Cold-formed Steel Design Manual 290.pdf

Missouri University of Science and Technology

Scholars' Mine AISI-Specifications for the Design of Cold-Formed Steel Structural Members

Wei-Wen Yu Center for Cold-Formed Steel Structures

1-1-1986

Cold-formed Steel Design Manual American Iron and Steel Institute

Follow this and additional works at: http://scholarsmine.mst.edu/ccfss-aisi-spec Part of the Structural Engineering Commons Recommended Citation American Iron and Steel Institute, "Cold-formed Steel Design Manual" (1986). AISI-Specifications for the Design of Cold-Formed Steel Structural Members. 60. http://scholarsmine.mst.edu/ccfss-aisi-spec/60

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IN TITUTE

•

~t'®

AMERICAN IRON AND STEEL INSTITUTE . 1000 16th STREET, NW WASHINGTON, DC 20036

This pUblication is for general infonnation only. The infonnation in it should not be used without first securing competent advice with respect to its suitability for any given application. The publication of the infonnation is not intended as a representation or warranty on the part of American Iron and Steel Institute-or any other person named herein-that the infonnation is suitable for any general or particular use or of freedom from infringement of any patent or patents. Anyone making use of the information assumes all liability arising from such use.

•

• 1st Printing-March 1987

Produced by W. P. Reyman Associates, Inc. New York Copyright American Iron and Steel Institute 1986

PREFACE This edition of the Cold-Formed Steel Design Manual is based on the August 19, 1986, Edition of the Specification for the Design of Cold-Formed Steel Structural Members. The Manual includes the following sections: Part I-Specification Part II-Commentary Part III-Supplementary Information Part IV -Illustrative Examples

Part V -C harts and Tables Part VI-Computer Aids Part VII-Test Procedures The Specification and the Commentary are both also available as separately bound booklets. American Iron and Steel Institute gratefully acknowledges the time and effort devoted to the preparation of the Manual by the Advisory Group on the Specification for the Design of Cold-Formed Steel Structural Members and its working subcommittees. A special thanks go to the following: the Cold-Formed Steel Design Manual Subcommittee-D. L. Johnson, Chairman, S. J. Errera, R. B. Haws, Herbert Klein, R. A. LaBoube, A. L. Johnson, and C. R. Clauer, Project Manager; the Editorial Subcommittee-C. W. Pinkham, Chairman, C. R. Clauer, D. A. Cuoco, S. J. Errera, A. L. Johnson, and T. B. Pekoz; W. R. Midgley, Clauer & Associates; and Jon Harrington and Associates.

American Iron and Steel Institute August 1986

American Iron and Steel Institute

•

1133 15th STREET. N.W .• WASHINGTON. D.C. 2000S-2701 Phone (202) 452-7100 Fax (202) 463-6573

July 25. 1991

Cold-Formed Steel Design Manual

RE:

Dear Friend of Cold-Formed Steel: Enclosed please find a complete 1986 edition of the Cold-Formed Steel Design Manual which consists of: Part I Part II Part Part Part Part Part

•

til IV V VI VII

1986 Edition of the Specification for the Design of Cold-Formed Steel Structural Members Commentary to the 1986 Edition of the Specification for the Design of Cold-Formed Steel Structural Members Supplementary Information Illustrative Examples Charts and Tables Computer Aids Test Procedures

Also enclosed Is a complimentary loose-leaf copy of the 1989 Addendum to the 1986 Edition of the Specification for the Design of Cold-Formed Steel Structural Members and its Commentary. The 1989 Addendum incorporates the results of research completed since the 1986 edition was issued. The Specification sections involving the more significant changes in the 1989 Addendum are: A3

C3.1.2 C3.1.2

04 05 E2.2 E2.6

Material Lateral Buckling Strength Beams Having One Range Through-Fastened to Deck or Sheathing Wall Studs and Wall Stud Assemblies Aoor. Roof or Wall Steel Diaphragm Construction (New Section) Arc Spot Welds Resistance Welds

In an effort to make the Specification and Manual more responsive to its users. a questionnaire has been included. Please take a few minutes and complete the survey and return it to AISI. Your input is important In determining the content of future SpeCifications. Thank you for your interest in cold-formed steel design. Sincerely yours, ,

" I

I ,--,:- ~-. ."7 \

~\.'-:.~,\ ..... J

\,-1

Richard B. Haws, P.E. Secretary Committee on Specifications RBHjldc

•@

AMERICAN IRON AND STEEL INSTITUTE 1133 15th Street, NW Washington, DC 20005

•

SURVEY OF USERS OF AlSI ·COLD-FORMED

DESIGN MANUAL·

Please Indicate the usefulness to you of the material In the COLO-FORMED STEEL DESIGN MANUAL by using the following rating system: 1 2 3 4

Very Useful Somewhat Useful Present Version not Useful No Interest; have not reviewed material

Part I

Specification

Part II

Commentary

Part III

Supplementary Information Section 1 - Unear Method Section 3 - Laterally Unbraced Compression Aanges Section 4 - Torsional - Flexural -Buckling

1 1 1

2 2 2

3 3 3

4 4 4

illustrative Examples Flexural Members - Examples 1-9 Compression Members - Examples 10-14 Beam-Column Members - Examples 15-17 Tension Members & Connections - Examples 18-22 PurUns - Examples 23-24 Calculation of Section Properties - Example 25

1 1 1 1 1 1

2 2 2 2 2 2

3 3 3 3 3 3

4 4 4 4 4 4

1 1

2 2 2

3 3 3

4 4 4

2 2

3 3 3 3

4 4 4 4

3 3

4 4

Part IV

•

STEE~

Part V

Part VI

Part VII

COMMENTS: 1. 2. 3. 4. 5.

Charts and Tables Torsional-Flexural Design Charts Full Area Tables - Tables 1-9 Effective Area Tables - Tables 10-15

Computer AIds (flow charts) Properties of Elements - Charts 82.1-86.2 Strength of Members - Charts C3.1-C5 Capacity of a Wall Stud - Chart 04.1 Connections - Charts E2.2-E3.2

1 1 1 1

Test Procedures Rotational-lateral Stiffness Stub-Column

1 1

2 2 2 2

Please use the back of this sheet to comment on the follOWing questions.

What software do you use In applying these specifications? What software would you desire reiated to these specifications? What suggestions do you have for additional examples? What suggestions do you have for Improving the specification and manual? Would additional section properties and load span tables be useful? Y N If yes, please list section profiles on reverse of this page.

Name:_______________________________________________________________

•

Add .....:

--------------------------------------------------------------

P.... return to the above address, 8Uentlon Richard B. Haws.

AInerican Iron and Steel Institute

•

1133 lSTH STREET, N.W., WASHINGTON, D.C. 2000S-2701

November 30, 1990 File No. SG-671

SUBJECT:

Errata to the 1986 Cold-Formed Steel Design Manual

Dear Friend of Cold-Formed Steel: The AISI Cold-Formed Steel Advisory Group has completed the errata to the 1986 Edition of the Specification for the Design of Cold-Formed Steel Structural Members, its Commentary and to the Cold-Formed Steel Design Manual. These updates are a result of user comments and questions. Please incorporate these revisions into your copies of the Specification, Commentary and Manual.

•

All users of the Specification, Commentary and Manual are invited to continue to offer their valuable comments and suggestions. Sincerely yours,

~(6.~~ Richard B. Haws, P.E. Program Manager Cold-Formed Steel Construction RBH/klc Attachment

•

American Iron and Steel Institute

•

Errata to the 1986 AISI Cold-Formed Specification and Commentary Line Number I

Page

Section

Reference

1-8

Symbols and Definitions

12 rrom bottom

1-10

Symbols and Definitions

6 from bottom-lye

Change:

E ModuJus of elasticity of sleel (29,000 ksi)

To:

E ModuJus of elasticity of steel (29,500 ksi)

Change:

03.1.1

To:

C3.1.2

Symbols and Definitions

above Ow

Insert:

Oy Factor of safety for shear rupture E4

1-21

B2.1

I from top

Change:

(3) If Section C3.1.2 is used, then the f =

To:

(3) Ir Section C3.1.2 is used, then f = Me Sr

Change:

Ct, Cl = Coefficients dermed in Figures B4-1 and B4-2

To:

CI, Cl = Coefficients defined in Figure B4-2

Change:

the yield stress, f" and la the thickness of the stiffener

To:

the yield stress, Fy, and la the thickness of the stiffener

1-27

1-28

1-30

1-32

1-37

B6.1

B6.2

C3.1.1

C3.1.2

8 from bouom

13 from bottom

Eq.B6.2-4

S from top

4 from top

21 from bottom MuoandMqo

1-41, 1-42

•

Revision

1-14

1-23

•

February 3,1990 File No. SG671/2E

03.2.1

&t.03.2.I-I, &t.03.2.1-2, &t.03.2.1-3, &/.03.2.1-4, &/.03.2.I-S, Eq. D3.2.I-6

Change:

k, ) when Cv > 0.8 Cv = -190 ( ...[F; hit F,

To:

Cv = 190 hIt

({¥.) F,

~rc

when Cv >0.8

Change:

Combined bending and web crippling shall be checked by provisions of Section C3.4

To:

Combined bending and web crippling shall be checked by provisions of Section C3.S

Change: bending moment (Section CS), Q, shall be taken as unity. To:

bending moment (Section CS), Cll' shaD be taken as unity.

Change:

Section C3 .12 (latera) buckling)

To:

Section C3 .1.2 (lateral buck.I ing)

Change: . 8 To:

sin 8

-1-

American Iron and Steel Institute

•

Errata to the 1986 AISI Cold-Formed Specification and Commentary Page I-58

Section Fl

Line Number I Reference Eq.FI-4

Revision Change: R R

To: 1-60

Appendices

I from top

Appendix

Eq. Bl.ltrl

=..jO.061tdE I fav ~(IOOcf I d) wr =..jO.0611dE I fav V(I00Cf I d)

Change:

To: Commentary F

II from bottom

2.5D + 2.5L

APPENDICES

Bl.l(b)

11-31

Change: APPENDICIES To:

1-61

= 2.5D + 2.5 L

Change:

Information on test

To:

Information on tests

•

• -2-

February 3,1990 File No. SG671!2E

February 3, 1990 File No. SG673E

American Iron and Steel Institute

•

Errata to the 1986 AISI Cold-Formed Steel Design Manual Page III-13

Section 1.2.3-9

Line Number I Reference 14 from top

Revision Change: To:

III-IS

2.1

12 from top

c = length of lip, see Figure 1.2.3-1 c = length of lip, see Figure 1.2.2-1

-, (!.), (-r

(ft = (flDa

Change:

- ,,~a' (

Example 4

14 from top

(X2

KtL

I )' +"""'2CT ( (ft-- = t2 a KtL

To: IV-19

+ CT _a_

Change:

D =d + 0.124 tan (912) = 0.600 + 0.124 tan (45°12)

=0.651 To:

D =d + 0.154 tan (912) = 0.600 + 0.154 tan (45°12)

=0.664 21 from top

24 from top

• 16 from bottom

IV-24

Example4A

5 from top

8 from bottom

3 from bottom

Change:

D/w = 0.651 1 1.471 = 0.443, 0.25 < D/w = 0.443 < 0.8

To:

D/w = 0.664 11.471 = 0.451, 0.25 < D/w = 0.451 < 0.8

Change:

k = [4.82 - 5(D/w)](IJI.)"+ 0.43 = [4.82 - 5(0.443)](1.082)1/1+ 0.43 = 3.139 k :S: 5.25 - 5(D/w) = 5.25 - 5(0.443) = 3.035 k =3.035

To:

k = [4.82 - 5(D/w)](IJI.)D+ 0.43 = [4.82 - 5(0.451)](1.082)112+ 0.43 = 3.097 k :S:5.25 -5(D/w) = 5.25 -5(0.451) = 2.994 k =2.994

Change:

= (1.052/ ..J3.035)(24.52)../50 129500 = 0.609 < 0.673

To:

= (1.052/ ..J2.994 )(24.52)../50 129500 = 0.614 < 0.673

Change:

To:

k =4 + 2(1- '1')3 + 2(1- '1') =4 + 2[1- (-1.000))3 + 2[1- (-1.000)]

Change:

0.064 cos 45° + (O.60012)cos 45° = 0.257

0.154

To:

(0.154 - 0.124 cos 45°) + (0.60012) sin 45° = 0.278

0.167

Change:

9.5 - 0.257 = 9.243

5.546

To:

9.5 -0.278= 9.221

5.533

• -1-

=4 + 2(1- '1'>' + 2(1 - 4) =4 + 2[i - (-1.000)]3 + 2[i - (-1.000)]

February 3.1990 File No. SG673E

American Iron and Steel Institute

•

Errata to the 1986 AISI Cold-Formed Steel Design Manual Line Number I Page IV-33

Section Example 5

Reference top line

bottom line

Revision Change:

V. = (l1SOOFy/E)ht = 11800(50(29500)(3.692)(0.06)

To:

V. =OAFyht = (0.4)(50)(3.692)(0.06)

Change:

Find Ieff at Ma = 31.3 kip-in.

To:

Find Ieff at Ma = 31.1 kip-in.

IV-38

Example 5

entire page

Change:

Replace with replacement page

IV-46

Example 6

22 from top

Change:

Mf =0.6Fy

To:

Mf = Sefr(0.6Fy)

Change:

2.629-

To:

1.629"

Change:

f\ =(1.048(2.629)(50) = 19.93 ksi (compression) f2 (1.306/2.629)(50) 24.84 ksi (tension) 'If = ftlf2 -24.84/19.93 = -1.246

IV-49

IV-50

Example 7

drawing at bottom

top line

•

= =

f\ =(1.048/1.629)(50) 32.17 ksi (compression) f2 = (1.306/1.629)(50) = 40.09 ksi (tension) 'If = ftlf2 = -40.09/32.17 = -1.246

To:

7 from top

=Seff(0.6Fy)

). = (1.052/..Jk)(w 1 t){fiE. f = f\

Change:

=(1.052/.J3iJ5)(17.44 )~19. 93/29500 ='t>.085 To:

). =(1.052/..Jk)(w 1 t)$7E. f =f\ = (1. 0521 ..J3iTs')(17. 44 )~32.17 1 29500

=0.108 20 from top

Change:

Se =h/(d - YeV = 2.47/ (4 - 1.731)

=1.09 in.'

Mn=SeFy =(1.09) (SO) =54.S kip-in. To:

Se =I lI /(d-Yc:a)=2A7 1(3-1.371}= l.S16 in.' Ma=SeFy -(1.516) (SO) =75.8 kip-in .

• -2-

American Iron and Steel Institute

•

Errata to the 1986 AISI Cold-Formed Steel Design Manual Page IV-51

Section Example 7

Line Number I Reference 17 from bottom

Revision Change: Mn shall not exceed 1.25 Se Fy = 1.25(54.5) = 68.1 kip-in. Therefore Mn = Se Fy = 54.5 kip-in. To:

Mn shall not exceed 1.25 SeFy = 1.25(75.8) = 94.8 kip-in. Therefore Mn= 1.25 SeFy = 94.8 kip-in.

3 from bottom

Change: M.=Mn / Or =68.1/1.67 = 40.8 kip-in. To:

IV-69

Example 8

6 from top

Ma=Mn / Or =94.8/1.67 = 56.7 kip-in.

Change: For interior reaction: Eq. C3.4-3 To:

•

For interior reaction: Eq. C3.4-4

IV-70

Example 9

entire page

Change: Replace with replacement page

IV-71

Example 10

13 from bottom

Change: a To:

12 from bottom

Change: b To:

11 from bottom

Change: c To:

IV-73

Example 10

14 from top - #13

Change:

fyfl = SOfl = 25.00 ksi

To:

Fyfl = 50fl = 25.00 ksi

15 from bottom-#14 Change: To:

(Eq.B4.~)

(Eq. B4.2-4)

8 from bottom-# 15 Change: To:

15. Determination of p.: 15. Determination of P.:

7 from boltom-# 15 Change: po =AeFn

•

February 3, 1990 File No. SG673E

To:

Pn =AeFn

3 from bottom-#15 Change: To:

p. =pnIOc P. =Pn!nc

-3-

February 3, 1990 File No. SG673E

American Iron and Steel Institute

•

Errata to the 1986 AISI Cold-Formed Steel Design Manual Page IV-75

Section Example 11

Line Number I Reference 2 from top - #4

19 from top - #7

27 from top - #9

29 from top - #9

32 from top - #9

33 from top - #9

•

IV-77

Example 11

12 from top - #15

13 from top - #15

Example 12

IV-78

Example 12

3 from bouom

4 from top - #1

Change:

Revision x

To:

-x

Change:

xo =~

To:

xo = -(x + m) = -(0.757 + 1.194)

Change:

[8(b)2(C) + 2m[2c(c - a) + b(2c - 3a)]

To:

(8(b)2(C) + 2m[2c(c -

(x + m) = -(0.757 + 1.194) a) + b(2c - 3a)]}

Change:

Cw = [(0.105)1ft).889] {0.757 x 0.889 x (3.395)2ft).105]

To:

Cw = [(0. 105)2ft). 889] {[ 0.757 x 0.889 x (3.395WO.I05]

Change: -1.657(1. 194)2ft). 105(2 x 3.395 + 4 x 0.848) To:

- 1.657(1.194)2ft).105 (2 x 3.395 + 4 x 0.848) + 1.194 (0.848)2/3 {8(1.895)2 x 0.848

Change:

+2x1.194 (2xO.848(0.848 - 3.395) + 1.895(2xO.848 - 3x3.395)])

To:

+2x1.l94[2xO.848(0.848 - 3.395) + 1.895(2xO.848 - 3x3.395)])

Change:

15. Detennination of pa:

To:

15. Detennination ofPa:

Change: P =AeF'n To:

Pn =AeF'n

Change:

2. Section: 4 x 4 x 0.065 Square Tube.

To:

2. Section: 3.5 x 3.5 x 0.105 channel with stiffened flanges.

Change:

from the sketch a = 2.914 in., b = 1.414 in., c = 0.607 in.

To:

from the sketch a = 2.914 in., b = 2.914 in., c = 0.607 in.

Change:

A =t[a+2b+2u+4c]

To:

A = t[a + 2b + 2c + 4u]

11 from top - #2

8 from bottom - #9 Change:

IV-79

•

Example 12

4 from top

C w= [(0.105)2/1.204] [1.445 x 1.204 x (3.395)2ft).105]

To:

C w= [(0.105)1/1.204] {[ 1.445 x 1.204 x (3.395WO.105]

Change:

To:

ro1

American Iron and Steel Institute

•

February 3,1990 File No. SG673E

Errata to the 1986 AISI Cold-Formed Steel Design Manual Page IV-89

Section Example 15

LIne Number I Reference 17 from bottom

Revision Change:

Ae = 1.551-0.105(7.415 -4.152) -0.105(0.508 -0.175) = 1.173 in.l Pno = 1.173 x 50 = 58.65 kips

= (5{3) + (3/8)R - (R3/8»] R = ~Fy 12Fe , Fe = 00 R =0

nc = 1.67 Pao = 58.65/1.67 =35.12kips To:

Ae = 1.551-0.105(7.415 -4.152)- 0.105(0.508 - 0.175)(2) = 1.139 in.l Pno = 1.139 X 50 = 56.95 kips

nc = 1.92 since the section is not fully effective Pao = 56.95/1.92 =29.66 kips IV-92

•

IV-93

Example 15

16 from top

13 from bottom

11 from bottom

IV-94

Example 15

5 from top

16 from top-#4

IV-98

Example 15

17 from top-#8

Change:

My = Sf Fy (Yield Moment)

To:

My=SrFy

Change:

Cmy = 0.6 - O.4(Ml 1Ml) ~ 0.4

To:

Cmy = 0.6 - O.4(Ml 1Ml)

Change:

0.6 - 0.4(-1.00) = 1.00 > 0.4

To:

0.6 - 0.4(-1.00) = 1.00

Change:

= (2.50{30.55) + (5.00124.34) = 0.082 + 0.205 = 0.287 < 1.0 OK

To:

= (2.50/29.66) + (5.00/24.34) = 0.084 + 0.205 = 0.289 < 1.0 OK

Change:

Pao = 30.55 K (ca1culated in part (a) 4).

To:

Pao = 29.66 kips (calculated in part (a) 4).

Change:

Cmx = 0.6 - 0.4(-1.0) = 1.0> 0.4 OK

To:

Cmx = 0.6 - 0.4(-1.0) = 1.0

14 from bottom-#9 Change: To:

•

ax =0.960

3 from bottom-# 15 Change:

To:

dx =0.960

(2.50{30.55) + (10.00/108.0) + (5.0/24.34) 0.082 + 0.093 + 0.205 = 0.380 < 1.0 OK (2.50/29.66) + (10.00/108.0) + (5.0124.34) 0.084 + 0.093 + 0.205 = 0.382 < 1.0 OK

-5-

American Iron and Steel Institute

February 3, 1990 File No. SG673E

Errata to the 1986 AISI Cold-Formed Steel Design Manual Line Number I

~ _p_ag_e~___S_~ __lo_n_______________________ R_ev_I_SI_o_n_________________________ Reference IV-loo Example 16 21 from bottom-{b) Change: Q.

To: 19 from bottom-{b) Change: To:

(fCR

= (1/2~)[(crex + (ftQ) - ~((fex + (ftQ)2 - 4~(fextQ ]

(fCR

= (1/2~{(crex + (ftQ)- ~((fex + (ftQ)2 - 4~(fex(ftQ ]

17 from bottom-{b) Change: To:

To:

Ot =(Qd 2 )/{4Ar.n Ot = (Qi2) / (4Ar;)

Change:

qo = 2.0 kip - in.

To:

Ci o = 2.0 kip /in.

Change:

=12 in.

To:

=12 in.

Change:

Ci = 2.0(2 -12 /12) = 2.0 kip - in.

To:

Ci = 2.0(2 -12 /12) =2.0 kip /in.

13 from bottom-{b) Change:

9 from bottom-{b)

8 from bottom-{b)

7 from bottom-{b)

~ IV-lOl

&ample 16

13 from bottom

Change: El =(25)( (68.5-25)[(3.57)2(0.00257)-{2.03)(0.257)] -(25)(2.03) [0.257-(2.03)(0.00257)] }/(68.5-25)(3.57)2(54.6-25) -[(25)(2.03)]2 To:

IV-1m

Example 16

9 from bottom

El =(25) {(68.5-25)[(3.57)2(0.00257)-{2.03)(0.257)] -(25){2.03) [0.257-(2.03)(0.00257)]) / {(68.5-25)(3.57)2(54.6-25) -[(25)(2.03)]2]

Change: D/w k

=0.275 =[4.82-5(0.275)](0.000936ft).OOO542)112+0.43

=4.96

D/w k

=0.290 =[4.82-5(0.290)](0.000936ft).OOO542)112+ 0.43

=4.86

5.25-5(0.275) =3.88 < 4.96, so use k =3.88 A. =(1.052/ "'3.88 )(32.17).J21.6/29500=O.465( S; 0.673)

To:

5.25-5(0.290) =3.80 < 4.86, so use k =3.80 A. = (1.052/ "'3.80 )(32.17W21.6/29500=O.470( S; 0.673)

~ -6-

February 3,1990 File No. SG673E

American Iron and Steel Institute

Errata to the 1986 AISI Cold-Formed Steel Design Manual •

Page IV-I25

IV-I26

•

Section Example 24

Example 25

Line Number I Reference

Revision

To:

a a

Eq.03.2.1-1, Eq.03.2.1-2, Eq.03.2.1-3

Change:

tan

12 from bottom, 8 from bottom, 4 from bottom

Change: To:

0.0833

11 from bottom

Change: To:

PI. =238Ibs. PI. =239Ibs.

5 from bottom, 4 from bottom

Delete:

0.5 before first bracket

8 from bottom

Change:

I' = I' (straight portions)+1' (Arcs)=O.0045+O.0114 = 0.0159 in.l I = I't = 0.0159 x 0.030 = 0.000477 in.4

To:

I' ~I' (straight portions)+I' (Arcs)=O.0045+O.0114 = 0.0159 in.l I ~I't = 0.0159 x 0.030 = 0.000477 in.4

11 from top

4 from bottom

Change:

To:

=4.76°, tan a = 0.083 =4.76°, sin a = 0.0830

a sin a

0.0830

Change:

lmin = [3.66t4~(W / t)2 - 4000 / Fy] but not less than (18t 4) = 0.000015 in 4 lmin

= [3.66 X (O.030)4~(79.8)2 -

lmin

= [3.66t4~(W / t)2 -

Imin

= [3.66 X (O.030)4~(79.8)2 -

To:

• -7-

4000 /50] = 0.000235 in 4 < 0.00477 in 4

0.136E / Fy] but not less than (18t 4 ) = 0.000015 in 4 (0.136)(29500) /50] = 0.0002: < 0.000477 in 4

February 3,1990 File No. SG673E

American Iron and Steel Institute

•

Errata to the 1986 AISI Cold-Formed Steel Design Manual Page IV-127

Section Example 25

Line Number I Reference 10 from bottom

7 from bottom

Revision Change:

S = 1.28..JETf = 1.28.../29500 /0.60(50) = 40.138

To:

S = 1.28..JETf = 1.28.../29500 / (50) = 31.091

Change:

Ia = (0.030t [115(86/40.138) + 5] = 0.000204 Is = 1'1 = 0.003 k =3.57(0.003ft).OOO204)I13+ 0.43 = 9.176 > 4

Ia = (0.030)4 [115(86(31.091) + 5] = 0.000262

To:

= =

Is Ixl 0.00090 k = 3.57(0.00090/0.000262)113 + 0.43 = 5.817 > 4 2 from bottom

Change:

b = pw = 0.474[3 - 3(0.140)]

= 1.233 in.

As= A's = 0.348 in.l for Is ~ Ia To:

b = pw = 0.474[3 - 3(0.140)]

= 1.223 in.

As= A's = 0.0348 in.l for Is ~ Ia

•

IV-I28

Example 25

entire page

Change:

Replace with replacement page

IV-129

Example 25

entire page

Change:

Replace with replacement page

IV-130

Example 25

Ly column in table

Change: To:

3.490 3.492 4.909

Change: To: Ll column in table Change: To: Change: Ll column in table To:

Ly column in table

4.911 3.550 3.544

To:

1.700 1.697 5.394 5.385

Ll column in table Change: Examp]e25

14 from bottom

Change: To:

be =0.030[(1.535/0.030)-O.10(79.8--{j()]=1.476 in. be = 0.030[(1.535/0.030)-0. 1O(79.8--{j()] = 1.476 in. for wit >60

Example 25

bottom line

Change: To:

be =0.030[(1.485/0.030)-0. 1O(68.033-{j()] = 1.458 in. be = 0.030[(1.485/0.030)-O.10(68.03~)]=1.461 in .

• -8-

American Iron and Steel Institute

•

Errata to the 1986 AISI Cold-Formed Steel Design Manual Page IV-13 I

V-25

•

February 3,1990 File No. SG673E

Line Number I Reference

Revision 1.458 1.461 16.460 16.463 3.490 3.492 2.938 2.944 17.089 17.097

Section Example 25

L column in table

Example 25

8 from bottom

Change: To:

Example 25

6 from bottom

Change: f =Fy since ycg < 2.030/2 = 1.015 To: f =Fy since ycg == 2.030/2 = LOIS

TablesGeneral Notes

3 from bottom

Change: (h) Tables 1-9 incl. are Full Area Tables. Tables 10-15 incl. are

Change: To: L column in table Change: To: Ly column in table Change: To: Ly column in table Change: To: Ly column in table Change: To:

ycg = 17.089/16.460 = 1.038 in. ycg = 17.097/16.463 =1.039 in.

Effective Area Tables. (Fy = 50 ksi) (h) All tables assume Fy =50 ksi.

To: V-26

Table 1

entire page

Change: Replace with replacement page

V-27

Table 1 (cond.)

entire page

Change: Replace with replacement page

V-28

Table 2

enlirepage

Change: Replace with replacement page

V-29

Table 3

entire page

Change: Replace with replacement page

V-30

Table 4

entire page

Change: Replace with replacement page

V-35 to V-38

Tables 10 to 13 entire page

VI-25

Computer Aids

diamond

Change: Remove pages Change:

To:

• -9-

IV-38

Examples Based on the August 19, 1986 Edition of the Cold-Fonned Specification

• b) Procedure IT

Calculate AI, Al

Detennine Cy

•

Calculate M"

Mn = 1.25ScFy

M" = ScFy

3. Allowable Bending Moment (Section C3.1)

M.=MJQr

Check if M...,. applied < M.

•

1....-_ _ _ _ _ _ _

(continued on next page)

Examples Based on the August 19, 1986 Edition of the Cold-Fonned Specification

IV-70

EXAMPLE NO.9

•

CYLINDRICAL TUBULAR SECTION

Outer diameter =8.000 in. Thickness =0.125 in.

•

Given:

Steel: Fy =50 ksi. Section: Shown in sketch above.

Required: Allowable bending moment Solution:

=1t[(0.0.)4 - (1.0.)4]/[32(0.0.)] = 1t[(8.00t - (7.75t]/[32(8.00)] =5.995 in.'

Ratio of outside diameter to wall thickness, O/t =8.00~.125 =64.00 O/t 0.5My = 21.0 kip-in. =My[1 - (M y/4Mc)] =42.0[1- 42.0/(4 x 1116.77)] = 41.61 kip-in. =41.61~.840 = 49.54 ksi

(Eq. C3.1.2-8)

To calculate effective section properties to obtain So at stress 49.54 ksi. we assume that the webs are fully effective. Compression flange:

A P b

=(1.052 1 -v4.(6)(70.62)..J49. 54 1 29500 = 1.522 > 0.673

tl -

(0.22/1.52~)/1.522 = 0.562 = =0.562 (7.415) = 4.167 in.

L Effective Length Element

•

Webs Upper Corners Lower Corners Compression Flange TenSion Flange Sum

(in.)

2 x 2.415 =4.830 2 x 0.377 = 0.754 2 x 0.377 =0.754 4.167 2 x 0.508 = 1.016

11.521

x Distance from Top Fiber (in.) 1.500 0.140 2.860 0.053 2.948

1'1 Lx (in. 2)

Lx2 (in.l)

7.245 0.106 2.156 0.221 2.995 12.723

10.868 0.015 6.167 0.012 8.830 25.892

About Own Axis (in.l) 2.347 -

2.347

IV-93

Examples Based on the the August 19, 1986 Edition of the Cold-Formed Specification

•

Distance from top fiber to y-axis is XCI = 12.723/11.521 = 1.104 in. To check if the webs are fully effective (Section B2.3): fl = [(1.104 - 0.293)/1.896] 49.54 = 21.19 ksi (compression) f2 =-[(1.104 - 0.293)/1.104) 49.54 = -36.39 ksi (tension) 'If =-36.39121.19 = -1.717 k =4 + 2[1- (-1.717W + 2[1- (-1.717)] =49.548

= (1.05~ / "'49.548 )(70. 62)..J21.19 / 29500 = 0.092 < 0.673 =2.415 In. =2.41512 = 1.208 in. =2.415/[3 - (-1.717)] = 0.512 in.

Compression portion of each web calculated on the basis of the effective section = 1.1 04 - 0.293 = 0.811 Since bl + bz = 1.720 in. > 0.811 in., bl + b2 shall be taken as 0.811 in. This verifies the assumption that the web is fully effective. I'y =25.892 + 2.347 - 11.521 (1.104)2 = 14.197 in.3 Actual Iy= 14.197 (0.105) = 1.491 in.' Sc = Iy/(3.ooo - xcJ = 1.491/(3.000 - l.104) =0.786in.3 = Mc SJSr Mny (Eq. C3.1.2-1) =41.61 (0.786)/0.840 = 38.94 kip-in.

•

Mny shall be the smaller of 40.65 kip-in. and 38.94 kip-in. Thus Mny = 38.94 kip-in. Or = 1.67 May =Mny/nr = 38.94/1.67 = 23.32 kip-in.

(Eq. C3.1-1)

7. Determination of Mayo: Mayo is the allowable moment about the centroidal axes determined in accordance with Section C3.1 excepting the provisions of Section C3.1.2 (excluding lateral buckling). Therefore Mn}O =40.65 kip-in. Or = 1.67 Mayo = 40.65/1.67 = 24.34 kip-in.

8. Cmy = 0.6 - 0.4 (Ml/M2) Ml/M2 = -1.00 (single curvature) 0.6 - 0.4 (-1.00) = 1.00 Cmy= 1.00

•

9. Determination of l/f1.y: Oc = 1.92 Per =1t2EIy/(KyLy)2 Iy = 1.786 in.' KyLy = 1.0 (16 X 12) = 192 in. Per = [r (29500) (1.786)]/(192)2 = 14.11 kips l/f1.y =1/[1 - (Oc PIPer)] 1/[1-(1.92x 2.5/14.11)] = 1.516 ex, =0.660

(Eq.C5-5)

(Eq.C5-4)

IV-I28

•

Examples Based on the August 19, 1986 Edition of the Cold-Fonned Specification

Element 9 from Section B3.2(a) w =0.415 -0.030 - 0.125 = 0.26 in. k =0.43 f < Fy Use Fy as conservative value.

A. P b

Element 3 from Section B4.2(a) w/t =[2-2(0.140)]/0.030=57.333 S D/w n I.

L k

P b d.

(Eq. B2.1-4)

= (1.052 / .J0.43 )(0.26/0.030)"/50/29500 = 0.572 = i for A. s 0.673 =W = 0.26 in.

(Eq. B2.l-1) (Eq. B4-1)

f=Fy [seeB2.1a(1)]

= 1.28$1f = 1.28../29500 / (SO) = 31.091 = [0.415 - 0.5(0.030)]1[2 - 2(0.140)] = 0.233 = 1/3 for wit > S = (O.030t [(57.333/31.091) (115) + 5] = 0.000176 for w/t? S = (1/12)bh3 = (1/12)(0.030)(0.415 - 0.125 - 0.030)3 = 0.000044 = 3.57(0.000044/0.000 176)1f3 + 0.43 = 2.679 < 4

(Eq. B4.2-13) (Eq. B4.2-10) (Eq. B2.l-4) (Eq. B2.l-3)

= (1.052 / .J2. 769 )(57.333)../50/29500 = 1.517 = (1- (0.22/1.517)j(I/1.517) = 0.564 = pw = 0.564[2 - 2(0.140)] = 0.970 in. = (IJI.)d'. = (0.000044/0.000176)(0.26) = 0.065 in. Element 1 2 3 4 5 6 7 8 9 10

•

L 1.160 1.223 0.970 0.660 3.440 4.788 2.396 2.068 0.065 0.440 17.210

(Eq. B4.2-11)

Ly2

0.321 0.Q15

0.372 0.018

0.120 -

0.015 0.066 1.015 2.015 1.840 2.015 0.188 1.964

oms

0.044 3.492 9.648 4.409 4.167 0.012 0.864 23.041

0.003 3.544 19.440 8.112 8.397 0.002 1.697 41.315

1'1 0.030

0.849

- - - - -0.879

Yea

= 23.041/17.210 = 1.339 in. =41.315 + 0.879 - 17.210(1.339)2 = 11.338 in.3 Ix = I'xt = (11.338)(0.030) = 0.340 in.4 S" = L/Yea 0.340/1.339 =0.254 in.3 Mn = S.Fy = 0.254(50) = 12.700 kip-in. M. =MJOc=12.700/1.67 = 7.605 kip-in.

1'"

Element 5 from Section B2.3(a) Yea = 1.339 in. f1 = [(1.339 - 0.125 - 0.030)/1.339](50) = 44.212 f1 = -[(2.030 - 0.125 - 0.030 - 1.339)/1.339](50) =-20.015 'If = f1/f1 =-20.015/44.212 = -0.453 k =4+2(1 + 0.453)3+ 2{l +0.453)= 13.041 >4

•

~~~1~h.J13.041 ){[2.030 -

2(0.155)] / 0.030}"/44.212 / 29500 = 0.647 < 0.673

Thus element 5 is fully effective so properties above are correct.lfb. < 1.72 then properties should

be recomputed for an exact solution.

(Eq. C3.1-1)

(Eq. B2.3-4) (Eq. B2.l-4) (Eq. B2.l-2)

IV-129

Examples Based on the the August 19, 1986 Edition of the Cold-Fonned Specification 3. Moment of Inertia for Deflection Detennination-Positive Bending

•

Element 2 from Section B4.2(b) f = Fy/1.67 = 30 ksi w = 3 - 3(0.140) = 2.580 in. A.: = 0.256+ 0.328(2.580 / 0.030)"50/29500 = 1.417 k =4

A P b A.

(Eq. B2.1-10)

~ fl.052 "'4.00 (2.580/0/030)..,130 /29500 ~ 1.443

(Eq. B2.1-4) (Eq. B2.1-9) (Eq. B2.1-2) (Eq. B4.2-12)

= 0.41+0.59 50/30 -(0 ..22/1.443)]{1/l.443)=0.706 = w = 0.706(2.580) = l.821 m = A'. = 0.348 in. 2

Element 3 from Section 4.2(b) f = 50/1.67=30 ksi w = 2 - 2(0.140)=1.720 in.

A.:

= 0.256 + 0.328(1. 720/0.030)"50/29500 = 1.030

(Eq. B2.1-10)

S I. k

=1.28,,29500 / 30 = 40.14 = [115(57.33/40.14) + 5](0.030)" = 0.000137 in.4 = 3.57(O.000044/0.ooo137YI3 + 0.43 = 2.875 = (1.052 / .J2.875){1.720 / 0.030)"30 / 29500 = 1.134

(Eq. B4-1) (Eq. B4.2-13) (Eq. B4.2-1O)

A P b

= ~0.41 + 0.59"-50 /30 - ~0 ..22 / 1.134)]{1 / 1.134) = 0.862 = w = 0.862(1.720) = 1.4 3 m. = (0.000044/0.000137)(0.260) = 0.084 in. Element 1 2 3 4 5 6 7 8 9 10

•

(Eq. (Eq. (Eq. (Eq.

L 1.160 l.821 1.483 0.660 3.440 4.788 2.396 2.068 0.084 0.440 18.340

0.321 0.015 0.015 0.066 1.015 2.015 1.840 2.015 0.197 1.964

0.372 0.027 0.022 0.044 3.492 9.648 4.409 4.167 0.017 0.864 23.062

Ly2

1'1

0.120

B2.1-4) B2.1-9) B2.1-2) B4.2-11)

0.003 3.544 19.440 8.112 8.397 0.003 1.697 41.316

0.030

0.849

- - - - -0.879

Yca

= 23.062/18.340 = 1.257 in. =41.316 + 0.879 - 18.340(1.257)2 = 13.217 in. 3 = I'"t = 13.217(0.030) = 0.397 in.4 Sa = 0.395/1.258 = 0.314 in.3 M = f"Sa = 30.0 x 0.314 = 9.426 kip-in. M. (from stress calculation) =7.605 kip-in. For deflection calculations, a stress level, f, should be used such that f"Sa will equal M. from SlltS.S calculations (see Examples 2 and 3). In this example, further iterations should be made, reducing f until f"Sa = M.. This will be left to the user to complete.

1'" 1..

4. Section Modulus for Load Determination-Negative Bending

•

Since the N.A. may be closer to the compression flange than to the tension flange, the compression stress is unknown, and therefore the effective width of the compression flange and section properties must be determined by an iterative method. Elements 1 • 2 • 3 • 4 • 5 • 9 and ] 0 do not vary with slress level.

•

TABLE 1

,-m

CHANNEL WITH STIFFENED FLANGES

V-25

Properties of Full Section Wgt

Size D In.

B In.

In.

Area

In.

In.2

pef Foot Lb.

Axisy-y

Axis x-x I. In.'

S. In.'

fx In.

Iy In.'

Sy In.'

fy In.

X In.

m In.

J In.'

Eff. S Prope

c. In.

In.

L In.'

12.000 3.500 0.135 1.010 0.188 2.706 9.199 O.IOS 0.900 0.188 2.rfJ7 7.129

56.266 9.378 4.560 43.836 7.306 4.572

4.037 1.560 1.222 3.090 1.181 1.214

0.912 1.487 0.01644 117.191 6.777 5.266 -2.332 0.883 1.461 0.00771 88.556 6.844 5.257 -2.291

55.387 40.904

10.000 3.500 0.135 1.010 0.188 2.436 8.281 0.105 0.900 0.188 1.887 6.415 0.075 0.720 0.094 1;344 4.568

36.526 7.305 3.872 28.505 5.701 3.887 20.533 4.107 3.909

3.823 1.533 1.253 2.929 1.160 1.246 2.035 0.792 1.231

1.006 1.582 0.01480 78.535 5.591 4.787 -2.520 0.975 1.553 0.00693 59.102 5.638 4.774 -2.476 0.932 1.473 0.00252 39.268 5.580 4.733 -2.367

35.957 26.513 17.571

9.000 3.250 0.135 0.105 0.075 0.060

1.000 0.840 0.700 0.610

0.188 0.188 0.094 0.094

2.230 1.717 1.228 0.976

7.584 5.836 4.176 3.319

27.157 21.077 15.287 12.182

6.035 4.684 3.397 2.707

3.489 3.504 3.528 3.533

3.072 2.300 1.627 1.265

1.344 0.987 0.689 0.530

1.174 1.157 1.151 1.138

0.965 0.921 0.888 0.862

1.507 1.458 1.393 1.364

0.01355 52.171 5.035 4.397 -2.404 0.00631 37.785 5.105 4.362 -2.326 0.00230 25.652 5.031 4.337 -2.244 0.00117 19.637 5.061 4.313 -2.196

27.157 20.030 13.551 9.703

8.000 3.000 0.135 0.105 0.075 0.060

0.930 0.810 0.700 0.600

0.188 0.188 0.094 0.094

2.009 1.553 1.116 0.885

6.831 5.279 3.793 3.008

19.371 15.125 11.045 8.791

4.843 3.781 2.761 2.198

3.105 3.121 3.147 3.152

2.356 1.794 1.290 0.997

1.127 0.844 0.600 0.458

1.083 1.075 1.075 1.061

0.909 0.876 0.851 0.822

1.409 1.375 1.322 1.288

0.01221 31.896 4.514 3.985 -2.250 0.00571 23.639 4.563 3.966 -2.198 0.00209 16.341 4.484 3.952 -2.135 0.00106 12.357 4.515 3.923 -2.080

19.371 14.727 9.965 7.397

8.000 1.625 0.105 0.075 0.060 0.048

0.820 0.820 0.600 0.500

0.188 0.094 0.094 0.094

1.266 0.927 0.720 0.569

4.305 3.153 2.447 1.935

10.647 7.996 6.190 4.889

2.662 1.999 1.548 1.222

2.900 2.936 2.932 2.931

0.402 0.316 0.222 0.167

0.332 0.261 0.177 0.131

0.564 0.584 0.555 0.542

0.412 0.414 0.369 0.347

0.709 0.706 0.645 0.618

0.00465 0.00174 0.00086 0.00044

5.656 4.364 2.925 2.168

4.971 4.686 4.992 5.131

3.141 3.184 3.143 3.126

-1.068 -1.083 ...{}.984 ...{}.941

10.647 7.996 6.190 4.447

7.000 2.750 0.135 0.105 0.075 0.060

0.880 0.880 0.700 0.600

0.188 0.188 0.094 0.094

1.793 1.410 1.003 0.795

6.097 4.794 3.411 2.702

13.266 10.553 7.659 6.098

3.790 3.015 2.188 1.742

2.720 2.736 2.763 2.770

1.777 1.438 1.000 0.772

0.940 0.761 0.517 0.393

0.996 1.010 0.999 0.986

0.859 0.859 0.815 0.786

1.320 1.335 1.251 1.217

0.01089 0.00518 0.00188 0.00095

18.778 15.341 9.940 7.469

3.992 3.995 3.950 3.977

3.584 3.618 3.570 3.541

-2.112 -2.141 -2.029 -1.973

13.266 10.548 7.033 5.368

6.000 2.500 0.135 0.105 0.075 0.060

0.820 0.820 0.820 0.600

0.188 0.188 0.094 0.094

1.574 1.240 0.909 0.705

5.353 4.215 3.089 2.396

8.575 6.843 5.124 4.012

2.858 2.281 1.708 1.337

2.334 2.349 2.375 2.386

1.293 1.051 0.805 0.583

0.764 0.621 0.478 0.333

0.906 0.921 0.941 0.909

0.808 0.808 0.814 0.752

1.229 1.244 1.232 1.148

0.00956 0.00456 0.00170 0.00085

10.264 8.436 6.425 4.257

3.485 3.491 3.408 3.456

3.185 3.219 3.249 3.164

-1.969 -1.999 -2.008 -1.869

8.575 6.843 4.944 3.606

6:000 1.625 0.105 0.075 0.060 0.048

0.820 0.820 0.600 0.500

0.188 0.094 0.094 0.094

1.056 0.777 0.600 0.473

3.591 2.643 2.039 1.608

5.247 3.972 3.085 2.441

1.749 1.324 1.028 0.814

2.229 2.260 2.268 2.271

0.370 0.291 0.206 0.155

0.324 0.255 0.173 0.128

0.592 0.611 0.585 0.573

0.483 0.486 0.437 0.412

0.798 0.791 0.722 0.692

0.00388 0.00146 0.00072 0.00036

3.074 2.388 1.555 1.140

3.304 3.154 3.330 3.412

2.613 2.650 2.600 2.580

-1.229 -1.240 -1.129 -1.081

5.247 3.972 3.085 2.334

•

TABLE 1 (continued)

CHANNEL WITH STIFFENED FLANGES

V-25

Prooerties of Full Section Axis y-y X m J Iy fy Sy

Wgt Area pef Foot

In.

In.z

Lb.

In.'

In.]

In.

In.'

In.]

In.

5.000 2.000 0.135 0.105 0.015 0.060 0.048

0.700 0.700 0.600 0.500 0.500

0.188 0.188 0.094 0.094 0.094

1.272 1.005 0.726 0.573 0.461

4.325 3.416 2.467 1.948 1.568

4.683 3.761 2.797 2.227 1.804

1.873 1.504 1.119 0.891 0.722

1.919 1.935 1.963 1.972 1.978

0.648 0.533 0.389 0.298 0.244

0.478 0.393 0.283 0.212 0.173

0.714 0.728 0.733 0.721 0.727

0.644 0.644 0.622 0.594 0.594

4.000 2.000 0.135 0.105 0.015 0.060 0.048

0.700 0.700 0.600 0.500 0.500

0.188 0.188 0.094 0.094 0.094

1.137 0.900 0.651 0.513 0.413

3.866 3.059 2.212 1.744 1.404

2.751 2.219 1.664 1.330 1.079

1.376 1.109 0.832 0.665 0.539

1.556 1.570 1.599 1.610 1.616

0.598 0.492 0.361 0.277 0.226

0.464 0.382 0.275 0.206 0.169

0.725 0.740 0.745 0.734 0.740

4.000 1.625 0.0150.600 0.060 0.500 0.048 0.500 0.036 0.500

0.094 0.094 0.094 0.094

0.594 0.468 0.317 0.285

2.021 1.591 1.282 0.969

1.448 1.155 0.938 0.715

0.724 0.577 0.469 0.357

1.561 1.571 1.577 1.584

0.219 0.167 0.137 0.106

0.201 0.150 0.123 0.095

3.625 1.625 0.015 0.060 0.048 0.036

0.600 0.500 0.500 0.500

0.094 0.094 0.094 0.094

0.566 0.445 0.359 0.271

1.925 1.514 1.221 0.923

1.148 0.918 0.746 0.569

0.633 0.506 0.412 0.314

1.424 1.436 1.442 1.448

0.211 0.162 0.133 0.102

3.500 2.000 0.135 0.105 0.075 0.060 0.048

0.700 0.700 0.600 0.500 0.500

0.188 0.188 0.094 0.094 0.094

1.069 0.847 0.613 0.483 0.389

3.636 2.880 2.085 1.642 1.323

2.003 1.620 1.222 0.979 0.795

1.144 0.926 0.698 0.559 0.454

1.368 1.383 1.412 1.424 1.430

3.000 1.750 0.105 0.015 0.060 0.048

0.700 0.530 0.530 0.410

0.188 0.094 0.094 0.094

0.742 0.528 0.426 0.332

2.523 1.794 1.450 1.130

1.017 0.767 0.628 0.499

0.678 0.512 0.418 0.332

2.500 1.625 0.015 0.060 0.048 0.036

0.600 0.500 0.500 0.500

0.094 0.094 0.094 0.094

0.482 0.378 0.305 0.231

1.638 1.285 1.037 0.785

0.481 0.388 0.317 0.242

0.384 0.311 0.254 0.194

Size

In.

Axis x-x

Eff. Se Prope

In.'

In.6

In.

0.987 1.002 0.949 0.915 0.921

0.00773 0.00369 0.00136 0.00069 0.00035

3.610 3.007 2.065 1.515 1.246

2.895 2.897 2.834 2.864 2.865

2.576 2.610 2.596 2.568 2.581

-1.563 -1.593 -1.533 -1.478 -1.491

4.684 3.761 2.760 2.053 1.632

0.712 0.712 0.689 0.660 0.660

1.054 1.069 1.009 0.972 0.979

0.00671 0.00331 0.00122 0.00062 0.00032

2.305 1.930 1.306 0.943 0.777

2.520 2.534 2.478 2.489 2.495

2.415 2.450 2.423 2.387 2.401

-1.699 -1.729 -1.661 -1.602 -1.614

2.751 2.219 1.644 1.223 0.972

0.601 0.597 0.603 0.609

0.539 0.511 0.511 0.511

0.818 0.785 0.791 0.797

0.00111 0.00056 0.00029 0.00012

0.802 0.577 0.477 0.370

2.260 2.291 2.294 2.296

2.132 2.104 2.118 2.132

-1.319 -1.266 -1.278 -1.290

1.448 1.143 0.895 0.663

0.199 0.148 0.122 0.094

0.611 0.602 0.608 0.614

0.564 0.536 0.536 0.536

0.841 0.801 0.813 0.819

0.00106 0.00053 0.00028 0.00012

0.660 0.471 0.390 0.303

2.126 2.148 2.153 2.157

2.067 2.037 2.050 2.064

-1.367 -1.313 -1.325 -1.337

1.148 0.908 0.712 0.527

0.568 0.468 0.344 0.264 0.216

0.456 0.375 0.271 0.203 0.166

0.729 0.743 0.749 0.739 0.745

0.753 1.093 0.00650 0.753 1.107 0.00311 0.729 1.043 0.00115 0.699 1.005 0.00058 0.699 1.011 0.00030

1.790 1.504 1.005 0.7]7 0.592

2.386 2.404 2.349 2.35] 2.358

2.359 2.394 2.358 2.318 2.333

-1.778 -1.808 - 1.734 -1.673 -1.686

2.003 1.620 1.208 0.899 0.7]5

1.171 1.206 1.213 1.225

0.318 0.224 0.185 0.138

0.300 0.202 0.167 0.120

0.654 0.651 0.658 0.644

0.689 1.016 0.00273 0.644 0.918 0.00099 0.644 0.926 0.00051 0.601 0.877 0.00026

0.835 0.486 0.406 0.272

2.100 2.045 2.054 2.051

2.128 2.050 2.068 2.011

-1.652 -1.525 -1.540 -1.460

1.017 0.767 0.617 0.442

0.999 1.014 1.019 1.025

0.184 0.141 0.116 0.089

0.190 0.141 0.116 0.090

0.618 0.611 0.617 0.622

0.656 0.626 0.626 0.627

0.337 0.230 0.191 0.149

1.859 1.856 1.864 1.873

1.937 1.896 1.910 1.924

-1.541 -1.481 -1.493 -1.505

0.481 0.385 0.303 0.224

0.923 0.885 0.891 0.897

0.00090 0.00045 0.00023 0.00010

Ix In.'

•

[~ RJ

TABLE 2

SHEAR

CE~~R ~

CHANNEL WITH UNSTIFFENED FLANGES

S -

- -

V-25 -

Area

per Foot

Properties of Full Section Axisy-y m x ly Sy ry

In.'

In.

In.'

In.

Wgl

Size

Axis x-x

]

In.

In.'

In.

0.393 0.381 0.366 0.360

0.596 0.600 0.597 0.599

0.00944 0.00447 0.00165 0.00085

5.522 4.426 3.264 2.650

4.843 4.856 4.887 4.894

3.094 ~.922 3.111 -{J.929 3.132 ~.925 3.140 -{J.929

0.399 0.404 0.407 0.410

0.284 0.272 0.257 0.25 I

0.416 0.421 0.418 0.420

0.00780 0.00370 0.00137 0.00070

1.805 1.459 1.086 0.885

4.611 4.619 4.653 4.656

2.582 -{J.633 2.598 ~.64O 2.622 ~.638 2.630 ~.641

0.166 0.132 0.096 0.078 0.063

0.414 0.419 0.423 0.425 0.427

0.310 0.298 0.283 0.277 0.272

0.447 0.451 0.447 0.449 0.451

0.00698 0.00331 0.00123 0.00063 0.00032

1.250 1.013 0.755 0.616 0.501

3.607 3.620 3.653 3.660 3.665

2.300 -{J.689 2.316 -{J.696 2.338 ~.692 2.346 ~.696 2.352 ~.698

0.089 0.067 0.054 0.044

0.090 0.066 0.054 0.043

0.347 0.350 0.353 0.355

0.256 0.241 0.235 0.230

0.376 0.372 0.374 0.376

0.00273 0.00102 0.00052 0.00027

0.395 0.297 0.244 0.199

3.001 3.036 3.042 3.047

1.919 ~.580 1.940 -{J.575 1.949 ~.579 1.955 ~.582

1.449 1.472 1.479 1.484

0.062 0.047 0.038 0.031

0.071 0.053 0.043 0.034

0.319 0.323 0.325 0.327

0.251 0.235 0.229 0.225

0.356 0.351 0.353 0.355

0.00225 0.00084 0.00043 0.00022

0.172 0.131 0.108 0.088

2.267 2.300 2.308 2.314

1.584 ~.555 1.604 ~.549 1.612 ..{).553 1.618 ~.555

0.424 0.324 0.265 0.215

1.120 1.141 1.147 1.153

0.057 0.043 0.035 0.029

0.069 0.051 0.041 0.033

0.336 0.340 0.342 0.344

0.292 0.275 0.269 0.264

0.398 0.390 0.392 0.393

0.00187 0.00070 0.00036 0.00019

0.086 0.066 0.054 0.045

1.598 1.625 1.634 1.641

1.331 1.345 1.353 1.360

0.241 0.187 0.154 0.126

0.773 0.792 0.798 0.804

0.050 0.038 0.031 0.025

0.064 0.048 0.039 0.032

0.351 0.356 0.358 0.360

0.355 0.335 0.329 0.324

0.451 0.438 0.440 0.441

0.00148 0.00056 0.00029 0.00015

0.032 0.025 0.021 0.017

U75 U91 1.200 1207

1.135 ..{).753 1.138 ~.736 1.145 ..{).738 U51 ~.741

In.

In.2

Lb.

In.'

8.000

2.000

0.135 0.105 0.075 0.060

0.188 0.188 0.094 0.094

1.554 1.216 0.880 0.706

5.284 4.135 2.993 2.402

13.075 10.335 7.599 6.127

3.269 2.584 1.900 1.532

2.901 2.915 2.938 2.945

0.485 0.386 0.283 0.229

0.302 0.238 0.173 0.140

0.559 0.563 0.567 0.569

7.000

1.500

0.135 O.IOS 0.075 0.060

0.188 1.284 0.188 1.006 0.094 .0.730 0.094 0.586

4.366 3.421 2.483 1.994

7.840 6.218 4.603 3.718

2.240 1.777 1.315 1.062

2.471 2.486 2.511 2.518

0.204 0.164 0.121 0.098

0.168 0.133 0.097 0.079

6.000

1.500

0.135 0.105 0.075 0.060 0.048

0.188 0.188 0.094 0.094 0.094

1.149 0.901 0.655 0.526 0.423

3.907 3.064 2.228 1.790 1.437

5.334 4.240 3.150 2.547 2.055

1.778 1.413 1.050 0.849 0.685

2.155 2.169 2.192 2.200 2.205

0.197 0.158 0.117 0.095 0.077

5.000

1.250

0.105 0.075 0.060 0.048

0.188 0.094 0.094 0.094

0.744 0.543 0.436 0.351

2.529 1.846 1.484 1.192

2.399 1.797 1.456 1.177

0.960 0.719 0.583 0.471

1.796 1.820 1.827 1.832

4.000

1.125

0.105 0.075 0.060 0.048

0.188 0.094 0.094 0.094

0.613 0.449 0.361 0.291

2.083 1.527 1.229 0.988

1.286 0.973 0.790 0.640

0.643 0.486 0.395 0.320

3.000

1.1~

0.105 0.075 0.060 0.048

0.188 0.094 0.094 0.094

0.508 0.374 0.301 0243

1.726 1.272 1.025 0.825

0.636 0.487 0.397 0.322

0.105 0.075 0.060 0.048

0.188 0.094 0.094 0.094

0.403 0.299 0.241 0.195

1.369 1.017 0.821 0.661

0.241 0.187 0.154 0.126

2.000

1.l2S

~.637 ~.627

~.631 ~.634

TABLE3Z-SECTION WITH STIFFENED FLANGES

s-- -----

[:J,

"2 - --

- - V-25 --

-I

Wgt.

Size t

In.

12000

3.500

0.135 0.105

1.010 0.900

10.000

3.500

0.135 0.105 0.075

Area

per

Axis x-x

Properties of Full Section Axis Axisy-y by X2 - X2 90"-8

Eff. S Prop

Foot

In.2

Lb.

In."

In.'

In."

0.188 0.188

2.706 2.097

9.199 7.129

56.267 9.378 43.836 7.306

4.560 4.573

5.967 1.738 4.535 1.315

1.485 13.151 1.006 13.803 1.471 10.096 0.999 13.596

0.01644 0.00771

162.474 123.250

55.387 40.904

1.010 0.900 0.720

0.188 0.188 0.094

2.436 1.887 1.344

8.281 6.415 4.568

36.526 7.305 28.506 5.701 20.533 4.107

3.873 3.887 3.909

5.967 1.738 4.535 1.315 3.109 0.898

1.S65 10.866 1.013 17.709 1.550 1.521

8.355 1.006 17.440 5.842 0.996 16.923

0.01480 0.00693 0.00252

108.445 82.180 54.811

35.957 26.513 17.571

In.]

In.

In."

----

In.]

In.

rmin In."

In.

Deg.

9.000

3.250

0.135 O.IOS 0.075 0.060

1.000 0.840 0.700 0.610

0.188 0.188 0.094 0.094

2.230 1.717 1.228 0.976

7.584 5.836 4.176 3.319

27.158 21.077 15.287 12.182

6.035 4.684 3.397 2.707

3.489 3.504 3.528 3.533

4.868 3.594 2.516 1.941

1.530 1.124 0.783 0.603

1.477 1.447 1.431 1.410

8.505 6.422 4.557 3.566

0.945 0.931 0.927 0.918

18.674 18.151 17.756 17.427

0.01355 0.00631 0.00230 0.00117

71.593 52.550 35.747 27.515

27.157 20.030 13.551 9.703

8.000

3.000

0.135 0.105 0.075 0.060

0.930 0.810 0.700 0.600

0.188 0.188 0.094 0.094

2.009 1.553 1.116 0.885

6.831 5.279 3.793 3.008

19.372 15.125 11.046 8.791

4.843 3.781 2.761 2.198

3.105 3.121 3.147 3.152

3.778 2.845 2.028 1.552

1.288 0.965 0.685 0.523

1.371 1.354 1.348 1.324

6.357 4.868 3.500 2.725

0.868 0.860 0.862 0.851

19.596 19.203 18.909 18.488

0.01221 0.00571 0.00209 0.00106

43.700 32.762 22.664 17.277

19.371 14.727 9.965 7.397

7.000

2750

0.135 0.105 0.075 0.060

0.880 0.880 0.700 0.600

0.188 0.188 0.094 0.094

1.793 1.410 1.003 0.795

6.097 4.794 3.411 2.702

13.266 10.553 7.659 6.099

3.790 3.015 2.188 1.742

2.720 2.736 2.763 2.770

2.900 2.355 1.607 1.227

1.081 0.873 0.592 0.451

1.272 1.292 1.266 1.242

4.636 3.727 2.612 2.033

0.794 0.805 0.796 0.785

20.907 21.140 20.399 19.922

0.01089 0.00518 0.00188 0.00095

25.576 20.824 13.678 10.388

13.266 10.548 7.033 5.368

6.000

2500

0.135 0.105 0.075 0.060

0.820 0.820 0.820 0.600

0.188 0.188 0.094 0.094

1.574 1.240 0.909 0.705

5.353 4.215 3.089 2.396

8.575 6.843 5.124 4.012

2.858 2.281 1.708 1.337

2.334 2.349 2.375 2.386

2.155 1.758 1.353 0.950

0.886 0.718 0.549 0.384

1.L70 1.191 1.220 1.161

3.235 2.610 1.977 1.463

0.716 0.728 0.746 0.718

22.609 22.874 23.180 21.845

0.00956 0.00456 0.00170 0.00085

13.873 11.356 8.532 5.865

8.575 6.843 4.944 3.606

5.000

2.000

0.135 0.1 OS 0.075 0.060 0.048

0.700 0.700 0.600 0.500 0.500

0.188 0.188 0.0')4

0.094 0.094

1.272 1.005 0.726 0.573 0.461

4.325 3.416 2.467 1.948 1.568

4.684 3.761 2.797 2.227 1.804

1.874 1.504 1.119 0.891 0.722

1.919 1.935 1.963 1.972 1.978

1.070 0.883 0.637 0.480 0.393

0.554 0.454 0.325 0.244 0.199

0.917 0.938 0.937 0.915 0.924

1.680 1.368 0.998 0.772 0.629

0.568 0.579 0.583 0.573 0.577

21.456 21.780 21.376 20.726 20.860

0.00773 0.00369 0.00136 0.00069 0.00035

4.904 4.063 2.805 2.094 1.719

4.684 3.761 2.760 2.053 1.632

0.135 0.105 0.075 0.060 0.048

0.700 0.700 0.600 0.500 0.500

0.188 0.188 0.094 0.094 0.094

1.137 0.900 0.651 0.513 0.413

3.866 3.059 2.212 1.744 1.404

2.752 2.219 1.664 1.330 1.079

1.376 1.110 0.832 0.665 0.539

1.556 1.599 1.610 1.616

1.070 0.883 0.637 0.480 0.393

0.554 0.454 0.325 0.244 0.199

0.970 0.991 0.990 0.967 0.976

1.313 1.071 0.786 0.610 0.498

0.556 0.567 0.570 0.561 0.565

28.685 29.031 28.426 27.572 27.717

0.00671 0.00331 0.00122 0.00062 0.00032

3.000 2.496 1.716 1.274 1.047

2.751 2.219 1.644 1.223 0.972

4.000

2000

1.S71

3.500

2.000

0.135 0.105 0.075 0.060 0.048

0.700 0.700 0.600 0.500 0.500

0.188 0.188 0.094 0.094 0.094

1.069 0.847 0.613 0.483 0.389

3.636 2.880 2.085 1.642 1.323

2.003 1.620 1.222 0.979 0.795

1.145 0.926 0.698 0.559 0.454

1.369 1.383 1.412 1.424 1.430

1.070 0.883 0.637 0.480 0.393

0.554 0.454 0.325 0.244 0.199

1.000 1.021 1.020 0.997 1.005

1.130 0.923 0.680 0.529 0.432

0.542 0.552 0.556 0.546 0.550

33.783 34.120 33.367 32.376 32.520

0.00650 0.00311 0.00115 0.00058 0.00030

2.242 1.871 1.282 0.947 0.780

2.003 1.620 1.208 0.899 0.715

3.000

1.750

O.IOS 0.075 0.060 0.048

0.700 0.530 0.530 0.410

0.188 0.094 0.094 0.094

0.742 0.528 0.426 0.332

2.523 1.794 1.45 1.130

1.017 0.767 0.628 0.499

0.678 0.512 0.418 0.332

1.171 1.206 1.213 1.225

0.618 0.418 0.346 0.251

0.364 0.244 0.201 0.145

0.912 0.890 0.900 0.868

0.610 0.437 0.360 0.274

0.487 0.480 0.485 0.472

35.937 34.107 34.302 32.822

0.00273 0.00099 0.00051 0.00026

0.990 0.617 0.514 0.362

1.017 0.767 0.617 0.442

•

TABLE 4

Z-SECTION WITH

UNSTIFFENEDFLANGES

V-25 Wgt.

Size

Area

Axis x-x

per Foot

Prooerties of Full Section Axis Axis v-v 1y X2-X2 90"-0 Iy Sy ry rmiD In.4 In.4 1n.3 In. In. Deg.

]

In.4

In.'

Eff. Section Properties 1

In.4

In.

1n.

Lb.

In.4

In.)

In.

8.000

2.000

0.135 0.105 0.075 0.060

0.188 0.188 0.094 0.094

1.554 1.216 0.880 0.706

5.284 4.135 2.993 2.402

13.076 lOj35 7 99 6.127

3.269 2.584 1.900 1.532

2.901 2.915 2.938 2.945

0.649 0.517 0.378 0.306

0.336 0.265 0.193 0.155

0.646 0.652 0.655 0.658

1.987 1.575 1.145 0.925

0.467 0.471 0.477 0.479

8.868 8.895 8.800 8.814

0.00944 0.00447 0.00165 0.00085

7.562 6.061 4.460 3.621

12.691 9.581 6.519 4.820

3.12 2.30 1.51 1.06

7.000

1.500

0.135 0.105 0.075 0.060

0.188 0.188 0.094 0.094

1.284 1.006 0.730 0.586

4.366 3.421 2.483 1.994

7.840 6.218 4.603 3.718

2.240 · 1.777 1.315 1.062

2.471 2.486 2.511 2.518

0.264 0.212 0.156 0.127

0.184 0.146 0.107 0.086

0.453 0.459 0.463 0.465

0.955 0.761 0.556 0.450

0.337 0.341 0.347 0.349

7.074 7.112 7.021 7.041

0.00780 0.00370 0.00137 0.00070

2.429 1.964 1.458 1.188

7.840 6.120 4.219 3.278

2.24 1.73 1.15 0.88

6.000

1.500

0.135 0.105 0.075 0.060 0.048

0.188 0.188 0.094 0.094 0.094

1.149 0.901 0.655 0.526 0.423

3.907 3.064 2.228 1.790 1.437

5.334 4.240 3.150 2.547 2.055

1.778 1.413 1.050 0.849 0.685

2.155 2.169 2.193 2.200 2.205

0.264 0.212 0.156 0.127 0.103

0.184 0.146 0.1 07 0.086 0.070

0.479 0.485 0.488 0.491 0.493

0.816 0.651 0.476 0.385 0.311

0.344 0.348 0.355 0.357 0.359

8.918 8.952 8.816 8.835 8.850

0.00698 0.00331 0.00123 0.00063 0.00032

1.715 1.389 1.032 0.842 0.685

5.334 4.168 2.868 2.223 1.716

1.77 1.37 0.91 0.69 0.52

5.000

1.250

0.105 0.075 0.060 0.048

0.188 0.094 0.094 0.094

0.744 0.543 0.436 0.351

2.529 1.846 1.484 1.192

2.399 1.797 1.456 1.177

0.960 0.719 0.583 0.471

1.796 1.820 1.827 1.832

0.120 0.089 0.073 0.059

0.100 0.073 0.060 0.048

0.401 0.405 0.408 0.410

0.370 0.272 0.221 0.179

0.287 0.294 0.296 0.298

9.003 8.830 8.853 8.870

0.00273 0.00102 0.00052 0.00027

0.543 0.407 0.333 0.272

2.399 1.700 1.320 1.024

0.96 0.66 0.50 0.38

4.000

1.500

0.060

0.094

0.406

1.382

0.965 0.483 1.541

0.127 0.086 0.559

0.256

0.369 15.693

0.00049

0.335

0.819

0.37

4.000

1.125

0.105 0.075 0.060 0.048

0.188 0.094 0.094 0.094

0.613 0.449 0.361 0.291

2.083 1.527 1.229 0.988

1.286 0.973 0.791 0.640

0.086 0.064 0.052 0.043

0.375 0.378 0.381 0.383

0.237 0.174 0.142 0.115

0.259 0.267 0.269 0.271

10.764 10.500 10.521 10.538

0.0022S 0.00084 0.00043 0.00022

0.240 0.181 0.149 0.122

1.286 0.938 0.730 0.565

0.64 0.46 0.35 0.26

3.000

1.500

0.060

0.094

0.346

1.178

0.494 0.329 1.194

0.127 0.086 0.606

0.191

0.364 23.054

0.00040

0.172

0.412

0.24

3.000

1.125

0.105 0.075 0.060 0.048

0.188 0.094 0.094 0.094

0.508 0.374 0.301 0.243

1.726 1.272 1.025 0.825

0.636 0.487 0.397 0.322

0.424 0.324 0.265 0.215

1.120 1.141 1.147 1.153

0.086 0.064 0.052 0.043

0.080 0.059 0.048 0.039

0.412 0.414 0:417 0.420

0.176 0.130 0.106 0.086

0.261 0.271 0.273 0.275

16.288 15.802 15.800 15.799

0.00187 0.00070 0.00036 0.00019

0.123 0.094 0.077 0.063

0.636 0.467 0.363 0.280

0.42 0.30 0.23 0.17

2.000

1.125

0.105 0.075 0.060 0.048

0.188 0.094 0.094 0.094

0.403 0.299 0.241 0.195

1.369 1.017 0.821 0.661

0.241 0.188 0.154 0.126

0.773 0.792 0.798 0.804

0.086 0.064 0.052 0.043

0.080 0.059 0.048 0.039

0.462 0.464 0.466 0.468

0.115 0.086 0.070 0.057

0.248 0.262 0.264 0.266

28.036 27.111 27.020 26.949

0.00148 0.00056 0.00029 0.00015

0.047 0.036 0.030 0.025

0.241 0.179 0.139 0.107

0.24 0.17 0.13 0.09

1.500

0.048 0.036

0.094 0.094

0.207 0.156

0.702 0.530

0.084 0.112 0.639 0.065 0.086 0.644

0.103 0.070 0.706 0.078 0.053 0.708

0.076 0.058

0.287 41.503 0.289 41.686

0.00016 0.00007

0.027 0.021

0.062 0.044

0.07 0.04

0.643 0.486 0.395 0.320

1.449 1.472 1.479 1.485

0.080 0.059 0.048 0.039

(/)

"'tJ

(")

jj (")

oz~

•

SPECIFICATION FOR THE DESIGN OF COLD-FORMED STEEL STRUCTURAL MEMBERS AUGUST 19,1986, EDITION

•

WITH DECEMBER 11, 1989 ADDENDUM

Cold-Formed Steel Design Manual - Part I

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AMERICAN IRON AND STEEL INSTITUTE 1133 15th STREET, NW WASHINGTON, DC 20005-2701

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Cold-Fonned Specification - August 19, 1986 Edition with December II, 1989 Addendum

• This publication is for general information only. The information in it should not be used without first securing competent advice with respect to its suitability for any given application. The publication of the information is not intended as a representation or warranty on the part of American Iron and Steel Institute - or any other person named herein - that the information is suitable for any general or particular use or of freedom from infringement of any patent or patents. Anyone making use of the information assumes all liability arising from such use.

• I st Printing - January, 1991

Produced by Computerized Structural Design, Inc. Milwaukee, Wisconsin Copyright American Iron and Steel Institute 1986, 1989

•

Cold-Fonned Specification - August 19. 1986 Edition with December II! 1989 Addendum

• PREFACE TO 1989 ADDENDUM

Several changes and additions to the 1986 Edition of AISI' s Specification for the Design ofCold-Fonned Steel Structural Members are contained in the 1989 Addendum to the Specification. The results of continuing research, advances in design techniques, development of new steels, and the needs of the design profession and consuming industries have all given impetus to the Addendum. AISI acknowledges the continuing support and hard work by the members of Advisory Group on the Specification and its subcommittees. The current membership lists follow this preface. Development and publication of the Specification is sponsored by AISI's Construction Marketing Committee, Light Construction Subcommittee, under the auspices of AISI's Committee on Construction Codes and Standards.

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All users of the Specification are encouraged to continue £0 provide their invaJuable recommendations for improvement. American Iron and Steel Institute December 11, 1989

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Cold-Fonned Specification - August 19, 1986 Edition with December 11 , 1989 Addendum

AISI Advisory Group On the Specification for the Design of Cold-Formed Steel Structural Members and its Subcommittees S.J. Errera, Chairman A.L. Johnson, Secretary RE. Albrecht R Bjorhovde R.L. Brockenbrough RE. Brown C.R Clauer D.A. Cuoco D.S. Ellifritt E.R Estes, Jr.

J.M. Fisher T.V. Galambos M. Golovin W.B. Hall G.S. Harris RB. Heagler N.Iwankiw D.L. Johnson TJ. Jones H. Klein

Subcommittee 3 - Connections J.N. Macadam, Chainnan R Bjorhovde E.R diGirolamo E.R Estes, Jr. A.L. Johnson

D.L. Johnson RA. LaBoube T.B. Pekoz W.W.Yu A.S. Zakrzewski

Subcommittee 5 - Channel & Z-Sections D.S. Ellifritt, Chairman R.L. Brockenbrough C.R Clauer J.M. Fisher M. Golovin G.S. Harris D.L. Johnson

RA. LaBollbe T.M. Murray J.N. Nunnery T.B. Pekoz D.C. Perry P.A. Seaburg

Subcommittee 7 - Editorial C.W. Pinkham, Chairman C.R. Clauer D.A. Cuoco

J.M. Fisher T.B. Pekoz

Subcommittee 11 - Welding R.E. Albrecht, Chainnan R Bjorhovde O.W. Blodgett D.S. Ellifritt A.L. Johnson

L.D. Luttrell W. McGuire C.W. Pinkham W.W.Yu

K.H. Klippstein R.A. LaBoube J.N. Macadam R.R. McClure W.R. Midgley TJ. Morrison J.A. Moses T.M. Murray G.G. Nichols J.N. Nunnery

T.B. Pekoz C.W. Pinkham P.G. Schurter R.M. Schuster P.A. Seaburg F.V. Slocum D.L. Tarlton D.S. Wolford W.W.Yu A.S. Zakrzewski

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Subcommittee 4 -Stud Design; Perforated Elements R.M. Schuster, Chairman T.W. Trestain, Secretary R. Bjorhovde F.M. Bollio R.E. Brown C.R. Clauer E.R. diGirolamo L. Hernandez H. Klein K.H. Klippstein

R.A. LaBoube J.P. Matsen, P.E. W.R. Midgley R.N. Parker T.B. Pekoz C. W. Pinkham G.S. Ralph J.E. Sullivan A.S. Zakrzewski

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Subcommittee 6 - Test Procedures W.B. Hall, Chairman E.R. Estes, Jr. D.L. Johnson K.H. Klippstein R.A. LaBoube R.W. Lautensleger

W.R. Midgley T.M. Murray T.B. Pekoz R.M. Schuster W.W.Yu A.S. Zakrzewski

Subcommittee 10 - Element Behavior D.L. Johnson, Chairman R.E. Albrecht SJ. Errera M. Golovin W.R. Midgley

T.M. Murray J.N. Nunnery T.B. Pekoz C.W. Pinkham T.W. Trestain

Subcommittee 13 - Diaphragms J.M. Fisher, Chainnan RE. Brown D.S. Ellifritt SJ. Errera R.B. Heagler

R.A. LaBoube L.D. Luttrell C. W. Pinkham T.S. Tarpy

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Cold-Fonned Specification - August 19, 1986 Edition with December 11, 1989 Addendum

•

Subcommittee 14 - International Standards

AL. Johnson, Chairman RE. Albrecht

T.B. Pekoz D.S. Wolford

Subcommittee 17 - Quality in Construction

W.R Midgley, Chairman RE. Albrecht E.R diGirolamo D.S. Ellifritt RA LaBoube

J.A. Moses T.B. Pekoz D.W. Wolford A.S. Zakrzewski

Subcommittee 19 - Applications Aids

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P.A. Seaburg, Chairman R.E. Brown E.R Estes, Jr. 1M. Fisher RS. Glauz R.E. Hodges, Jr.

M. Johanningsmeier D.L. Johnson R.A LaBoube T.M. Murray RM. Schuster W.W.Yu

Subcommittee 21-Research Needs

RL. Brockenbrough, Chairman Chairman D.L. Johnson R Bjorhovde T.M. Murray E.R Estes, Jr. J.N. Nunnery 1M. Fisher T.B. Pekoz RB. Heagler R.M. Schuster RA LaBoube W.W. Yu Subcommittee 23 - LRFD

K.H. Klippstein, Chairman R Bjorhovde D.S. Ellifritt T.V. Galambos M. Golovin D.H. Hall W.B. Hall

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RB. Heagler D .L. Johnson A.S. Nowak T.B. Pekoz C.W. Pinkham R.M. Schuster W.W.Yu

Subcommittee 25 - Commentary

D.S. Ellifritt, Chairman RE. Albrecht R.A LaBoube

T.B. Pekoz D.S. Wolford W.W.Yu

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Subcommittee 15 - Materials; Ductility

E.R. Estes, Jr., Chairman D.L. Johnson RA LaBoube J.N. Macadam

T.B. Pekoz F.V. Slocum D.S. Wolford

Subcommittee 18 - Cylindrical Members

R.M. Schuster, Chairman T.B. Pekoz D.R. Sherman

D.S. Wolford W.W.Yu

Subcommittee 20 - Simplification

D.A Cuoco, Chairman RE. Brown c.R. Clauer R.B. Haws R.B. Heagler K.H. Klippstein

R.A. LaBoube T.B. Pekoz C. W. Pinkham R.M. Schuster D.S. Wolford

Subcommittee 22-Compression Members

IN. Macadam

R. Bjorhovde,

1 Crews D.S. Ellifritt N.Iwankiw

J.N. Macadam T.B. Pekoz

Subcommittee 24 - Flexural Members

RA. LaBoube, Chairman R.E. Albrecht R. Bjorhovde R.E. Brown D.S. Ellifritt E.R. Estes, Jr. T. V. Galambos M. Golovin RB. Heagler

D.L. Johnson K.H. Klippstein J.N. Macadam J.N. Nunnery T.B. Pekoz R.M. Schuster F.V. Slocum T.W. Trestain W.W.Yu

Subcommittee 26 - Design Manual

D.L. Johnson, Chairman c.R. Clauer R.B. Haws

H. Klein R.A LaBoube

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Cold-Formed Specification - August 19 , 1986 Edition with December 11 , 1989 Addendum

Joint AISC/AISI Specification Coordination N. Iwankiw, Chainnan R. Bjorhovde R.L.Brockenbrough D.S. Ellifritt J.M. Fisher T.V. Galambos

RA. LaBoube T.M. Murray T.B. Pekoz C.W. Pinkham W.W.Yu

ML/SFA-AISI Joint Task Force C. Bissey R.L. Brockenbrough R.R. Garris L. Hernandez A.L. Johnson K.H. Klippstein RA. LaBoube

RN. Parker T.B. Pekoz N. Peterson G.S. Ralph RM. Schuster J .E. Sullivan T.W. Trestain

Ad Hoc Task Force on Purlin Stock J.N. Macadam, Chainnan RL. Brockenbrough E.R. Estes, Jr.

R.A. LaBoube T.B. Pekoz

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Steering Committee S.J. Errera, Chainnan A.L. Johnson, Secretary

C.R Clauer D.L. Johnson

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Cold-Fonned Specification - August 19. 1986 Edition with December 11. 1989 Addendum

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PERSONNEL RE. Albrecht C. Bissey R Bjorhovde O.W. Blodgett F.M. Bolio RL. Brockenbrough RE. Brown C.R. Clauer J. Crews D.A Cuoco E.R diGirolamo D.S. Ellifritt S.J. Errera E.R Estes, Jr. J.M. Fisher T.V. Galambos RR Garris RS. Glauz M. Golovin D.H. Hall W.G. Hall RB. Haws G.S. Harris RB. Heagler L. Hernandez RE. Hodges, Jr. N.lwankiw M. Johanningsmeier A.L. Johnson D.L. Johnson TJ. Jones H. Klein K.H. Klippstein RA LaBoube RW. Lautensleger L.D. Luttrell J.N. Macadam J.P. Matsen RM. McClure W. McGuire W.R Midgley TJ. Morrison J.A. Moses T.M. Murray G.G. Nichols AS. Nowak

H.H. Robertson Company Kansas State University University of Pittsburgh Lincoln Electric Company Marino Industries Corporation USS Division USX Corporation Wheeling Corrugating Company Clauer Associates Litton UHS/AMS Lev Zetlin Associates, Inc. E.R. diGirolamo, P.E., P.C. University of Florida Bethlehem Steel Corporation Old Dominion University Computerized Structural Design University of Minnesota Dale Industries The Marley Cooling Tower Company The Ceco Corporation Bridge Software Development Int. University of Waterloo H.H. Robertson Company MBMA United Steel Deck, Inc. Western Metal Lath Varco-Pruden Buildings AISC Building Technologies Corporation American Iron and Steel Institute Butler Manufacturing Company Structural Engineer Unarco Industries, Inc. Structural Engineer University of Missouri-Rolla Armco Inc. West Virginia University Armco, Inc. Matsen Ford Design Associates, Inc. BOCA Cornell University Midgley, Clauer & Associates IntI. Conference of Bldg. Officials Unistrut Virginia Polytechnic Institute SBCCI University of Michigan

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Cold-Fonned Specification - August 19,1986 Edition with December 11,1989 Addendum

PERSONNEL J.N. Nunnery R. Parker T.B. Pekoz D.C. Perry N. Peterson C.W. Pinkham G.S. Ralph P.G. Schurter R.M. Schuster P.A. Seaburg D.R. Sherman F.V. Slocum J.E. Sullivan D.L. Tarlton T.S. Tarpy T.W. Trestain D.S. Wolford W.W.Yu A.S. Zakrzewski

AMCA International Bostwick Steel Framing, Inc. Cornell University Southern Bldg. Code Congress Int. DEVCO Engineering, Inc. S.B. Barnes Associates Dietrich Industries, Inc. Dofasco, Inc. University of Waterloo Pennsylvania State University University of Wisconsin National Steel Corporation Unimast, Inc. CSSBI S.D. Lindsay and Associates T.W.J. Trestain Structural Engineering Consultant University of Missouri-Rolla Proen Consultants

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Cold-Formed Specification - August 19, 1986 Edition with December II, 1989 Addendum

• PREFACE In memory of George Winter, in recognition of his many contributions and achievements to the enhancements of cold-formed steel design. The newly published Edition of AISI's Specification for the Design of Cold-Formed Steel Structural Members represents a major revision, with many changes made to keep the Specification responsive to the needs of users. It reflects the results of research projects and improvements in design techniques. Moreover, it embodies the results of efforts to simplify the use of the Specification by changes in its format, organization, and content. To accomplish this simplification, relevant sections needed to design a particular member, such as a beam or a column, have been collected together as much as possible.

•

AISI acknowledges the devoted efforts of the members of the Advisory Group on the Specification of the Design of Cold-Formed Steel Structural Members. This group, comprised of consulting engineers, researchers, designers from companies manufacturing coldformed steel members, components, assemblies, and complete structures, and specialists from the steel producing industry, has met two to three times per year since its establishment in 1973. Its current members, who have made extensive contributions of time and effort in developing and reaching consensus on the changes which have been described above, are: R. E. Albrecht Reidar Bjorhovde R. E. Brown C. R. Clauer D. A. Cuoco D. S. Ellifritt S. 1. Errera, Chairman E. R. Estes, Jr. 1. M . Fisher S. R. Fox T. V. Galambos Gerhard Haaijer R. W. Haussler

R. B. Heagler A. L. Johnson, Secretary D. L. Johnson T. J. Jones (Assoc.) Herbert Klein K. H. Klippstein* R. A. LaBoube J. N. Macadam T.1. McCabe R. M. McClure J. A. Moses T. M. Murray G. G. Nichols

A. J. Oudheusden T. B. Pekoz D. C. Perry C. W. Pinkham T. G. Ryan P. G. Schurter R. M. Schuster P. A. Seaburg J. S. Traw D. S. Wolford* D. R. Wootten Wei-Wen Yu A. S. Zakrzewski

The activities of the Advisory Group are sponsored by AISl's Committee of Sheet Steel Producers. The Specification is issued under the auspices of AISI' s Committee on Construction Codes and Standards. Users of the Specification are invited to continue to offer their valuable comments and suggestions. The cooperation of all involved, the users as well as the writers, is needed to continue to keep the Specification up to date and a useful tool for the designer.

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American Iron and Steel Institute August 19, 1986

*Past Chairman

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Cold-Fonned Specification - August 19, 1986 Edition with December II , 1989 Addendum

•

TABLE OF CONTENTS SPECIFICATION FOR THE DESIGN OF

COLD-FORMED STEEL STRUCTURAL MEMBERS AUGUST 19, 1986 EDITION WITH DECEMBER 11, 1989 ADDENDUM PREFACE TO 1989 ADDENDUM ............................................... AISI ADVISORY GROUP AND SUBCOMMITTEE MEMBERS .................... PERSONNEL ................................................................ PREFACE TO 1986 EDITION .................................................. SYMBOLS AND DEFINITIONS ................................................. A. GENERAL PROVISIONS .. .. .. . . . .. . . .. . .. . . . . . .. .. . . . . . . . . . . .. . . .. .. .. . ... A 1 Limits of Applicability and Terms .......................................... . A 1.1 Scope and Limits of Applicability ..................................... . Al.2 Terms ........................................................... . Al.3 Units of Symbols and Terms ......................................... . A2 Non-Conforming Shapes and Construction ................................... . A3 Material ............................................................... . A3.1 Applicable Steels .................................................. . A3.2 Other Steels ...................................................... . A3.3 Ductility ......................................................... . A3.4 Delivered Minimum Thickness ....................................... . A4 Loads ................................................................ . A4.1 Dead Load ....................................................... . A4.2 Live Load ........................................................ . A4.3 Impact Load ...................................................... . A4.4 Wind or Earthquake Loads ........................................... . A4.5 Ponding ......................................................... . A5 Structural Analysis and Design ............................................ . A5.1 Design Basis ...................................................... . A5.2 Yield Point and Strength Increase from Cold Work of Forming .............. . AS.2.l Yield Point ........................................... . AS.2.2 Strength Increase from Cold Work of Forming ............... . A5.3 Serviceability and Durability ............ . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. A6 Reference Documents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. B. ELEMENTS............................................................... B I Dimensional Limits and Considerations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. B1.1 Flange Flat-Width-to-Thickness Considerations .......................... B 1.2 Maximum Web Depth-to-Thickness Ratio ............................... B2 Effective Widths of Stiffened Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. B2.1 Uniformly Compressed Stiffened Elements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. B2.2 Uniformly Compressed Stiffened Elements with Circular Holes .............. B2.3 Effective Width of Webs and Stiffened Elements with Stress Gradient ......... B3 Effective Widths of Un stiffened Elements ..................................... B3.1 Uniformly Compressed Un stiffened Elements ............................ B3.2 Un stiffened Elements and Edge Stiffeners with Stress Gradient ............... B4 Effective Widths of Elements with an Edge Stiffener or One Intermediate Stiffener .... B4.1 Uniformly Compressed Elements with an Intermediate Stiffener .............. B4.2 Uniformly Compressed Elements with an Edge Stiffener ... 0' • • • • • • • • • • • • • • • •

1-3 1-4

1-7 1-9 1-13 1-23 1-23 1-23 1-23 1-24 1-24 1-24 1-24 1-25 1-25 1-26 1-26 1-26 1-26 1-26 1-26 1-26 1-26 1-26 1-27

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1-27 1-27 1-28 1-29 1-31 1-31 1-31 1-32 1-33 1-33 1-34 1-35 1-35 1-35 1-36 1-37 1-37 1-38

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Cold-Fonned Specification - August 19, 1986 Edition with December 11, 1989 Addendum

•

B5 Effective Widths of Edge Stiffened Elements with Intermediate Stiffeners or Stiffened Elements with More Than One Intermediate Stiffener. . . . . . . . . . . . . . . . . . .. B6 Stiffeners.................................................. . ... .. .... ... B6.1 Transverse Stiffeners ........................ .... ............... ..... B6.2 Shear Stiffeners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. B6.3 Non-Conforming Stiffeners. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. C. MEMBERS........................................ . . . . . . .. ................ C 1 Properties of Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. C2 Tension Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. C3 Flexural Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. C3.1 Strength for Bending Only . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

1-39 1-40 1-40 1-41 1-42 1-43 1-43 1-43 1-43 1-43

C3.1.1 Nominal Section Strength ................................ 1--43 C3.1.2 Lateral Buckling Strength ................................ 1-44 C3.1.3 Beams Having One Flange Through-Fastened to Deck or Sheathing 1--47 C3.2 Strength for Shear Only ...................... ...... .... . . . . . . . . . . . . .. C3.3 Strength for Combined Bending and Shear .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. C3.4 Web Crippling Strength .............................................. C3.5 Combined Bending and Web Crippling Strength .......................... C4 Concentrically Loaded Compression Members ................................. C4.1 Sections Not Subject to Torsional or Torsional-Flexural Buckling ............ C4.2 Ooubly- or Singly-Symmetric Sections Subject to Torsional or Torsional-Flexural Buckling .......................................... C4.3 Nonsymmetric Sections ....................... ........... .... . . . . . . .. C5 Combined Axial Load and Bending .................... . ... . ................. C6 Cylindrical Tubular Members ............................................... C6.1 Bending ........................................ .... .. ... ......... C6.2 Compression................................ ............. .......... C6.3 Combined Bending and Compression ................................... D. STRUCTURAL ASSEMBLIES.. . .. .. .. . .. . . .. . . .. . . . . . .. .. . . . . . . . .. . . . . . . ... 01 Built-Up Sections .................................... .. ...... ... ......... 01.1 I - Sections Composed of Two Channels ........... . .................... 01.2 Spacing of Connections in Compression Elements ......................... 02 Mixed Systems ................................... ....... .... . .......... 03 Lateral Bracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 03.1 Symmetrical Beams and Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 03.2 Channel-Section and Z-Section Beams ........ ..... ....................

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I-II

1-48 1-48 1-49 I-51 I-51 I-52 I-53 I-53 I-53 I-54 I-54 I-55 I-55 I-56 I-56 I-56 I-57 I-57 I-57 I-57 I-57

D3.2.1 Anchorage of Bracing for Roof Systems Under Gravity Load With Top Flange Connected to Sheathing . . . . . . . . . . . . . . . . . . .. I-58 D3.2.2 Neither Flange Connected to Sheathing. . . . . . . . . . . . . . . . . . . . .. I-59

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03.3 Laterally Unbraced Box Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 04 Wall Studs and Wall Stud Assemblies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 04.1 Wall Studs in Compression ................... ....... . . ............... 04.2 WaH Studs in Bending ............................................... 04.3 Wall Studs with Combined Axial Load and Bending ....................... D5 Floor, Roof or Wall Steel Diaphragm Construction .............................. E. CONNECTIONS AND JOINTS .............................................. E 1 General Provisions ....................................................... E2 Welded Connections ...................................................... E2.l Groove Welds in Butt Joints .......................................... E2.2 Arc Spot Welds ....................................................

1-60 1-60 1-61 1-63 1-63 1-64 1-65 1-65 1-65 1-65 1-65

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Cold-Fonned Specification - August 19. 1986 Edition with December II. 1989 Addendum

E2.3 Arc Seam Welds ................................................... . E2.4 Fillet Welds ...................................................... . E2.S Flare Groove Welds ....................... ... ...................... . E2.6 Resistance Welds .................................................. . E3 Bolted Connections ...................................................... . E3.1 Spacing and Edge Distance .......................................... . E3.2 Tension in Connected Part ........................................... . E3.3 Bearing .. ...... .. ......... ........... .... .................. ... ... . E3.4 Shear and Tension in Bolts ............ . ...... . ................ ... ... . E4 Shear Rupture ....... . ..................................... . .... ........ . ES Connections to Other Materials ........................................ . ... . ES.l Bearing .......................................................... . ES.2 Tension ...... ... ................................................. . ES.3 Shear ............................................................ . F. TESTS FOR SPECIAL CASES ............................................. . FI Tests for Determining Structural Performance ................................. . F2 Tests for Conftrming Structural Performance ..... ... ......................... . F3 Tests for Determining Mechanical Properties ................................. . F3.1 Full Section . ..................................................... . F3.2 Flat Elements of Formed Sections ..................................... . F3.3 Virgin Steel ...................................................... .

1-69 1-70 1-71 1-73 1-73 1-74 1-7S 1-7S 1-76 1-78 1-78 1-78 1-78 1-79 1-80 1-80 1-80 1-81 1-81 1-81 1-82

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Cold-Fonned Specification - August 19,1986 Edition with December 11, 1989 Addendum

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1-13

SYMBOLS AND DEFINITIONS

Symbol

Definition

Section

A A Ab

C3.l.l, C3.1.2, C4, C6.2, 04.1 Full unreduced cross-sectional area of the member ES.l Contact area bIt + As, for transverse stiffeners at interior support and under B6.1, E3.4 concentrated load, and b2t + As, for transverse stiffeners at end support

18t2 + As, for transverse stiffeners at interior support and under concentrated load, and 10t 2 + As, for transverse stiffeners at end support

B6.l

Ae An As A's ASl Awn Al A2 a

Effective area at the stress Fn Net area of cross section Cross-sectional area of transverse stiffeners Effective area of stiffener Gross area of shear stiffener Net web area Bearing area Full cross sectional area of concrete support Shear panel length of the unreinforced web element. For a reinforced web element, the distance between transverse stiffeners

C4, C6.2, 04.1 C2, E3.2 B4, B4.l, B4.2, B6.1 B4, B4.l, B4.2 B6.2 E4 ES.1 ES.l B6.2, C3.2, 03.2

Lateral deflection of the compression flange at assumed load, q.

C3.1.3

a B Be b

Length of bracing interval Stud spacing Term for determining the tensile yield point of comers Effective design width of compression element

03.2 04,04.1 AS.2.2 B2.l, B2.2, B2.3, B3.1, B3.2, B4.1, B4.2, BS

b bd be bo C

Overall width of compression flange, C or Z Effective widths for deflection calculations Effective design width of sub--element or element See Figure B4.l For flexural members, ratio of the total comer crosssectional area of the controlling flange to the full crosssectional area of the controlling flange

03.2.l B2.1, B2.2 Al.2, B2.3, B5 B4, B4.l, BS AS.2.2

Cb Cm

Bending coefficient dependent on moment gradient End moment coefficient in interaction formula

C3.l.l CS

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Cold-Fonned Specification - August 19, 1986 Edition with December II, 1989 Addendum

SYMBOLS AND DEFINITIONS

Symbol

Definition

Section

Cms Cmx, Cmy Cs CTF Cth, CtT Cv Cw Cy Co CI Cz c

Coefficient for lateral bracing of C- and Z-section End moment coefficient in interaction formula Coefficient for lateral torsional buckling End moment coefficient in interaction formula Coefficient for lateral bracing of C- and Z-sections Shear stiffener coefficient Torsional warping constant of the cross-section Compression strain factor Initial column imperfection Term used to compute shear strain in wall board Coefficient as defined in Figure B4-2 Distance from the neutral axis to the extreme fiber of untwisted section

03.2.1 C5 C3.1.1 C3.1.1 03.2.1. B6.2 C3.1.1 C3.1.1 04.1 B4, B4.1, 04.2 B4, B4.2 C3.1.3

D D D 0 Do d

Amount of curling Outside diameter of cylindrical tube Dead load, includes weight of the test specimen Overall depth of lip Shear stiffener coefficient Initial column imperfection Depth of section

Bl.lb C6.1, C6.2, 04.2 F1 B1.1, B4, 01.1 B6.2 04.1 B 1.l b, B4, C3.1.1, C3.1.3, 01.1,03.2.1,04,04.1, E3.4

d d d da da de de dh ds d's dwc E

Width of arc seam weld Visible diameter of outer surface of arc spot weld Diameter of bolt A verage diameter of the arc spot weld at mid-thickness of t A verage width of seam weld Effective diameter of fused area Effective width of arc seam weld at fused surfaces Diameter of standard hole Reduced effective width of stiffener Actual effective width of stiffener Coped web depth Modulus of elasticity of steel (29,500 ksi)

E2.3 E2.2 E3, E3.1, £3.2 E2.2 E2.3 E2.2 E2, E2.3 B2.2, E3.1 E4 B4, B4.2 B4, B4.2 E4 B1.1b, B2.1, B6.1, C3.1.1, C3.1.3, C3.2, C3.S.2, C4, C4.1, C5, C6.l, 01.2, 04.1, 04.2, E2.2

Initial column imperfection; a measure of the initial twist of the stud from the initial, ideal, unbuckled location

04.1

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Cold-Fonned Specification - August 19,1986 Edition with December 11 , 1989 Addendum

•

SYMBOLS AND DEFINITIONS

Symbol

•

1-15

Definition

Section

El E' emin

Tenn used to compute shear strain in wallboard Inelastic modulus of elasticity Minimum allowable distance measured in the line of force from the centerline of a weld to the nearest edge of an adjacent weld or to the end of the connected part which the force is directed

D4.I D4.1 E2.2

emin

The distance e measured in the line of force from the center of a standard hole to the nearest edge of an adjacent hole or to the end of the connected part toward which the force is directed

E3.1

ey FD Fe

Yield strain = Fy/E Dead load factor Elastic buckling stress

C3.I.I Fl C4, C4.1, C4.2, C4.3, C6.2, D4.1

FL Fn Fp Fsy Ft F't

Live load factor Nominal buckling stress Allowable bearing stress Yield point as specified in Sections A3.1 or A3.2 Nominal tension stress limit on net section Allowable tension stress for bolts subject to combination of shear and tension

Fl C4, C6.2, D4.2 E3.3, E5.1 A3.3.2, E2.2, E3.I, E3.2 E3.2, E3.4 E3.4

Tensile strength as specified in Sections A3.l or A3.2, or as reduced for low ductility steel

A3.3, A3.3.2, E2.2, E2.3, E2.4, E2.5, E3.1, E3.2, E3.3, E4

Fuv

Ultimate tensile strength of virgin steel specified by Section A3 or established in accordance with Section F3.3

A5.2.2, E2.2

Fv Fwy Fxx Fy

Allowable shear stress on the gross area of a bolt Yield point for design of transverse stiffeners Strength level designation in AWS electrode classification Yield point used for design, not to exceed the specified yield point or established in accordance with Section F3, or as increased for cold work of fonning in Section A5.S.2 or as reduced for low ductility steels in Section A3.3.2

E3.4 86.1 E2.2, E2.3, E2.4, E2.5 A1.2, A3.3, AS.2.l , AS.2.2, B2.1, B5, B6.1, C2, C3.l, C3.I.I, C3.I.3, C3.2, C3.5.2, C4, C6.1, C6.2, D 1.2, D4, D4.2, E2

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•

SYMBOLS AND DEFINITIONS

Symbol

Definition

Section

Fya Fyc Fyf Fys Fyv

A verage yield point of section Tensile yield point of corners Weighted average tensile yield point of the flat portions Yield point of stiffener steel Tensile yield point of virgin steel specified by Section A3 or established in accordance with Section F3.3

A5.2.2 A5.2.2 F3.2, A5.2.2 B6.1 A5.2.2

Stress in the compression element computed on the basis of the effective design width

B2.1, B2.2, B3.2, B4, B4.1

fav

A verage computed stress in the full, unreduced flange width

BI.lb

Maximum bending stress equal to the bending moment divided by appropriate section modulus of member

C3.1.3

fc f'c fd

Computed stress at design load in the cover plate or sheet Specified compression stress of concrete Computed compressive stress in the element being considered. Calculations are based on the effective section at the load for which deflections are detennined.

01.2 E5.1 B2.1, B2.2, B3.1, B4.1, B4.2

fdl, fd2

Computed stresses fl and f2 as shown in Figure B2.3-1. Calculations are based on the effective section at the load for which deflections are deteremined

B2.3

fd3

Computed stress f3 in edge stiffener, as shown in Figure B4-2. Calculations are based on the effective section at the load for which deflections are detennined

B3.2

The computed maximum compressive stress due to twisting and lateral bending

C3.I.3

fv fl, f2 f3

Computed shear stress on a bolt Web stresses defined by Figure B2.3-1 Edge stiffener stress defined by Figure B4.2 Shear modulus for steel = 11,300 ksi Inelastic shear modulus Vertical distance between two rows of connections nearest to the top and bottom flanges

E4 B2.3 B3.2 C3.1.1,04.1 04.1 01.1

G G' g

•

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Cold-Fonned Specification - August 19, 1986 Edition with December 11 , 1989 Addendum

SYMBOLS AND DEFINITIONS Symbols

Definition

L L L

Length of seam weld not including the circular ends Length of fillet weld Unbraced length of member

E2.3 E2.4, E2.S C3.1.2, C3.1.3, C4.1, 01.1, 04, 04.1

L La

Live load Length of the portion of the span between supports where the flange that is not connected to the sheathing is in compression

FI C3.1.3

LSI LI L.

Length of transverse stiffener Unbraced length of compression member for torsion Unbraced length of compression member for bending about x-axis

B6.1 C3.l.1 C3.1.l

Unbraced length of compression member for bending about y-axis

C3.1.1

M Ma

Applied bending moment Allowable bending moment permitted if bending stress only exists

C3.3, C3.S.I, C3.S.2 C3.1, C3.3, C3.S.1, C3.S.2, C6.1

Max. May Allowable moments about the centroidal axes determined in accordance with Section C3

Section

•

Maxo Mayo

Allowable moments about the centroidal axes determined in accordance with Section 3.1 excluding the provisions of Section 3.1.2

C3.3, C3.S

Me Me Mn

Critical moment Elastic critical moment Nominal moment strength

C3.1.2 C3.1.2 C3.1, C3.1.1, C3.1.2, C3.1.3, C6.1

Mx,My Applied moments about the centroidal axes determined in accordance with Section C3

My M\ M2 m

B2.1, C3.1 C3.1.1, CS C3.1.1, CS 03.2.2, D1.1

Moment causing a maximum strain of ey Smaller end moment Larger end moment Distance from the shear center of one channel to the mid-plane of its web

•

Cold-Fonned Specification - August 19.1986 Edition with December II. 1989 Addendum

•

SYMBOLS AND DEFINITIONS Symbol

• II

•

Definition

Section

m N n np P P P P P.

0.192 (Fuv/Fyv) - 0.068 Actual length of bearing Number of holes Number of parallel purlin lines Concentrated load or reaction Applied axial load Force transmitted by bolt Force transmitted by weld Allowable concentrated load or reaction for one transverse stiffener

AS.2.2 03.6 E4 03.2.1 C3.S CS,04.l E3, E3.1 E2, E2.2 B6.1

Pao

Allowable axial load determined in accordance with Section C4 for L =0

PL Pn Pn

Force to be resisted by intermediate beam brace Nominal axial strength of member Nominal strength of connection component

B3.2.2 C4, C6.2 E2, E2.2, E2.3, E2,4, E2.5

Oesign shear rigidity for sheathing on both side of the wall assembly

04.1

q qw

Uniformly distributed load in the plane of the web Allowable uniform load

C3.1.3,01.1 C3.1.3

Oesign shear rigidity for sheathing per inch of stud spacing

04.1

qo qu R R R R r r

Factor used to determine design shear rigidity Maximum uniformly distributed load in the plane of the web Inside bend radius Reduction Factor Coefficient Required load carrying capacity Radius of gyration of full unreduced cross section Force transmitted by the bolt or bolts at the section considered, divided by the tension force in member at that section

04.1 C3.1.3 AS.2.2, C3,4 C3.1.3 C4, C6.2 Fl C3.1.1, C4, C4.1 E3.2

rey

Radius of gyration of one channel about its centroidal axis parallel to web

01.1

Polar radius of gyration of cross section about the shear center

C3.1.1, C4.2, 04.1

Radius of gyration of cross section about centroidal principal axis

C3.1.1

r~.

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Cold-Fonned Specification - August 19, 1986 Edition with December 11 , 1989 Addendum

SYMBOLS AND DEFINITIONS Symbol

Definition

Section

Radius of gyration of I-section about the axis perp-pendicular to the direction in which buckling would occur for the given conditions of end support and intermediate bracing

01.1

1. 28.JE / f In-plane load carrying capacity for diaphragms Elastic section modulus of the effective section calculated at a stress Me/Sf in the extreme compression fiber

B4, B4.1

Sa Sc

Elastic section modulus of the effective section calculated with extreme compression or tension fiber at Fy

C3.l.1, C3.1.3

Elastic seciton modulus of full unreduced section for the extreme compression fiber

C3.1.1, C3.1.2, C6.1

Sf Smax

Nominal diaphragm shear strength Maximum permissible longitudinal spacing of welds or other connectors joining two channels to form an I-section

OS 01.1

s s

Fastener spacing Spacing in line of stress of welds, rivets, or bolts connecting a compression coverplate or sheet to a non-integral stiffener or other element

D1.2,04.1 E3.2

s Ta Tn Ts t

Weld spacing Allowable tensile strength Nominal tensile strength Strength of connection in tension Base steel thickness of any element or section

01.1 C2 C2 01.1 Al.2, A3.4, A5.2.1, B1.1, BUb, B1.2, B2.1, B4, B4.1, B4.2, B5, B6.1, C3.1.1., C3.1.3, C3.2, C3.4, C3.S.2, C4, C6.1, C6.2, D 1.2, D4, E2.4, E2.S

ts tw V Va

Total thickness of the two welded sheets Thickness of thinnest connected part Equivalent thickness of a multiple-stiffened element Effective throat of weld Actual shear force Allowable shear force

E2.2 E2.2, E3.1, E4 BS, B6.1 E2.4, E2.5 C3.3 B6.2, C3.2. C3.3

•

OS C3. 1.1 , C3.1.2, C4

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Cold-Fonned Specification - August 19,1986 Edition with December 11, 1989 Addendum

•

SYMBOLS AND DEFINITIONS

Symbol

Total load supported by the purl in lines between adjacent supports, lbs.

D3.2.1.

Flat width of element exclusive of radii

AI.2, Bl.1, B2.1,B2.2, B3.I, B4, B4.1, B4.2, BS, C3.I.l., C3.I.3, C4, D1.2

Flat width of the beam flange which contacts the bearing plate

C3.S

Width of flange projection beyond the web or half the distance between webs for box- or U-type sections

Bl.I

Projection of flanges from inside face of web Leg on weld Distance from concentrated load to brace Distance from shear center to centroid along the principal x-axis

Dl.I E2.4 D3.2 C3.I.I, C4.2, D4.1

Yield point of web steel divided by yield point of stiffener steel Magnification factors

B6.2 CS

Coefficient Actual shear strain in the sheathing

C4.2, D4.I D4.1

Permissible shear strain of the sheathing Angle between web and bearing surface >4S o but not more than 90 0

D4.1 C3.4

Angle between the vertical and the plane of the web of the Z-section, degrees

D3.2.t

a aCR at

Stress related to shear strain in sheathing Theoretical elastic buckling stress Torsional buckling stress Reduction factor Slenderness factors fufl Factor of safety for bearing Factor of safety for axial compression

D4.l D4.1 C3.l.I, C4.2, D4.1 B2.1 B2.1, C3.S B2.3 E3.3 B6.1. C4. C5. C6.2, D4.1

x xo

l/ax l/ay ~

Y y

•

Section

Definition

WI,W2

•

1-21

A, A.: 'II Ob

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Cold-Formed Specification - August 19, 1986 Edition with December 11 , 1989 Addendum

SYMBOLS AND DEFINITIONS

Symbol

Oe Of Os OSI 01 OV Ow

Definition Factor of safety for sheet tearing Factor of safety for flexure Factor of safety for diaphragm shear Factor of safety for end crushing of transverse stiffener Factor of safety for tension on net section Factor of safety for shear rupture Factor of safety for welded connections

Section

•

E2.2, E3.! C3.1, C6.1 D5 B6.1 C2, E3.2 E4 E2

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Cold-Fonned Specification - August 19,1986 Edition with December 11, 1989 Addendum

•

SPECIFICATION FOR THE DESIGN OF COLD-FORMED STEEL STRUCTURAL MEMBERS AUGUST 19,1986 EDITION WITH DECEMBER 11, 1989 ADDENDUM A. GENERAL PROVISIONS A1 limits of Applicability and Terms A1.1 Scope and limits of Applicability This Specification shall apply to the design of structural members cold-formed to shape from carbon or low-alloy steel sheet, strip, plate or bar not more than one inch in thickness and used for load-carrying purposes in buildings. It may also be used for structures other than buildings provided appropriate allowances are made for dynamic effects. Appendices to this Specification shall be considered as integral parts of the Specification.

A1.2 Terms

•

II /'

Where the following terms appear in this Specification they shall have the meaning herein indicated: (a) Stiffened or Partially Stiffened Compression Elements. A stiffened or partially stiffened compression element is a flat compression element (i.e., a plane compression flange of a flexural member or a plane web or flange of a compression member) of which both edges paral\el to the direction of stress are stiffened either by a web, flange, stiffening lip, intermediate stiffener, or the like. (b) Unstiffened Compression Elements. An un stiffened compression element is a flat compression element which is stiffened at only one edge parallel to the direction of stress. (c) Multiple-Stiffened Elements. A multiple-stiffened element is an element that is stiffened between webs, or between a web and a stiffened edge, by means of intermediate stiffeners which are parallel to the direction of stress. A sub-element is the portion between adjacent stiffeners or between web and intermediate stiffener or between edge and intermediate stiffener. (d) Flat-Width-to-Thickness Ratio. The flat width of an element measured along its plane, divided by its thickness. (e) Effective Design Width. Where the flat width of an element is reduced for design purposes, the reduced design width is termed the effective width or effective design width. (f) Thickness. The thickness, t, of any element or section shall be the base steel thickness, exclusive of coatings. (g) Torsional-Flexural Buckling. Torsional-flexural buckling is a mode of buckling in which compression members can bend and twist simultaneously. (h) Point-Symmetric Section. A point-symmetric section is a section symmetrical about a point (centroid) such as a Z-section having equal flanges. (i) Yield Point. Yield point, Fy or Fsy, as used in this Specification shall mean yield point or yield strength.

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Cold-Formed Specification - August 19, 1986 Edition with December II, 1989 Addendum

U) Stress. Stress as used in this Specification means force per unit area. (k) Confirmatory Test. A confinnatory test is a test made, when desired, on members, connections, and assemblies designed according to the provisions of Sections A through E of this Specification or its specific references, in order to compare actual versus calculated perfonnance.

(I)

(m) (n) (0)

(p )

•

Performance Test. A perfonnance test is a test made on structural members, connections, and assemblies whose perfonnance cannot be detennined by the provisions of Sections A through E of this Specification or its specific references. Virgin Steel. Virgin steel refers to steel as received from the steel producer or warehouse before being cold worked as a result of fabricating operations. Virgin Steel Properties. Virgin steel properties refer to mechanical properties of virgin steel such as yield point, tensile strength, and elongation. Specified Minimum Yield Point. The specified minimum yield point is the lower limit of yield point which must be equaled or exceeded in a specification test to qualify a lot of steel for use in a cold-fonned steel structural member designed at that yield point. Cold-Formed Steel Structural Members. Cold-fonned steel structural members are shapes which are manufactured by press-braking blanks sheared from sheets, cut lengths of coils or plates, or by roll fonning cold- or hot-rolled coils or sheets; both fonning operations being perfonned at ambient room temperature, that is, without manifest addition of heat such as would be required for hot forming.

A1.3 Units of Symbols and Terms The Specification is written so that any compatible system of units may be used except where explicitly stated otherwise in the text of these provisions.

•

A2 Non-Conforming Shapes and Construction The provisions of the Specification are not intended to prevent the use of alternate shapes or constructions not specifically prescribed herein. Such alternates shall meet the provisions of Section F of the Specification and be approved by the appropriate building code authority.

A3 Material A3.1 Applicable Steels This Specification requires the use of steel of structural quality as defined in general by the provisions of the following specifications of the American Society for Testing and Materials: ASTM A36/A36M, Structural Steel ASTM A242/A242M, High-Strength Low-Alloy Structural Steel ASTM A441M, High-Strength Low-Alloy Structural Manganese Vanadium Steel ASTM A446/A446M (Grades A, B, C, D, & F) Steel, Sheet, Zinc-Coated (Galvanized) by the Hot-Dip Process, Structural (Physical) Quality ASTM A500, Cold-Fonned Welded and Seamless Carbon Steel Structural Tubing in Rounds and Shapes ASTM A529/A529M, Structural Steel with 42 ksi Minimum Yield Point 0/2 in. Maximum Thickness)

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Cold-Fonned Specification - August 19, f 986 Edition with December II! 1989 Addendum

•

ASTM A570/A570M Steel, Sheet and Strip, Carbon, Hot-Rolled, Structural Quality ASTM A572/A572M, High-Strength Low-Alloy Columbium-Vanadium Steels of Structural Quality ASTM A588/A588M, High-Strength Low-Alloy Structural Steel with 50 ksi Minimum Yield Point to 4 in. Thick ASTM A606 Steel, Sheet and Strip, High Strength, Low Alloy, Hot-Rolled and ColdRolled, with Improved Atmospheric Corrosion Resistance ASTM A607 Steel Sheet and Strip, High Strength, Low Alloy, Columbium or Vanadium, or both, Hot-Rolled and Cold-Rolled ASTM A611 (Grades A, B, C, & D) Steel, Sheet, Carbon, Cold-Rolled, Structural Quality ASTM A 715 (Grades 50 and 60) Sheet Steel and Strip, High-Strength, Low-Alloy, HotRolled, With Improved Formability ASTM A792 (Grades 33, 37,40 & 50) Steel Sheet, Aluminum-Zinc Alloy-Coated by the Hot-Dip Process, General Requirements

A3.2 Other Steels The listing in Section A3.1 does not exclude the use of steel up to and including one inch in thickness ordered or produced to other than the listed specifications provided such steel conforms to the chemical and mechanical requirements of one of the listed specifications or other published specification which establishes its properties and suitability, and provided it is subjected by either the producer or the purchaser to analyses, tests and other controls to the extent and in the manner prescribed by one of the listed specifications and Section A3.3.

•

A3.3 Ductility Steels not listed in Section A3.1 and used for structural members and connections shall comply with one of the foJ/owing ductility requirements: A3.3.1 The ratio of tensile strength to yield point shall not be less than 1.08, and the total elongation shall not be Jess than 10 percent for a two-inch gage length or 7 percent for an eight-inch gage length standard specimen tested in accordance with ASTM A370--77£. If these requirements cannot be met, the following criteria shall be satisfied: (1) local elongation in a 1/2 inch gage length across the fracture shall not be less than 20%, (2) uniform elongation outside the fracture shall not be less than 3%*. When material ductility is determined on the basis of the local and uniform elongation criteria, the use of such material is restricted to the design of purlins and girts** in accordance with Sections C3.1.1 (a), C3.1.2, and C3.1.3. For purlins and girts subject to combined axial load and bending moment (Section C5), PIP. shall not exceed 0.15. The provisions of Chapters B through E of this Specification are I imited to steels conforming to these requirements. A3.3.2 Steels conforming to ASTM A446 Grade E and A611 Grade E and other steels which do not meet the provisions of Section A3.3.1 may be used for particular configurations provided (1) the yield strength, F y , used for design in Chapters B, C and D

•

* Further infonnation on the test procedures should be obtained from the Commentary. ** Horizontal structural members which support roof deck or panel covering and applied loads principally by bending.

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Cold-Fonned Specification - August 19, 1986 Edition with December 11 , 1989 Addendum

is taken as 75 percent of the specified minimum yield point or 60 ksi, whichever is less and (2) the tensile strength, Fu, used for design in Chapter E is taken as 75 percent of the specified minimum tensile stress or 62 ksi, whichever is less. Alternatively, the suitability of such steels for the configuration shall be demonstrated by load tests in accordance with Section Fl. Allowable loads based on these tests shall not exceed the loads calculated according to Chapters B through E, using the specified minimum yield point, Fsy, for Fy and the specified minimum tensile strength, Fu. Allowable loads based on existing use shall not exceed the loads calculated according to Chapters B through E, using the specified minimum yield point, Fsy, for Fy and the specified minimum tensile strength, Fu.

•

A3.4 Delivered Minimum Thickness The uncoated minimum steel thickness of the cold-formed product as deli vered to the job site shall not at any location be less than 95 percent of the thickness, t, used in its design; however, thicknesses may be less at bends, such as corners, due to cold-forming effects.

A4 Loads A4.1 Dead Load The dead load to be assumed in design shall consist of the weight of steelwork and all material permanently fastened thereto or supported thereby.

A4.2 Live Load The live load shall be that stipulated by the applicable code or specification under which the structure is being designed or that dictated by the conditions involved.

•

A4.3 Impact Load For structures carrying live loads which induce impact, the assumed live load shall be increased sufficiently to provide for impact.

A4.4 Wind or Earthquake Loads

Where load combinations specified by the applicable building code include wind or earthquake loads, the resulting forces may be multiplied by 0.75 for strength determination.

A4.5 Ponding Unless a roof surface is provided with sufficient slope toward points of free drainage or adequate individual drains to prevent the accumulation of rainwater, the roof system shall be investigated by rational analysis to assure stability under ponding conditions.

A5 Structural Analysis and Design A5.1 Design Basis This Specification is based upon the allowable stress concept presented in terms of allowable moments and loads. The allowable moments and loads are determined by dividing the corresponding nominal capacities by an accepted factor of safety.

•

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Cold-Fonned Specification - August 19.1986 Edition with December II. 1989 Addendum

•

AS.2 Yield Point and Strength Increase from Cold Work of Forming AS.2.1 Yield Point The yield point used in design, Fy, shall not exceed the specified minimum yield point of steels as listed in Section A3.1 or A3.2, as established in accordance with Chapter F, or as increased for cold work of forming in Section A5.2.2, or as reduced for low ductility steels in Section A3.3.2.

AS.2.2 Strength Increase from Cold Work of Forming Strength increase from cold work of forming may be obtained by substituting Fya for Fy, where Fya is the average yield point of the full section. Such increase shall be limited to Sections C3.1 (excluding Section C3.l.1(b)), C4. C5, C6 and D4. The limitations and methods for determining Fya are as follows: (a) For axially loaded compression members and flexural members whose proportions are such that the quantity p is unity as determined according to Section B2 for each of the component elements of the section, the design yield stress, F ya, of the steel shall be determined on the basis of one of the following ,methods: (1) full section tensile tests [see paragraph (a) of Section F3.1]

(2) stub column tests [see paragraph (b) of Section F3.1] (3) computed as follows: Fya = CFyc + (1 - C) Fyf

•

(Eq. A5.2.2-l)

where Fya = Average tensile yield pofnt of the steel in the full flange sections of flexural members C

= For compression members, ratio of the total comer cross-sectional area to the total cross-sectional area of the full section; for flexural members, ratio of the total comer cross-sectional area of the controlling flange to the full cross-sectional area of the controlling flange

Fyf = Weighted average tensile yield point of the flat portions established in accordance with Section F3.2 or virgin yield point if tests are not made. Fye = BeFyv/(R/t)m, tensile yield point of comers (Eq. A5.2.2-2) when Fuv/Fyv > 1.2, R/t < 7, minimum included angle < 1200 Be = 3.69 (Fuv/Fyv) - 0.819 (Fuv/Fyv)2 - 1.79 m = 0.192 (Fuv/Fyv) - 0.068 R = Inside bend radius. Fyv

(Eq. A5.2.2-3) (Eq. A5.2.2-4)

= Tensile yield point of virgin steel* specified by Section A3 or established in accordance with Section F3.3

Fuv

•

= Ultimate tensile strength of virgin steel * specified by Section A3 or

established in accordance with Section F3.3 (b) For axially loaded tension members the yield point of the steel shall be determined by either method (1) or method (3) prescribed in paragraph (a) ofthis Section.

* Virgin steel refers to the condition (i.e., coiled or straight) of the steel prior to the cold-fonning operation.

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Cold-Fonned Specification - August 19,1986 Edition with December 11,1989 Addendum

(c) The effect of any welding on mechanical properties of a member shall be determined on the basis of tests of full section specimens containing within the gage length, such welding as the manufacturer intends to use. Any necessary allowance for such effect shall be made in the structural use of the member.

•

A5.3 Serviceability and Durability A structure shaH be designed to perform its required functions during its expected life, including serviceability and durability considerations.

AS Reference Documents This Specification recognizes other published and latest approved specifications and manuals for designs contemplated herein, as follows: o American National Standards Institute, ANSI A58.1-1982, "Minimum Design Loads in Buildings and Other Structures,"* American National Standards Institute, Inc. (ANSI), 1430 Broadway, New York, New York ID018 o American Institute of Steel Construction, "Specification for the Design, Fabrication and Erection of Structural Steel for Buildings," American Institute of Steel Construction (AISC), One East Wacker Drive, Chicago, Illinois 60601, November I, 1978 o American Welding Society, AWS 01.3-81, "Structural Welding Code - Sheet Steel," American Welding Society (AWS), 550 N.W. Lejeune Road, Miami, Florida 33126 o Research Council on Structural Connections, Allowable Stress Design, "Specification for Structural Joints Using ASTM A325 or A490 Bolts," Research Council on Structural Connections (RCSC), American Institute of Steel Construction (AISC), One East Wacker Drive, Chicago, Illinois 60601, November 13, 1985.

•

o Metal Building Manufacturers Association, Low Rise Building Systems Manual, Metal Building Manufacturers Association (MBMA), 1230 Keith Building, Cleveland, Ohio 44115 o Steel Deck Institute, "Design Manual for Composite Decks, Formed Decks, and Roof Decks," Steel Deck Institute (SOl), Inc., P.O. Box 9506, Canton, Ohio 44711, 1984 o Steel Joist Institute, "Standard Specifications Load Tables and Weight Tables for Steel Joists and Joist Girders," Steel Joist Institute (S1I), Suite A, 1205 48th Avenue North, Myrtle Beach, South Carolina 29577, 1986 o Rack Manufacturers Institute, " Specification for the Design, Testing and Utilization ofIndustrial Steel Storage Racks," Rack Manufacturers Institute (RMI), 8720 Red Oak Boulevard, Suite 201, Charlotte, North Carolina 28210,1985 o American Iron and Steel Institute, "Stainless Steel Cold-Formed Structural Design Manual," 1974 Edition, American Iron and Steel Institute (AISI), 1133 15th Street, N.W., Washington, D.C. 20005 o American Society of Civil Engineers, "ASCE Standard, Specification for the Design and Construction of Composite Slabs, "American Society of Civil Engineers (ASCE), 345 East 47th Street, New York, New York lO(H7, October, 1984

* For further infonnation contact ASCE, 345 East 47th Street, New York, New York 10017.

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Cold-Fonned Specification - August 19,1986 Edition with December 11 , 1989 Addendum

•

o American Iron and Steel Institute, "Tentative Criteria for Structural Applications of Steel Tubing and Pipe," American Iron and Steel Institute (AISI), 1133 15th Street, N.W., Washington, D.C. 20005, August, 1976 In addition to the above references this Specification recognizes the following standards from the American Society for Testing and Materials (ASTM), 1916 Race Street, Philadelphia, Pennsylvania 19013: ASTM A36/ A36M-84a, Structural Steel ASTM A 194--88, Carbon and Alloy Steel Nuts for Bolts for High-Pressure and High-Temperature Service ASTM A242/A242M-85, High-Strength Low-Alloy Structural Steel ASTM A307-84 (Type A), Carbon Steel Externally and Internally Threaded Standard Fasteners ASTM A325-84, High Strength Bolts for Structural Steel Joints ASTM A354--84 (Grade BD), Quenched and Tempered Alloy Steel Bolts, Studs, and Other Externally Threaded Fasteners (for diameter of bolt smaller than liz inch) ASTM A370-77 E Mechanical Testing of Steel Products ASTM A441M-85, High-Strength Low-Alloy Structural Manganese Vanadium Steel ASTM A446/A446M-85 (Grades A, B, C, D, & F) Steel, Sheet, Zinc-Coated (Galvanized) by the Hot-Dip Process, Structural (Physical) Quality ASTM A449-84a, Quenched and Tempered Steel Bolts and Studs (for diameter of bolt smaller than liz inch) ASTM A490-84, Quenched and Tempered Alloy Steel Bolts for Structural Steel Joints. ASTM A500-84, Cold-Formed Welded and Seamless Carbon Steel Structural Tubing in Rounds and Shapes ASTM A529/A529M-85, Structural Steel with 42 ksi Minimum Yield Point (liz in. Maximum Thickness) ASTM A563-88a, Carbon and Alloy Steel Nuts ASTM A570/A570M-85 Steel, Sheet and Strip, Carbon, Hot-Rolled, Structural Quality ASTM A572/A572M-85, High-Strength Low-Alloy Columbium-Vanadium Steels of Structural Quality , ASTM A588/A588M-85 , High-Strength Low-Alloy Structural Steel with 50 ksi Minimum Yield Point to 4 in. Thick ASTM A606-85 Steel, Sheet and Strip, High Strength, Low Alloy, Hot-Rolled and Cold-Rolled, with Improved Atmospheric Corrosion Resistance ASTM A607-85 Steel Sheet and Strip, High Strength, Low Alloy, Columbium or Vanadium, or both, Hot-Rolled and Cold-Rolled ASTM A611-85 (Grades A, B, C, & D) Steel, Sheet, Carbon, Cold-Rolled, Structural Quality ASTM A715-85 (Grades 50 & 60) Sheet Steel and Strip, High-Strength, Low-Alloy, Hot-Rolled, With Improved Formability ASTM A792-85a (Grades 33, 37,40 & 50) Steel Sheet, Aluminum-Zinc AlloyCoated by the Hot-Dip Process, General Requirements ASTM F436-86, Hardened Steel Washers

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Cold-Fonned Specification - August 19, 1986 Edition with December II, 1989 Addendum

ASTM F844--83(1988), Washers, Steel, Plain (Flat), Unhardened for General Use ASTM F959-85, Compressible Washer-Type Direct Tension Indicators for Use with Structural Fasteners

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Cold-Fonned Specification - August 19. 1986 Edition with December 11.1989 Addendum

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B. ELEMENTS 81 Dimensional Limits and Considerations 81.1 Flange Flat-Width-to-Thickness Considerations (a) Maximum Flat-Width-to-Thickness Ratios Maximum allowable overall flat-width-to-thickness ratios, wIt, disregarding intermediate stiffeners and taking as t the actual thickness ofthe element, shall be as follows:

(1) Stiffened compression element having one longitudinal edge connected to a web or flange element, the other stiffened by: Simple lip

Any other kind of stiffener having Is > Ia and D/w < 0.8 according to Section B4.2

(2) Stiffened compression element with both longitudinal edges connected to other stiffened elements

•

(3) Un stiffened compression element and elements with an edge stiffener having Is < Ia and D/w ~ 0.8 according to Section B4.2

500

Note: Unstiffened compression elements that have wIt ratios exceeding approximately 30 and stiffened compression elements that have wIt ratios exceeding approximately 250 are likely to develop noticeable deformation at the full allowable load, without affecting the ability of the member to carry design loads. Stiffened elements having wIt ratios larger than 500 may be used with safety to support loads, but substantial deformation of such elements under load may occur and may render inapplicable the design formulas of this Specification. (b) Flange Curling Where the flange of a flexural member is unusually wide and it is desired to limit the maximum amount of curling or movement of the flange toward the neutral axis, the following formula applies to compression and tension flanges, either stiffened or unstiffened:

•

= -J0.061tdE/fav V(lOOcf / d)

where wr= Width of flange projecting beyond the web; or half of the distance between webs for box- or U-type beams t = Flange thickness d =Depth of beam Cr =Amount of curling fav=Average stress in the full, unreduced flange width. (Where members are designed by the effective design width procedure, the average stress equals

(Eq. B1.1-1)

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Cold-Fonned Specification - August 19. 1986 Edition with December 11. 1989 Addendum

the maximum stress multiplied by the ratio of the effective design width to the actual width.) (c) Shear Lag Effects - Unusually Short Spans Supporting Concentrated Loads

•

Where the span of the beam is less than 30wr (wr as defined below) and it carries one concentrated load, or several loads spaced farther apart than 2wr, the effective design width of any flange, whether in tension or compression, shall be limited to the following:

TABLE B1.1 SHORT, WIDE FLANGES MAXIMUM ALLOWABLE RATIO OF EFFECTIVE DESIGN WIDTH TO ACTUAL WIDTH L/wr 30 25 20 18 16

Ratio

L/wr

Ratio

1.00 0.96 0.91 0.89 0.86

14 12 10 8 6

0.82 0.78 0.73 0.67 0.55

where L =Full span for simple beams; or the distance between inflection points for continuous beams; or twice the length of cantilever beams. Wr= Width of flange projection beyond the web for I-beam and similar sections or half the distance between webs of box or V-type sections.

•

For flanges of I-beams and similar sections stiffened by lips at the outer edges, Wr shall be taken as the sum of the flange projection beyond the web plus the depth of the lip.

B1.2 Maximum Web Depth-to-Thickness Ratio The ratio, hIt, of the webs of flexural members shall not exceed the following limitations: (a) For unreinforced webs: (h/t)max = 200 (b) For webs which are provided with transverse stiffeners satisfying the requirements of Section B6.1: (1) When using bearing stiffeners only, (h/t)max = 260 (2) When using bearing stiffeners and intermediate stiffeners, (h/t)max = 300 In the above, h = Depth of flat portion of web measured along the plane of web t = Web thickness Where a web consists of two or more sheets, the hit ratio shall be computed for the individual sheets.

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Cold-Fonned Specification - August 19, 1986 Edition with December 11,1989 Addendum

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82 Effective Widths of Stiffened Elements 82.1 Uniformly Compressed Stiffened Elements (a) Load Capacity Determination The effective widths, b, of unifonnly compressed elements shall be detennined from the following fonnulas: b = w when A. ~ 0.673 (Eq. B2.1-l) b =pw when A. > 0.673 (Eq. B2.1-2) where w =Flat width as shown in Figure B2.1 p =(1 - 0.22/A. )/A. (Eq. B2.l-3) A is a slenderness factor detennined as follows:

A.= 1.0S2(W)

..Jk

(Eq. B2.l-4)

where f for load capacity detennination is as follows: For flexural members: (1)

•

If Procedure I of Section C3.1.1 is used, f = Fy if the initial yielding is in compression in the element considered. If the initial yielding is in tension, the compressive stress, f, in the element considered shall be detennined on the basis of the effective section at My (moment causing initial yield).

(2) If Procedure II of Section C3.1.1 is used then f is the stress in the element considered at Mn detennined on the basis of the effective section. (3) If Section C3.1.2 is used, then f = Me as described in that Section in determining Sc Sf

•

For compression members f is taken equal to Fn as detennined in Section C4 or 04 as applicable. E = Modulus of elasticity k = Plate buckling coefficient = 4 for stiffened elements supported by a web on each longitudinal edge. Values for different types of elements are given in the applicable sections. (b) Deflection Determination The effective widths, bd, used in computing deflections shall be detennined from the following fonnulas: bd = w when A. ~ 0.673 (Eq. B2.I-S) bd =pw when A. > 0.673 (Eq. B2.1-6) where w =Aat width p =Reduction factor detennined by either of the following two procedures: (1 ) Proced ure I. A low estimate of the effective width may be obtained from Eqs. B2.1-3

Cold-Fonned Specification - August 19, 1986 Edition with December 11, 1989 Addendum

1-34

{I I I

D _________ L-J

---------~f

I I

Actual Element

•

~---------~

Effective Element, b, and Stress, f, on Effective Elements

Figure 82.1-1 Stiffened Elements

and B2.1-4 where fd is substituted for f where fd is the computed compressive stress in the element being considered. (2) Procedure II. For stiffened elements supported by a web on each longitudinal edge an improved estimate of the effective width can be obtained by calculating p as follows:

p = 1 when 'A ~ 0.673 P =(1.358 - 0.461/'A )/'A when 0.673 < "A < Ac P =(0.41 + 0.59 ~Fy 1fd - 0.22/'A)/"A when 'A ~ Ac

(Eq. B2.1-7) (Eq. B2.1-8) (Eq. B2.1-9)

p shall not exceed 1.0 for all cases. where

Ac =0.256 + 0.328 (w/t)~Fy 1E

(Eq. B2.1-1O)

•

and 'A is as defined by Eq. B2.1-4 except that fd is substituted for f.

82.2 Uniformly Compressed Stiffened Elements with Circular Holes (a) Load Capacity Determination

The effective width, b, of stiffened elements with uniform compression having circular holes shall be determined as follows: for 0.50 ~ ~ ~ 0, and w

~ 70

center-to--center spacing of holes> 0.50w, and 3dh, b =W - dh when "A ~ 0.673

(Eq. B2.2-1)

W[l- (0.22) _ (0.8d h)] b=

when 'A > 0.673

(Eq. 82.2-2)

b shall not exceed w - dh where w = Flat width dh =Diameter of holes 'A is as defined in Section B2.1. (b) Deflection Determination The effective width, bd, used in deflection calculations shall be equal to b deter-

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Cold-Fonned Specification - August 19, 1986 Edition with December 11, 1989 Addendum

•

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mined in accordance with Procedure I of Section B2.2a except that fd is substituted for f, where fd is the computed compressive stress in the element being considered.

82.3 Effective Width of Webs and Stiffened Elements with Stress Gradient Load Capacity Determination The effective widths, bl and b2, as shown in Figure B2.3-l shall be detennined from the following formulas: bl =be/(3 - 'II) For", :5: - 0.236 b2 = be/2 bl + b2 shall not exceed the compression portion of the web calculated on the basis of effective section For",> - 0.236 b2=be -bl where be = Effective width b detennined in accordance with Section B2.l with fl substituted for f and with k detennined as follows: k =4 + 2(1- 'II? + 2(1 - 'II) 'II =f2/fl fl, f2 = Stresses shown in Figure B2.3-1 calculated on the basis of effective section. fl is compression (+) and f2 can be either tension (-) or compression. In case fl and f2 are both compression, fl ~ f2 (b) Deflection Determination The effective widths in computing deflections at a given load shall be determined in accordance with Section B2.3a except that fdl and fd2 are substituted for fl and f2, where fdl, fd2 = Computed stresses fl and f2 as shown in Figure B2.3-1. Calculations are based on the effective section at the load for which deflections are determined.

(a)

•

83 Effective Widths of Unstiffened Elements 83.1 Uniformly Compressed Unstiffened Elements (a) Load Capacity Determination

Effective widths, b, of un stiffened compression elements with unifonn compression shall be detennined in accordance with Section B2.1 a with the exception that k shall be taken as 0.43 and w as defined in Figure B3.I-I. (b) Deflection Determination The effective widths used in computing deflections shall be detennined in accordance with Procedure I of Section B2.1 b except that fd is substituted for f and k = 0.43.

•

(Eq. B2.3-l) (Eq. B2.3-2)

(Eq.B2.3-3)

(Eq. B2.3-4)

Cold-Fonned Specification - August 19, 1986 Edition with December 11 , 1989 Addendum

1-36

• Actual Element

:jj---

•

f 2(tension)

Effective Elements and Stresses on Effective Elements

Figure 82.3-1 Stiffened Elements with Stress Gradient and Webs

Stress f ....... L..I_ _ _---II

~~~~~J

( Actual Element

Effective Element and Stress on Effective Element

Figure 83.1-1 Unstiffened Element with Uniform Compression

83.2 Unstiffened Elements and Edge Stiffeners with Stress Gradient (a) Load Capacity Determination

Effective widths, b, of un stiffened compression elements and edge stiffeners with stress gradient shall be determined in accordance with Section B2.1 a with f =f3 as in Figure B4-2 in the element and k = 0.43. (b) Deflection Determination Effective widths, b, of un stiffened compression elements and edge stiffeners with

•

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Cold-Fonned Specification - August 19, 1986 Edition with December 11, 1989 Addendum

•

stress gradient shall be determined in accordance with Procedure I Section B2.t b except that fd3 is substituted for f and k = 0.43.

84 Effective Widths of Elements with an Edge Stiffener or One Intermediate Stiffener The following notation is used in this section. = 1.28.JEjf (Eq. B4-1) k = Buckling coefficient = Dimension defined in Figure B4-1 bo d, w, D = Dimensions defined in Figure B4-2 ds = Reduced effective width of the stiffener as specified in this section. ds, calculated according to Section B4.2, is to be used in computing the overall effective section properties (see Figure B4-2) d's = Effective width of the stiffener calculated according to Section B3.1 (see Figure B4-2) CI, C2 = Coefficients defined in Figure B4-2 As = Reduced area of the stiffener as specified in this section. As is to be used in computing the overall effective section properties. The centroid of the stiffener is to be considered located at the centroid of the full area of the stiffener, and the moment of inertia of the stiffener about its own centroidal axis shall be that of the full section of the stiffener. Ia = Adequate moment of inertia of stiffener, so that each component element will behave as a stiffened element. Is, A's = Moment of inertia of the full stiffener about its own centroidal axis parallel to the element to be stiffened and the effective area of the stiffener, respectively. For edge stiffeners the round comer between the stiffener and the element to be stiffened shall not be considered as a part of the stiffener. S

•

For the stiffener shown in Figure B4-2: = (d 3t sin29)/12 = d'st

Is A's

(Eq. B4-2) (Eq. B4-3)

84.1 Uniformly Compressed Elements with an Intermediate Stiffener Load Capacity Determination Case I: bolt ~ S Ia =0 (no intermediate stiffener needed) b =w As =A's Case II: S < bolt < 3S IaN =[50(bo/t)/S] - 50 b and As shall be calculated according to Section B2.la where k =3(lslla)I/2+ 1 ~4 As=A's(Islla) ~ A's Case III: bolt ~ 3S lalt4 = [128(bo/t)/S] - 285 b and As are calculated according to Section B2.la where k =3(lsIIa)1/3 + 1 ~ As=A's (Islla) ~ A's (b) Deflection Determination Effective widths shall be determined as in Section B4.1 a except that fd is substituted for f.

(a)

•

(Eq. (Eq. (Eq. (Eq. (Eq. (Eq.

B4.1-1) B4.1-2) B4.1-3) B4.1-4) B4.1-5) B4.1-6)

(Eq. B4.1-7) (Eq. B4.1-8) (Eq. B4.1-9) (Eq. B4.l-1O) (Eq. B4.1-11)

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Cold-Fonned Specification - August 19, 1986 Edition with December 11, 1989 Addendum Stress f

f -----

[IIIIIII[ ~ ~ ~ ~ ] 1111111111111111111m~ ~ ~ ~ ~ ~ ]IIIIIIr

-~.a~iV~~i

(

------~

•

Effective Elements and Stress on Effective Element

Actual Elements

Stiffener Section

Figure 84-1 Elements with Intermediate Stiffener

84.2 Uniformly Compressed Elements with an Edge Stiffener (a) Load Capacity Determination Case I: wit 5: S/3 Ia =0 (no edge stiffener needed) b =w cis =d's for simple lip stiffener As =A's for other stiffener shapes Case II: S/3 < wit < S Ialt4 =399{ [(w/t)/S] - 0.33}3 n =1/2 C2 = Is/la 5: 1 CI =2- C2 b shall be calculated according to Section B2.1 where k =[4.82 - 5(D/w)](Is/la)n + 0.435: 5.25 - 5(D/w) for 0.8 ~ D/w > 0.25 k =3.57{1s/la)n + 0.435: 4.0 for (D/w) 5: 0.25 cis = d's (ls/la) 5: d's for simple lip stiffener As=A's (ls/la) 5: A's for other stiffener shape Case III: wit ~ S Ialt4 =[115 (w/t)/S] + 5 CI, C2, b, k, ds, As are calculated per Case II with n = 1/3. (b) Deflection Determination Effective widths shall be determined as in Section B4.2a except that fd is substituted for f.

(Eq. (Eq. (Eq. (Eq. (Eq.

B4.2-1) B4.2-2) B4.2-3) B4.2-4) B4.2-5)

•

(Eq. B4.2--6) (Eq. B4.2-7) (Eq. B4.2-8) (Eq. B4.2-9) (Eq. B4.2-1O) (Eq. B4.2-11) (Eq. B4.2-12)

(Eq. B4.2-13)

•

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Cold-Formed Specification - August 19, 1986 Edition with December 11, 1989 Addendum

•

Effective Stiffener used lor Calculating Overall Section Properties

Actual Stiffener

Stress I lor Flange

rmmTn]-----

WillWJ _____

u.J..j",j"J".I.J.UJJ.lj

Stress 13 lor lip

, , ", ' , ,"

Effective Element and Stress on Effective Element

•

Figure 84-2 Elements with Edge Stiffener

85 Effective Widths of Edge Stiffened Elements with Intermediate Stiffeners or Stiffened Elements with More Than One Intermediate Stiffener For the determination of the effective width, the intermediate stiffener of an edge stiffened element or the stiffeners of a stiffened element with more than one stiffener shall be disregarded unless each intermediate stiffener has the minimum Is as follows:

Imin

= [3.66~( (w I t)2 - (O.136E) I Fy 4

•

)}4

but not less than 18.4 t where wit =Width-thickness ratio of the larger stiffened sub-element Is =Moment of inertia of the full stiffener about its own centroid axis parallel to the element to be stiffened (a) If the spacing of intermediate stiffeners between two webs is such that for the sub-element between stiffeners b < w as determined in Section B2.1, only two intermediate stiffeners (those nearest each web) shall be considered effective. (b) If the spacing of intermediate stiffeners between a web and an edge stiffener is such that for the sub--element between stiffeners b < w as determined in Section B2.1, only one intermediate stiffener, that nearest the web, shall be considered effective. (c) If intermediate stiffeners are spaced so closely that for the elements between stiffeners b = w as determined in Section B2.1, all the stiffeners may be considered effective. In computing the flat-width to thickness ratio of the entire multiple-stiffened element, such element shall be considered as replaced by an "equivalent element" without intermediate stiffeners whose width, bo, is the full width between webs or from web to edge stiffener, and whose equivalent thickness, ts, is determined as fol-

(Eq. B5-1)

Cold-Fonned Specification - August 19, 1986 Edition with December II, 1989 Addendum

1-40

lows: ts

= \I12I sf I b o

(Eq. BS-2)

where Isf = Moment of inertia of the full area of the multiple-stiffened element, including the intermediate stiffeners, about its own centroidal axis. The moment of inertia of the entire section shall be calculated assuming the "equivalent element" to be located at the centroidal axis of the multiple stiffened element, including the intermediate stiffener. The actual extreme fiber distance shall be used in computing the section modulus. (d) If wit> 60, the effective width, be, of the sub-element or element shall be determined from the following formula:

~=~_O.lO[w -60] t

(Eq. BS-3)

where: w/t=flat-width ratio of sub-element or element b = effective design width determined in accordance with the provisions of Section B2.1, in. be =effective design width of sub-element or element to be used in design computations, in. For computing the effective structural properties of a member having compression sub-elements or element subject to the above reduction in effective width, the area of stiffeners (edge stiffener or intermediate stiffeners) shall be considered reduced to an effective area as follows:

For 60 < wit < 90: Aer=aAs! where

= (3 -

•

2 be I

• (Eq. BS-4)

w) -

3~ [ 1- ~

I 7]

(Eq. BS-S)

For wit ~ 90: (Eq. BS-6) Aer= (be/w) As! In the above expressions, Aef and As! refer only to the area of the stiffener section, exclusive of any portion of adjacent elements. The centroid of the stiffener is to be considered located at the centroid of the full area of the stiffener, and the moment of inertia of the stiffener about its own centroidal axis shall be that of the full section of the stiffener.

86 Stiffeners 86.1 Transverse Stiffeners Transverse stiffeners attached to beam webs at points of concentrated loads or reactions, shall be designed as compression members. Concentrated loads or reactions shall be applied directly into the stiffeners, or each stiffener shall be fitted accurately to the flat portion of the flange to provide direct load bearing into the end of the stiffener. Means for shear transfer between the stiffener and the web shall be provided according to Chapter E. The concentrated loads or reactions shall not exceed the smaller of the allowable loads, Pa. given by (a) and (b) as follows:

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Cold-Formed Specification - August 19, 1986 Edition with December 11 , 1989 Addendum

•

(a) Pa =Pn/QsI where Pn =FwyAc UsI=2.00 Ac = 18t2 + As, for transverse stiffeners at interior support and under concentrated load Ac = I Ot2+ As, for transverse stiffeners at end support Fwy=Lower value of beam web, Fy or stiffener section, Fys (b) Pa =Pn/Qc where Pn =Nominal axial load evaluated according to Section C4(a) with Ae replaced by Ab Qc =Factor of safety for axial compression evaluated according to Section C4(a) Ab =blt + As, for transverse stiffeners at interior support and under concentrated load Ab = b2t + As, for transverse stiffeners at end support As =Cross sectional area of transverse stiffeners bl =25t [0.0024(LsJt) + 0.72] ::; 25t b2 =12t [O.0044(LsJt) + 0.83]::; 12t LsI = Length of transverse stiffener t =Base thickness of beam web

1-41

(Eq. B6.1-1) (Eq.B6.1-2) (Eq. B6.1-3) (Eq. B6.l-4) (Eq. B6.l-5)

(Eq. B6.1-6) (Eq. B6.1-7) (Eq. B6.1-8) (Eq. B6.1-9)

The wits ratio for the stiffened and unstiffened elements of cold-formed steel transverse stiffeners shall not exceed 1.28 ~(E I Fys) and 0.37 ~(E I Fys) respectively, where Fys is the yield stress, Fy, and ts the thickness of the stiffener steel.

86.2 Shear Stiffeners Where shear stiffeners are required, the spacing shaH be such that the web shear force shall not exceed the allowable shear force, Va, permitted by Section C3.2, and the ratio a/h shall not exceed [260/(h/t)F nor 3.0. The actual moment of inertia, Is, of a pair of attached shear stiffeners, or of a single shear stiffener, with reference to an axis in the plane of the web, shall have a minimum value of Ismin = 5ht3[h/a - 0.7(a/h)] ~ (h/50)4 The gross area of shear stiffeners shall be not less than

ASI=I-Cv[~_ 2

(a/h)2

(a/h)+~I+(a/h)2

]YDht

(Eq. B6.2-1)

(Eq. B6.2-2)

where C v = 45,000kv

when Cv::;' 0.8

Fy(h/t)2

•

Cv = 190

hit

-(~v: Fy

when Cv > 0.8

h a/h < 10 kv = 4.00+ 5.34 2 wen . (a/h)

(Eq. B6.2-3)

(Eq. B6.2-4) (Eq. B6.2-5)

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Cold-Fonned Specification - August 19, 1986 Edition with December 11, 1989 Addendum

kv = 5.34 + 4.00 when alb > 1.0 (a/h/ a =Distance between transverse stiffeners Yield point of web steel Y = Yield point of stiffener steel D = 1.0 for stiffeners furnished in pairs D = 1.8 for single-angle stiffeners D = 2.4 for single-plate stiffeners t and h are as defined in Section B 1.2

(Eq. B6.2-6)

•

86.3 Non-Conforming Stiffeners The allowable load carrying capacity of members with transverse stiffeners that do not meet the requirements of Sections B6.1 or B6.2, such as stamped or rolled-in transverse stiffeners shall be determined by tests in accordance with Chapter F of this Specification.

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Cold-Fonned Specification - August 19, 1986 Edition with December 11 , 1989 Addendum

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1-43

C.MEMBERS C1 Properties of Sections Properties of sections (cross-sectional area, moment of inertia, section modulus, radius of gyration, etc.) shall be determined in accordance with conventional methods of structural design. Properties shall be based on the full cross section of the members (or net sections where the use of net section is applicable) except where the use of a reduced cross section, or effective design width, is required.

C2 Tension Members For axially loaded tension members, the applied tensile force shall not exceed T a determined as follows: Ta = TnlQ I (Eq. C2-1) where Tn

= Strength of member when loaded in tension = AnFy Q = Factor of safety for tension = 1.67 An = Net area of the cross section Fy = Design yield stress as determined in Section AS.2.1

(Eq. C2-2)

C3 Flexural Members C3.1 Strength for Bending Only

•

In flexural members, the applied moment uncoupled from axial load, shear, and local concentrated forces or reactions shall not exceed the allowable Ma calculated as follows: (Eq. C3.1-l) Ma = MnlQf where Mn = Smaller of the nominal moment strengths calculated according to Sections C3.l.1, C3.1.2, and C3.1.3 Qf Factor of safety for bending 1.67

= =

C3.1.1 Nominal Section Strength Section strength shall be calculated either on the basis of initiation of yielding in the effective section (Procedure I) or on the basis of the inelastic reserve capacity (Procedure II) as applicable. (a)

•

Procedure I - Based on Initiation of Yielding Effective yield moment based on section strength, Mn, shall be determined as follows:

= SeFy

where F y = Design yield stress as determined in Section A5.2.1 Se = Elastic section modulus of the effective section calculated with the extreme compression or tension fiber at Fy

(Eq. C3.1.1-l)

Cold-Fonned Specification - August 19, 1986 Edition with December II, 1989 Addendum

1-44

•

(b) Procedure II - Based on Inelastic Reserve Capacity The inelastic flexural reserve capacity may be used when the following conditions are met: (1) The member is not subject to twisting or to lateral, torsional, or torsional-

flexural buckling. (2) The effect of cold forming is not included in determining the yield point F y. (3) The ratio of the depth of the compressed portion of the web to its thickness does not exceed AI. (4) The shear force does not exceed 0.35Fy times the web area, h x t. (5) The angle between any web and the vertical does not exceed 30 degrees. The nominal moment strength, Mn, shall not exceed either 1.25 SeFy determined according to Procedure I or that causing a maximum compression strain of Cyey (no limit is placed on the maximum tensile strain). where ey E

= Yield strain = FylE =Modulus of elasticity =Compression strain factor determined as follows: (a) Stiffened compression elements without intermediate stiffeners Cy = 3 for wIt :::; AI C y = 3 - 2( wIt - AI) for AI < w < A2

A2 -AI

C y = 1 for wIt ~ A2 where

A _ 1-

1.11

~Fy

1.28

~Fy IE

(Eq. C3.1.1-2) (Eq. C3.1.1-3)

•

(b) Unstiffened compression elements Cy

(c) Multiple-stiffened compression elements and compression elements with edge stiffeners Cy = I When applicable, effective design widths defined in Section B3.1 shaH be used in calculating section properties. Mn shall be calculated considering equilibrium of stresses, assuming an ideally elastic-plastic stress-strain curve which is the same in tension as in compression, assuming small deformation and assuming that plane sections remain plane during bending. Combined bending and web crippling shall be checked by provisions of Section C3.S.

C3.1.2 Lateral Buckling Strength

For the laterally unbraced segments of singly-, doubly-, and point-symmetric sections* subject to lateral budding, Mn shall be determined as follows: Me Mn =SeSf

(Eq. C3.1.2-1)

The provisions of this Section apply to 1-, lr-, C- and other singly-symmetric section flexural members (not including multiple-web deck, U- and closed box-type members, and curved or arch members). The provisions of this Section do not apply to laterally unbraced compression flanges of otherwise laterally stable sections. Refer to C3.I.3 for C- and Z-purlins in which the tension flange is attached to sheathing.

•

Cold-Fonned Specification - August 19, J 986 Edition with December J I, 1989 Addendum

•

1-45

where Sf = Elastic section modulus of the full unreduced section for the extreme compression fiber Se = Elastic section modulus of the effective section calculated at a stress Me / Sf in the extreme compression fiber Me = Critical moment calculated according to (a) or (b) below: (a) For singly-, doubly-, and point-symmetric sections: For Me > O.5My Me

=My(I-~J 4Me

(Eq. C3.1.2-2)

For Me:5: O.5My (Eq. C3.1.2-3) Me = Me where My = Moment causing initiaJ yield at the extreme compression fiber of the full section (Eq. C3.1.2-4) =SfFy =Elastic critical moment computed by the following equations: Me

=CbroA~creycrt for bending about the symmetry axis. For

(Eq. C3.1.2-5)

singly-symmetric sections, x-axis is the axis of symmetry oriented such that the shear center has a negative x-coordinate. For point-symmetric sections, use 0.5 Me. Alternatively, Me can be calculated using the formula for doubly-symmetric I-sections or point-symmetric sections given in (b) below

•

= CsAcre j + Cs~ j2 + r;( crt / crex) ] / CTF for bending about the (Eq. C3.1.2-6) centroi al axis perpendicular to the symmetry axis for singly -symmetric sections only = +1 for moment causing compression on the shear center side of the centroid =-1 for moment causing tension on the shear center side of the centroid 1t2E = (Eq. C3.1.2-7) (KxLx / rx)2

Cs Cs crex

crey

1t 2 E

(Eq. C3.1.2-8)

{KyLy / ry)2 crt

•

A Cb Cb

_1_ [GJ + ,,'Ee. ]

Ar;

(K tL t )2 = Full cross-sectional area = Bending coefficient which can conservatively be taken as unity, or calculated from = 1.75 + 1.05[(MtlM2)] + 0.3 [(MtlM2)F :5: 2.3 where MI is the smaller and M2 the larger bending moment at the ends of the unbraced length, taken about the strong axis of the mem-

(Eq. C3.1.2-9)

Cold-Fonned Specification - August 19, 1986 Edition with December 11, 1989 Addendum

1-46

•

ber, and where M 1/M2, the ratio of end moments, is positive when MI and M2 have the same sign (reverse curvature bending) and negative when they are of opposite sign (single curvature bending). When the bending moment at any point within an unbraced length is larger than that at both ends of this length, and for members subject to combined axial load and bending moment (Section C5), Cb shall be taken as unity. =0.6 - 0.4 (MI/M2) where MI is the smaller and M2 the larger bending moment at the ends of the unbraced length, and where MI/M2, the ratio of end moments, is positive when MI and M2 have the same sign (reverse curvature bending) and negative when they are of opposite sign (single curvature bending). When the bending moment at any point within an unbraced length is larger than that at both ends of this length, and for members subject to combined axial load and bending moment (Section C5), CTF shall be taken as unity. = Polar radius of gyration of the cross section about the shear center

CTF

=~r; +r; +x~ (Eq. C3.1.2-1O) =Radii of gyration ofthe cross section about the centroidal principal axes E = Modulus of elasticity G =Shear modulus Kx, K y, K t =Effective length factors for bending about the x- and y-axes, and for twisting Lx, Ly, L t = Unbraced length of compression member for bending about the x- and y-axes, and for twisting xo =Distance from the shear center to the centroid along the principal x-axis, taken as negative J =St. Venant torsion constant of the cross section Cw =Torsional warping constant of the cross section rx, ry

_l_[r X3dA+f x y2 dA]-x o 2Iy J A

•

(Eq. C3.1.2-11)

(b) For 1- or Z-sections bent about the centroidal axis perpendicular to the web (xaxis): In lieu of (a), the following equations may be used to evaluate Me: For Me> 2.78My Me

= My

(Eq.C3.1.2-12)

For 2.78My > Me > 0.56My

= 10 M (1- lOM y ) 9 y 36M

(Eq. C3.1.2-13)

For Me $; 0.56My Me where

= Me

(Eq.C3.1.2-14)

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Cold-Fonned Specification - August 19, 1986 Edition with December 11 , 1989 Addendum

•

1-47

Me = Elastic critical moment detennined either as defined in (a) above or as follows: dIye - 2EC b -1t -

~ dou bl y-symmetnc . I-sections . lor

(Eq. C3.1.2-15)

_ 1t 2 EC b dIye

(Eq. C3.1.2-16) for point-symmetric Z-sections 2U d = Depth of section L = Unbraced length of the member lye = Moment of inertia of the compression portion of a section about the centroidal axis of the entire section parallel to the web, using the full unreduced section

Other tenns are defined in (a).

C3.1.3 Beams Having One Flange Through-Fastened to Deck or Sheathing This section does not apply to a continuous beam for the region between inflection points adjacent to a support, or to a cantilever beam. The nominal moment strength of a Channel or Z-section loaded in a plane parallel to the web, with the tension flange attached to deck or sheathing and with the compression flange laterally unbraced shall be detennined as follows:

•

Mn = RSeFy where R =0.40 for simple span C sections =0.50 for simple span Z sections =0.60 for continuous span C sections =0.70 for continuous span Z sections Se and Fy are defined in Section C3.1.1 The reduction factor, R, shall be limited to roof and wall systems meeting the following conditions:

•

Member depth less than 11.5 inches The flanges are edge stiffened compression elements 60 ~ depth/thickness ~ 170 2.8 ~ depth/flange width ~ 4.5 16 ~ flat width/thickness of flange ~ 43 For continuous span systems, the lap length at each interior support in each direction (distance from center of support to end of lap) shall not be less than: 1.5d for zee sections 3.0d for channel sections Member span length no greater than 33 feet For continuous span systems, the longest member span shall not be more than 20% greater than the shortest span Both flanges are prevented from moving laterally at the supports Roof or wall panels shall be steel sheets, minimum of 0.0 19 in. coated thickness, having a minimum rib depth of 1 in., spaced a maximum of 12 in. on centers and attached in a manner to effectively inhibit relative movement between the panel and purlin flange

(Eq. C3.1.3-l)

Cold-Fanned Specification - August 19, 1986 Edition with December 11 , 1989 Addendum

1--48

•

Insulation shall be glass fiber blanket 0 to 6 inches thick compressed between the member and panel in a manner consistent with the fastener being used Fastener type: minimum No. 12 self~rilling or self-tapping sheet metal screws or 3/16 - in. rivets, washers 1/2 in. diameter Fasteners shall not be standoff type screws Fasteners shall be spaced not greater than 12 in. on centers and placed near the center of the beam flange If variables fall outside any of the above stated limits, the user must perform full scale tests in accordance with Section Fl of the Specification, or apply another rational analysis procedure. In any case, the user is permitted to perform tests, in accordance with Section FI, as an alternate to the procedure described in this section.

C3.2 Strength for Shear Only The shear force at any section shall not exceed the allowable shear, Va, calculated as follows: (a)

Forh/t~1.38~Ekv/Fy Va =0.38t2~ ~O.4Fyht

(b)

(Eq. C3.2-l)

For h / t > 1.38~Ekv / Fy

Va =0.53Ekvt3 / h

(Eq. C3.2-2)

•

where t = Web thickness h = Depth of the flat portion of the web measured along the plane of the web kv = Shear buckling coefficient determined as follows : 1. For unreinforced webs, kv = 5.34 2. For beam webs with transverse stiffeners satisfying the requirements of Section B6 when a/h ~ 1.0 kv =4.00+ 5.34 (a / h)2 when a/h > 1.0

(Eq . C3.2-3)

kv = 5.34 + 4.00 (Eq. C3.2-4) (a/h)2 where a =the shear panel length for unreinforced web element =distance between transverse stiffeners for web elements. For a web consisting of two or more sheets, each sheet shall be considered as a separate element carrying its share of the shear force.

C3.3 Strength for Combined Bending and Shear

For beams with unreinforced webs, the moment, M, and shear, V, shall satisfy the following interaction equation: (M/Maxo)2 + (VN a)2 ~ 1.0 For beams with transverse web stiffeners, the moment, M, and shear, V, shall not exceed Ma and Va, respectively. When MlMaxO> 0.5 and VN a> 0.7, then M and V shall satisfy the following interaction equation:

•

.11

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Cold-Formed Specification - August 19, 1986 Edition with December II, 1989 Addendum

0.6 (M/Maxo) + (VNa)::; 1.3 In the above: Ma = Allowable moment when bending alone exists Maxo = Allowable moment about the centroidal axes determined in accordance with Section C3.1 excluding the provisions of Section C3.1.2, Va = Allowable shear force when shear alone exists

C3.4 Web Crippling Strength

•

These provisions are applicable to webs of flexural members subject to concentrated loads or reactions, or the components thereof, acting perpendicular to the longitudinal axis of the member, acting in the plane of the web under consideration, and causing compressive stresses in the web. To avoid crippling of unreinforced flat webs of flexural members having a flat width ratio, hit, equal to or less than 200, concentrated loads and reactions shall not exceed the values of P a given in Table C3.4-I. Webs of flexural members for which hit is greater than 200 shall be provided with adequate means of transmitting concentrated loads andlor reactions directly into the webs. The formulas in Table C3.4-1 apply to beams when R/t ::; 6 and to deck when R/t::; 7, Nit::; 210 and Nih::; 3.5. Pa represents the concentrated load or reaction for one solid web connecting top and bottom flanges. For two or more webs, P a shall be computed for each individual web and the results added to obtain the allowable load or reaction for the multiple web. For built-up I-sections, or similar sections, the distance between the web connector and beam flange shall be kept as small as practical.

TABLE C3.4-1

Pa Shapes Having Single Webs Un stiffened Stiffened Flanges Flanges Opposing Loads Spaced> 1.5h(2)

Opposing Loads Spaced ~ 1.5h(5)

•

Shapes Having Multiple Webs(l) Stiffened and Unstiffened Ranges

End Reaction(3)

Eq. C3.4-1

Eq. C3.4-2

Eq. C3.4-3

Interior Reaction(4)

Eq. C3.4-4

Eq. C3.4-S

End Reaction(3)

Eq. C3.4-6

Eq. C3.4-7

Interior Reaction(4)

Eq. C3.4-8

Eq. C3.4-9

Footnotes and Equation References to Table C3.4-1 : (1) I-sections made oftwo channels connected back to back or similar sections which provide a high degree of restraint against rotation of the web (such as I-sections made by welding two angles to a channel). (2) At locations of one concentrated load or reaction acting either on the top or bottom flange, when the clear distance between the bearing edges of this and adjacent opposite concentrated loads or reactions is greater than 1.Sh. (3) For end reactions of beams or concentrated loads on the end of cantilevers when the distance from the edge of the bearing to the end of the beam is less than 1.5h.

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Cold-Fonned Specification - August 19, 1986 Edition with December 11, 1989 Addendum

(4) For reactions and concentrated loads when the distance from the edge of bearing to the end of the beam is equal to or greater than 1.5h. (5) At locations of two opposite concentrated loads or of a concentrated load and an opposite reaction acting simultaneously on the top and bottom flanges, when the clear distance between their adjacent bearing edges is equal to or less than 1.5h. Equations for Table C3.4--1 : (Eq. t2kC3C4Ce[179 -O.33(h/t)] [1 + 0.0 1(N/t)] (Eq. t2 kC3C4Ce[117 - 0.15(h/t)] [1 + 0.01 (N/t)] When N/t > 60, the factor [1 + 0.01 (N/t)] may be increased to [0.71 + 0.0 15(N/t)] (Eq. t2FyC6(5.0 + 0. 63.JNTt) 2 (Eq. t kCIC2Ce[291- 0.40(h/t)] [1 + 0.007(N/t)]

• C3.4--1) C3.4--2) C3.4--3) C3.4--4)

When N/t > 60, the factor [l + 0.007(N/t)] may be increased to [0.75 + O.Oll(N/t) t2FyC5(0.88+0.12m)(7.50 + 1.63~N / t) t2 kC3C4Ce[132 - 0.31(h/t)] [1 + 0.01 (N/t)] t2FyCs(0.64+0.31m) (5.0 + O. 63.JNTt) t2 kCIC2Ce[417 -1.22(h/t)] [1 + 0.00 13(N/t)]

(Eq. C3.4--5) (Eq. C3.4--6) (Eq. C3.4--7) (Eq. C3.4--8) (Eq. C3.4--9)

In the above-referenced formulas: Pa = Allowable concentrated load or reaction per web, kips Cl =(1.22 - 0.22k) C2 =(1.06 - 0.06R/t) ~ 1.0 C3 =(1.33 - 0.33k) C4 =0.50 < (1.15 - 0.15R/t) ~ 1.0 C5 =(1.49 - 0.53k) ~ 0.6 C6=1+(h/t) when h/t~150 750 = 1.20, when hit > 150 C7 = 11k, when hit ~ 66.5 = [1.10- h / tJ~ 665 k' C s = [ 0.98 -

Ce Fy h k m t

when h / t > 66.5

~~; ] ~

=0.7 + 0.3 (9/90)2 = Design yield stress of the web, see Section A5.2.1 = Depth of the flat portion of the web measured along the plane of the web =Fy/33 =t/0.075 =Web thickness, inches

N = Actual length of bearing, inches. For the case of two equal and opposite concentrated loads distributed over unequal bearing lengths, the smaller value of N shall be taken R =Inside bend radius

(Eq. (Eq. (Eq. (Eq. (Eq.

C3.4--1O) C3.4--11) C3.4--12) C3.4--13) C3.4--14)

•

(Eq. C3.4--15) (Eq. C3.4--16) (Eq. C3.4--17) (Eq. C3.4--18) (Eq. C3.4--19) (Eq. C3.4--20)

(Eq. C3.4--21) (Eq. C3.4--22)

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Cold-Fonned Specification - August 19, 1986 Edition with December 11 , 1989 Addendum

•

I-51

=Angle between the plane of the web and the plane ofthe bearing surface ~ 45°, but not more than 90°

C3.5 Combined Bending and Web Crippling Strength Unreinforced flat webs of shapes subjected to a combination of bending and concentrated load or reaction shall be designed to meet the following requirements: For shapes having single unreinforced webs:

1.2 (PlPa) + (M/Maxo) < 1.5

(Eq. C3.5-l)

Exception: At the interior supports of continuous spans, the above formula is not applicable to deck or beams with two or more single webs, provided the compression edges of adjacent webs are laterally supported in the negative moment region by continuous or intermittently connected flange elements, rigid cladding, or lateral bracing, and the spacing between adjacent webs does not exceed 10 inches. For shapes having multiple unreinforced webs such as I-sections made of two channels connected back-to-back, or similar sections which provide a high degree of restraint against rotation of the web (such as I-sections made by welding two angles to a channel);

1.1 (PlPa) + (M/Maxo) < 1.5

(Eq. C3.5-2)

Exception: When hIt ~ 2.331 ~(Fy I E) and A~ 0.673, the allowable concentrated load or reaction may be determined by Section C3.4 .

• II

In the above formulas: P =Concentrated load or reaction in the presence of bending moment Pa = Allowable concentrated load or reaction in the absence of bending moment determined in accordance with Section C3.4 M =Applied bending moment at, or immediately adjacent to, the point of application of the concentrated load or reaction Maxo = Allowable moment about the centroidal axes determined in accordance with Section C3.1 excluding the provisions of Section C3.1.2, w =Flat width of the beam flange which contacts the bearing plate t =Thickness of the web or flange A =Slendemess factor given by Section B2.l

C4 Concentrically Loaded Compression Members This section applies to members in which the resultant of all loads acting on the member is an axial load passing through the centroid of the effective section calculated at the stress, Fn, defined in this section. (a) The axial load shall not exceed P a calculated as follows: Pa = PolO c

•

(Eq . C4-I)

where Pn = AeFn (Eq. C4-2) A,; = Effective area at the stress Fn. For sections with circular holes, Ae shall be determined according to Section B2.2a, subject to the limitations of that section. If the number of holes in the effective length region times the hole diameter divided by the effective length does not exceed 0.015, Ae can be determined ignoring the holes. Fn is determined as follows:

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Cold-Fonned Specification - August 19, 1986 Edition with December 11, 1989 Addendum

(Eq. C4-3) For Fe > Fy/2 Fn = Fy (1 - Fy/4Fe) (Eq. C4-4) For Fe::;; Fy/2 Fn = Fe Fe is the least of the elastic flexural, torsional and torsional-flexural buckling stress detennined according to Sections C4.1 through C4.3. = Factor of safety for axial compression = 1.92, except when Fe is detennined according to Section C4.1 for fully effective sections having wall thicknesses greater than or equal to 0.09 inches and Fe> Fy/2. In this case,

•

n =~+lR-!R3 3

where

R = ~(Fy / 2Fe) (b) For C- and Z-shapes, and single-angle sections with unstiffened flanges, Pn shall be taken as the smaller of Pn calculated above and Pn calculated as follows: Pn = where A w t

A1t 2 E

25. 7{w It)

(Eq. C4-5)

= Area of the full, unreduced cross section = Flat width of the un stiffened element = Thickness of the unstiffened element

(c) Angle sections shaH be designed for the applied axial load, P, acting simultaneously with a moment equal to PL/IOOO applied about the minor principal axis causing compression in the tips of the angle legs.

•

(d) The slenderness ratio, KL/r, of all compression members preferably should not exceed 200, except that during construction only, KL/r preferably should not exceed 300.

C4.1 Sections Not Subject to Torsional or Torsional-Flexural Buckling

For doubly-symmetric sections, closed cross sections and any other sections which can be shown not to be subject to torsional or torsional-flexural buckling, the elastic flexural buckling stress, Fe, shall be detennined as follows:

E (KL / r)2 1t 2

Fe=---,,where E K L r

(Eq. C4.1-1)

= Modulus of elasticity = Effective length factor* = Unbraced length of member = Radius of gyration of the full, unreduced cross section

* In frames where lateral stability is provided by diagonal bracing, shear walls, attachment to an adjacent structure having adequate lateral stability, or floor slabs or roof decks secured horizontally by walls or bracing systems parallel to the plane of the frame, and in trusses, the effective length factor. K. for compression members which do not depend upon their own bending stiffness for lateral stability of the frame or truss. shall be taken as unity, unless analysis shows that a smaller value may be used. In a frame which depends upon its own bending stiffness for lateral stability. the effective length, KL, of the compression members shall be determined by a rational method and shall not be less than the actual unbraced length.

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I-53

C4.2 Doubly- or Singly-Symmetric Sections Subject to Torsional or Torsional-Flexural Buckling For sections subject to torsional or torsional-flexural buckling, Fe shall be taken as the smaller of Fe calculated according to Section C4.1 and Fe calculated as follows: Fe = 21p [( a ex + at) -

~( a ex + at)2 -

4paex at ]

(Eq. C4.2-1)

Alternatively, a conservative estimate of Fe can be obtained using the following equation: Fe = ata ex (Eq. C4.2-2) at + a ex where at and aex are as defined in C3.1.2(b) (Eq. C4.2-3)

For singly-symmetric sections, the x-axis is assumed to be the axis of symmetry.

C4.3 Nonsymmetric Sections For shapes whose cross sections do not have any symmetry, either about an axis or about a point, Fe shall be determined by rational analysis. Alternatively, compression members composed of such shapes may be tested in accordance with Chapter F.

•

C5 Combined Axial Load and Bending The axial force and bending moments shall satisfy the following interaction equations: (Eq. CS-l)

~+ Mx + My :S1.0 Paa

Max

May

(Eq. CS-2)

When P/Pa ~ O.lS, the following formula may be used in lieu ofthe above two formulas:

~+ Mx + My :S1.0 Pa

•

Max

May

(Eq. CS-3)

where P = Applied axial load Mx and My =Applied moments with respect to the centroidal axes of the effective section determined forthe axial load alone. For angle sections, My shall be taken either as the applied momentortheappliedmomentplusPL/l 000, wh icheverresultsin a lower value of Pa. Pa =Allowable axial load determined in accordance with Section C4 Pao = Allowable axial load determined in accordance with Section C4, with Fn = Fy Max and May = Allowable moments about the centroidal axes determined in accordance with Section C3 1/ (Xx, 1/ (Xy = Magnification factors = 1/[1 -(OcP/Pcr)] (Eq. CS-4) nc =Factor of safety used in determining Pa Ib = Moment of inertia of the full, unreduced cross section about the axis of bending

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Cold-Fonned Specification - August 19. 1986 Edition with December 11. 1989 Addendum

n 2Eh

= (KbLb) 2

Per

(Eq. C5-5)

=Actual unbraced length in the plane of bending =Effective length factor in the plane of bending =Coefficients whose value shall be taken as follows:

•

1. For compression members in frames subject to joint translation (sidesway) Cm = 0.85 2. For restrained compression members in frames braced against joint translation and not subject to transverse loading between their supports in the plane of bending Cm = 0.6 - 0.4 (MI/M2) (Eq. C5-6) where MI/M2 is the ratio of the smaller to the larger moment at the ends of that portion of the member under consideration which is unbraced in the plane of bending. MI/M2 is positive when the member is bent in reverse curvature and negative when it is bent in single curvature.

3. For compression members in frames braced against joint translation in the plane of loading and subject to transverse loading between their supports. the value ofCm may be determined by rational analysis. However, in lieu of such analysis, the following values may be used:

•

(a) for members whose ends are restrained, Cm = 0.85, (b) for members whose ends are unrestrained, Cm = 1.0.

(:6 Cylindrical Tubular Members The requirements of this Section apply to cylindrical tubular members having a ratio of outside diameter to wall thickness, O/t, not greater than 0.441 E/Fy.

C6.1 Bending For flexural members, the actual moment uncoupled from axial load, shear, and local concentrated forces or reactions shall not exceed Ma calculated as follows: Ma = Mn/Q f (Eq. C6.1-1) where Mn = Nominal moment n f = Factor of safety for bending = 1.67 For O/t ~ 0.070 E/Fy (Eq. C6.1-2) Mn = 1.25 FySf For 0.070 E/Fy < O/t ~ 0.319 E/Fy

=[0.970 + 0.020 (E / Fy ) ]FySf

O/t For 0.319 E/Fy < O/t ~ 0.441 E/Fy Mn = [0.328E/(0/t)]Sf where Sf Elastic section modulus of the full, unreduced cross section

(Eq. C6.1-3)

(Eq. C6.1-4)

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Cold-Fonned Specification - August 19, 1986 Edition with December II , 1989 Addendum

•

I-55

CS.2 Compression The requirements of this Section apply to members in which the resultant of all loads and moments acting on the member is equivalent to a single force in the direction of the member axis passing through the centroid of the section. The axial load shall not exceed P a calculated as follows: Pa = PnlQc (Eq. C6.2-1) where

Pn = Fn Ae For Fe greater than Fy/2 Fn = Flexural buckling stress = Fy [1 - Fy/4Fe] Fe = The elastic flexural buckling stress determined according to Section C4.1 nc = Factor of safety for axial compression

(Eq. C6.2-4)

(Eq. C6.2-5)

Ao =

3 8 8 ~Fy /2Fe

7 [OoOi + 0.667]A $. A for D$. 0.441 ~ __y t Fy

tE A = Area of the unreduced cross section For Fe $. Fy/2 Fn

= Fe

nc = Factor of safety for axial compression Ae

= 1.92 =A

CS.3 Combined Bending and Compression Combined bending and compression shall satisfy the provisions of Section C5.

•

(Eq. C6.2-3)

= ~+~R-.!.R3 Ae = [1 - (1 - R2)(l - Ao/A)]A

•

(Eq. C6.2-2)

(Eq. C6.2-6) (Eq. C6.2-7)

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Cold-Fonned Specification - August 19,1986 Edition with December II, 1989 Addendum

D. STRUCTURAL ASSEMBLIES 01 Built-Up Sections 01.1 I - Sections Composed of Two Channels The maximum pennissible longitudinal spacing of welds or other connectors Sm.x, joining two channels to fonn an I-section shall be (a) For compression members: Lrey Smax = - (Eq. Dl.I-l) 2rI where L = Unbraced length of compression member rl = Radius of gyration of the I-section about the axis perpendicular to the direction in which buckling would occur for the given conditions of end support and intennediate bracing rey = Radius of gyration of one channel about its centroidal axis parallel to the web (b) For flexural members: Sm.x= L/6 (Eq.D1.1-2) In no case shall the spacing exceed the value 2gTs Sm.x = - (Eq. Dl.l-3) mq where L = Span of beam Ts = Strength of connection in tension g = Vertical distance between the two rows of connections nearest to the top and bottom flanges q = Intensity of load on the beam (For methods of detennination, see below). m = Distance from the shear center of one channel to the mid-plane of its web. For simple channels without stiffening lips at the outer edges,

=---'----

= wrdt [Wrd + 2D(d _ 4D2)]

2wr+d/3 For channels with stiffening lips at the outer edges, 4Ix

= Projection of flanges

= Pm/2g

•

(Eq. Dl.l-4)

(Eq. Dl.1-5)

from the inside face of the web (For channels with flanges of unequal width, Wr shall be taken as the width of the wider flange) d = Depth of channel or beam D = Overall depth of lip Ix = Moment of inertia of one channel about its centroidal axis nonnal to the web. The intensity of load, q, is obtained by dividing the magnitude of concentrated loads or reactions by the length of bearing. For beams designed for a unifonnly distributed load, q shall be taken equal to three times the intensity of the unifonnly distributed design load. If the length of bearing of a concentrated load or reaction is smaller than the weld spacing, s, the required strength of the welds or connections closest to the load or reaction is The required maximum spacing of connections, Smax, depends upon the intensity of the load directly at the connection. Therefore, if unifonn spacing of connections is

•

(Eq. Dl.l-6)

•

Cold-Fonned Specification - August 19 , 1986 Edition with December II , 1989 Addendum

•

used over the whole length of the beam, it shall be determined at the point of maximum local load intensity. In cases where this procedure would result in uneconomically close spacing, either one of the following methods may be adopted: (a) the connection spacing may be varied along the beam according to the variation of the load intensity; or (b) reinforcing cover plates may be welded to the flanges at points where concentrated loads occur. The shear strength ofthe connections joining these plates to the flanges shall then be used for Ts, and g shall be taken as the depth of the beam.

01.2 Spacing of Connections in Compression Elements The spacing, s, in the line of stress, of welds, rivets, or bolts connecting a cover plate, sheet, or a non-integral stiffener in compression to another element shall not exceed (a)

(b)

that which is required to transmit the shear between the connected parts on the basis of the design strength per connection specified elsewhere herein; nor 1.16t ~ (E I fc ), where t is the thickness of the cover plate or sheet, and fc is the stress at design load in the cover plate or sheet; nor

(c) three times the flat width, w, of the narrowest unstiffened compression element tributary to the connections, but need not be less than 1.11 t

~(E I Fy) , or 1.33t ~(E I Fy) if wit ? quired by (a) or (b) above.

•

~(E I Fy ) if wit < 0.50

0.50~(E I Fy), unless closer spacing is re-

In the case of intermittent fillet welds parallel to the direction of stress, the spacing shall be taken as the clear distance between welds, plus one-half inch. In all other cases, the spacing shall be taken as the center-to--center distance between connections. Exception: The requirements of this Section do not apply to cover sheets which act only as sheathing material and are not considered as load-carrying elements.

Mixed Systems

The design of members in mixed systems using cold-formed steel components in conjunction with other materials shall conform to this Specification and the applicable specification of the other material.

03 Lateral Bracing Braces shall be designed to restrain lateral bending or twisting of a loaded beam or column, and to avoid local crippling at the points of attachment.

03.1 Symmetrical Beams and Columns Braces and bracing systems, including connections, shall be designed considering strength and stiffness requirements.

03.2 Channel-Section and Z-Section Beams

•

The following provisions for bracing to restrain twisting of channels and Z-sections used as beams loaded in the plane of the web, apply only when (a) the top flange is connected to deck or sheathing material in such a manner as to effectively restrain lateral deflection of the connected flange *, or (b) neither flange is so connected. When both flanges are so connected, no further bracing is required .

* Where the Specification does not provide an explicit method for design, funher infonnation should be obtained from the Commentary.

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•

03.2.1 Anchorage of Bracing for Roof Systems Under Gravity Load With Top Flange Connected to Sheathing For channels and Z-sections designed according to Section C3.I.l, and having deck or sheathing fastened directly to the top flanges in such a manner shown to effectively inhibit relative movement between the deck or sheathing and the purlin flange, provisions shall be made to restrain the flanges so that the maximum top flange lateral displacements with respect to the purlin reaction points do not exceed the span length divided by 360. If the top flanges of all purl ins face in the same direction, anchorage of the restraint system must be capable of satisfying the requirements of Sections D3.2.1(a) and D3 .2.l(b). If the top flanges of adjacent lines of purl ins face in opposite directions, the provisions of Section D3.2.I(a) and D3.2.1(b) do not apply. Anchored braces may be connected to only one line ofpurlins in each purl in bay of each roof slope if provision is made to transmit forces from other purlin lines through the roof deck and its fastening system. Anchored braces shall be as close as possible to the flange which is connected to the deck or sheathing. Anchored braces shall be provided for each purlin bay. For bracing arrangements other than those covered in Sections D3.2.l (a) and D3.2.1 (b), tests in accordance with Chapter F shall be performed so that the type and I or spacing of braces selected are such that the test strength of the braced Z-section assembly is equal to or greater than 5/3 times its flexural design strength, instead of that required by Chapter F. (a)

(b)

Channel Sections For roof systems using channel sections for purlins with all compression flanges facing in the same direction, a restraint system capable of resisting 0.05W, in addition to other loading, shall be provided where W is the load supported by all purlin lines being restrained. Where more than one brace is used at a purlin line, the restraint force 0.05W shall be divided equally between all braces.

•

Z-Sections For roof systems having a diaphragm stiffness of at least 2,000 Ib/in., having four to twenty Z-purlin lines with all top flanges facing in the direction of the upward roof slope, and with restraint braces at the purlin supports, midspan or one-third points, each brace shall be designed to resist a force determined as follows: (I) Single-Span System with Restraints at the Supports: 50 0.220b1. . e]w L - 0. -sm

P - 5[

n~ · 72dO·90to.60

(Eq. D3.2.I-I)

(2) Single-Span System with Third-Point Restraints: PL=0.5[ 0.474 b 1.22 -sine]w n ~ . 57 d 0.89tO.33

(Eq. D3.2.l-2)

(3) Single-Span System with Midspan Restraint: •n.L

224b 1.32 ng· d 0.83tO.50

= [0.65

. e]w -SIn

(4) Multiple-Span System with Restraints at the Supports: with Ctr =0.63 for braces at end supports of multiple-span systems

(Eq. D3.2.l-3)

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•

PL = e tr

[

0.OS3b1.88LO.13 . -sme W O 94 n~·95d 1.07t .

I-59

(Eq.03.2.1-4)

Cr =0.87 for braces at the first interior supports etr =0.81 for all other braces (S) Multiple-Span System with Third-Point Restraints:

PL = eth

[

0. 181b1.15Lo.25 . -sme W n~·54d I.1lt O.29

(Eq.03.2.1-S)

with Ch =0.S7 for outer braces in exterior spans Ch =0.48 for all other braces

(6) Multiple-Span System with Midspan Restraints:

0.116b1.32U.18 . PL = ems -sme W [ nO.70d1.00to.5o with P ems = 1.0S for braces in exterior spans ems =0.90 for all other braces where b d t L e

=Flange width. in. =Oepth of section, in . =Thickness, in. =Span length, in. =Angle between the vertical and the plane of the web of the Z-section, degrees np = Number of parallel puriin lines W = Total load supported by the purlin lines between adjacent supports, pounds

•

The force, PL, is positive when restraint is required to prevent movement of the purl in flanges in the upward roof slope direction. For systems having less than four purlin lines, the brace force can be determined by taking 1.1 times the force found from Equations 03.2.1-1 through 03.2.1--{), with np = 4. For systems having more than twenty purl in lines, the brace force can be determined from Equations 03.2.1-1 through 03.2.1--{), with np = 20.

03.2.2 Neither Flange Connected to Sheathing Each intermediate brace. at the top and bottom flange, shaH be designed to resist a lateral force, PL, determined as follows:

•

(a)

For uniform loads, PL = I.SK' times the load within a distance O.Sa each side of the brace.

(b)

For concentrated loads, PL = 1.0K' times each concentrated load within a distance 0.3a each side ofthe brace, plus 1.4K'[I-(x/a)] times each concentrated load located farther than 0.3a but not farther than 1.0a from the brace .

In the above formulas: For channels and Z-sections: x =Oistance from the concentrated load to the brace

(Eq.03.2.1--{)

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1-60

a = Distance between center line of braces For channels: K' =m/d

(Eq. D3.2.2-1)

where m =Distance from the shear center to the mid-plane of the web, as specified in Section D 1.1 d = Depth of channel

•

For Z-sections:

K' =Jxy/lx

(Eq. D3.2.2-2)

where

Ixy =Product of inertia of the full section about centroidal axes parallel and perpendicular to the web

Ix = Moment of inertia of the full section about the centroidal axis perpendicular to the web Braces shall be designed to avoid local crippling at the points of attachment to the member. Braces shall be attached both to the top and bottom flanges of the sections, at the ends and at intervals not greater than one-quarter of the span length, in such a manner as to prevent tipping at the ends and lateral deflection of either flange in either direction at intermediate braces. If one-third or more of the total load on the beam is concentrated over a length of one-twelfth or less of the span of the beam, an additional brace shall be placed at or near the center of this loaded length. Exception: When all loads and reactions on a beam are transmitted through members which frame into the section in such a manner as to effecti vely restrain the section against rotation and lateral displacement, no other braces will be required.

•

03.3 Laterally Un braced Box Beams For closed box-type sections used as beams subject to bending about the major axis, the ratio of the laterally unsupported length to the distance between the webs of the section shall not exceed 0.086 E/Fy.

04 Wall Studs and Wall Stud Assemblies

The safe load-carrying capacity of a stud may be computed on the basis of Section C (neglecting sheathing and using steel only) or on the basis that sheathing (attached to one or both sides of the stud) furnishes adequate lateral and rotational support to the stud in the plane of the wall, provided that the stud, sheathing, and attachments comply with the following requirements: Both ends of the stud shall be braced to restrain rotation about the longitudinal stud axis and horizontal displacement perpendicular to the stud axis; however, the ends mayor may not be free to rotate about both axes perpendicular to the stud axis. The sheathing shall be connected to the top and bottom members of the wall assembly to enhance the restraint provided to the stud and stabilize the overall assembly. When sheathing is utilized for stability of the wall studs, the sheathing shall retain adequate strength and stiffness for the expected service life of the wall and additional bracing shall be provided as required for adequate structural integrity during construction and in the completed structure.

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Cold-Formed Specification - August 19, 1986 Edition with December 11, 1989 Addendum

•

1-61

The equations given are based on solid-web steel studs and are applicable within the following limits: Yield point, Fy $ 50 ksi Section depth, d $ 6.0 in. Thickness, t $ 0.075 in. Overall length, L ::;; 16 ft. Stud spacing, B, not less than 12 in. nor greater than 24 in. Studs with perforations shall be designed using the results of stub column tests and/or rational analysis.

04.1 Wall Studs in Compression For studs having identical sheathing attached to both flanges, and neglecting any rotational restraint provided by the sheathing* , the applied axial load, P, shall not exceed P. calculated as follows: (Eq.04.1-1) P. =AeFn/Qc where Ae =Effective area determined at Fn Qc =Factor of safety for axial compression, i.e., in accordance with Section C4(a)

when either Sections 04.I(a) or 04.I(b) govern or 1.92 when Section 04.I(c) governs. Fn = The lowest value determined by the following three conditions:

•

(a) To prevent column buckling between fasteners in the plane of the wall, Fn shall be calculated according to Section C4 with KL equal to two times the distance between fasteners. (b) To prevent flexural and/or torsional overall column buckling, Fn shall be calculated in accordance with Section C4 with Fe taken as the smaller of the two O"CR values specified for the following section types, where O"CR is the theoretical elastic buckling stress under concentric loading. (I) Singly-symmetric channels and C-Sections

(Eq.04.1-2)

O"CR = 0" ey + Q. O"CR

= 21~ [( O"ex + O"tQ) - ~( O"ex + O"tQ)2 - (4~O"exO"tQ) ]

(Eq.04.1-3)

(2) Z-Sections

(Eq.04.1-4)

O"CR = cr t + Qt (JcR=

~{(O"ex +O"ey +0.)-

[(O"ex +O"ey +0./ -4(O"exO"ey +O"exO. -0"2 exy )]} (Eq. 04.1-5)

(3) I-Sections (doubly-symmetric) O"CR = crey + Q. crCR = crex In the above formulas: n 2E O"ex = 2 (L / rx) *Studs with sheathing on one flange only, or with unidentical sheathing on both flanges, or having rotational restraint that is not neglected, or having any combination of the above, shall be designed in accordance with the same basic analysis principles used in deriving the provisions of this Section.

(Eq. 04.1-6) (Eq.04.1-7)

(Eq.04.1-8)

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1-62

(Eq.04.1-9)

crey

1t 2E

(L I ry)

(Eq.04.1-1O)

crt = _1_[GJ + n ECw Ar~

crtQ Q q B Qa A L Qt d Ixy (c)

(L)2

(Eq.04.1-11)

= crt + Qt (Eq. 04.1-12) = q B = Design shear rigidity for sheathing on both sides of wall assembly = Design shear rigidity for sheathing per inch of stud spacing (see Table 04) = -Stud spacing = QI A (Eq.04.1-13) = Area of full unreduced cross section = Length of stud (Eq.04.1-14) = (Qd 2 )1 (4Ar;) = Depth of section = Product of inertia

To prevent shear failure of the sheathing, a value of Fn shall be used in the following equations so that the shear strain of the sheathing, y, does not exceed the permissible shear strain, y. The shear strain, y, shall be determined as follows: y = (n /L) [CI + (EI d/2)] (Eq.04.1-15) where C I and E I are the absolute values of C I and EI specified below for each section type:

•

(1) Singly-Symmetric Channels and C-Sections

= (Fn Co)1 (crey

(Eq.04.1-16)

- Fn + Qa)

Fn [( cr ex - Fn)( r~Eo - xoOo) - Fnxo(Oo - xoEo)] (cr ex -Fn)r~(crtQ -Fn)-(FnXo)

(Eq.04.1-17)

(2) Z-Sections

Fn[Co(crex -Fn)- Docrexy]

- (crey - Fn + Qa)( cr ex - Fn) - cr~xy EI = (Fn Eo) I (crtQ - Fn )

(Eq.04.1-18) (Eq.D4.1-19)

(3) I-Sections

CI = (FnCo)/(crey-Fn +Q a ) EI = 0 where Xo =distance from shear center to centroid along principal x-axis, in. (absolute value) Co, Eo, and Do are initial column imperfections which shall be assumed to be at least Co = L/350 in a direction parallel to the wall Do = LnOO in a direction perpendicular to the wall Eo = L/(d x 10,(00), rad., a measure of the initial twist of the stud from the initial, ideal, unbuckled shape

(Eq.04.1-20)

(Eq.04.1-21) (Eq.04.1-22) (Eq .04.1-23)

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Cold-Fonned Specification - August 19,1986 Edition with December II, 1989 Addendum

•

1-63

If Fn > O.S F y, then in the definitions for O"ey, O"ex, O"exy and O"tQ, the parameters E and G shall be replaced by E' and G', respectively, as defined below (Eq.04.1-24) E' =4EFn (Fy - Fn )/Fl (Eq.04.1-2S) G' =G (E'IE)

Sheathing parameters and may be determined from representative fullscale tests, conducted and evaluated as described by published documented methods (see Commentary), or from the small-scale-test values given in Table 04.

04.2 Wall Studs in Bending For studs having identical sheathing attached to both flanges, and neglecting any rotational restraint provided by the sheathing, * the allowable moments are Maxo and Mayo where Maxo and

Mayo

=Allowable moments about the centroidal axes determined in accordance with Section C3.1, excluding the provisions of Section C3.1.2 (lateral buckling)

04.3 Wall Studs with Combined Axial Load and Bending

•

The axial load and bending moments shall satisfy the interaction equations of Section CS with the following redefined terms: P a =Allowable axial load determined according to Section 04.1 Max and May in Equations CS-l and CS-3 shall be replaced by allowable moments, Maxo and Mayo, respectively.

TABLE 04 Sheathing Parameters(1) -(3)

qo Sheathing(2) 3/8 to S/8 in. thick gypsum Lignocellulosic board Fiberboard (regular or impregnated) Fiberboard (heavy impregnated)

k/in.

Y in./in.

2.0 1.0 0.6 1.2

0.008 0.009 0.007 0.010

(I) The values given are subject to the following limitations: All values are for sheathing on both sides of the wall assembly. All fasteners are No.6, type S-12, self-drilling drywall screws with pan or bugle head, or equivalent, at 6- to 12-inch spacing. (2) All sheathing is lI2-inch thick except as noted. (3)

•

q = qo (2 - s/12) where s = fastener spacing, in. For other types of sheathing, qo and y may be determined conservatively from rep-

* Studs with sheathing on one flange only, or with unidentical sheathing on both flanges, or having rotational restraint that is not neglected, or having any combination of the above, shall be designed in accordance with the same basic analysis principles used in deriving the provisions of this Section.

(Eq.04.1-26)

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•

resentative small-specimen tests as described by published documented methods (see Commentary).

D5 Floor, Roof or Wall Steel Diaphragm Construction The in-phme structural performance of floor, roof or wall steel diaphragm construction shall be established by calculation or test. The allowable in-plane load carrying capacity Sa shall be: (Eq. D5-l)

Sa =SnlUs where Sn = the nominal diaphragm shear strength O s =the factor of safety for diaphragm shear as specified below: =3.0 for welded connections or for combinations of welds and mechanical connections subjected to earthquake loads , or subjected to load combinations which include earthquake loads. =2.5 for mechanical connections subjected to earthquake loads, or subjected to load combinations which include earthquake loads. For backed-up fasteners (bolts, rivets, spreading back fasteners or the like) O s may be taken as 2.3. =2.75 for welded connections or for combinations of welds and mechanical connections subjected to wind loads or subjected to load combinations which include wind loads. =2.35 for mechanical connections subjected to wind loads or subjected to load combinations which include wind loads. For backed-up fasteners (bolts, rivets, spreading back fasteners or the like) Os may be taken as 2. 1.

•

Although Section A4.4 of the Specification allows forces to be multiplied by 0.75 when the loading consists of wind or seismic loads acting either alone or in combination with other loads, this decrease in loads is not permitted for diaphragms. For load combinations not involving wind or seismic loads: O s = 2.75 0.75

for welded connections or for combinations of welds and mechanical connections.

O s = 2.35 0.75

for mechanical connections.

•

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•

E. CONNECTIONS AND JOINTS E1 General Provisions Connections shall be designed to transmit the maximum load in the connected member. Proper regard shall be given to eccentricity.

E2 Welded Connections

Arc welds on steel where each connected part is over 0.18 inch in thickness shall be made in accordance with AISC Specification (Section A6). Except as modified herein, arc welds on steel where at least one of the connected parts is 0.18 inch or less in thickness shall be made in accordance with the AWS 0-1.3 (Section A6) and its Commentary. Welders and welding procedures shall be qualified as specified in A WS DI.3. These provisions are intended to cover the welding positions as shown in Table E2. Resistance welds shall be made in conformance with the procedures given in AWS C1.1-66, "Recommended Practices for Resistance Welding" or AWS CI.3-70, "Recommended Practice for Resistance Welding Coated Low Carbon Steels."

Square Groove Connection Butt Weld

•

Sheet to Sheet

Sheet to Supporting Member

TABLE E2 Welding Position Fillet Arc Seam Arc SJot Weld, Weld WeI Lap orT

OH -

FlareBevel Groove

FCare-V roove Weld

H V

(F =flat, H = horizontal, V = vertical, OH =overhead)

The load on each weld shall not exceed Pa, calculated as follows: Pa = PnlQw

where Qw

= Factor of safety for arc welded connections = 2.50

Pn = Nominal strength of welds determined according to Sections E2.1 through E2.5.

E2.1 Groove Welds in Butt Joints

•

The maximum load for a groove weld in a butt joint, welded from one or both sides, shall be determined on the basis of the lower strength base steel in the connection, provided that an effective throat equal to or greater than the thickness of the material is consistently obtained .

E2.2 Arc Spot Welds Arc spot welds permitted by this Specification are for welding sheet steel to thicker supporting members in the flat position. Arc spot welds (puddle welds) shall not

(Eq. E2-l)

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Cold-Formed Specification - August 19, 1986 Edition with December 11, 1989 Addendum

•

be made on steel where the thinnest connected part is over 0.15 inch thick, nor through a combination of steel sheets having a total thickness over 0.15 inch. Weld washers, Figures E2.2(A) and E2.2(B), shall be used when the thickness of the sheet is less than 0.028 inch. Weld washers shall have a thickness between 0.05 and 0.08 inch with a minimum prepunched hole of 3/8 - inch diameter.

Arc Spot Weld

•

Figure E2.2A Typical Weld Washer

, ", , ', ,;

Optional Lug Washer

, ...

m..........+i

Figure E2.2B Arc Spot Weld Using Washer

Arc spot welds shall be specified by minimum effective diameter of fused area, de. Minimum allowable effective diameter is 3/8 inch. The nominal shear load, Pn, on each arc spot weld between sheet or sheets and supporting member shall not exceed the smaller of either

= 0.625 de2 Fxx ; or

For (da!t):5 0.815

(Eq. E2.2-1)

~(E / Fu) :

P n = 2.20 t da Fu ;

ForO.815~(E/Fu)«da/t)< 1.397 ~(E/Fu):

(Eq. E2.2-2)

•

Cold-Fonned Specification - August 19, 1986 Edition with December 11 , 1989 Addendum

•

Pn = 0.280 1+ 5. 59t-JEj r;:;- tdaFu; [ d a 'Y Fu

(Eq. E2.2-3)

For (dalt) ~ 1.397 ~ (E / Fu) : Pn where d da

de de

Fxx Fsy Fu

= 1.40 t da Fu

(Eq. E2.2-4)

= Visible diameter of outer surface of arc spot weld

= Average diameter of the arc spot weld at mid-thickness of t [where da =(d - t) for a single sheet, and (d - 2t) for multiple sheets (not more than four lapped sheets over a supporting member)] = Effective diameter of fused area = 0.7d - 1.5t but ~ 0.55d (Eq. E2.2-5) = Total combined base steel thickness (exclusive of coatings) of sheets involved in shear transfer = Stress level designation in AWS electrode classification = Yield point as specified in Section A3.1 or A3.2. = Tensile strength as specified in Section A3.1 or A3.2 or as reduced for low ductility steel.

Note: See Figures E2.2(C) and E2.2(0) for diameter definitions

•

The distance measured in the line of force from the centerline of a weld to the nearest edge of an adjacent weld or to the end of the connected part toward which the force is directed shall not be less than the value of emi" as given below:

d a= d - t d e= O.7d - 1.5t:s; O.55d (C) Arc Spot Weld-Single Thickness of Sheet

d a =d-2t

•

1-67

d e= O.7d - 1.5t:s; O.55d

14---da--~

(D) Arc Spot Weld-Double Thickness of Sheet

Figure E2.2 C, 0 Arc Spot Welds

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1--68

em in =e where

(Eq.

E2.2~)

(Eq. E2.2-7)

Fut Q e =Factor of safety for sheet tearing =2.0 when Fu/Fsy ~ 1.15 =2.22 when Fu/Fsy < 1.15 P = Force transmitted by weld t =Thickness of thinnest connected sheet

•

Note: See Figures E2.2(E) and E2.2(F) for edge distances of arc welds. In addition, the distance from the centerline of any weld to the end or boundary of the connected member shall not be less than 1.5d. In no case shall the clear distance between welds and the end of member be less than 1.Od.

• (E) Single Sheet

(F) Double Sheet

Figure E2.2 E, F Edge DIstances for Arc Spot Welds

•

Cold-Fonned Specification - August 19, 1986 Edition with December 11 z 1989 Addendum

•

1-69

The nominal tension load, Pn, on each arc spot weld between sheet and supporting member, shall not exceed:

= 0.7 t d. Fu

(Eq. E2.2-8)

The following additional limitations for use in Eq. 2.2-8 shall apply: emin~

Fxx Fu t

~ ~

d 60 ksi 60 ksi 0.028 in.

If it can be shown by measurement that a given weld procedure will consistently give a larger effective diameter, de, or average diameter, da, as applicable, this larger diameter may be used providing the particular welding procedure used for making those welds is followed.

E2.3 Arc Seam Welds Arc seam welds [Figure E2.3(A)J covered by this Specification apply only to the following joints: (a) Sheet to thicker supporting member in the flat position. (b) Sheet to sheet in the horizontal or flat position. The shear load, Pn, on each arc seam weld shall not exceed either

•

d; LDe] 2.5Fxx; =[ 4+-3-

Pn = 2.5 tFu(0.25L + 0.96 da) where d = width of arc seam weld L = Length of seam weld not including the circular ends (For computation purposes, L shall not exceed 3d.) da = Average width of seam weld where da = (d - t) for a single sheet, and (d - 2t) for a double sheet de = Effective width of arc seam weld at fused surfaces de = 0.7d-l.5t and Fu and Fxx are defined in Section E2.2. The minimum edge distance shall be as determined for the arc spot weld, Section E2.2 [see Figure E2.3(B)]. If it can be shown by measurement that a given weld procedure will consistently give a larger effective width, de or da as applicable, this value may be used providing the particular welding procedure used for making the welds that are measured is followed .

(Eq. E2.3-1) (Eq. E2.3-2)

(Eq. E2.3-3) (Eq. E2.3-4) (Eq. E2.3-5)

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1-70

• j

d LWidth

Figure E2.3A Arc Seam Welds - Sheet to Supporting Member in Flat Position

•

Figure E2.38 Edge Distances for Arc Seam Welds

E2.4 Fillet Welds Fillet welds covered by this Specification apply to the welding of joints in any position, either (a) Sheet to sheet, or (b) Sheet to thicker steel member. The shear load, Pn, on a fillet weld in lap and T-joints shall not exceed the following: For longitudinal loading: For Lit < 25 :

= (1- O.~IL }LFu

For Lit ~ 25: P n = 0.75 tLFu For transverse loading: Pn = tLFu where t = Least value of t\ or 12, Figure E2.4

(Eq. E2.4-l)

(Eq. E2.4-2) (Eq. E2.4-3)

In addition, for t > 0.150 inch the allowable load for a fillet weld in lap and T-joints shall not exceed: (Eq. E2.4-4) Pn = 0.75 twLFxx where L = Length of flliet weld

•

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•

1-71

= Effective throat =0.707 WI or 0.707 W2, whichever is smaller. A larger effective

throat may be taken if it can be shown by measurement that a given welding procedure will consistently give a larger value providing the particular welding procedure used for making the welds that are measured is followed. WI and W2 = leg on weld (see Figure E2.4). Fu and Fxx are defined in Section E2.2.

(A) Lap Joint

(8) T-Joint

Figure E2.4 Fillet Welds

•

E2.S Flare Groove Welds Flare groove welds covered by this Specification apply to welding of joints in any position, either: (a) Sheet to sheet for f1are-V groove welds, or (b) Sheet to sheet for flare-bevel groove welds, or (c) Sheet to thicker steel member for flare-bevel groove welds. The shear load, Pn, on a weld shall be governed by the thickness, t, of the sheet steel adjacent to the weld. The load shall not exceed: For flare-bevel groove welds, transverse loading [see Figure E2.5(A)]: Pn = 0.833tLFu (Eq. E2.5-1) For flare groove welds, longitudinal loading [see Figures E2.5(B), E2.5(C), and E2.5(O)] : If the effective throat, tw, is equal to or greater than t but less than 2t or if the lip height is less than weld length, L, then: Pn

= 0.75tLFu

(Eq. E2.5-2)

If tw is equal to or greater than 2t and the lip height is equal to or greater than L, then: Pn

= 1.50tLFu

(Eq. E2.5-3)

In addition, if t > 0.15 inch, then: Pn = 0.75twLFxx

•

(Eq. E2.5-4)

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• Figure E2.SA Flare-Bevel Groove Weld

P" P (B) Flare Bevel Groove

•

(e) Flare V-Groove

jt tw

.....---fl-~----I~ (0) Throat

Figure E2.S B, C, D Shear In Rare Groove Welds

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CoJd-Fonned Specification - August 19, J 986 Edition with December II , 1989 Addendum

•

E2.6 Resistance Welds In sheets joined by spot welding the nominal shear strength per spot, Pn, is as follows:

TABLE E2.6 Thickness of Thinnest Outside Sheet, in. 0.010 0.020 0.030 0.040 0.050 0.060 0.070

•

Nominal Shear Strength per Spot, kips 0.13 0.48 1.00 1.42 1.65 2.28 2.83

Thickness of Thinnest Outside Sheet, in. 0.080 0.090 0.100 0.110 0.125 0.190 0.250

Nominal Shear Stength per Spot, kips 3.33 4.00 4.99 6.07 7.29 10.16 15.00

E3 Bolted Connections The following requirements govern bolted connections of cold-formed steel structural members in which the thickness of the thinnest connected part is less than 3/!6 inch and there are no gaps between connected parts. For bolted connections in which the thinnest connected part is equal to or greater than 3/!6 inch, refer to AISC Specification (Section A6). Bolts, nuts, and washers shall generally conform to one of the following specifications: ASTM A 194 Carbon and Alloy Steel Nuts for Bolts for High-Pressure and High-Temperature Service ASTM A307(Type A), Carbon Steel Externally and Internally Threaded Standard Fasteners ASTM A325 High Strength Bolts for Structural Steel Joints ASTM A354 (Grade BD), Quenched and Tempered Alloy Steel Bolts, Studs,and Other Externally Threaded Fasteners (for diameter of bolt smaller than liz inch) ASTM A449 Quenched and Tempered Steel Bolts and Studs (for diameter ofbolt smaller than liz inch) ASTM A490 Quenched and Tempered Alloy Steel Bolts for Structural Steel Joints. ASTM A563 Carbon and Alloy Steel Nuts ASTM F436 Hardened Steel Washers ASTM F844 Washers, Steel, Plain (Flat), Unhardened for General Use ASTM F959 Compressible Washer-Type Direct Tension Indicators for Use with Structural Fasteners

•

When other than the above are used, drawings shall indicate clearly the type and size of fasteners to be employed and the allowable force assumed in design . Bolts shall be installed and tightened to achieve satisfactory performance of the connections involved under usual service conditions. The holes for bolts shall not exceed the sizes specified in Table E3, except that larger holes may be used in column base details or structural systems connected to concrete walls.

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Cold-Formed Specification - August 19, 1986 Edition with December 11 , 1989 Addendum

TABLE E3 Maximum Size of Bolt Holes, Inches Nominal Bolt Diameter, d in.

< Ih

Standard Hole Diameter, d in. d+ 1/32 d+ I/!6

"?,Ih

Oversized Hole Diameter, d in. d+ I/!6 d + I/S

Short-Slotted Hole Dimensions in. (d + 1/32) by (d + 1/4) (d + 1/16) by (d + 1/4)

Long-Slotted Hole Dimensions in.

•

(d + 1/32) by (2 Ihd) (d + 1/16) by (2 Ihd)

Standard holes shall be used in bolted connections, except that oversized and slotted holes may be used as approved by the designer. The length of slotted holes shall be normal to the direction of the shear load. Washers or backup plates shall be installed over oversized or short-slotted holes in an outer ply unless suitable performance is demonstrated by load tests in accordance with Section F.

E3.1 Spacing and Edge Distance The distance, e, measured in the line of force from the center of a standard hole to the nearest edge of an adjacent hole or to the end of the connected part toward which the force is directed shall not be less than the value of emin determined as follows: emin = e (Eq. E3.1-1) where p e=(Eq. E3.1-2) Fut

•

(a) When FulFsy"?' 1.15: ne =Factor of safety for sheet tearing =2.0 (b) When FulFsy < 1.15: ne =Factor of safety for sheet tearing =2.22 where P =Force transmitted by bolt t =Thickness of thinnest connected part Fu =Tensile strength of the connected part as specified in Sections A3.1 or A3.2 Fsy = Yield point of the connected part as specified in Sections A3.1 or A3.2 In addition, the minimum distance between centers of bolt holes shall provide sufficient clearance for bolt heads, nuts, washers and the wrench but shall not be less than 3 times the nominal bolt diameter, d. Also, the distance from the center of any standard hole to the end or other boundary of the connecting member shall not be less than 11 h d. For oversized and slotted holes, the distance between edges of two adjacent holes and the distance measured from the edge of the hole to the end or other boundary of the connecting member in the line of stress shall not be less than the value of [emin- (dtJ2)], in which .emin is the required distance computed from the applicable equation given above, and dh is the diameter of a standard hole defmed in Table E3. In no case shall the clear

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Cold-Fonned Specification - August 19! 1986 Edition with December II! 1989 Addendum

•

1-75

distance between edges of two adjacent holes be less than 2d and the distance between the edge of the hole and the end of the member be less than d.

E3.2 Tension in Connected Part The tension force on the net section of a bolted connection shall not exceed T afrom Section C2 or Pacalculated as follows: Pa = Pni nl (Eq. E3.2-1) where Pn = AnFt An = Net section area Ft and n 1 are determined as follows: (a) When t ~ 3/16 in.: See AISC Specification (Reference 3 of Section A6) (b) When t < 3/16 inch and washers are provided under both the bolt head and the nut Ft =(1.0 - 0.9r + 3rd/s) Fu ~ Fu nl =Factor of safety for tension on the net section =2.0 for double shear = 2.22 for single shear

•

(Eq. E3.2-2)

(c) When t < 3116 inch and either washers are not provided underthe bolt head and nut, or only one washer is provided under either the bolt head or nut Fl =(1.0 - r + 2.5rd/s) Fu ~ Fu (Eq. E3.2-3) nt = Factor of safety for tension on the net section =2.22 where r =Force transmitted by the bolt or bolts at the section considered, divided by the tension force in the member at that section. If r is less than 0.2, it may be taken equal to zero. s = Spacing of bolts perpendicular to line of stress. In the case of a single bolt, s = Width of sheet Fl =Nominal tension stress limit on net section Fu =Tensile strength of the connected part as specified in Sections A3.1 or A3.2 d and t are defined in Section E3.1

E3.3 Bearing The bearing force shall not exceed Pa calculated as follows: Pa = PnlQb

•

where Pn = Qb = = Fp =

Fpdt Safety factor for bearing 2.22 Nominal bearing stress as given in Tables E3.3-1 and E3.3-2.

For conditions not shown, forces shall be determined on the basis of test data using a factor of safety of 2.22

(Eq. E3.3-1) (Eq. E3.3-2)

Cold-Formed Specification - August 19, 1986 Edition with December II, 1989 Addendum

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•

TABLE E3.3-1 Nominal Bearing Stress for Bolted Connections with Washers under Both Bolt Head and Nut Nominal Thickness of Fu/Fsy ratio of bearing connected part Type of joint connected part stress, Fp m. Inside sheet of double shear connection ~0.024

but < 3116

~ 3116

Single shear and outside sheets of double shear connection

1.15

3.33 Fu

< 1.15

3.00 Fu

No limit

3.00 Fu

See AISC Specification (Reference 3 of Section A6)

TABLE E3.3-2 Nominal Bearing Stress for Bolted Connections Without Washers Under Both Bolt Head and Nut, or With Only One Washer Thickness of connected part in.

Type of joint

Inside sheet of double shear connection

Fu/Fsy ratio of connected part

Nominal bearing stress, Fp

1.15

3.00 Fu

1.15

2.22 Fu

•

0.036 but < 3116

~ 3116

Single shear and outside sheets of double shear connection

See AISC Specification (Reference 3 of Section A6)

E3.4 Shear and Tension in Bolts The bolt force resulting from shear, tension or combination of shear and tension shall not exceed allowable bolt force, Pa, calculated as follows (The factor of safety is included in Tables E3.4-1 and E3.4-2):

Pa = AbF where Ab = Gross cross-sectional area of bolt F is given by Fv, Ft or F't in Tables E3.4-1 and E3.4-2.

(Eq. E3.4-l)

•

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Cold-Fonned Specification - August 19. 1986 Edition with December 11, 1989 Addendum

•

TABLE E3.4-1 Allowable Shear Stress*, Fv, ksi Threads not Excluded from Shear Plane

Description of Bolts A325 Bolts A354 Grade B Bolts (1/4 in. ::; d < 1/2 in.) A449 Bolts (1/4 in. ::; d < 1/2 in.) A490 Bolts

Threads Excluded from Shear Plane

Allowable Tension Stress, FI, ksi

21 24

30 40

44 49

A307 Bolts, Grade A (1/4 in. ::; d < 1/2 in.) A307 Bolts, Grade A (d ~ 1/2 in.)

* Applies to bolts in holes as limited by Table E3.

•

Washers or back-up plates shall be installed over long-slotted holes and the capacity of connections using long-slotted holes shall be determined by load tests in accordance with Section F.

The pullover strength of the connected sheet at the bolt head, nut or washer should

be considered where bolt tension is involved, See Section E5.2. When bolts are subject to a combination of shear and tension, the tension force shall not exceed the allowable force, Pa, based on F'I, given in Table E3.4-2, where fv, the shear stress produced by the same forces, shall not exceed the allowable value Fv given above.

TABLE E3.4-2 Allowable Tension Stress, F't for Bolts Subject to the Combination of Shear and Tension Description of Bolts A325 Bolts A354 Grade BD Bolts A449 Bolts A490 Bolts

•

A307 Bolts, Grade A When lJ4 in. ~ d < 1/2 in. When d ~ 1/2 in.

Threads Not Excluded from Shear Planes 55 61 50 68 -

1.8fv ::; 44 1.8fv::; 49 1.8fv ::; 40 1.8fv ::; 54

Threads Excluded from Shear Planes 55 61 50 68 -

23 - 1.8fv ~ 18 26 - 1.8fv ::; 20

1.4fv ::; 44 1.4fv ::; 49 1.4fv ::; 40 1.4fv ::; 54

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Cold-Fonned Specification - August I9? 1986 Edition with December II? 1989 Addendum

•

E4 Shear Rupture At beam-end connections, where one or more flanges are coped and failure might occur along a plane through the fasteners, the shear force shall not exceed the allowable shear force Va, calculated as follows: Va

= Vn/Qv

(Eq. E4-1)

where Vn = 0.6 FuAwn Awn = (dwc - ndh)t dwc = coped web depth n = number of holes in the critical plane dh = hole diameter Fu = Tensile strength as specified in Sections A3.1 or A3.2 t = Thickness of coped web Qv = Factor of safety for shear rupture = 2.00

(Eq. E4-2) (Eq. E4-3)

ES Connections to Other Materials ES.1 Bearing Proper provisions shall be made to transfer bearing forces resulting from axial loads and moments from steel components covered by the Specification to adjacent structural components made of other materials. The bearing force in the contact area shall not exceed the allowable bearing force P a calculated as follows: Pa

= FpA

where A = Contact area Fp = Allowable bearing stress. (The factor of safety is included in values for Fp.)

•

In the absence of code regulations for other materials, the following allowable stresses may be used: Fp Fp Fp Fp

= 0.40 ksi on sandstone and limestone = 0.25 ksi on brick in cement mortar = 0.35 f'c on the full area of a concrete support = 0.35f~ ~(A2 / AI) ~ O. 7f~ on less than the full area of a concrete support

where f'c = Specified compression strength of concrete AI = Bearing area A2 = Full cross-sectional area of concrete support

ES.2 Tension The pull-over shear/tension forces in the steel sheet around the head of the fastener should be considered as well as the pull-out force resulting from axial loads and bending moments transmitted onto the fastener from various adjacent structural components in the assembly. The allowable tensile strength of the fastener and the allowable imbedment strength of the adjacent structural component shall be determined by applicable product code approvals, or product specifications and/or product literature.

•

Cold-Fonned Specification - August 19, 1986 Edition with December 11 , 1989 Addendum

•

E5.3 Shear Proper provisions shall be made to transfer shearing forces from steel components covered by this Specification to adjacent structural components made of other materials. The allowable shear and/or bearing forces on the steel components shall not exceed that allowed by this Specification. The allowable shear force on the fasteners and other material shall not be exceeded. hnbedment requirements are to be met. Proper provision shall also be made for shearing forces in combination with other forces.

•

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Cold-Fonned Specification - August 19, 1986 Edition with December 11, 1989 Addendum

•

F. TESTS FOR SPECIAL CASES (a) Tests shall be made by an independent testing laboratory or by a testing laboratory of a manufacturer. (b) The provisions of Chapter F do not apply to cold-formed steel diaphragms.

F1 Tests for Determining Structural Performance Where the composition or configuration of elements, assemblies, connections, or details of cold-formed steel structural members are such that calculation of their safe load-carrying capacity or deflection cannot be made in accordance with the provisions of this Specification, their structural performance shall be established from tests and evaluated in accordance with the following procedure. (a) Where practicable, evaluation oftests results shall be made on the basis ofthe mean values resulting from tests of not fewer than three identical specimens, provided the deviation of any individual test result from the mean value obtained from all tests does not exceed ±1O percent. If such deviation from the mean exceeds 10 percent, at least three more tests of the same kind shall be made. The average of the three lowest values of all tests made shall then be regarded as the result of the series of tests. (b) The required load-carrying capacity shall be: R =D Fo + L FL

(Eq. FI-I)

where D and L are the dead and live loads, respectively, D shall include the weight ofthe test specimen. Fo and FL are the dead and live load factors specified below. R shall be taken as the largest applicable value determined as follows: (1) The minimum load-carrying capacity, R, shall be calculated from the formula R

1.5D + 2L

• (Eq. FI-2)

R shall be multiplied by 1.25 for steels not listed in Section A3.1 R may be divided by 11/3 when the loading consists of wind or earthquake loads alone, or in combination with dead, live, or snow loads, but shall not be less than R calculated for the combination of dead and live loads only, without wind or earthquake loads. (2) The load at which distortions interfere with the proper functioning of the specimen in actual use shall not be less than: R~D

+ 1.5L

(Eq. FI-3)

(3) The load carrying capacity when limited by connection failure shall not be less than: R

~2.5D

+ 2.5L

(c) If the yield point of the steel from which the tested sections are formed is larger than the specified value, the test results shall be adjusted down to the specified minimum yield point of the steel which the manufacturer intends to use. The test results shall not be adjusted upward if the yield point of the test specimen is less than the minimum specified yield point. Similar adjustments shall be made on the basis of tensile strength instead of yield point where tensile strength is the critical factor. Consideration must also be given to any variation or differences which may exist between the design thickness and the thickness of the specimens used in the tests.

F2 Tests for Confirming Structural Performance The procedures and formulas specified in Section FI are not applicable to confmnation tests on specimens whose capacities can be computed according to this Specification or its

(Eq. FI-4)

•

Cold-Formed Specification - August 19, 1986 Edition with December II, 1989 Addendum

•

specific references. A successful confirmatory test shall demonstrate a safety factor not less than that implied in the Specification for the type of behavior involved.

F3 Tests for Determining Mechanical Properties F3.1 Fu" Section Tests for determination of mechanical properties of full sections to be used in Section A5.2.2 shall be made as specified below:

(a) Tensile testing procedures shall agree with Standard Methods and Definitions for Mechanical Testing of Steel Products, ASTM A370. Compressive yield point determinations shall be made by means of compression tests of short specimens of the section. (b) The comprehensive yield stress shall be taken as the smaller value of either the maximum compressive strength of the sections divided by the cross section area or the stress defined by one of the following methods: (1) For sharp yielding steel, the yield point shall be determined by the autographic dia-

gram method or by the total strain under load method.

•

(2) For gradual yielding steel, the yield point shall be determined by the strain under load method or by the 0.2 percent offset method. When the total strain under load method is used, there shan be evidence that the yield point so determined agrees within 5 percent with the yield point which would be determined by the 0.2 percent offset method (c) Where the principal effect of the loading to which the member will be subjected in service will be to produce bending stresses, the yield point shall be determined for the flanges only. In determining such yield points, each specimen shall consist of one complete flange plus a portion of the web of such flat width ratio that the value of p for the specimen is unity. (d) For acceptance and control purposes, two fun section tests shall be made from each lot of not more than 50 tons nor less than 30 tons of each section, or one test from each lot of less than 30 tons of each section. For this purpose a lot may be defined as that tonnage of one section that is formed in a single production run of material from one heat. (e) At the option of the manufacturer, either tension or compression tests may be used for routine acceptance and control purposes, provided the manufacturer demonstrates that such tests reliably indicate the yield point of the section when subjected to the kind of stress under which the member is to be used.

F3.2 Flat Elements of Formed Sections

•

Tests for determining mechanical properties of flat elements of formed sections and representative mechanical properties of virgin steel to be used in Section A5.2.2 shall be made in accordance with the following provisions: The yield point of flats, Fyf, shall be established by means of a weighted average of the yield points of standard tensile coupons taken longitudinally from the flat portions of a representative cold-fonned member. The weighted average shall be the sum of the products of the average yield point for each flat portion times its cross sectional area, divided by the total area of flats in the cross section. The exact number of such coupons will depend on the shape of the member, i.e. ,on the number of flats in the cross section. At least one tensile coupon shall be taken from the middle of each flat. If the actual virgin yield point exceeds the specified minimum yield point, the yield point of the flats, Fyf,

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Cold-Fonned Specification - August 19] 1986 Edition with December 11 , 1989 Addendum

shall be adjusted by multiplying the test values by the ratio of the specified minimum yield point to the actual virgin yield point.

F3.3 Virgin Steel

•

The following provisions apply to steel produced to other than the ASTM Specifications listed in Section A3.1 when used in sections for which the increased yield point of the steel after cold fonning shall be computed from the virgin steel properties according to Section A5.2.2. For acceptance and control purposes, at least four tensile specimens shall be taken from each lot as defined in Section F3.1(d) for the establishment of the representative values of the virgin tensile yield point and ultimate strengtn. Specimens shall be taken longitudinally from the quarter points of the width near the outer end of the coil.

•

.' American Iron and Steel Institute 113315th Street, NW Washington, DC 20005

•

41 s'

CD c.

,• ~

." en C) ?>

•

SPECIFICATION FOR THE DESIGN OF COLD-FORMED STEEL STRUCTURAL MEMBERS AUGUST 19,1986, EDITION

•

Cold -Formed Steel Design Manual- Part I

~®

AMERICAN IRON AND STEEL INSTITUTE 1000 16th STREET, NW WASHINGTON, DC 20036

AUGUST 19, 1986

1-2 COLD-FORMED SPECIFICATION

This publication is for general information only. The information in it should not be used without first securing competent advice with respect to its suitability for any given application. The publication of the information is not intended as a representation or warranty on the part of American Iron and Steel Institute-or any other person named herein-that the information is suitable for any general or particular use or of freedom from infringement of any patent or patents. Anyone making use of the information assumes all liability arising from such use.

•

• 1st Printing-March 1987

Produced by W. P. Reyman Associates, Inc. New York Copyright American Iron and Steel Institute 1986

•

AUGUST 19, 1986

COLD-FORMED SPECIFICATION

PREFACE In memory of George Winter, in recognition of his many contributions and achievements to the enhancements of cold-formed steel design. The newly published Edition of AISI's Specification for the Design of Cold-Formed Steel Structural Members represents a major revision, with many changes made to keep the Specification responsive to the needs of users. It reflects the results of research projects and improvements in design techniques. Moreover, it embodies the results of efforts to simplify the use of the Specification by changes in its format, organization, and content. To accomplish this simplification, relevant sections needed to design a particular member, such as a beam or a column, have been collected together as much as possible. AISI acknowledges the devoted efforts of the members of the Advisory Group on the Specification of the Design of Cold-Fonned Steel Structural Members. This group, comprised of consulting engineers, researchers, designers from companies manufacturing cold-formed steel members, components, assemblies, and complete structures, and specialists from the steel producing industry, has met two to three times per year since its establishment in 1973. Its current members, who have made extensive contributions of time and effort in developing and reaching consensus on the changes which have been described above, are: R. E. Albrecht R. B. Heagler A. J. Oudheusden Reidar Bjorhovde A. L. Johnson, Secretary T. B. Pekoz R. E. Brown D. L. Johnson D. C. Perry C. R. Clauer T. J. Jones (Assoc.) C. W. Pinkham D. A. Cuoco Herbert Klein T. G. Ryan D. S. Ellifritt K. H. Klippstein* P. G. Schurter S. J. Errera, Chairman R. A. LaBoube R. M. Schuster J. N. Macadam P. A. Seaburg E. R. Estes, Jr. J. M. Fisher T. J. McCabe J. S. Traw S. R. Fox R. M. McClure D. S. Wolford* T. V. Galambos J. A. Moses D. R. Wootten Gerhard Haaijer T. M. Murray Wei-Wen Yu R. W. Haussler G. G. Nichols A. S. Zakrzewski The activities of the Advisory Group are sponsored by AISI's Committee of Sheet Steel Producers. The Specification is issued under the auspices of AISI's Committee on Construction Codes and Standards. Users of the Specification are invited to continue to offer their valuable comments and suggestions. The cooperation of all involved, the users as well as the writers, is needed to continue to keep the Specification up to date and a useful tool for the designer. American Iron and Steel Institute August 19, 1986

*Past Chairman

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1-4 COLD-FORMED SPECIFICATION

AUGUST 19, 1986

• TABLE OF CONTENTS SPECIFICATION FOR THE DESIGN OF COL~FORMEDSTEELSTRUCTURALMEMBERS PREFACE ...................................................................... 3 SYMBOLS AND DEFINITIONS . ................................................... 7 A. GENERAL PROVISIONS . ..................................................... 15 Al Limits of Applicability and Terms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 15 A1.1 Scope and Limits of Applicability .................................... 15 A1.2 Terms........................................................... 15 A1.3 Units of Symbols and Terms ........................................ 16 A2 Non-Conforming Shapes and Constructions ................................. 16 A3 Material................ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 16 A3.1 Applicable Steels ......... . ........................................ 16 A3.2 OtherSteels .................................. . ................... 17 A3.3 Ductility ......................................................... 17 A3.4 Delivered Minimum Thickness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 17 A4 Loads .................................................................. 17 A4.1 DeadLoad ....................................................... 17 A4.2 Live Load ........................................................ 17 A4.3 Impact Load ...................................................... 17 A4.4 Wind or Earthquake Loads ................... . ..................... 17 A4.5 Ponding ............... . .......................................... 18 A5 Structural Analysis and Design ..................... . ...................... 18 A5.1 Design Basis ...................................................... 18 A5.2 Yield Point and Strength Increase from Cold Work of Forming .............................................. 18 A5.2.1 Yield Point. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 18 A5.2.2 Strength Increase from Cold Work of Forming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 18 A5.3 Serviceability and Durability ....................................... 18 A6 Reference Documents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 18 B. ELEMENTS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 19 B1 Dimensional Limits and Considerations ..................................... 19 B1.1 Flange Flat-Width-to-Thickness Considerations. . . . . . . . . . . . . . . . . . . . . .. 19 B1.2 Maximum Web Depth-to-Thickness Ratio ............................. 20 B2 Effective Widths of Stiffened Elements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 20 B2.1 Uniformly Compressed Stiffened Elements ........................... 20 B2.2 Uniformly Compressed Stiffened Elements with Circular Holes ......... 21

•

AUGUST 19, 1986

COLD-FORMED SPECIFICATION

• B2.3

•

Effective Widths of Webs and Stiffened Elements with Stress Gradient ............................................... 22 B3 Effective Widths of Unstiffened Elements ................................... 23 B3.1 Uniformly Compressed Unstiffened Elements. . . . . . . . . . . . . . . . . . . . . . .. 23 B3.2 Unstiffened Elements and Edge Stiffeners with Stress Gradient ......... 23 B4 Effective Widths of Elements with an Edge Stiffener or One Intermediate Stiffener. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 23 B4.1 Uniformly Compressed Elements with an Intermediate Stiffener ........ 24 B4.2 Uniformly Compressed Elements with an Edge Stiffener ............... 24 B5 Effective Widths of Edge Stiffened Elements with Intermediate Stiffeners or Stiffened Elements with More Than One Intermediate Stiffener. . . . . . . . . . . . . .. 25 B6 Stiffeners ............................................................... 27 B6.1 Transverse Stiffeners. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 B6.2 Shear Stiffeners ................................................... 27 B6.3 Non-Conforming Stiffeners ......................................... 28 C. MEMBERS . ................................................................. 28 Cl Properties of Sections .................................................... 28 C2 Tension Members ........................................................ 28 C3 Flexural Members. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 28 C3.1 Strength for Bending Only .......................................... 28 C3.1.1 Nominal Section Strength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 29 C3.1.2 Lateral Buckling Strength .................................. 30 C3.1.3 Beams Having One Flange Attached to Deck or Sheathing ...... 32 C3.2 Strength for Shear Only ............................................ 32 C3.3 Strength for Combined Bending and Shear. . . . . . . . . . . . . . . . . . . . . . . . . .. 33 C3A Web Crippling Strength ............................................ 33 C3.5 Combined Bending and Web Crippling Strength ....................... 35 C4 Concentrically Loaded Compression Members ............................... 35 C4.1 Sections Not Subject to Torsional or Torsional-Flexural Buckling. . . . . . .. 36 C4.2 Doubly- or Singly-Symmetric Sections Subject to Torsional or Torsional-Flexural Buckling .................... 36 C4.3 Nonsymmetric Sections ............................................ 37 C5 Combined Axial Load and Bending ......................................... 37 C6 Cylindrical Tubular Members. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 38 C6.1 Bending .......................................................... 38 C6.2 Compression ...................................................... 38 C6.3 Combined Bending and Compression. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 39 D. STRUCTURAL ASSEMBLIES . ................................................ 39 Dl Built-UpSections ........................................................ 39 D1.1 I-Sections Composed of Two Channels ............................... 39 D1.2 Spacing of Connections in Compression Elements ...................... 40

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1-6 COLD-FORMED SPECIFICATION

AUGUST 19,1986

• D2 D3

Mixed Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 40 Lateral Bracing ........................................................ , 40 D3.1 Symmetrical Beams and Columns. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 40 D3.2 Channel-Section and Z-Section Beams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 40 D3.2.1 Anchorage of Bracing for Roof Systems Under Gravity Load With 'lbp Flange Connected to Sheathing ................ 41 D3.2.2 Neither Flange Connected to Sheathing ...................... 42 D3.3 Laterally Unbraced Box Beams ..................................... 43 D4 Wall Studs and Wall Stud Assemblies ....................................... 43 D4.1 Wall Studs in Compression. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 43 D4.2 Wall Studs in Bending .............................................. 45 D4.3 Wall Studs with Combined Axial Load and Bending .................... 45 E. CONNECTIONS AND JOINTS . ............................................... , 46 E 1 General Provisions ....................................................... 46 E2 Welded Connections ...................................................... 46 E2.1 Groove Welds in Butt Joints ......................................... 47 E2.2 Arc Spot Welds ................................................... 47 E2.3 Arc Seam Welds ................................................... 49 E2.4 Fillet Welds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 50 E2.5 Flare Groove Welds ................................................ 51 E2.6 Resistance Welds .................................................. 52 E3 Bolted Connections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 53 E3.1 Spacing and Edge Distance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 E3.2 Tension in Connected Part .......................................... 54 E3.3 Bearing ........................................................ " 55 E3.4 Shear and Tension in Bolts .......................................... 56 E4 Shear Rupture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 57 E5 Connections to Other Materials ............................................ 57 E5.1 Bearing.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 57 E5.2 Tension .......................................................... 57 E5.3 Shear ............................................................ 57 F. TESTS FOR SPECIAL CASES . ................................................ 58 Fl Tests for Determining Structural Performance ............................... 58 F2 Tests for Confirming Structural Performance ................................ 58 F3 Tests for Determining Mechanical Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 F3.1 Full Section ....................................................... 59 F3.2 Flat Elements of Formed Sections ..................... " .. " ........ 59 F3.3 VIrgin Steel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 59 APPENDICES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 60 Appendix A5.2.2 Strength Increase from Cold Work of Forming . . . . . . . . . . . . . . . . . .. 60 Appendix B1.l(b) Flange Curling ............................. " ...... , ... '" ... 61 Appendix Bl.l(c) Shear Lag Effects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 61

•

AUGUST 19, 1986

•

SYMBOLS AND DEFINITIONS Symbol

Full unreduced cross-sectional area of the member

A Ab

Contact area bit + A" for transverse stiffeners at interior support and under concentrated load, and b2 t + A>, for transverse stiffeners at end support 18t2 + A" for transverse stiffeners at interior support and under concentrated load, and lOt2 + A" for transverse stiffeners at end support Effective area at the stress F n

Net area of cross section Cross-sectional area of transverse stiffeners

A' •

Effective area of stiffener

A,t

Gross area of shear stiffener

Am.

a a B Be b

Net web area Bearing area FUll cross sectional area of concrete support Shear panel length of the unreinforced web element. For a reinforced web element, the distance between transverse stiffeners Lateral deflection of the compression flange at assumed load, q. Length of bracing interval Stud spacing Term for determining the tensile yield point of corners Effective design width of compression element

Overall width of compression flange, Cor Z

bd be

Effective widths for deflection calculations Effective design width of sub-element or element

See Figure B4.1

For flexural members, ratio of the total corner cross-sectional area of the controlling flange to the full cross-sectional area of the controlling flange Bending coefficient dependent on moment gradient End moment coefficient in interaction formula Coefficient for lateral bracing of C- and Z- section End moment coefficient in interaction formula End moment coefficient in interaction formula Coefficient for lateral torsional buckling End moment coeffic,ient in interaction formula Coefficient for lateral bracing of C- and Z-section Coefficient for lateral bracing of C- and Z-section

•

Definition

•

COLD-FORMED SPECIFICATION

Al ~ a

Cb Cm Cms Cmx Cmy C. CTF Cth Ctr

Section

C3.1.1, C3.l.2, C4, C6.2, D4.1 E5.1 B6.1, E3.4

B6.1

C4, C6.2, D4.1 C2, E3.2 B4, B4.1, B4.2, B6.1 B4, B4.1, B4.2 B6.2 E4 E5.1 E5.1 B6.2, C3.2, D3.2 C3.l.3 D3.2 D4.1 A5.2.2 B2.1, B2.2, B2.3, B3.1, B3.2, B4.1, B4.2, B5, D3.2.1 B2.1, B2.2 A1.2, B2.3, B5 B4, B4.1, B5 A5.2.2

C3.1.1 C5 D3.2.1 C5 C5 C3.1.1 C3.1.1 D3.2.1 D3.2.1

1-7

AUGUST 19,1986

1-8 COLD-FORMED SPECIFICATION

SYMBOLS AND DEFINITIONS Definition

Symbol

Cv Cw Cy Co C1

Shear stiffener coefficient Torsional warping constant of the cross-section Compression strain factor Initial column imperfection Term used to compute shear strain in wall board

C2 c cf D

Coefficient as defined in Figure B4-2 Distance from the neutral axis to the extreme fiber of untwisted section Amount of curling Outside diameter of cylindrical tube

Dead load, includes weight of the test specimen

Overall depth of lip

D Do d

Shear stiffener coefficient Initial column imperfection Depth of section

d d d

Width of arc seam weld Visible diameter of outer surface of arc spot weld Diameter of bolt

da da d. de dh

Average diameter of the arc spot weld at mid-thickness oft Average width of seam weld Effective diameter of fused area Effective width of arc seam weld at fused surfaces Diameter of standard hole

ds d' s d wc E

Reduced effective width of stiffener Actual effective width of stiffener· Coped web depth Modulus of elasticity of steel (29,000 ksi)

Initial column imperfection; a measure of the initial twist of the stud from the initial, ideal, unbuckled location

Section

B6.2 C3.l.1 C3.l.1 D4.1 B4, B4.1, D4.2 B4, B4.2 C3.l.3

•

Bl.1b C6.1, C6.2, D4.2 Fl Bl.1, B4, Dl.1 B6.2 D4.1 Bl.1b, B4, C3.l.1, C3.l.3, Dl.1, D3.2.1, D4.1, E3.4 E2.3 E2.2 E3, E3.1, E3.2 E2.2 E2.3 E2.2 E2, E2.3 B2.2, E3.1, E4 B4, B4.2 B4, B4.2 E4 Bl.1b, B2.1, B6.1, C3.l.1, C3.l.3, C3.2, C3.5.2, C4, C4.1, C5, C6.1, Dl.2, D4.1, D4.2, E2.2 D4.1

•

AUGUST 19,1986

•

SYMBOLS AND DEFINITIONS Symbol

ey Fn Fe

FL Fn Fp Fsy

Live load factor Nominal buckling stress Allowable bearing stress Yield point as specified in Sections A3.1 or A3.2

Ft F' t

Nominal tension stress limit on net section Allowable tension str{lss for bolts subject to combination of shear and tension Tensile strength as specified in Sections A3.1 or A3.2, or as reduced for low ductility steel

Fuv Fv Fwy Fxx

•

Definition

Term used to compute shear strain in wallboard Inelastic modulus of elasticity Minimum allowable distance measured in the line of force from the centerline of a weld to the nearest edge of an adjacent weld or to the end of the connected part toward which the force is directed The distance e measured in the line of force from the center of a standard hole to the nearest edge of an adjacent hole or to the end of the connected part toward which the force is directed Yield strain = F /E Dead load factor Elastic buckling stress

El E' e min

emin

•

COLD-FORMED SPECIFICATION

Ultimate tensile strength of virgin steel specified by Section A3 or established in accordance with Section F3.3 Allowable shear stress on the gross area of a bolt Yield point for design oftransverse stiffeners Strength level designation in AWS electrode classification

Yield point used for design, not to exceed the specified yield point or established in accordance with Section F3, or as increased for cold work of forming in Section A5.5.2 or as reduced for low~ ductility steels in Sections A3.2.2

Fya Fyc Fyf

Average yield point of section Tensile yield point of corners Weighted average tensile yield point of the flat portions

Fys

Yield point of stiffener steel

Section

D4.1 D4.1 E2.2

E3.1

C3.1.1 F1 C4, C4.1, C4.2, C4.3, C6.2, D4.1 F1 C4, C6.2, D4.2 E3.3, E5.1 A3.3.2, E2.2,· E3.1, E3.2 E3.2, E3.4 E3.4 A3.3, A3.3.2, E2.2, E2.3, E2.4, E2.5, E3.1, E3.2, E3.3, E4 A5.2.2, E2.2 E3.4 B6.1 E2.2, E2.3, E2.4, E2.5 Al.2, A3.3, A5.2.1, A5.2.2, B2.1, B5, B6.1, C2, C3.1, C3.2, C3.5.2, C3.1.3, C4, C6.1, C6.2, D1.2, D4.2, E2 A5.2.2 A5.2.2 F3.2, A5.2.2 B6.1

1-9

AUGUST 19, 1986

1-10 COLD-FORMED SPECIFICATION

SYMBOLS AND DEFINITIONS Symbol

Fyv f

fav fb fe

f' c fd

fdl fd2 fd3

ft fv fl' f2 fa

G G' g h

Definition

Tensile yield point of virgin steel specified by Section A3 or established in accordance with Section F3.3 Stress in the compression element computed on the basis of the effective design width Average computed stress in the full, unreduced flange width Maximum bending stress equal to the bending moment divided by appropriate section modulus of member Computed stress at design load in the cover plate or sheet Specified compression stress of concrete Computed compressive stress in the element being consi~ered. Calculations are based on the effective section at the load for which deflections are determined Computed stresses fl and f2 as shown in Figure B2.3-1. Calculations are based on the effective section at the load for which deflections are determined Computed stress f3 in edge stiffener, as shown in Figure B4-2. Calculations are based on the effective section at the load for which deflections are determined The computed maximum compressive stress due to twisting and lateral bending Computed shear stress on a bolt Web stresses defmed by Figure B2.3-1 Edge stiffener stress defmed by Figure B4.2 Shear modulus for steel = 11,300 ksi Inelastic shear modulus Vertical distance between two rows of connections nearest to the top and bottom flanges Depth of flat portion of web measured along the plane of web

Section

A5.2.2 B2.1, B2.2, B3.2, B4, B4.1 Bl.1b C3.1.3 D1.2 E5.1 B2.1, B2.2, B3.1; B4.1, B4.2 B2.3

B3.2

C3.1.3 E4 B2.3 B3.2 C3.1.1, D4.1 D4.1 Dl.1

Adequate moment of inertia of stiffener so that each component element will behave as a stiffened element

Moment of inertia of the full unreduced section about the bending axis Moment of inertia of effective section about its m;;ljor axis

Actual moment of inertia of the full stiffener about its own centroidal axis parallel to the element to be stiffened

Isc

Moment of inertia of the full area of the multiple stiffened element, including the intermediate stiffeners, about its own centroidal axis parallel to the element to be stiffened Moment of inertia of the compression portion of a section about the gravity axis of the entire section about the y-axis Moment of inertia of full section about principal axis

Bl.1, B4, B4.1, B4.2, B5 B5

D3.2.2, D1.1

Product of inertia of full section about major and minor centroidal axes St. Venant torsion constant

D3.2.2, D4.1 C3.1.1

lye

Ix,Iy Ixy

•

B1.2, B6.2, C3.2, C3.4, C3.5.2 BI.I, B4, B4.1, B4.2

•

C3.1.3

D3.l.1

•

COLD-FORMED SPECIFICATION

AUGUST 19, 1986

•

SYMBOLS AND DEFINITIONS Symbol j

Definition

Section property for torsional-flexural buckling Effective length factor A constant Effective length factor in the plane of bending Effective length factor for torsion Effective length factor for bending about x-axis Effective length factor for bending about y-axis Plate buckling coefficient

kv L L L L

•

Lst Lt Lx Ly M

Live load Length of the portion of the span between supports where the flange that is not connected to the sheathing is in compression Length of transverse stiffener U nbraced length of compression member for torsion U nbraced length of compression member for bending about x-axis U nbraced length of compression member for bending about y-axis Applied bending moment

Allowable bending moment permitted if bending stress only exists

Max May Maxo Mayo

Allowable moments about the centroidal axes determined in accordance with Section C3 Allowable moments about the centroidal axes determined in accordance with Section C3.1 excluding the provisions of Section C3.l.2 Critical moment Elastic critical moment Nominal moment strength

L Ls

Me Me Mn

Mx. My

•

Shear buckling coefficient Full span for simple beams, distance between inflection points for continuous beams, twice the length of cantilever beams Length of seam weld not including the circular ends Length of fillet weld Unbraced length of member

My Ml M2 m m

Applied moments about the centroidal axes determined in accordance with Section C3 Moment causing a maximum strain of ey Smaller end moment Larger end moment ~istance from the shear center of one channel to the mid-plane of its web O.192(F uJF yv) - 0.068

Section

C3.1.1 C3.l.3, C4, C4.1, C5 03.2.2 C5 C3.1.2 C3.1.2 C3.1.2 B2.1, B2.3, B3.1, B3.2, B4, B4.1, B4.2 B6.2, C3.2 B1.1c, 03.2.1 E2.3 E2.4, E2.5 C3.l.2, C3.l.3, C4.1, 01.1 F1 C3.l.3 B6.1 C3.1.1 C3.1.1 C3.1.1 C3.3, C3.5.1, C3.5.2 C3.1, C3.3, C3.5.1, C3.5.2, C6.1 C5 C5,04.2

C3.l.2 C3.l.2 C3.1, C3.1.1, C3.l.2, C6.1 C5 B2.1, C3.1 C3.1.1, C5 C3.1.1, C5 03.2.2, 01.1 A5.2.2

1-11

AUGUST 19, 1986

1-12 COLD-FORMED SPECIFICATION

SYMBOLS AND DEFINITIONS Symbol

N n np P P P P Pa

P ao PL Pn Pn

Definition

Actual length of bearing Number of holes N umber of parallel purlin lines Concentrated load or reaction Applied axial load Force transmitted by bolt Force transmitted by weld Allowable concentrated load or reaction for one transverse stiffener Allowable axial load determined in accordance with Section C4 for Force to be resisted by intermediate beam brace Nominal axial strength of member Nominal strength of connection component

q qw q qo qu R R R r

Radius of gyration of full unreduced cross section

Force transmitted by the bolt or bolts at the section considered, divided by the tension force in member at that section 'Radius of gyration of one channel about its centroidal axis parallel to web Polar radius of gyration of cross section about the shear center

ro r x' ry r,

S Se Se S,

D3.6 E4 D3.2.1 C3.5 C5, D4.1 E3, E3.1 E2, E2.2 B6.1

•

L=O

Design shear rigidity for sheathing on both sides of the wall assembly Uniformly distributed load in the plane of the web Allowable uniform load Design shear rigidity for sheathing per inch of stud spacing Factor used to determine design shear rigidity Maximum uniformly distributed load in the plane of the web Required load carrying capacity Coefficient Inside bend radius

rey

Section

Radius of gyration of cross section about centroidal principal axes Radius of gyration of I -section about the axis perpendicular to the direction in which buckling would occur for the given conditions of end support and intermediate bracing l.28 VElf Elastic section modulus of the effective section calculated at a stress M/S, in the extreme compression fiber Elastic section modulus of the effective section calculated with extreme compression or tension fiber at F y Elastic section modulus of full unreduced section for the extreme compression fiber

B3.2.2 C4, C6.2 E2, E2.2, E2.3, E2.4, E2.5 D4.1 C3.l.3, Dl.1 C3.l.3 D4.1 D4.1 C3.l.3 FI C4, C6.2 A5.2.2 C3.4 C3.1.1, C4, C4.1 E3.2

•

Dl.1 C3.1.1, C4.2, D4.1 C3.1.1 Dl.1

B4, B4.1 C3.1.1, C3.1.2, C4 C3.1.1 C3.1.1, C3.1.2, C6.1

•

AUGUST 19, 1986

•

SYMBOLS AND DEFINITIONS Symbol

t t

Total thickness of the two welded sheets Thickness of thinnest connected part

ts tw V Va

Equivalent thickness of a multiple-stiffened element Effective throat of weld Actual shear force Allowable shear force

Total load supported by the purlin lines between adjacent supports, Ibs. Flat width of element exclusive of radii

s s

s Ta Tn

•

Definition

Maximum permissible longitudinal spacing of welds or other connectors joining two channels to form an I-section Fastener spacing Spacing in line of stress of welds, rivets, or bolts connecting a {!ompression coverplate or sheet to a non-integral stiffener or other element Weld spacing Allowable tensile strength Nominal tensile strength Strength of connection in tension Base steel thickness of any element or section

Smax

•

COLD-FORMED SPECIFICATION 1-13

w wr wr WI

w2 x xo

Flat width of the beam flange which contacts the bearing plate Width of flange projection beyond the web or half the distance between webs for box- or U-type sections Projection of flanges from inside face of web Leg on weld Leg on weld Distance from concentrated load to brace Distance from shear center to centroid along the principal x-axis

Section

DI.I D1.2, D4.1 E3.2

Dl.1 C2 C2 Dl.1 A1.2, A3.4, A5.2.1, BI.I, BUb, B1.2, B2.1, B4, B4.1, B4.2, B5, B6.1, C3.1.1, C3.1.3, C3.2, C3.4, C3.5.2, C4, C6.1, C6.2, D1.2, E2.4, E2.5 E2.2 E2.2, E3.1, E4 B5, B6.1 E2.4, E2.5 C3.3 B6.2, C3.2, C3.3 D3.2.1 A1.2, BU, B2.1, B2.2, B3.1, B4, B4.1, B4.2, B5, C3.1.1, C3.1.3, C4, D1.2 C3.5 Bl.1 DI.I E2.4 E2.4 D3.2 C3.U, C4.2, D4.1

AUGUST 19,1986

1-14 COLD-FORMED SPECIFICATION

SYMBOLS AND DEFINI1"IONS Symbol

Definition

Section

Y 1/ax 1/ay

Yield point of web steel divided by yield point of stiffener steel Magnification factors

B6.2 C5

Coefficient Actual shear strain in the sheathing Permissible shear strain of the sheathing

C4.2, D4.1 D4.1 D4.1

Angle between web and bearing surface> 45° but no more than 90° Angle between the vertical and the plane of the web of the Z-section, degrees Stress related to shear strain in sheathing Theoretical elastic buckling stress Torsional buckling stress

C3.4 D3.2.1

'Y 'Y

9 9 0' O'eR O't

A, Ae

Reduction factor Slenderness factors f2/f)

'fibfie"

Factor of safety for bearing Factor of safety for axial compression

fi, fie fist fit fiw

Factor of safety for flexure Facto,r of safety for sheet tearing Factor of safety for end crushing of transverse stiffener Factor of safety for tension on net section Factor of safety for welded connections

D4.1 D4.1 C3.1.1, C4.2, D4.1 B2.1 B2.1, C3.5.2 B2.3 E3.3 B6.1, C4, C5, C6.2, D4.1 C3.1, C6.1 E2.2, E3.1 B6.1 C2, E3.2 E2

•

AUGUST 19, 1986

•

COLD-FORMED SPECIFICATION

SPECIFICATION FOR THE DESIGN OF COLD-FORMED STEEL STRUCTURAL MEMBERS AUGUST 19,1986 A. GENERAL PROVISIONS A1 Limits of Applicability and Terms A1.1 Scope and Limits of Applicability

This specification shall apply to the design of structural members cold-formed to shape from carbon or low-alloy steel sheet, strip, plate or bar not more than one inch in thickness and used for load-carrying purposes in buildings. It may also be used for structures other than buildings provided appropriate allowances are made for dynamic effects. Appendices to this Specification shall be considered as integral parts of the Specification. A1.2 Terms

•

Where the following terms appear in this Specification they shall have the meaning herein indicated: (a) Stiffened or Partially Stiffened Compression Elements. A stiffened or partially stiffened compression element is a flat compression element (i.e., a plane compression flange of a flexural member or a plane web or flange of a compression member) of which both edges parallel to the direction of stress are stiffened by a web, flange, stiffening lip, intermediate stiffener, or the like. (b) Unstiffened Compression Elements. An unstiffened compression element is a flat compression element which is stiffened at only one edge parallel to the direction of stress. (c) Multiple-Stiffened Elements. A multiple-stiffened element is an element that is stiffened between webs, or between a web and a stiffened edge, by means of intermediate stiffeners which are parallel to the direction of stress. A sub-element is the portion between adjacent stiffeners or between web and intermediate stiffener or between edge and intermediate stiffener. (d) Flat-Width-to- Thickness Ratio. The flat width of an element measured along its plane, divided by its thickness. (e) Effective Design Width. Where the flat width of an element is reduced for design purposes, the reduced design width is termed the effective width or effective design width. (f) Thickness. The thickness, t, of any element or section shall be the base steel thickness, exclusive of coatings. (g) Torsional-Flexural Buckling. Thrsional-flexural buckling is a mode of buckling in which compression members can bend and twist simultaneously. (h) Point-Symmetric Section. A point-symmetric section is a section symmetrical about a point (centroid) such as a Z-section having equal flanges. (i) Yield Point. Yield point, Fy or F.y, as used in this Specification shall mean yield point or yield strength . (j) Stress . Stress as used in this Specification means force per unit area. (k) Confirmatory Test. A confirmatory test is a test made, when desired, on members, connections, and assemblies designed according to the provisions of Sections A through E of this Specification or its specific references, in order to compare actual versus calculated performance.

1-15

1-16 COLD-FORMED SPECIFICATION

Performance Test. A performance test is a test made on structural members, connections, and assemblies whose performance cannot be determined by the provisions of Sections A through E of this Specification or its specific references. (m) Virgin Steel. Vrrgin steel refers to steel as received from the steel producer or warehouse before being cold worked as a result of fabricating operations. (n) Virgin Steel Properties. Virgin steel properties refer to mechanical properties of virgin steel such as yield point, tensile strength, and elongation. (0) Specified Minimum Yield Point. The specified minimum yield point is the lower limit of yield point which must be equalled or exceeded in a specification test to qualify a lot of steel for use in a cold-formed steel structural member designed at that yield point. (p) Cold-Forrned'Ste,el Structural Members. Cold-formed steel structural members are shapes which are manufactured by press-braking blanks sheared from sheets, cut lengths of coils or plates, or by roll forming cold- or hot-rolled coils or sheets; both forming operations being performed at ambient room temperature, that is, without manifest addition of heat such as would be required for hot forming.

AUGUST 19, 1986

(I)

•

A1.3 Units of Symbols and Terms

The Specification is written so that any compatible system of units may be used except where explicitly stated otherwise in the text of these provisions. A2 Non-Conforming Shapes and Construction

The provisions of the Specification are not intended to prevent the use of alternate shapes or constructions not specifically prescribed herein. Such alternates shall meet the provisions of Section F of the Specification and be approved by the appropriate building code authority. A3 Material A3.1 Applicable Steels

This Specification requires the use of steel of structural quality as defined in general by the provisions of the following specifications of the American Society for Testing and Materials: ASTM A36/A36M-84a, Structural Steel ASTM A242/ A242M-85, High-Strength Low-Alloy Structural Steel ASTM A441M-85, High-Strength Low-Alloy Structural Manganese Vanadium Steel ASTM A446/ A446M-85 (Grades A, B, C, D, & F) Steel, Sheet, Zinc-Coated (Galvanized) by the Hot-Dip Process, Structural (Physical) Quality ASTM A500-84, Cold-Formed Welded and Seamless Carbon Steel Structural Tubing in Rounds and Shapes ASTM A529/ A529M-85, Structural Steel with 42 ksi Minimum Yield Point (y2 in. Maximum Thickness) ASTM A570/A570M-85 Steel, Sheet and Strip, Carbon, Hot-Rolled, Structural Quality ASTM A572/ A572M-85, High-Strength Low-Alloy Columbium-Vanadium Steels of Structural Quality ASTM A588/ A588M-85, High-Strength Low-Alloy Structural Steel with 50 ksi Minimum Yield Point to 4 in. Thick ASTM A606-85 Steel, Sheet and Strip, High Strength, Low Alloy, Hot-Rolled and ColdRolled, with Improved Atmospheric Corrosion Resistance ASTM A607-85 Steel Sheet and Strip, High Strength, Low Alloy, Columbium or Vanadium, or both, Hot-Rolled and Cold-Rolled ASTM A611-85 (Grades A, B, C, & D) Steel, Sheet, Carbon, Cold-Rolled, Structural Quality ASTM A715-85 (Grades 50 and 60) Sheet Steel and Strip, High-Strength, Low-Alloy, HotRolled, With Improved Formability ASTM A792-85a (Grades 33,37,40 & 50) Steel Sheet, Aluminum-Zinc Alloy-Coated by the Hot-Dip Process, General Requirements

•

AUGUST 19, 1986

COLD-FORMED SPECIFICATION

A3.2 Other Steels

•

The listing in Section A3.1 does not exclude the use of steel up to and including one inch in thickness ordered or produced to other than the listed specifications provided such steel conforms to the chemical and mechanical requirements of one of the listed specifications or other published specification which establishes its properties and suitability, and provided it is subjected by either the producer or the purchaser to analyses, tests and other controls to the extent and in the manner prescribed by one of the listed specifications and Section A3.3. A3.3 Ductility

Steels not listed in Section A3.1 and used for structural members and connections shall comply with one of the following ductility requirements: A3.3.1 The ratio of tensile strength to yield point shall not be less than 1. 08, and the total elongation shall not be less than 10 percent for a two-inch gage length or 7 percent for an eight-inch gage length standard specimen tested in accordance with ASTM A370-77'. The provisions of Chapters B through E of this Specification are limited to steels conforming to these requirements.

•

A3.3.2 Steels conforming to ASTM A446 Grade E and A611 Grade E and other steels which do not meet the provisions of Section A3.3.1 may be used for particular configurations provided (1) the yield strength, F y' used for design in Chapters B, C and D is taken as 75 percent of the specified minimum yield point or 60 ksi, whichever is less and (2) the tensile strength, Fu' used for design in Chapter E is taken as 75 percent of the specified minimum tensile stress or 62 ksi, whichever is less. Alternatively, the suitability of such steels for the configuration shall be demonstrated by load tests in accordance with Section F1. Allowable loads based on these tests shall not exceed the loads calculated according to Chapters B through E, using the specified minimum yield point, Fsy , for Fy and the specified minimum tensile strength, Fu' Allowable loads based on existing use shall not exceed the loads calculated according to Chapters B through E, using the specified minimum yield point, Fsy , for Fy and the specified minimum tensile strength, Fu' A3.4 Delivered Minimum Thickness

The uncoated minimum steel thickness of the cold-formed product as delivered to the job site shall not at any location be less than 95 percent of the thickness, t, used in its design; however, thicknesses may be less at bends, such as corners, due to cold-forming effects. A4 Loads A4.1 Dead Load

The dead load to be assumed in design shall consist of the weight of steelwork and all material permanently fastened thereto or supported thereby. A4.2 Live Load

The live load shall be that stipulated by the applicable code or specification under which the structure is being designed or that dictated by the conditions involved. A4.3 Impact Load

•

For structures carrying live loads which induce impact, the assumed live load shall bp increased sufficiently to provide for impact. A4.4 Wind or Earthquake Loads

Where load combinations specified by the applicable building code include wind or earthquake loads, the resulting forces may be multiplied by 0.75.

1-17

1-18 COLD-FORMED SPECIFICATION

AUGUST 19,1986

A4.5 Ponding

Unless a roof surface is provided with sufficient slope toward points of free drainage or adequate individual drains to prevent the accumulation of rainwater, the roof system shall be investigated by rational analysis to assure stability under ponding conditions. A5 Structural Analysis and Design

•

A5.1 Design Basis

This Specification is based upon the allowable stress concept presented in terms of allowable moments and loads. The allowable moments and loads are determined by dividing the corresponding nominal capacities by an accepted factor of safety. A5.2 Yield Point and Strength Increase from Cold Work of Forming A5.2.1 Yield Point

The yield point used in design, Fy , shall not exceed the specified minimum yield point, or as established in accordance with Chapter F, or as increased for cold work of forming in Section A5.2.2, or as reduced for low ductility steels in Section A3.3.2. A5.2.2 Strength Increase from Cold Work of Forming

Provisions for the strength increase from cold work of forming are given in Appendix A5.2.2. A5.3 Serviceability and Durability

A structure shall be designed to perform its required functions during its expected life, including serviceability and durability considerations. A6 Reference Documents

This Specification recognizes other published and latest approved specifications and manuals for designs contemplated herein, as follows:

•

1. American National Standards Institute, ANSI A58.1-1982, "Minimum Design Loads in

Buildings and Other Structures:' * American National Standards Institute, Inc., (ANSI), 1430 Broadway, New York, New York 10018

2. Applicable standards of the American Society for Testing and Materials, (ASTM), 1916 Race Street, Philadelphia, Pennsylvania 19013 3. American Institute of Steel Construction, "Specification for the Design, Fabrication and Erection of Structural Steel for Buildings," American Institute of Steel Construction, (AISC), 400 North Michigan Avenue, Chicago, Illinois 60611, November 1, 1978 4. American Welding Society, AWS D1.3-81, "Structural Welding Code-Sheet Steel," American Welding Society, (AWS), 550 N.W. LeJeune Road, Miami, Florida 33126 5. Research Council on Structural Connections, Allowable Stress Design, "Specification for Structural Joints Using ASTM A325 or A490 Bolts," Research Council on Structural Connections, (RCSC), American Institute of Steel Construction (AISC) 400 North Michigan Avenue, Chicago, Illinois 60611, November 13,1985. 6. Metal Building Manufacturers Association, Low Rise Building Systems Manual, Metal Building Manufacturers Association (MBMA), 1230 Keith Building, Cleveland, Ohio 44115 7. Steel Deck Institute, "Design Manual for Composite Decks, Formed Decks, and Roof Decks," Steel Deck Institute, Inc., P.O. Box 9506, Canton, Ohio, 44711,1984 8. Steel Joist Institute, "Standard Specifications Load Tables and Weight Tables for Steel *For further information contact ASeE, New York, New York.

•

COLD-FORMED SPECIFICATION 1-19

AUGUST 19, 1986

••

Joists and Joist Girders," Steel Joist Institute, (SJI), Suite A, 12Q5 48th Avenue North, Myrtle Beach, South Carolina 29577, 1986 9. Rack Manufacturers Institute, "Specification for the Design, Testing and Utilization of Industrial Steel Storage Racks," Rack Manufacturers Institute, (RMI) 8720 Red Oak Boulevard; Suite 201, Charlotte, North Carolina 28210, 1985 10. American Iron ahd Steel Institute, "Stainless Steel Cold-Formed Structural Design Manual," 1974 Edition, American Iron and Steel Institute, (AISI), 1000 16th Street, N.W., Washington, D.C. 20036 11. American Society of Civil Engineers, "ASCE Standard, Specification for the Design and Construction of Composite Slabs," American Society of Civil Engineers, (ASCE), 345 East 47th Street, New York, New York 10017, October, 1984

12. American Iron and Steel Institute, "Tentative Criteria for Structural Applications of Steel Tubing and Pipe," American Iron and Steel Institute, (AISI), 1000 16th Street, N.W., Washington, D.C. 20036, August, 1976

B.ELEMENTS 81 Dimensional Limits and Considerations 81.1 Flange Flat-Width-to-Thickness Considerations (a)

Maximum Flat-Width-to-Thickness Ratios Maximum allowable overall flat-width-to-thickness ratios, wit, disregarding intermediate stiffeners and taking as t the actual thickness of the element, shall be as follows: (1)

•

(2)

(3)

Note:

(b)

•

(c)

Stiffened compression element having one longitudinal edge connected to a web or flange element, the other stiffened by: Simple lip

Any other kind of stiffener having Is> Ia and D/w.. > 0.673 where w = Flat width as shown in Figure B2.1 p = (1-0.22/>..)/>.. >.. is a slenderness factor determined as follows: >.. = 1.052

v'k

(~) i t

(Eq. B2.1-1) (Eq. B2.1-2)

(Eq . B2.1-3)

(Eq. B2.1-4)

V"E

•

where f for load capacity determination is as follows: For flexural members: (1)

If Procedure I of Section C3.1.1 is used, f = F y if the initial yielding is in compression in the element considered. If the initial yielding is not in compression in the element considered, then the stress f shall be determined for the element considered on the basis of the effective section at My(moment causing initial yield).

(2)

If Procedure II of Section C3.1.1 is used, th~n f is the stress in the element considered at Mn determined on the basis of the effective section.

---------D~f D ---------

Actual Element

I I

(I."'.I---------I.~.i\ I I

b/2

bl2

Effective Element and Stress on Effective Elements

Figure 82.1-1 Stiffened Elements

I I

•

AUGUST 19, 1986

1-21

If Section C3.1.2 is used, then the f= ~e as described in that Section in determining Se' f

(3)

•

COLD-FORMED SPECIFICATION

For compression members f is taken equal to F n as determined in Section C4 or D4 as applicable. E = Modulus of elasticity k = Plate buckling coefficient = 4 for stiffened elements supported by a web on each longitudinal edge. Values for different types of elements are given in the applicable sections. (b)

Deflection Determination The effective widths, bd , used in computing deflections shall be determined from the following formulas: bd =w Whenh::50.673 bd = pw when h > 0.673 where w = Flat width P . = Reduction factor determined by either of the following two procedures:

•

(1)

Procedure 1. A low estimate of the effective width may be obtained from Eqs. B2.1-3 and B2.1-4 where fd is substituted for f where fd is the computed compressive stress in the element being considered.

(2)

Procedure II. For stiffened elements supported by a web on each longitudinal edge an improved estimate of the effective width can be obtained by calculating p as follows: p =1 whenh::50.673 p = (1.358 -0.461/h)/h when 0.673 < A< he p = (0.41 + 0.59YF y/fd -0.22/h)/A when A~ he where Ac = 0.256+0.328 (w/t)YF/E and Ais as defined by Eq. B2.1-4 except that fd is substituted for f.

(Eq. B2.1-5) (Eq. B2.1-6)

(Eq. B2.1-7)

CEq. B2.1-8) (Eq. B2.1-9)

(Eq. B2.1-1O)

82.2 Uniformly Compressed Stiffened Elements with Circular Holes (a)

Load Capacity Determination The effective width, b, of stiffened elements with uniform compression having circular holes shall be determined as follows: d

forO.50~~~O,and

w t

-::570

center-to-centerspacing of holes> O.50w, and 3d h , b =w-d h whenA::50.673 w [ 1- (0.:2) _ (O.!d h )

b =

•

]

when A>O.673

where w = Flat width d h = Diameter of holes Ais as defined in Section B2.1. (b)

(Eq. B2.2-1)

Deflection Determination The effective width, bd, used in deflection calculations shall be equal to b determined in accordance with Procedure I of Section B2.2a except that fd is substituted for f, where fd is the computed compressive stress in the element being considered.

CEq. B2.2-2)

AUGUST 19,1986

1-22 COLD-FORMED SPECIFICATION

B2.3 Effective Width of Webs and Stiffened Elements with Stress Gradient (a)

Load Capacity Determination The effective widths, b l and b2 , as shown in Figure B2.3-1 shall be determined from the following formulas: b l = b e /(3 -1/1) For 1/1 ~ -0.236 b2 = b e /2 b l + b2 shall not exceed the compression portion of the web calculated on the basis of effective section For 1/1 > -0.236 b 2 = be -b l where be = Effective width b determined in accordance with Section B2.1 with fl substituted for f and with k determined as follows: k = 4+2(1-1/1)3+2(1-1/1) 1/1 = f2/fl

• (Eq. B2.3-1) (Eq. B2.3-2)

(Eq. B2.3-3)

(Eq. B2.3-4)

fl' f2 = Stresses shown in Figure B2.3-1 calculated on the basis of effective section. fl is compression ( + ) and f2 can be either tension ( - ) or compression. In case fl and f2 are both compression, f\ ~ f2 (b)

Deflection Determination The effective widths in computing deflections at a given load shall be determined in accordance with Section B2.3a except that fdl and fd2 are substituted for fl and f2' where fdl • fd2 == Computed stresses f\ and f2 as shown in Figure B2.3-1. Calculations are based on the effective section at the load for which deflections are determined.

• Actual Element

:j)--Effective Elements and Stresses on Effective Elements

Figure B2.3-1 StIffened Elements with StrNa GrMIIent and Webs

•

COLD-FORMED SPECIFICATION

AUGUST 19, 1986

1-23

83 Effective Widths of Unstiffened Elements

•

83.1 Uniformly Compressed Unstiffened Elements

Load Capacity Determination Effective widths, b, of unstiffened compression elements with uniform compression shall be determined in accordance with Section B2.1a with the exception that k shall be taken as 0.43 and w as defined in Figure B3.1-1. (b) Deflection Determination The effective widths used in computing deflections shall be determined in accordance with Procedure I of Section B2.1 b except that fa is substituted for f and k = 0.43. (a)

83.2 Unstiffened Elements and Edge Stiffeners with Stress Gradient

Load Capacity Determination Effective widths, b, of unstiffened compression elements and edge stiffeners with stress gradient shall be determined in accordance with Section B2.1a with f = f3 as in Figure B4-2 in the element and k = 0.43. (b) Deflection Determination Effective widths, b, of unstiffened compression elements and edge stiffeners with stress gradient shall be determined in accordance with Procedure I Section B2.1b except that fa3 is substituted for f and k = 0.43.

(a)

----.,

Stress f ......... 1

I-

•

(I I I

----..I

-I

(i. Actual Element

Effective Element and Stress on Effective Element

FIgure 83.1-1 Unstlffened Element with Uniform Compression

84 Effective Widths of Elements with an Edge Stiffener or One Intermediate Stiffener

The following notation is used in this section.

•

k bo d,w,D

d' s

CI> C2 As

= =

l.28v'E/f Buckling coefficient Dimension defined in Figure B4-1 Dimensions defined in Figure B4-2 Reduced effective width of the stiffener as specified in this section. ds ' calculated according to Section B4.2, is to be used in computing the overall effective section properties (see Figure B4-2) Effective width of the stiffener calculated according to Section B3.1 (see Figure B4-2) Coefficients defined in Figures B4-1 and B4-2 Reduced area of the stiffener as specified in this section. As is to be used in computing the overall effective section properties. The centroid of the stiffener is to be considered located at the centroid of the full a:rea of the stiffener, and the moment of inertia of the stiffener about its own centroid~l axis shall be that of the full section of the stiffener. Adequate moment of inertia of stiffener, so that each component element will behave as a stiffened element.

(Eq. B4-1)

1-24

COLD-FORMED SPECIFICATION

Is, A' s

AUGUST 19, 1986

Moment of inertia of the full stiffener about its own centroidal axis parallel to the element to be stiffened and the effective area of the stiffener, respectively. For edge stiffeners the round corner between the stiffener and the element to be . stiffened shall not be considered as a part of the stiffener.

•

For the stiffener shown in Figure B4-2, =

(d 3t

d'st

sin 2

(Eq. B4-2) (Eq. B4-3)

6)/12

Stress f

ffiIIIII]= =====_IIIIIIIIIIIIIIIIIIIIIIIII-======ffiIIIII]1 ~-------i~;i~~W2~-------~

·1

'u'

(

E·ffective Elements and Stress on Effective Element

Actual Elements

Stiffener Section Figure 84-1 Elements with Intermediate Stiffener

B4.1 Uniformly Compressed Elements with an Intermediate Stiffener (a)

Load Capacity Determination Case I:

Case II:

Case III:

bolt $ S

B4.1-1) B4.1-2) B4.1-3) B4.1-4)

= 0 (no intermediate stiffener needed)

b As

Ia/t4 b and k A"

= [50(bo/t)/S] -50

(Eq. B4.1-5) (Eq. B4.1-6)

As shall be calculated according to Section B2.1a where = 3(1./1.)112 + 1 $4 = A' "(1./1.) $ A' s

(Eq. B4.1-7) (Eq. B4.1-8)

w A's

= S < bolt < 3S

•

bo/t~3S

1./t4 = [128(bo/t)/S] -285 b and As are calculated according to Section B2.1a where

(b)

(Eq. (Eq. (Eq. (Eq.

= 3(1./1.)113 + 1 $

= A's(l.lla)$A's

(Eq. B4.1-9) (Eq. B4.1-1O) (Eq. B4.1-11)

Deflection Determination Effective widths shall be determined as in Section B4.1a except that fd is substituted forf.

B4.2 Uniformly Compressed Elements with an Edge Stiffener (a)

Load Capacity Determination Case I:

wit $ S/3 la = 0 (no edge stiffener needed) =w b d.

for simple lip stiffener A'. for other stiffener shapes

(Eq. (Eq. (Eq. (Eq. (Eg.

B4.2-1) B4.2-2) B4.2-3) B4.2-4) B4.2-5)

•

COLD-FORMED SPECIFICATION

AUGUST 19,1986

Case II:

•

S/360, the effective width, be' of the sub-element or element shall be determined from the following formula: b [W ] tbe ="t0.10 T- 60

(Eq. B5-3)

where:

wit = flat-width ratio of sub-element or element b be

= effective design width determined in accordance with the provisions of Section B2.1, in. = effective design width of sub-element or element to be used in design computations, in.

•

For computing the effective structural properties of a member having compression subelements or element subject to the above reduction in effective width, the area of stiffeners (edge stiffener or intermediate stiffeners) shall be considered reduced to an effective area as follows: For 60: (Eq. E2.2-4)

P n = 1.40td a F u where d = Visible diameter of outer surface of arc spot weld da = Average diameter of the arc spot weld at mid-thickness oft [where da = (d -t) for a single sheet, and (d -2t) for mUltiple sheets (not more than four lapped sheets over a supporting member)] de = Effective diameter of fused area de =O.7d-1.5tbut:::;O.55d t = TOtal combined base steel thickness (exclusive of coatings) of sheets involved in shear transfer F xx = Stress level designation in AWS electrode classification Fay = Yield point as specified in Sections A3.1 or A3.2 F u = Tensile strength as specified in Sections A3.1 or A3.2 or as reduced for low-ductility steel. Note: See Figures E2.2(C) and E2.2(D) for diameter definitions The distance measured in the line of force from the centerline of a weld to the nearest edge of an adjacent weld or to the end of the connected part toward which the force is directed shall not be less than the value of e min as given below:

•

(Eq.E2.2-5)

(Eq. E2.2-6)

where (Eq. E2.2-7)

Oe = = = P = t =

Factor of safety for sheet tearing 2.0 when FjFsy~1.15 2.22 when F u/FSY < 1.15 Force transmitted by weld Thickness of thinnest connected sheet

•

d-t

d. _ O.7d - 1.5t:s;; O.55d

d. - - - . I

d. - d-2t d. _ O.7d-1.5t~O.55d

d.--~

(D) Arc Spot Weld-Double Thickness of Sheet

Figure E2.2 C, D Arc Spot w.lda

•

COLD-FORMED SPECIFICATION 1-49

AUGUST 19, 1986 Note:

•

See Figures E2.2(E) and E2.2(F) for edge distances of arc welds. In addition, the distance from the centerline of any weld to the end or boundary of the connected member shall not be less than 1.5d. In no case shall the clear distance between welds and the end of member be less than 1.0d.

(E) Single Sheet

• (F) Double Sheet

Figure E2.2 E, F Edge Distances for Arc Spot Welds

If it can be shown by measurement that a given weld procedure will consistently give a

larger effective diameter, de' or average diameter, da , as applicable, this larger diameter may be used providing the particular welding procedure used for making those welds is followed. E2.3 Arc Seam Welds

Arc seam welds [Figure E2.3(A)] covered by this Specification apply only to the following joints: (a) Sheet to thicker supporting member in the flat position. (b) Sheet to sheet in the horizontal or flat position. The shear load, Po, on each arc seam weld shall not exceed either 2

Ld e] 2.5 F xx,or . P 0_- [de 4+3

•

= 2.5tF u(O.25L + O.96da)

where d = width of arc seam weld L = Length of seam weld not including the circular ends (For computation purposes, L shall not exceed 3d.)

(Eq. E2.3-1) CEq. E2.3-2)

AUGUST 19, 1986

I-50 COLD-FORMED SPECIFICATION

da = Average width of seam weld where da = (d -t) for a single sheet, and (d - 2t) for a double sheet de = Effective width of arc seam weld at fused surfaces de = O.7d -lo5t

(Eq. E2.3-3) (Eq. E2.3-4) (Eq. E2.3-5)

and F u and F xx are defined in Section E2.2. The minimum edge distance shall be as determined for the arc spot weld, Section E2.2 [see Figure E2.3(B)].

•

If it can be shown by measurement that a given weld procedure will consistently give a larger effective width, de or da as applicable, this value may be used providing the particular welding procedure used for making the welds that are measured is followed.

d LWidth

•

Figure E2.3A Arc Seam Welda-Sheet to Supporting Member In Flat Poaltlon

Figure E2.3B Edge Distances for Arc Seam Welda

E2.4 Fillet Welds

Fillet welds covered by this Specification apply to the welding of joints in any position, either (a) Sheet to sheet, or (b) Sheet to thicker steel member. The shear load, Pn, on a fillet weld in lap and T-joints shall not exceed the following: For longitudinal loading: For L/t 0.150 inch the allowable load for a fillet weld in lap and T-joints shall not exceed: Pn = o. 75twLFxx

(Eq. E2.4-4)

where L = Length of fillet weld tw = Effective throat = o. 707w I or 0.707w 2 , whichever is smaller. A larger effective throat may be taken if it can be shown by measurement that a given welding procedure will consistently give a larger value providing the particular welding procedure used for making the welds that are measured is followed. and W 2 = leg on weld (see Figure E2.4). F u and F xx are defined in Section E2.2.

•

(A)

Lap Joint

(8) T -Joint

Figure E2.4 Fillet Welda

E2.S Flare Groove Welds

Flare groove welds covered by this Specification apply to welding of joints in any position, either: (a) Sheet to sheet for flare- V groove welds, or (b) Sheet to sheet for flare-bevel groove welds, or (c) Sheet to thicker steel member for flare-bevel groove welds. The shear load, Pn' on a weld shall be governed by the thickness, t, of the sheet steel adjacent to the weld. The load shall not exceed: For flare-bevel groove welds, transverse loading [see Figure E2.5(A) ]: (Eq. E2.5-l)

Pn = O.833tLF u

•

Figure E2.5A Flare-Bevel Groove Weld

AUGUST 19,1986

I-52 COLD-FORMED SPECIFICATION

For flare groove welds, longitudinal loading [see Figures E2.5(B), E2.5(C), and E2.5(D)]: If the effective throat, t w' is equal to or greater than t but less than 2t or if the lip height is less than weld length, L, then: P n = O. 75tLF u

(Eq. E2.5-2)

Iftw is equal to or greater than 2t and the lip height is equal to or greater than L, then: P n = 1.50tLF u

•

(Eq. E2.5-3)

In addition, ift:> 0.15 inch, then: (Eq. E2.5-4)

P n = O. 75twLF xx

(B) Flare Bevel Groove

• (C) Flare V-Groove

(0) Throat

Figure E2.S B, C, D Shear In Flare Groove Welda

E2.& Resistance Welds

In sheets joined by spot welding the allowable shear per spot, P a' shall be as follows (the safety factor is included in Table E2.6):

•

COLD-FORMED SPECIFICATION

AUGUST 19, 1986

TABLE E2.6

•

Thickness of Thinnest Outside Sheet, in.

Allowable Shear Strength per Spot, kips

Thickness of Thinnest Outside Sheet, in.

Allowable Shear Strength per Spot, kips

0.010 0.020 0.030 0.040 0.050 0.060

0.050 0.175 0.400 0.570 0.660 0.910

0.080 0.094 0.109 0.125 0.188 0.250

1.330 1.725 2.395 2.88 4.00 6.00

E3 Bolted Connections

•

The following requirements govern bolted connections of cold-formed steel structural members in which the thickness of the thinnest connected part is less than 31I6 inch and there are no gaps between connected parts. For bolted connections in which the thinnest connected part is equal to or greater than 0/16 inch, refer to AISC Specification (Reference 3 of Section A6). Bolts, nuts, and washers shall generally conform to one of the following specifications: ASTM A307-84 (Type A), Carbon Steel Externally and Internally Threaded Standard Fasteners ASTM A325-84, High Strength Bolts for Structural Steel Joints ASTM A354-84 (Grade BD), Quenched and Tempered Alloy Steel Bolts, Studs, and Other Externally Threaded Fasteners (for diameter of bolt smaller than Y2 inch) ASTM A449-84a, Quenched and Tempered Steel Bolts and Studs (for diameter of bolt smaller than Y2 inch) ASTM A490-84, Quenched and Tempered Alloy Steel Bolts for Structural Steel Joints. When other than the above are used, drawings shall indicate clearly the type and size of fasteners to be employed and the allowable force assumed in design. Bolts shall be installed and tightened to achieve satisfactory performance of the connec- . tions involved under usual service conditions. The holes for bolts shall not exceed the sizes specified in Table E3, except that larger holes may be used in column base details or structural systems connected to concrete walls. TABLE E3 Maximum Size of Bolt Holes, Inches

•

Nominal Bolt Diameter, d in.

Standard Hole Diameter, d in.

Oversized Hole Diameter, d In.

Short-Slotted Hole Dimensions in.

Long-Slotted Hole Dimensions in.

1/2 ;::: 1/2

d + 1/32 d + 1/16

d + 1/16 d+ 1/8

(d + 1/32)by(d + 1/4) (d + 1/16)by(d + 1/4)

(d + 1/32)by(2-1/2 d) (d + 1/16)by(2-1/2 d)

Standard holes shall be used in bolted connections, except that oversized and slotted holes may be used as approved by the designer. The length of slotted holes shall be normal to the direction of the shear load. Washers or backup plates shall be installed over oversized or shortslotted holes in an outer ply unless suitable performance is demonstrated by load tests in accordance with Section F. E3.1 Spacing and Edge Distance

The distance, e, measured in the line of force from the center of a standard hole to the nearest edge of an adjacent hole or to the end of the connected part toward which the force is directed shall not be less than the value of emin detennined as follows:

I-53

I-54

COLD-FORMED SPECIFICATION

AUGUST 19, 1986

(Eq . E3.1-1)

where P e=Fu t

(Eq. E3.1-2)

When Fu/Fsy~ 1.15: fie = Factor of safety for sheet tearing = 2.0 (b) When FjFsy < 1.15: fie = Factor of safety for sheet tearing = 2.22 where P = Force transmitted by bolt t = Thickness of thinnest connected part F u = Tensile strength of the connected part as specified in Sections A3.1 or A3.2. F sy = Yield point of the connected part as specified in Sections A3.1 or A3.2. (a)

In addition, the minimum distance between centers of bolt holes shall provide sufficient clearance for bolt heads; nuts, washers and the wrench but shall not be less than 3 times the nominal bolt diameter, d. Also, the distance from the center of any standard hole to the end or other boundary of the connecting member shall not be less than lY2 d. For oversized and slotted holes, the distance between edges of two adjacent holes and the distance measured from the edge of the hole to the end or other boundary of the connecting member in the line of stress shall not be less than the value of [ e min - (dh /2)], in which e min is the required distance computed from the applicable equation given above, and d h is the diameter of a standard hole defined in Thble E3. In no case shall the clear distance between edges of two adjacent holes be less than 2d and the distance between the edge of the hole and the end of the member be less than d.

•

E3.2 Tension In Connected Part

The tension force on the net section of a bolted connection shall not exceed Ta from Section C2 or p. calculated as follows: P a = Pn/fi t

•

(Eq. E3.2-1)

where P n = AnFt An = Net section area F t and fit are determined as follows: (a)

When t~3/16 in.: See AISC Specification (Reference 3 of Section A6)

(b) When t < 3/16 inch and washers are provided under both the bolt head and the nut F t = (1.0 -0.9r + 3rd/s)F uS F u fit = Factor of safety for tension on the net section = 2.0 for double shear = 2.22 for single shear (c)

When t < 3/16 inch and either washers are not provided under the bolt head and nut, or only one washer is provided under either the bolt head or nut F t = (1.0-r+2.5rd/s)FusFu fit = Factor of safety for tension on the net section = 2.22 . where r = Force transmitted by the bolt or bolts at the section considered, divided by the tension force in the member at that section. Ifr is less than 0.2, it may be taken equal to zero.

(Eq. E3.2-2)

(Eq. E3.2-3)

•

COLD-FORMED SPECIFICATION

AUGUST 19, 1986

•

I-55

= Spacing of bolts perpendicular to line of stress.

In the case of a single bolt, s = Width of sheet F t = Nominal tension stress limit on net section F u = Tensile strength of the connected part as specified in Sections A3.1 or A3.2 d and t are defined in Section E3.1. E3.3 Bearing

The bearing force shall not exceed Pa calculated as follows: Pa

= Pn/fib

(Eq. E3.3-I)

where

Pn = Fpdt = Safety factor for bearing

(Eq. E3.3-2)

fib Fp

= 2.22 = Nominal bearing stress as given in Tables E3.3-1 and E3.3-2.

For conditions not shown, forces shall be determined on the basis oftest data using a factor of safety of 2.22. TABLE E3.3-1 Nominal Bearing Stress for Bolted Connections with Washers under Both Bolt Head and Nut

Thickness of connected part in.

•

Type of joint

F u/F sy ratio of connected part

Inside sheet of double shear connection ~0.024

but F y/2. In this case Oc varies from 1.92 to 1.67 1. 92 against column buckling 1. 92 for computing the permissable shear strain in sheathing material. 2.50 against ultimate test value 2.50 against ultimate test value 2.0 when F u/F y~ 1.15 2.22 when F jF y< 1.15 2.0 when washers are provided under bolt head and nut 2.22 when only one washer is used, or no washers 2.22 against bearing failure 2.25-2.52 against shear failure of bolts A twenty five percent reduction of nominal safety factor is permissable provided that the section thus designed is not less than that required for combination of dead and live load.

11-14

Commentary on the August 19,1986 Edition of the Cold-Formed Specification

B. ELEMENTS This edition of the Specification differs from previous editions because a unified design approach has been adopted for treating compression elements. The effective width approach, previously applied only to stiffened compression elements, is being universally applied to all compression elements. Commentary Section B2 discusses the effective width approach. 81

Dimensional limits and Considerations

Because of the relatively large flat-width-to-thickness ratios (wit) that are possible in cold-formed steel construction, dimensional limits are established in the Specification. Also, phenomena not germane to hot-rolled steel construction, e.g., flange curling and shear lag effects, are given consideration in the Specification. 81.1

Flange Flat-Width-to-Thickness Considerations

(a)

Maximum wit Ratios The limits imposed in Specification Section B1.1a are unchanged from previous editions of the Specification. Field experience has indicated that these limits are reasonable and achievable for typical cold-formed construction. In such cases where the limits are exceeded, tests in accordance with Specification Chapter Fare required. The note regarding noticeable deformations for larger flat-width-to-thickness ratios is a caution and is not intended to prevent the use of such compression elements.

(b)

Flange Curling Unusually wide, thin, but stable flanges tend to curl, i.e., deflect toward the neutral axis, during loading. An approximate, analytical treatment of the problem is given in Reference 24. Equation B1.1b-1 (Appendix B) enables the evaluation of the maximum admissible flange width, wr, for a given amount of curling, cr. The Specification does not stipUlate the amount of curling; this is subjective because the distortions mayor may not be offensive depending upon the application. The suggested curling of 5 percent of the member depth is not considered excessive under usuaJ conditions.

(c)

Shear Lag Effects For beams having relatively small span-to-flange-width ratios, L/wr , shear deformations may significantly alter the stress distribution in both the compression and tension flanges. Table B1.1c (Appendix B) is based on analytical and experimental data summarized in Reference 25. It should be noted that the flange width in this case is the projection beyond the web, not the flat portion of the flange, as in the case in subsequent sections of Chapter B.

81.2

Maximum Web-Depth-to-Thickness Ratio

The limits prescribed in Section B1.2 are unchanged from the 1980 AISI Specification. These limitations are based on the studies reported in References 26-28. However, because the definition for h, the depth of the flat portion of the web measured along the plane of the web, differs from previous editions of the Specification, the prescribed limits may appear to be more liberal. An unpublished study by LaBoube concluded that the new definition for h had negligible influence on the web strength. 82

Effective Widths of Stiffened Elements

The use of effective widths for stiffened compression elements is not new to the Specification. Previous editions of the Specification have treated only uniformly compressed stiffened elements by using an effective width approach. The scope of application for effective widths has been expanded to include (1) uniformly compressed stiffened elements, (2) uniformly compressed stiffened elements with circular holes and (3) webs and stiffened elements with stress gradients.

Commentary on the August 19,1986 Edition of the Cold-Formed Specification

82.1

Uniformly Compressed Stiffened Elements

(a)

Load Capacity Determination A non-dimensional format for presentation of Specification provisions has been adopted. See Reference 29 for a thorough discussion of the basis for this format as well as the research basis for the minor differences in numerical results. Therefore, the equations of Section B2.1a, although in outward appearance different from the 1980 AISI Specification, are, in fact, nearly identical to equations as developed by Winter (References 24,30-32). In addition to the non-dimensional format, Equation B2.1-4 is given with k, the plate buckling coefficient, as a variable. The factor k depends upon the boundary conditions of the plate element and the manner of loading. Presenting the Equation in this form, enables its use for all compression elements in the Specification. The equations of Section B2.1a are a common thread that runs through Sections B2 through B4 of the Specification.

(b)

Deflection Determination The design engineer has the option of using two procedures for determining the effective width to be used for deflection calculations. Procedure I uses the effective width Equation of Section B2.1a evaluated at the actual stress level. This is consistent with the practice of the 1980 AISI Specification. Procedure II is based upon recently completed research (Reference 29) and yields a more accurate estimate of the effective width for deflection analysis.

82.2

Uniformly Compressed Stiffened Elements with Circular Holes

These are new provisions and have a limited application as stated in the Specification. Reference 29 summarizes the background studies relative to this section. 82.3

Effective Width of Webs and Stiffened Elements with Stress Gradient

The use of effective widths for web elements subjected to a stress gradient is a deviation from the past practice of using a full area in conjunction with a reduced stress to account for local buckling and post-buckling strength (Reference 23). The effective widths are based upon Winter's effective width equation distributed as shown by Figure B2.3-1 of the Specification. Background regarding the development of the provisions of Section B2.3 is provided in Reference 29. 83

Effective Widths of Unstiffened Elements

The 1986 edition of the Specification marks the first time that unstiffened compression elements are treated using an effective width approach. The provisions of this section are based upon analytical and experimental data reported in Reference 29. The research demonstrated that Winter's effective width equation was an adequate predictor of section capacity if the appropriate buckling coefficient, k, is employed. 83.1

Uniformly Compressed Unstlffened Elements

The theoretical buckling coefficient, as given by Reference 33, is 0.425. This value has been rounded to two significant figures in Specification Section B3.1 83.2

Unstlffened Elements and Edge Stiffeners with Stress Gradient

There is a very limited amount of information on the behavior of unstiffened plate elements with a stress gradient. Cornell research (Reference 29), into the behavior of edge stiffeners for flexural members, has demonstrated that by using Winter's effective width equation in conjunction with a k == 0.43 (uniform compression), good correlation was achieved between test and calculated capacity. This same trend was also true for deflection determination.

11-15

II-16 84

Commentary on the August 19,1986 Edition of the Cold-Formed Specification Effective Widths of Elements with an Edge Stiffener or One Intermediate Stiffener

The provisions of Specification Section B4 represent the latest research findings in regard to stiffeners (Reference 29). Previous specifications treated stiffeners as fully effective plate elements. By using effective areas for stiffeners, all compression elements are analyzed on the basis of effective widths or areas. The design provisions, which are based on both critical local buckling and ultimate strength criteria, recognize the interaction of the plate elements (i.e., flange and stiffener). Also, for the first time, provisions for analyzing partially stiffened, as well as adequately stiffened, compression elements are contained in the Specification. 84.1

Uniformly Compressed Elements with an Intermediate Stiffener

The 1980 AISI Specification contained provisions for the minimum required moment of inertia, which was based on the assumption that an intermediate stiffener needed to be twice as rigid as an edge stiffener. Subsequent research (Reference 34) has developed expressions for evaluating the required stiffener rigidity based upon the geometry of the contiguous flat elements. Using the ratio of actual stiffener moment of inertia, Is, to adequate stiffener moment of inertia, la' (i. e., Islla) to evaluate the buckling coefficient and the stiffener area, a partially stiffened compression flange can also be evaluated. 84.2

Uniformly Compressed Elements with an Edge Stiffener

Specification Section B4.2 recognizes that the necessary stiffener rigidity depends upon the slenderness of the plate element being stiffened. Thus, Cases, I, II and III, each contain different definitions for an adequate stiffener moment of inertia. The interaction of the plate elements, as well as the degree of edge support, full or partial, is compensated for in the expressions for k, ds and~. For more in-depth coverage of this topic see Reference 29. 85

Effective Widths of Edge Stiffened Elements with Intermediate Stiffeners or Stiffened Elements with More Than One Intermediate Stiffener

There has been no research to further our understanding of the behavior of multiple stiffened elements. Thus the Specification has retained Equation B5-1 from the 1980 Specification for evaluating the minimum required rigidity, I min , of an intermediate stiffener fQr a multiple-stiffened element. This value of I min is used when evaluating the effective widths in Specification Section B4. In addition, Specification Section B5(a) stipulates that only intermediate stiffeners adjacent to web elements (see Figure A1.2-1(c)(1» shall be counted as effective. Additional stiffeners would have two or more sub-elements between themselves and the nearest sheartransmitting element (i.e., web) and hence, could be ineffective. Specification Section B5(b) applies the same reasoning to intermediate stiffeners between a web and an edge stiffener. If intermediate stiffeners are spaced so closely that the sub-elements are fully effective, i.e., b < w, no plate buckling of the sub-elements will occur. Therefore, the entire assembly of sub-elements and intermediate stiffeners between webs behaves like a single compression element whose rigidity is given by the moment of inertia, Is, of the full, multiple-stiffened element, including stiffeners. Although the effective width calculations are based upon an equivalent element having width, ws' and thickness, t s ' the actual thickness must be used when calculating section properties. 86

Transverse Stiffeners

Design requirements for attached transverse stiffeners and for intermediate stiffeners were added in the 1980 AISI Specification and are unchanged in the 1986 Specification. Equation B6.1-1 serves to prevent end crushing of the transverse stiffeners, while Equation B6.1-5 is to prevent column-type buckling of the web-stiffeners. The equations for computing the effective areas (Ab and Ac) and the effective widths (bl and b2) were adopted with minor modifications from Reference 28.

Commentary on the August 19,1986 Edition of the Cold-Formed Specification

The requirements for intermediate stiffeners included in Specification Section B6.2 were adapted from Section 1.10.5.3 of the AISC Specification (Reference 10). The equations for determining the minimum required moment of inertia (Eq. B6.2-1) and the minimum required gross area (Eq. B6.2-2) of attached intermediate stiffeners are based on the studies summarized in Reference 28. In Equation B6.2-1, the minimum value of (h/50)4 was selected from the AISC Specification. Tests on rolled-in transverse stiffeners covered in Specification Section B6.3 were not made in the experimental program reported in Reference 28. Lacking reliable information, the required dimensions and the allowable loads should be determined by special tests.

C.MEMBERS To simplify the use of the Specification, all design provisions relative to a specific member type, e.g., beam, column or beam-column, have been assembled in one location within the Specification. Also, design provisions are given in terms of allowable load or moment, instead of allowable stress, as was the approach in previous specifications. To enable a clearer understanding of the phenomenon being evaluated, the nominal capacity and required safety factor are explicitly stated.

Properties of Sections

The geometric properties of a member, i.e., area, moment of inertia, section modulus and radius of gyration, shall be evaluated using conventional methods of structural design. These properties are based upon either full cross-section dimensions, effective widths or net section, as applicable. For flexural members and axially loaded members both the full and effective dimensions are used. The full dimensions are used when calculating the critical load or moment, while the effective dimensions, evaluated at the stress corresponding to the critical load or moment, are used to calculate the nominal capacity. References 29 and 35 discuss this concept in more detail. The net section is employed when computing the capacity of a tension member. C2

Tension Members

There is a very limited amount of data regarding the capacity of cold-formed steel tension members. Because the provisions of the 1980 AISI Specification have been field tested with no known deficiency, they have been carried forward to the 1986 Specification. C3

Flexural Members

The provisions contained in Section C3 of the Specification address the various design aspects related to cross-section capacity, that is, flexure strength, shear strength, combined bending and shear strength, web crippling strength and combined bending and web crippling strength. For brace design, see Specification Section D3. C3.1

Strength for Bending Only

Flexural strength is a function of the geometry of the member in question, as well as the degree of lateral restraint, i.e., bracing, provided. The provisions of Specification Section C3.1 encompass these considerations. C3.1.1

Nominal Section Strength

Beams not subject to lateral (flexural), torsional or torsional-flexural buckling, are designed on the basis of the yield strength being achieved in the extreme fibers. Depending upon the cross-section geometry, initial yielding may occur in either the extreme tension or compression fibers. This is the premise in Section C3.1.la, which is consistent with previous editions of the Specification. For certain beam members, depending upon geometry, the potential exists for partial yielding of the cross section. The 1980 AISI Specification introduced guidelines which enabled design engineers to take advantage of this increased moment capacity. The

II-17

11-18

Commentary on the August 19,1986 Edition of the Cold-Formed Specification

provisions of the 1986 Specification have been modified by removing the requirement that the depth-to-thickness ratio of the entire web does not exceed 640/~ This restriction had been adopted from the AISC Specification (Reference 10) and was based on research on the plastic rotation capacity of hot-rolled, doubly symmetric wide-flange beams. For typical cold-formed sections, this limitation is redundant because the requirement of Specification Section C3.1.1b(3), the ratio of the depth of the compression portion of the web to its thickness not exceed ~l = 1. l1/v'Fy/E is the governing restriction. A.detailed discussion of the inelastic reserve capacity of flexural members is given in Reference 36. The development of this procedure is described in Reference 29. C3.1.2

Lateral Buckling Strength

The design expressions for laterally unbraced segments of flexural members in Specification Section C3.1.2 represent an improvement over previous specifications. The approach that has been adopted enables direct consideration of the interaction between local and overall buckling by a reduction of the critical moment. This reduction is equal to the ratio of the effective section modulus to the full section modulus. Unlike previous specifications, the 1986 Specification is expressed in terms of moment instead of stress. The critical moment for I-and Z-sections employ the same critical buckling stress equations that formed the basis for the 1980 AISI Specification (References 23 and 37-40). For singly symmetric sections for which the x-axis is the axis of symmetry, new, more theoretically based equations are given. The background for these equations is given in Reference 41. The case oflaterally un braced compression flanges is treated in Part III, Section 3, of the Manual, based on Reference 42. A slightly different approach is given in Reference 43. C3.1.3

Beams Having One Flange Attached to Deck or Sheathing

Studies (References 44, 45) of simple span C- and Z-purlin roof systems under uplift load have demonstrated that the roof panel, although attached to the tension flange, does provide some degree of restraint. This restraint is a function of the rotational stiffness of the panel-to-purlin connection which can be evaluated by the test procedure given in Part VII of the Manual. For continuous purlin systems, the analytical procedure described in Reference 44 is a rational analysis provided limitations in specimen dimension and construction details in supporting test evidence are recognized, and proper consideration is given for the behavior of continuous-span systems. In lieu of a rational analysis, tests may be conducted in accordance with Chapter F. C3.2

Strength for Shear Only

The Specification provisions are applicable for slender webs of beams and decks either with or without stiffeners. These provisions are identical to Section 1.10.5.2 for the design of plate girders and rolled beams in the 1978 AISC Specification (Reference 10). The acceptance of the AISC equations for cold-formed sections is based upon the study summarized in Reference 46. C3.3

Strength for Combined Bending and Shear

For cantilever beams and continuous beams, high bending stresses often combine with high shear stresses at the supports. In the design of such members, it has been the practice to use Specification Equation C3.3-1 to safeguard against buckling of flat webs due to the combination of bending and shear stresses (References 7 and 33). In addition, a new interaction equation (Eq. C3.2-2) was included in the 1980 Specification for beam webs with adequate transverse stiffeners. The correlations between the test data and both formulas are given in Reference 47. Limitations remain imposed on Ma and Va as loads, in contrast to removal of limits when stress interaction equations were used.

Commentary on the August 19,1986 Edition of the Cold-Formed Specification

C3.4

Web Crippling Strength

Section C3.4 of the Specification provides design equations to prevent web crippling of flexural members having flat single webs (channels, Z-sections, hat sections, tubular members, roof deck, floor deck, etc.) and I -beams (made of two channels connected back to back, by welding two angles to a channel, or by connecting three channels). Different design equations are used for different loading conditions. As shown in Figure C3.4-I, .Equations C3.4-I, C3.4-2, and C3.4-3 are used for end one-flange loading; Equations C3.4-4 and C3.4-5 for interior one-flange loading; Equations C3.4-6 and C3.4-7 for end two-flange loading; and Equations C3.4-8 and C3.4-9 for interior two-flange loading. These design equations are based on experimental evidence (Reference 27) and the distribution ofloads or reactions into the web as shown in Figure C3.4-2. The distribution of loads or reactions into the web as shown in Figure C3.4-2 are independent of the flexural response of the beam. Due to flexure, the point of bearing will vary relative to the plane of bearing resulting in non-uniform bearing load distribution into the web. The value ofPa will vary because ofa transition from the interior one-flange loading (Figure C3.4-2(b» to the end one-flange loading (Figure C3.4-2) condition. These discrete conditions represent the experimental basis on which the design provisions were founded (Reference 27). C3.5

Combined Bending and Web Crippling Strength

This Specification section contains two interaction formulas for the combination of bending and web crippling. These formulas are based on studies at the University of Missouri-Rolla on the effect of bending on the reduction of web crippling loads (Reference 23, 27, 48 and 49). For embossed webs, crippling strength should be determined by tests according to Specification Chapter F. The exception clause in Specification Section C3.5.I applies to the interior supports of continuous spans using decks and beams, as shown in Figure C3. 5-1. Results of continuous beam tests of steel decks (References 49) and several independent studies by manufacturers indicate that, for these types of members, the post-buckling behavior of webs at interior supports differs from the type of failure mode occurring under concentrated loads on single span beams. This post-buckling strength enables the member to redistribute the moments in continuous spans. For this reason, Equation C3.5-I is not applicable to the interaction between bending and the reaction at interior supports of continuous spans. This exception applies only for the members shown in Figure C3.5-I and similar situations explicitly described in Specification Section C3. 5. The exception clause should be interpreted to mean that the effects of combined bending and web crippling need not be checked for determining load carrying capacity. Furthermore the positive bending resistance of the beam should be at least 90 percent of the negative bending resistance in order to insure the factor of safety implied by the Specification. U sing this procedure the allowable loads may (1) produce slight deformations in the beam over the support, (2) increase the actual compressive bending stresses over the support to as high as 0.8 F Y' and (3) result in additional bending deflection of up to 22 percent due to elastic moment redistribution. If load carrying capacity is not the primary design concern because of the above behaviors, the designer is urged to use Equation C3.5-1. With regard to Equation C3.5-2, previous tests indicate that when the hit ratio of an I-beam web does not exceed 2.33/VF yiE and when A::S 0.673, the bending moment has little or no effect on the web crippling load. For this reason, the allowable reaction or concentrated load can be determined by the formulas given in Specification Section C3.4 without reduction for the presence of bending. C4

Concentrically Loaded Compression Members

The provisions of this Specification section represent a significant improvement over previous provisions for concentrically loaded compression members subject to either flexural, torsional or torsional-flexural buckling. A unified approach is presented wherein Equations C4-1 through C4-4 are general equations for the three buckling modes. The variation in the

11-19

II-20

Commentary on the August 19,1986 Edition of the Cold-Formed Specification

(a)

< 1.Sh

-_+----M-

Eq. C3.4-1, -2, or-3 End One-Flange Loading

Eq. C3.4-4 or-S Interior One-Flange Loading

Eq. C3.4-8 or -9 Interior Two-Flange Loading

(b)

--...~to+--

< 1.Sh

Eq. C3.4-1, -2, or-3 End One-Flange Loading

Eq. C3.4-1, -2. or-3 End One-Flange Loading

-.+---+-- < 1.Sh

---+----1-- < 1.Sh C3.4-8 or-9 Interior Two-Flange Loading

Eq. C3.4-4 or -5 Interior One-Flange Loading

--If----+--

< 1.5h

Eq. C3.4-6 or-7 End Two-Flange Loading

0.673 p = [1-(0.22/0.893)]/0.893 = 0.844 be = 0.844 X 5.692 = 4.804 in. b2 = be /2 = 4.804/2 = 2.402 in. bl = b e /(3 -$) = 4.804/[3 -( -0.842)] = 1.250 in. b l + b2 = 1.250 + 2.402 = 3.652 in. =

(Eq. B2.3-2) (Eq. B2.3-1)

compression portion of the web calculated on the basis of the effective section = Y cg -0.154 = 3.244 - 0.154 = 3.090 in. Since b l + b2 = 3.652 in. > 3.090 in., b l + b2 shall be taken as 3.090 in. This verifies the assumption that the web is fully effective. I~

= Ly2+I'I-LY~g = 110.504 + 15.368 -8.339 x (3.244)2

= 38.116 in. 3

Actual Ix

= I~t

= 38.116 x 0.060 = 2.287

in.4

Ix/Ycg

= 2.287/3.244

= 0.705

= Se Fy

in. 3

= 0.705 x 50 = 35.25 kip-in.

(Eq. C3.1.1-1)

Examples Based on the August 19,1986 Edition of the Cold-Formed Specification

IV-7

= 1.67 = Mn/nf

(Eq. C3.1-1)

35.25/1.67 = 21.11 kip-in. (positive bending)

2. Calculation of Effective moment of inertia based on procedure I for deflection determination at the allowable moment: The procedure is iterative: one assumes the actual compressive stress f under this allowable moment. Knowing f, proceed as usual to obtain Se and check to see if (f x Se) is equal to Ma as it should. If not reiterate until one obtains the desired level of accuracy. a. For the first iteration, assume a compression stress of f = F y/2 = 25 ksi in the top fibers of the section and that the web is fully effective. Compression flange: A = (1.052/V0.43) (24. 52)V25/29500 = 1.145> 0.673 p = [1 - (0.22/1.145)]/1.145 = 0.706 bd = pw = 0.706 x 1.471 = 1.039 in.

(Eq. B2.1-6)

Effective section properties about x-axis: L = 8.339 -0.786 + 1.039 = 8.592 in. Ly = 27.052 -0~024 + 1.039 x 0.030 = 27.059 in. 2 Ly2 = 110.504 -0.001 + 1.039 x (0.030)2 = 110.504 in. 3 I~ = 15.368 in. 3 Y cg = 27.059/8.592 = 3.149 in. greater than one half beam depth. Thus top compression fiber controls in determination of Se.

Th check if web is fully effective: (Section B2.3-(a),(b)) fl = [(3.149 -0.154)/3.149] x 25 = 23.78 ksi. f2 = - [(2.851 -0.154)/3.149] x 25 = -21.41 ksi. \fJ = -21.41/23.78 = -0.900 k = 4 + 2[1-( -0.900)]3 + 2[1-( -0.900)] = 21.518 A = (1.052/V21.518) (94. 87)V(23. 78/29500) = 0.611 < 0.673 be = w = 5.692 in. b 2 = 5.692/2 = 2.846 in. b i = 5.692/[3 -( -0.900)] = 1.459 in. compression portion of the web calculated on the basis of the effective section = 3.149 -0.154 = 2.995 in. Since b i + b2= 4.305 in. > 2.995 in., b i + b 2 shall be taken as 2.995 in. This verifies the assumption that the web is fully effective. I~ = 110.504 + 15.368 -8.592 x (3.149)2 = 40.672 in. 3 Actual Ix = 40.672 x 0.060 = 2.440 in.4 Se = 2.440/3.149 = 0.775 in. 3 M = f x Se = 25 x 0.775 = 19.38 k -in. < Ma = 21.11 kip-in. Need to do another iteration and also to increase f. b. For the second iteration, assume f = 27.65 ksi in the top fibers of the section and that the web is fully effective. Compression flange: A= (1.052/V0.43) (24. 52)V27. 65/29500 = 1.204> 0.673 p bd

= [1-(0.22/1.204)]/1.204 = 0.679 =

0.679 x 1.471 = 0.999 in.

(Eq. B2.l-l)

IV-8

Examples Based on the August 19,1986 Edition of the Cold-Fonned Specification

Effective section properties about x-axis: L = 8.339-0.786+0.999=8.552in. Ly = 27.052 -0.024 + 0.999 x 0.030 = 27.058 in. 2 Ly2 = 110.504 -0.001 + 0.999 x (0.030)2 = 110.504 in. 3 Ii = 15.368 in. 3

Ycg = 27.058/8.552 = 3.164 in. greater than one half beam depth, thus top compression fiber controls in detennination of Se' To check if web is fully effective: f} = [(3.164 -0.154)/3.164] x 27.65 = 26.30 ksi. f2 = -[(2.836 -0.154)/3.164] x 27.65 = -23.44 ksi. tfJ = -23.44/26.30 = -0.891 k = 4 + 2[1-( -0.891)]3 + 2[1-( -0.891)] = 21.306 A = (1.052/Y21.306) (94.87)Y26.30/29500 = 0.646 < 0.673 be = 5.692 in. b2 = 5.692/2 = 2.846 in. b i = 5.692/[3 -( -0.891)] = 1.463 in. Compression portion of the web calculated on the basis of the effective section = 3.164 -0.154 = 3.010 in. Since bi + b2 = 4.309 in. > 3.010 in., b i + b2 shall be taken as 3.010 in. This verifies the assumption that·the web is fully effective. I~ = 110.505 + 15.368 -8.552 x (3.164)2 = 40.259 in. 3 Actual Ix = 40.259 x 0.060 = 2.416 in.4 Se = 2.416/3.164 = 0.764 in. 3 M = fxS e =27.65 X O.764 = 21.12 k -in. close enough to Ma = 21.11 kip-in. Thus Ix = 2.416 in. 4 using procedure I for deflection detennination.

Examples Based on the August 19,1986 Edition of the Cold-Formed Specification

IV-9

EXAMPLE NO.2 C-SECTION 1.317"

T_O_.154_"_....L--t;d==~~ ~"

154

rIO.

5.692" 6.000"

---------x

0.079"

~---L~=====::::: 0.075"

Given:

·0.450"

1.625"

1. Steel: F y = 50 ksi. 2. Section: 6 x 1.625 x 0.060 channel with stiffened flanges. 3. Compression flange braced against lateral buckling.

Required: 1. Allowable moment based on initiation of yielding.

2. Effective moment of inertia based on procedure I for deflection determination at the allowable moment. Solution:

1. Calculation of the allowable moment: Properties of 90 0 comers: r = R + t/2 = 3/32 + 0.060/2 = 0.124 in. length of arc, u= 1.57r= 1.57 x 0.124=0.195in. Distance of c.g. from center of radius, c = 0.637r = 0.637 x 0.124 = 0.079 in.

Computation of Ix: for the first approximation, assume a compression stress of f = F y = 50 ksi in the top fibers of the section and that the web is fully effective. Compression flange: = 1.317 in. w wit = 1.317/0.060=21.95 S = 1.28 VE/f = 1.28 V~29~500"""'--"-/50- = 31.09 S/3 = 10.36«w/t)=21.95 0.673 =ll-(0.22/~)]/~

(Eq. B2.1-3)

= [1-(0.22/0.831)]/0.831 = 0.885

=pw

(Eq. B2.1-2)

= 0.885 x 5.692 = 5.037 in.

= be /2

(Eq. B2.3-2)

= 5.037/2 = 2.519 in. be /(3 -t\J) = 5.037/[3-(-0.970)] = 1.269 in.

(Eq. B2.3-1)

bi + b2 = 1.269 + 2.519 = 3.788 in. Compression portion of the web calculated on the basis of the effective section Ycg -0.154 = 3.043 -0.154 = 2.889 in. Since b i + b2= 3.788 in. > 2.889 in., b i + b2shall be taken as 2.889 in. This verifies the assumption that the web is fully effective. I~

= Ly2 + 1'1 -

LY~g

= 121.478 + 15.370 -9.542(3.043)2 = 48.491 in. 3 Actual Ix

= I~t = 48.491 x 0.060 = 2.909 in.4

= IJYcg = 2.909/3.043 = 0.956 in. 3

= SeFy

(Eq. C3.1.1-1)

0.956 x 50 = 47.80 kip-in.

= 1.67 Mn/nc = 47.80/1.67 = 28.62 kip-in.

2. Calculation of the effective moment of inertia based on procedure I for deflection detennination at the allowable moment: The procedure is iterative: one assumes the actual compressive stress f under this allowable moment. Knowing f, one proceeds as usual to obtain Se and checks to see if (f x Se) is equal to Ma as it should. If not, reiterate until one obtains the desired level of accuracy. [Section B2.1-(b)-(1)]

CEq. C3.1-1)

IV-12

Examples Based on the August 19,1986 Edition of the Cold-Formed Specification

(a) For the first iteration, assume a compression stress of f = Fy /2 = 25 ksi in the top fibers of the section and that the web is fully effective. Compression flange: S = 1. 28 V~29'--50-0""""'/2-5 = 43.97 S/3 = 14.66«w/t)=21.953.540 k

= 3.540

= (1.052jv'3.540) (21.95) V25/29500 = 0.357 3.540 k

= 3.540

= (1.052/V3.540) (21.95) Y28. 85 129500 = 0.384 < 0.673 = 1.317 in. (i.e. ~ompression flange fully effective)

Compression (upper) stiffener: f conservatively taken as for top compression fiber A = (1.052/V0.43) (4.93) V28.85/29500 = 0.247 < 0.673 d~ = 0.296 in. Since IsiIa = 2.89 > 1.0 it follows that d s = d~ = 0.296 in. (i.e. compression stiffener fully effective). Thus the section is fully effective. Ycg =

6/2 = 3.000 in. (from symmetry)

FUll section properties are the same as were found in the first iteration. Thus, as before, top compression fiber may be used in computing Se.

Th check if web is fully effective: f1 = [(3.000 -0.154)/3.000] x 28.85 = 27.37 ksi (compression) f2 = -27.37 ksi (tension) \fI = -27.37/27.37 = -1.000 k = 24.000 A = (1.052/\1'24) (94.87) Y27.37/29500 = 0.621 < 0.673 be = w = 5.692 in. Hence, as in first iteration, b i + b2 = 2.846 in. and thus the web is fully effective as assumed.

Ix Se M

= 2.975 in.4

= 0.992 in. 3 = fx Se = 28.85 x 0.992 = 28.62 kip-in. = Ma OK

Thus Ix = 2.975 in.4 using procedure I for deflection determination.

IV-13

IV-14

Examples Based on the August 19,1986 Edition of the Cold-Formed Specification

EXAMPLE NO.3 C-SECTION BRACED

6.000"

5.692"

0.079" 0.600"

0.075"

1. 2. 3. Required: 1. 2.

Given:

1.625"

Steel: F y = 50 ksi. Section: 6 x 1.625 x 0.060 channel with stiffened flanges. Compression flange braced against lateral buckling. Allowable moment based on initiation of yielding. Effective moment of inertia based on procedure I for deflection determination at the allowable moment.

Solution: 1. Calculation of the allowable moment:

Properties of 90° corners: r = R + t/2 = 3/32 + 0.060/2 = 0.124 in. length of arc, u = 1.57r = 1.57 x 0.124 = 0.195 in. Distance of c.g. from center of radius, c = 0.637r = 0.637 x 0.124 = 0.079 in. Computation of Ix: for the first approximation, assume a compression stress of f = F y = 50 ksi in the top fibers of the section and that the web is fully effective. Compression flange: w = 1.317 in. wit = 1.317/0.060=21.95 S = 1.28V(E7fj = 1.28v'29500/50 = 31.09 S/3 = 10.36 compression portion of the web = 2.846 in.

k A

be b2 b} b} + b2

= -28.46 ksi (tension)

(Eq. B2.1-1)

Thus bl + b2 shall be taken as 2.846 in. This verifies the assumption that the web is fully effective. Full section properties are the same as were found in determination of Ma since the section is fully effective. . Ix = 3.324 in.4, Se = 1.108 in. 3 M = fxSe=30x 1.108 = 33.24 k -in. close enough to Ma = 33.17 k -in. and no need for other iterations. = 3.324 in. 4 using procedure I for deflection determination. Thus Ix

IV-22

Examples Based on the August 19,1986 Edition of the Cold-Formed Specification

EXAMPLE NO. 4A DEEP-Z SECTION w/STIFFENED FLANGE

1.471"

t=0.060"

9.500" 9.192"

0.079"

l 1.625" 0.075"

Given:

1. Steel: F y = 50 ksi. 2. Section: 9.5 x 1.625 x 0.060 Z-section with stiffened flanges. 3. Compression flange braced against lateral buckling.

Required: 1. Allowable moment based on initiation of yielding. 2. Effective moment of inertia based on procedure I for deflection determination at the allowable moment. Solution: 1. Calculation of the allowable moment: .Properties of 90° corners: . r = R + t/2 = 3/32 + 0.060/2 = 0.124 in. length of arc, u = 1.57r= 1.57 x 0.124 = 0.195 in. Distance of c.g. from center of radius, c = 0.637r = 0.637 x 0.124 = 0.079 in.

Ex~ples

Based on the August 19,1986 Edition of the Cold-Fonned Specification

IV-23

Properties of 135° corners: r = R + t/2 = 3/32 + 0.060/2 = 0.124 in. length of arc, u = (45°/180°) (3.14)r = 0.785r = 0.785 x 0.124 = 0.097 in. Distance of c.g. from center of radius, c] = r sin 6/6 = {0.124 sin 45°/[(45/180) x 3.14} = 0.112 in. Computation of Ix: For the first approximation, assume a compression stress of f = F y = 50 ksi in the top fibers of the section and also assume that the web is fully effective. Compression flange: = 1.471 in. w w /t = 1.471/0.060 = 24.52 = 1.28 VE/f 8 = 1. 28 V~29':-'500---:-/5~0 = 31. 09 8/3 = 10.360.673

= (1-(0.22/1.362)]/1.362 = 0.616 be . = 0.616 X 9.192 = 5.662 in. b2 = 5.662/2 = 2.831 in. bI = 5.662/[3 -( -0.960)] = 1.430 in. b I + b2 = 4.261 in. close enough to 4.260 in. thus the solution stabilizes.

Hence we now compute the location ofN .A. and moment of inertia using b I = 1.430 in. and b2 = 2.831 in.

Examples Based on the August 19,1986 Edition ofthe Cold-Fonned Specification

IV-27

Effective section properties about x-axis:

Element

L (in.)

bi b2 + (9.5 -YCg) -0.154 Compression flange Compression stiffener Top 900 corner Top 1350 corner Bottom 1350 corner Bottom 90 0 corner Bottom stiffener Tension flange Sum

1.430 7.333 1.471 0.600 0.195 0.097 0.097 0.195 0.600 1.471 13.489

Y Distance from Top Fiber (in.) 0.869 5.680 0.030 0.257 0.075 0.042 9.458 9.425 9.243 9.470

Ly (in. 2)

Ly2 (in. 3)

1.243 41.651 0.044 0.154 0.015 0.004 0.917 1.838 5.546 13.930 -65.342

1.080 236.578 0.001 0.040 0.001

8.673 17.323 51.262 131.917 446.875

I'I About Own Axis (in. 3 )

0.244 32.860 -

0.009 -

0.009

-- 33.122

Distance of x-axis from top fiber is Ycg = 65.342/13.489 = 4.844 in. Since distance of top compression fiber from neutral axis is greater than one half the beam depth ( = 4.750 in.), a compression stress of 50 ksi will govern as assumed. I~

= = =

Ly2 + I 1 - LY~g 446.875 + 33.122 -13.489 (4.844)2 163.487 in. 3 I

Actual Ix = I~t = 163.487 x 0.060 = 9.809 in.4 Section modulus Se = IxlYcg = 9.809/4.844 = 2.025 in. 3 == SeFy 2.025 x 50 101.25 kip-in.

(Eq. C3.1.1-1)

= = =

1.67

= Mn/O f

= 101.25/1.67 =

60.63 kip-in.

2. Calculation of the effective moment of inertia based on procedure I for deflection determination at the allowable moment: The procedure is iterative: one assumes the actual compressive stress f under this allowable moment. Knowing f, one proceeds as usual to obtain Se and checks to see if (f x Se) equals Ma as it should. If not, reiterate until one obtains the desired level of accuracy [Section B2.1-(b)-(1)]. (a) For the first iteration, assume a compressive stress of f = 30 ksi in the top fibers of the section and that the web is fully effective.

(Eq. C3.1-l)

IV-28

Examples Based on the August 19,1986 Edition of the Cold-Formed Specification

Compression flange: S = 1.28 V~29::"--50"""""'0"""""/3~0 = 40.14 S/3 = 13.38 1.0, it follows that d s = d~ = 0.600 in. (i.e. compression stiffener fully effective). Thus section is fully effective (since web was assumed fully effective) Ycg

= 9.5/2 = 4.750 in. (from symmetry)

1b check if the web is fully effective: fl = [(4.750 -0.154)/4.750] (30) = 29.03 ksi f2 = -29.03 ksi ~ = -29.03/29.03 = -1.000 k = 24.000 A = (1.052/V24) (153.20) V29.03/29500 = 1.032> 0.673 p = [1-(0.22/1.032)]/1.032 = 0:'762 be = 0.762 X 9.192 = 7.004 in. = 7.004/2 = 3.502 in. b2 bi = 7.004/[3 -( -1.000)] = 1. 751 in.

compression portion of the web = y cg - 0.154 = 4.750 - 0.154 = 4.596 in. b i + b 2 = 5.253 in. > 4.596 in. Thus b i + b 2 shall be taken as 4.596 in. This verifies the assumption that the web is fully effective. FUll section properties about x-axis:

Element Web Stiffeners 90° corners 135° corners Flanges Sum

L (in.)

y Distance from Centerline of Section (in.)

9.192 2 x 0.600 = 1.200 2 x 0.195 = 0.390 2 x 0.097 = 0.194 2 x 1.471 = 2.942

4.493 4.675 4.708 4.720

I'I Ly2 (in. 3) _

24.224 8.524 4.300 65.543 102.591

About Own Axis (in. 3) 64.722 0.018 -

-64.740

Examples Based on the August 19,1986 Edition of the Cold-Formed Specification I~ =Ly2+I~

= 102.591 + 64.740 = 167.331 in. 3 Ix = 167.331 (0.060) = 10.040 in.4 Se = Ix/Yell: = 10.040/4.750 = 2.114 in. 3 M = f X Se = 30 X 2.114 = 63.42 kip-in. not equal to Ma = 60.63 kip-in. thus need to reiterate. However, one sees that we need to assume a smaller stress than 30 ksi and hence since the section was fully effective for f = 30 ksi, it will be fully effective for f < 30 ksi. Thus Se = 2.114 in. 3 Therefore, the correct actual f at Ma = Ma/Se = 60.63/2.114 = 28.68 ksi. And Ix = 10.040 in.4 using procedure I for deflection determination. Remark: It was clearly seen that in the calculation of Ma the assumption of the web being fully effective was not true. However, it would be interesting to see the percentage of error if one neglected the partial effectiveness of the web and proceeded with the assumption of a fully effective web. To demonstrate: neglect in the first approximation in the calculation of Ma the partial effectiveness of the web. Thus the whole section is fully effective. Full section properties about x-axis (from part 2): Ix = 10.040 in.4 Se =2.114in. 3 Ma = (2.114 X 50)/1.67 = 63.29 kip-in. 01

7'0

error -

63.29 -60.63 x 100 01'0 60.63 7(

= 4.39% Since percentage of error is small, one could rationalize that in practical cases to get a first-hand quick answer one could assume web being fully effective.

IV-29

IV-30

Examples Based on the August 19,1986 Edition of the Cold-Formed Specification

EXAMPLE NO.5 HAT SECTION Complete Flexural Design, Stiffened Compression Flange

0.101

9.000" 8._69_2_"_ _ _ _ _ _ _

if-c.. . - -_ _ _ _ _ _ _ _ _

R=3/32"

X--+---H--_· - - - - . - - - - - -

--._--

-4+---X

~~==~~~~~=*~

0.079" 0.075"

1. Steel: F y = 50 ksi. 2. Section: As shown in sketch. 3. Span: L = 8 ft., with simple supports, no overhang, and 6-in. support bearing lengths. 4. Loading: Live = 300 lb/ft.; Dead = 20 lb/ft.

Given:

Required: Check adequacy of section for: 1. Bending moment 2. Shear 3. Web Crippling 4. Deflection Solution: 1. Properties of 90° Corners: Radius to centerline, r = R + t/2 = 3/32 + 0.060/2 = 0.124 in. Length of arc, u = 1.57r = 1.57(0.124) = 0.195 in. Distance of c.g. from center of radius, c = 0.637r = 0.637(0.124) = 0.079 in. I of corner about its own centroidal axis is negligible Equations referenced from p. 111-7 of Supplementary ~nformation I

2. Nominal Section Strength (Section C3.1.1) (a) Procedure I-Based on Initiation of Yielding Computation of lx, fIrst approximation: • Assume a compressive stress of f = F y = 50 ksi in the top fibers of the section . • Also assume web is fully effective. Element@}: hit = 3.692/0.060 = 61.53 < (h/t)max = 200 OK [Section B1.2-(a)] Assumed fully effective

3.000"

IV-31

Examples Based on the August 19,1986 Edition of the Cold-Formed Specification

Element@: wit = 8.692/0.060= 144.90.673 p = (1-0.22/2.431)/2.431 = 0.374

(Eq. B2.1-3) (Eq. B2.1-6)

bd =pw

= 0.374 (8.692) 3.251 in.

Element

L Effective Length (in.) 2 x 0.596 = 4 x 0.195 = 2 x 2.692 = 2 x 3.692 =

1.192 0.780 5.384 7.384 3.251 2 x 0.195 = 0.390 18.381

1 2 3 4 5 6 Sum

I'1

y Distance from Thp Fiber (in.) 3.548 3.925 3.970 2.000 0.030 0.075

Ly (in. 2)

Ly2 (in. 3)

4.229 3.062 21.375 14.768 0.098 0.029 -43.561

15.005 12.016 84.857 29.536 0.003 0.002 141.419

About Own Axis (in. 3) 0.035 -

8.388 -

-8.423

Distance of neutral axis from top fiber, Ycg = Ly/L = (43.561/18.381) = 2.370 in.

= Ly2+ I~ -LY~g = 141.419 + 8.423 -18.381 (2.370)2 = 46.60 in. 3 Actual letT = tI~tT = (0.060) (46.60) = 2.80 in.4 Check Web • Should be fully effective

-0.154" fc=30 ksi

~=.-=

-+---...- - -

N.A.

----~---------

I) fl f2

= (2.216/2.370) (30) = 28.05 ksi (compression) = (1.476/2.370) (30) = 18.68 ksi (tension)

IV-35

Examples Based on the August 19,1986 Edition of the Cold-Formed Specification

= f2/fl = -18.68/28.05 = -0.665 = 4 + 2 (1 - tV )3 + 2 (1 - tV ) = 4 + 2 [1-( -0.665»)3 + 2 [1-( -0.665)] = 16.56

CEq. B2.1-4)

f=fl = (1.052/Yk) (w/t) v'f/E , = (1.052/YI6.56) (61.53) V28.05/29500 = 0.491 For A 2.216 (compressive portion of web)

Therefore, web is fully effective. = leff/Ycg=2.80/2.370= 1.18 in.3

Seer Mf =o.6F y

= SerlO.6F y) =(1.18)(30) = 35.4 kip-in.

10 determine leer at M = 31.1, extrapolate using

CD M =52.0, I =2.56in.4 @ M=35.4, I =2.80in. 4 @M=31.1,1=? (31.1-35.4)/(1 -2.80) = (35.4 -52.0)/(2.80 -2.56) -4.30 = -69.17 (1-2.80) 0.0622 = 1-2.80 1= 2.86 in.4

M (kip-in.)

60 50 40 30 20 10

Use I = 2.86 in.4 in deflection calculations

0 0

Deflection = 5wL4/384EI

1.0

2.0

3.0

(b) Procedure II

(Eq. B2.1-10)

Ac = 0.2J6+ 0.328(w/t) v'Fy!E = 0.256 + 0.328(144.9) V""'-50-/2-9-500= 2.213

Computation of left'; Check case of f = F y X =3.138 (from pg. IV-31) For A>Xc p = (0.41 + 0.59 v'F y!r'-O.22/X)/X p = (l-O.22/X)/X p = 0.296, which is the same value for ,Load Capacity Determination

(Eq. B2.1-9)

IV-36

Examples Based on the August 19,1986 Edition of the Cold-Formed Specification

Computation of leff; Assume a compressive stress f= 0.6F y = 30 ksi in top fiber of section

Note: Web is fully effective A = 2.431 (from pg. IV-34) For A>Ac p = [0.41 + 0.59 YF y/f -(0.·22/A) ]/A

(Eq. B2.1-9)

= [0.41 + 0.59 Y50/30 -(0.22/2.431)]/2.431 = 0.445 For A>0.673 bd = pW = 0.445 (8.692) = 3.868 in.

Element

L Effective Length (in.)

1 2 3 4 5 6 Sum

2 x 0.596 = 1.192 4 x 0.195 = 0.780 2 x 2.692 = 5.384 2 x 3.692 = 7.384 3.868 2 x 0.195 =0.390 18.998

(Eq. B2.1-6)

y Distance from Top Fiber (in.) 3.548 3.925 3.970 2.000 0.030 0.075

Ly (in. 2)

Ly2 (in. 3 )

4.229 3.062 21.375 14.768 0.116 0.029 -43.579

15.005 12.016 84.857 29.536 0.004 0.002 141.420

I'1 About Own Axis (in. 3 ) 0.035

8.388 -

- 8.423

Distance of neutral axis from top fiber, Ycg = Ly /L = 43.579/18.998 = 2.294 in. = Ly2 + I~ - LY~g = 141.420 + 8.423 -(18.998) (2.294)2 = 49.87 in. 3

I;rr

Actual leff = tI;ff = (0.06) (49.87) = 2.99 in.4 = leff/Ycg = 2.99/2.294 = 1.30 in. 3

M f =o.6Fy

= Ser~0.6F y) = (1. 30) (30) = 39.0 kip-in.

To determine leffat M = 31.1, extrapolate using

CD M = 52.0, I = 2.56 in.4 @ M=39.0, 1=2.99in. 4 @M=31.1,1=? (31.1-39.0)/(1 -2.99) = (39.0 -52.0)/(2.99 -2.56) -7.9 = -30.23(1-2.99) 0.26 = 1-2.99 1= 3.25 in.4 Use I = 3.25 in. 4 in deflection calculations Deflection = 5w L4 /384EI

Examples Based on the August 19,1986 Edition of the Cold-Fonned Specification

IV-37

1. Determine Properties of 90° Corners

2. Nominal Section Strength (Section C3.1.1)

Assume: 1. Compressive stress in top fiber, f= F y 2. Web fully effective

Check web depth to thickness ratio (Section Bl. 2)

Determine compression flange properties: 1) wit (Section B1.1) 2) k [Section B2.1 (a)] 3) b [Section B2.1 (a)]

Calculate Section properties: Ycg' Ix

Assume new value of compressive stress

-----II~

(continued on next page)

IV-38

Examples Based on the August 19,1986 Edition of the Cold-Fonned Specification

Calculate AI' A2

3. Allowable Bending Moment (Section C3.1)

Check if Mmax applied < Ma ------tl~

(continued on next page)

Examples Based on the August 19,1986 Edition of the Cold-Fonned Specification

4. Strength for Shear Only (Section C3.2)

Va by Part (b)

Va by Part (a)

Check if Va applied 38 (Case III) Ia = t4 {[128(bo/t)/S] -285} = 0.00180 in. 4

= 0.00345 in. 4 (from pg. IV-42)

= 3(18/ l a)113 + 1 s; 4

(Eq. B4.1-9)

(Eq. B4.1-10)

Since lalla> 1, k = 4

wit

= 68.30

= (1.052/Yk) (w/t)

v'f7E,

f=25.24ksi

Examples Based on the August 19,1986 Edition of the Cold-Fonned Specification

IV-47

= (1.052/\1'4) (68.30) V25.24/29500 = 1.051

For A>0.673 p = (1-0.22/A)/A = (1-0.22/1.051)/1.051 = 0.752 b

(Eq. B2.1-3)

(Eq. B2.1-2)

= pw

= 0.752(4.098) = 3.082 in. Stiffener, Element ®: As = A~(lJla) ~ A' s

(Eq. B4.1-11)

Since Is/Ia> 1 As =A~ = 0.0888 in. 2 Ls = As/t = 0.0888/0.060 = 1.480 in.

Element

L Effective Length (in.)

1 2 3 4 5 6 7 Sum

2 x 0.596 = 1.192 4 x 0.195 = 0.780 2 x 2.692 = 5.384 2 x 3.692 = 7.384 2 x 3.082 = 6.164 2 x 0.195 = 0.390 Stiffener 1.480 22.774

y Distance from Thp Fiber (in.) 3.548 3.925 3.970 2.000 0.030 0.075 0.329

Ly (in. 2)

Ly2 (in. 3 )

4.229 3.062 21.375 14.768 0.185 0.029 0.487 -44.135

15.005 12.016 84.857 29.536 0.006 0.002 0.160 141.582

I'1 About Own Axis (in. 3 ) 0.035 -

8.388 -

0.058 8.481

Distance of neutral axis from top fiber, Ycg = (Ly /L) = (44.135/22.774) = 1.938 in. = Ly2+ I~ -LY~g = 141.582 + 8.481-22.774(1.938)2 = 64.53 in. 3

Actual letT = tI~ff = (0.060) (64.53) = 3.87 in.4 Seff = [leff/(4 -YCg)] = [3.87/(4 -1.938)] = 1.88 in. 3 Mr=25.24 Use I

ksi

= (1.88) (25.24) = 47.5 kip-in. Close enough

= 3.87 in. 4 in deflection calculations

7. Comparison of sections with and without intermediate stiffeners

Section

(in.2)

Allowable Moment Capacity (kip-in.)

No Stiffener Stiffener

1.43 1.49

31.1 49.7

Thtal

Area

Increase in weight = [(1.49 -1.43)/1.43] x 100% = 4.2% Increase in moment capacity = [(49.7 -31.1)/31.1] x 100% = 59.8%

Examples Based on the August 19,1986 Edition of the Cold-Formed Specification

IV-48

EXAMPLE NO.7 HAT SECTION Inelastic Reserve

~0.323"---..I" I

4.500"

It---.~3.8-=----54"~·I 'I '0

R=3/16"

I T

0.135" -0.162"

-0.161" 1.670"

1.347" 7.570"

1. 2. 3. 4.

Given:

Steel: F y = 50 ksi. Section: Shown in sketch. Top flange continuously supported. Span = 8 ft. (simply supported).

Required: Determine flexural strength of section. Solution:

1. Properties of 90° Corners: Radius to centerline, r = R + t/2 = 3/16 + 0.135/2 = 0.255 in. Length of arc, u = 1.57r = 1.57(0.255) = 0.400 in. Distance of c.g. from center of radius, c = 0.637r = 0.637(0.255) = 0.162 in. I' of comer about its own centroidal axis = 0.149r3 = 0.149(0.255)3 = 0.003 in. 3. This is negligible. Equations referenced from p. III -7 of Supplementary Information 2. Nominal Section Strength (Section C3.1.1) (a) Procedure I-Based on Initiation of Yielding Computation of Ix, fIrst approximation: • Assume a compressive stress of f = F y = 50 ksi in the top fibers of the section . • Assume web is fully effective. Element@: hit = 2.354/0.135= 17.440.673 p = (l-0.22/'A)/'A = (1-0.22/0.22/1.101)/1.101 = 0.727 =pw = 0.727 ( 1. 000 ) = 0.727 in.

(Eq. B2.1-3)

(Eq. B2.1-2)

Element@: Same as element @ in positive bending case b = 1.926 in. Element@: w /t = 2.000/0.060 = 33.33 < 60 OK [Section B1.1-(a)-(3)] Conservative check.

= 1.28 VE/f = 1.28 Y29500/50 = 31.09

~--

For wit> S Ia =t4 {[115(w/t)/S]+5} = (0.060)4 {[115 (33.33)/31.09] + 5} = 0.00166 in.4 Is = (d 3t sin2e) /12 = (1.000)3 (0.060) (sin 75.96°)2/12 = 0.00471 in.4 D

= =

0.121 + 1.000 1.121 in.

D/w

= 1.121/2.000 = 0.561

For 0.25 < D/w < 0.8 k = [ 4.82 -5 (D /w)] (Is/Ia)1I3 + 0.43::s 5.25 -5 (D /w)

(Eq. B4.2-9)

[4.82 -5(D/w)] (If;/Ia) 1/3 + 0.43 = [4.82 -5(0.561)] (0.00471/0.00166)113 = 2.856 5.25 -5(D/w) = 5.25 -5(0.561) = 2.445 k = 2.445 'A

= (1.052/Vk) (w/t) Vf/E = (1.052/Y2.445) (33.33) V50/29500 = 0.923

(Eq. B2.1-4)

IV-58

Examples Based on the August 19,1986 Edition of the Cold-Fonned Specification

For A>0.673 P = (1-0.22/A)/A = (1-0.22/0.923)/0.923 = 0.825

(Eq. B2.1-3)

b=pw = 0.825(2.000) = 1.650 in. Element®: Is = 0.00471 in. 4 (calculated previously) Ia = 0.00166 in. 4 (calculated previously) d = 1.000 in. Assume max stress in element, f = F y = 50 ksi although it will be actually less. k = 0.43 wit = 1.000/0.060 = 16.670.673 p = (1-0.22/A)/A = (1-0.22/1.101)/1.101 = 0.727 b

(Eq. B2.1-3)

(Eq. B2.1-2)

=pw = 0.727 (1.000) = 0.727 = 0.727 in. = d~ (ls/Ia):5 d~

(Eq. B4.3-11)

Since Is/Ia> 1 d s = d~ = 0.727 in. I~ = (d s)3 sin26/12 = (0.727)3 (sin 75.96°)2/12 = 0.030 in. 3 Distance of centroid of reduced section from top fiber, y = 4 -0.147 -(0.727/2) cos 14.04° = 3.500 in. y Distance from Top Fiber (in.)

Element

L Effective Length (in.)

1 2 3 4 5 6 7 8 Sum

0.727 5 x 0.206 = 1.030 4 x 3.821 = 15.284 2 x 2.000 = 4.000 1.926 4 x 0.206= 0.824 0.727 1.650 26.168

Distance of neutral axis from top fiber,

Ycg

3.970 3.928 2.000 0.030 3.970 0.072 3.500 3.970

Ly (in. 2)

Ly2 (in. 3)

2.886 4.046 30.568 0.120 7.646 0.059 2.545 6.551 -54.421

11.458 15.892 61.136 0.004 30.355 0.004 8.906 26.005 153.760

I'1 About Own Axis (in. 3) -

17.500 -

0.030 -

17.530

= (Ly/L) = (54.421/26.168) = 2.080 in.

Since the distance of the top compression fiber from the neutral axis is greater than onehalf the deck depth, a compressive stress of F y will not govern as assumed. The compressive stress will be slightly less.

Examples Based on the August 19,1986 Edition of the Cold-Fonned Specification

IV-59

(:)

co o N 2.080 ( 0 k ') f1=1.920 5 Sl =54.17 ksi>Fy

fc =50ksi

Computation of Ix, second approximation: • Assume a compressive stress of f= 45 ksi • Assume web is fully effective. Element®: wit = 16.67 k

= 0.43

= (1.052/Yk) (w It) v'f7E = (1.052/v'0.43) (16.67) Y'--45-/2-9-500= 1.045

For p

(Eq. B2.1-4)

~>0.673

= (1-0.22/~)/~ = (1-0.22/1.045)/1.045 = 0.756

(Eq. B2.1-3)

pw = 0.756 (1.000) = 0.756 in.

(Eq. B2.1-2)

Element@: wit = 33.33

= (1.052/V'k) (w/t) Vf/E = (1.052/V4) (33.33) Vr--45--:-/2-9-50-0 = 0.685

For

(Eq. B2.1-4)

~>0.673

= (1-0.22/~)/~ = (1-0.22/0.685)/0.685 = 0.991

(Eq. B2.1-3)

= pw

(Eq. B2.1-2)

= 0.991 (2.000) = 1.982 in. Element®: wit = 33.33 S

vE7f

= 1.28 = 1. 28 Y.-29l...-500----,-/4-5 = 32.77

(Eq. B4-1)

For w/t>S

= t4 [115(w /t)/S] + 5

(Eq. B4.2-13)

IV-60

Examples Based on the August 19,1986 Edition of the Cold-Formed Specification = (0.060)4 {[115(33.33)/32. 77] + 5}

= 0.00158 in.4 Is = 0.00471 in.4 (calculated previously) D = 1.121 in. (calculated previously) D/w = 0.561 (calculated previously) For 0.250.673 p = (l-0.22/A)/A = (1-0.22/1.045)/1.045 = 0.756 b

=pw = (0.756) (1.000) = 0.756 in. = 0.756 in. = d~ (Is/Ia) :::; d~

Since Ig/Ia> 1 d s = d~ = 0.756 in. I~ = (dg)3 sin28/12 = (0.756)3 (sin 75.96°)2/12 = 0.034 in. 3 Distance of centroid of reduced section from top fiber, y

(Eq. B2.1-4)

= 4 -0.147 -(0.756/2) cos 14.04 = 3.486 in.

(Eq. B2.1-3)

(Eq. B2.1-2)

(Eq. B4.2-11)

Examples Based on the August 19,1986 Edition of the Cold-Formed Specification

Element

L E ffecti ve Length (in.)

1 2 3 4 5 6 7 8 Sum

0.756 5 x 0.206 = 1.030 4 x 3.821 = 15.284 2 x 2.000 = 4.000 1.982 4 x 0.206= 0.824 0.756 1.710 26.342

y Distance from Top Fiber (in.) 3.970 3.928 2.000 0.030 3.970 0.072 3.486 3.970

IV-61

Ly (in. 2)

Ly2 (in. 3 )

3.001 4.046 30.568 0.120 7.869 0.059 2.635 6.789 -55.087

11.915 15.892 61.136 0.004 31.238 0.004 9.187 26.951 156.327

Distance of neutral axis from top fiber, Ycg = Ly /L = 55.087/26.342 = 2.091 in.

2.091 ( k ') ft= 1.909 45 SI

o o

=49.29 ksi Satisfactory

fc =45ksi

Check Web 0.147"

_I----r-----

:.::== =--.=.

c;;

o C\i

N.A.

'/ = =~---------'-----

.&._----'

fc= 45 ksi

0.147"

= (1.762/1.909) (45) =41.53 ksi (compression) = (1.944/1.909) (45) = 45.83 ksi (tension)

= f2/fl

= 4 + 2 (1 -

= -45.83/41.53 = -1.104 ~ )3 + 2 (1 - ~ )

= 4 + 2 [1-( -1.104))3 + 2 [1-( -1.104)] = 26.84

I'1 About Own Axis (in. 3 ) -

17.500 -

0.034

-- 17.534

IV-62

Examples Based on the August 19, 1986 Edition of the Cold-Formed Specification

= (1.052/v'k) (w/t) vf7E, f=fI = (1.052/V26.84) (63.68) V 41.53/29500 = 0.485 ForA 1. 765 (compression portion of web) Therefore web is fully effective. Check Element (1): Maximum stress in element, f= 41.54 ksi k = 0.43 wit = 16.67

= (1.052/vk) (w/t) vf7E = (1.052/Y0.43) (16.67) V~41-.5---3~/2~9--50-0 = 1.003

For A>0.673 p = (1-0.22/A)/A = (1-0.22/1.003)/1.003 = 0.778 b

=pw = (0.778) (1.000) = 0.778 in.

= 0.778 in. = d~ (IJl a) ~ d~

Since Is/Ia> 1 ds = d~ = 0.778 in. I; = (d s )3 sin26/12 = (0.778)3 (sin 75.96°)2/12 = 0.037 in. 3 Distance of centroid of reduced section from top fiber, y = 4 -0.147 -(0.778/2) cos 14.04° = 3.476 in. Determine section properties, but only the properties of element ® have changed aL

= 0.778 -0.756 = 0.022 in. aLy = (0.778) (3.476) -2.635 = 0.069 in. 2 aLy2 = 0.778(3.476)2-9.187 = 0.213 in.a aI~ = 0.037 -0.034 = 0.003 in. 3 Therefore, L = 26.342 + 0.022 = 26.364 in.

(Eq. B2.1-4)

(Eq. B2.1-3)

(Eq. B2.1-2)

(Eq. B4.2-11)

Examples Based on the August 19,1986 Edition of the Cold-Formed Specification

Ly Ly2

= =

IV-63

55.087 + 0.069 = 55.156 in. 2 156.327 + 0.213 = 156.540 in. 3 17.534 + 0.003 = 17.537 in. 3

Distance of neutral axis from top fiber, Ycg = Ly /L = 55.156/26.364 = 2.092 in.

= (2.092/1.908)(45) = 49.34ksi = 50ksi OK

= Ly2 + I~ -

LY~g

156.540 + 17.537 -26.364(2.092)2 = 58.70 in. 3

Actual Ix = =

tI~

(0.060) (58.70)

= 3.52 in.4 = I)Ycg = 3.52/2.092 = 1.68 in. 3

= =

SeFy (1.68) (50) = 84.0 kip-in.

(Eq. C3.1.1-1)

Mn/Of 84.0/1.67 = 50.3 kip-in.

(Eq. C3.1-1)

= =

5. Moment of Inertia for Deflection Determination-Negative Bending Computation of I eff , first approximation: • Assume a compressive stress of f = 27 ksi in the bottom fiber of the section . • Since the web was fully effective at a higher stress gradient, it will be fully effective at this stress level. Element (1): wit = 16.67 0.43

= (1.052/v'k) (w/t) v'f/E = (1.052/v'0.43) (16.67) Vr7"".27~/2~9~50:--0

(Eq. B2.1-4)

= 0.809

For A>0.673 p = (1-0.22/A)/A = (1-0.22/0.809)/0.809 = 0.900

(Eq. B2.1-3)

(Eq. B2.1-2)

=pw = (0.900) (1.000)

= 0.900 in. Element@: wit = 33.33 k =4 A

= (1.052/Vk) (w It) v'f/E = (1.052/\14) (33.33) v'' ' '-27---:"/2-9-50-0

(Eq. B2.1-4)

= 0.530 For A0.673 p = (l-0.22/A)/A = (1-0.22/0.809)/0.809 = 0.900 b

=pw

(Eq. B2.1-3)

(Eq. B2.1-2)

= (0.900) (1.000) d~

= 0.900 in. = 0.900 in.

= d~ (Is/Ia) :5 d~

Since Is/Ia> 1 d s = d~ = 0.900 in. I~ = (d s )3 sin26/12 = (0.900)3 (sin 75.96°)2/12 = 0.057 in. 3

(Eq. B4.2-11)

Examples Based on the August 19,1986 Edition of the Cold-Formed Specification

IV-65

Distance of centroid of reduced section from top fiber, Y = 4 -0.147 -(0.900/2) cos 14.04° = 3.416 in.

L Element

Effective Length (in.)

1 2 3 4 5 6 7 8 Sum

0.900 5 x 0.206 = 1.030 4 x 3.821 = 15.284 2 x 2.000 = 4.000 2.000 4 x 0.206= 0.824 0.900 1.992 26.930

Y Distance from Top Fiber (in.) 3.970 3.928 2.000 0.030 3.970 0.072 3.416 3.970

Ly (in. 2)

Ly2 (in. 3)

3.573 4.046 30.568 0.120 7.940 0.059 3.074 7.908 -57.288

14.185 15.892 61.136 0.004 31.522 0.004 10.502 31.396 164.641

I'1 About Own Axis (in. 3) -

17.500 -

0.057

-- 17.557

Distance of neutral axis from top fiber, Ycg = Ly /L = 57.288/26.930 = 2.127 in. I~ff

= Ly2 + I~ - LY~g = 164.641 + 17.557 -26.930(2.127)2 = 60.36 in. 3

Actual Ieff = tI~ff = (0.060) (60.36) = 3.62 in.4 = Iefrl(d -YCg) = 3.62/(4 -2.127) = 1.93 in. 3

Seff M fc =27

ksi

= (1.93) (27) = 52.1 ksi > Ma = 50.3 ksi

N .G.

Computation of I eff , second approximation • Assume a compressive stress in the bottom fiber of the section using extrapolation.

(!) f= 45 ksi, M = 84.0 kip-in.

@ f= 27 ksi, M = 52.1 kip-in. @ f=?

M = 50.3 kip-in.

(f -27) (27 -45) = (50.3 -52.1) (52.1-84.0) f=26.0 ksi Element CD: wit = 16.67 k ~

For p

= 0.43 = (1.052/v'k) (w/t) Vf/E

(Eq. B2.1-4)

= (1.052/\1'0.43) (16.67) V'--26-'/2"""""'9-=-500'-= 0.794 ~>0.673

= (1-0.22/)")/~ = (1-0.22/0.794)/0.794 = 0.911

(Eq. B2.1-3)

IV-66

Examples Based on the August 19,1986 Edition of the Cold-Formed Specification

=pw

(Eq. B2.1-2)

= (0.911) (1.000) = 0.911 in.

Element@: Fully effective at f= 27 ksi It will also be fully effective at f= 26 ksi b = 2.000 in. Element@: wit = 33.33

= 1.28 YE/f = 1.28 yr29'--50-0-/2-6 = 43.12

(Eq. B4-1)

ForS/3 1 k = 2.445 A

= (l.052/V'k) (wit) v17E = (l.052/Y2.445) (33.33) Y26/29500

(Eq. B2.1-4)

= 0.666 For A 1 d = 1.000 in. Assume maximum stress in element, f = 26 ksi although it will be actually less. k

= 0.43

wit = 16.67

= (l.052/Yk) (wit) Vf/E

(Eq. B2.1-4)

= (1.052/V0.43) (16.67) V=-26:--:-/2~9~50-:-0 = 0.794 For A>0.673 p = (1-0.22/A)/A = (1-0.22/0.794)/0.794 = 0.911 b

=pw

= (0.911) (1.000) = 0.911 in. d~

= 0.911 in.

Since Is/Ia> 1 ds = d~ = 0.911 in. I~ = (d s)3 sin29/12 = (0.911)3 (sin 75.96°)2/12 = 0.059 in. 3 Distance of centroid of reduced section from top fiber, y = 4 -0.147 -(0.911/2) cos 14.04° = 3.411 in.

(Eq. B2.1-3)

(Eq. B2.1-2)

IV-67

Examples Based on the August 19,1986 Edition of the Cold-Formed Specification

Element

L Effective Length (in.)

1 2 3 4 5 6 7 8 Sum

0.911 5 x 0.206 = 1.030 4 x 3.821 = 15.284 2 x 2.000 = 4.000 2.000 4 x 0.206 = 0.824 0.911 2.000 26.960

y Distance from Top Fiber (in.) 3.970 3.928 2.000 0.030 3.970 0.072 3.411 3.970

I'1 Ly (in. 2)

Ly2 (in. 3)

3.617 4.046 30.568 0.120 7.940 0.059 3.107 7.940 -57.397

14.358 15.892 61.136 0.004 31.522 0.004 10.599 31.522 165.037

About Own Axis (in. 3) -

17.500

0.059

-- 17.559

Distance of neutral axis from top fiber y cg = Ly /L = 57.397/26.960 = 2.129 in. = Ly2+I~-LY~g = 165.037 + 17.559 -26.960(2.129)2 = 60.40 in. 3 Actual Ieff = tI;ff = (0.060) (60.40) = 3.62 in.4 = Iefrl(d -YCg) = 3.62/4 -2.129) = 1.93 in. 3

Seff Mfc =26

ksi

= (1.93) (26) = 50.2ksi = Ma = 50.3ksi OK

Note: A slight adjustment could be made for element ® since the actual maximum stress is less than f = 26 ksi, but the net effect will be negligible. 6. Summary Positive Bending: Ma leff Negative Bending: Ma leff

= 50.3 kip-in. = 3.64 in. 4 = 50.3 kip-in.

= 3.62 in. 4

7. Compute Allowable Uniform Load For a continuous deck over three equal spans, the maximum bending moment is negative and occurs over the interior supports. It is given by: M=0.10OwL2 Therefore, the maximum uniform load is w = M/0.100L2 = 50.3/0.100(10' x 12"/1)2=0.0349 kip/in. w = 0.419 kip/ft. The maximum deflection occurs at a distance of 0.446L from the exterior supports. It is given by: ~

= 0.OO69wL4/EI

This deflection is limited to, ~ = L/240 for live load. Therefore, the maximum live load which will satisfy the deflection requirements is W LL

= EI/240(0.0069)L3 = 29500(3.64)/240(0.0069) (10 x 12)3 = 0.0375 kip/in.

W LL

= 0.450 kip/ft.

IV-68

Examples Based on the August 19,1986 Edition of the Cold-Fonned Specification

w < w LL' therefore allowable bending moment governs. Allowable Uniform Load = 0.419 kip/ft. 8. Check Shear Strength (Section C3.2) kv = 5.34, unreinforced web 1.38 VEKv/Fy = 1.38 V29500(5.34)/50 = 77.46 hit = 3.821/0.060 = 63.68 For h/t< 1.38 VEKjFy Va = 0.38t2 V~FyE = (0.38) (0.060)2 V~5.~34~(~50~)-=-=(2-=-:95~00~) = 3.84k

(Eq. C3.2-1)

Va = (11800 F y/E) ht = (11800) (50/29500) (3.821) (0.060) = 4.59k Va = 3.84k controls (per web) Thtal Va for section: Va = 4(3.84k) = 15.36k The maximum shear force is given by V = 0.600wL = (0.600) (0.419) (10) = 2.51k

= 2.51k < Va =

15.36k OK

9. Check Strength for Combined Bending and Shear (Section C3.3) At the interior supports there is a combination of web bending and web shear. Ma = 50.3 kip-in. Va = 15.36 k

M = 0.100wL2 V = 0.600wL

For unreinforced webs (M/Ma)2 + (V /Va)2:-=; 1.0 Solve for w: {[O.I00w( 10 x 12)2]/50.3}2 + ([0.600w( 10 x 12) ]/15.36}2 = 1.0 819.58w2+ 21.97w2 = 1.0 841.55w2 = 1.0 w = 0.0345 kip/in. = 0.414 kip/ft. Allowable Uniform Load = 0.414 kip/ft. 10. Check Web Crippling Strength (Section C3.4) h

= 3.821 in.

= 0.060 in.

hit = 3.821/0.060 = 63.68 0.705 in., b l + b 2 shall be taken as 0.705 in. This verifies the assumption that the web is fully effective.

= LX2 + 1'1 -

Lx~

=25.895 + 2.374 -12.819(0.998)2 = 15.501 in. 3 Actually = I ~t = 15.501 (0.105) = 1.628 in.4

(Eq. B2.3-2) (Eq. B2.3-1)

Examples Based on the August 19,1986 Edition of the Cold-Formed Specification

IV-92

Mny

= Iy/(3.000 -Xeg) = 1.628/(3.000 -0.998) = 0.813 in.a = SeFy

(Eq. C3.1.1-1)

= 0.813(50)

= 40.65 kip-in.

(b) Section C3.1.2: Mny will be calculated on the basis of the lateral buckling strength. (y-axis is the axis of bending) For the full section: Iy = 1.786in.4 Xeg = X+ t/2 = 0.820 + 0.105/2 = 0.873 in. Sf = Iy/xeg = 1. 786/0.873 = 2.046 in.a My = SfFy (Yield Moment) = 2.046(50) = 102.30 kip-in. Cs A u ex

(Eq. C3.1.2-5)

= + 1.00 = 1.551 in. 2

= 76.93 ksi = 10.26 ksi Ml/M2 = -1.00 (single curvature) CTF = 0.6-0.4(M 1 /M2)

= 0.6 -0.4 ( -1.00) = 1.00

ro j Me

Me Me

= 3.961 in. = 4.568

= CsAaex[j + Cs Yj2 + ro2(uti 0.5 My = 51.15 kip-in. = My[1-(My/4M e)]

(Eq. C3.1.2-8)

= 102.30{1-[102.30/(4 X 1116.77)]}

= 99.96 kip-in. Me/Sf = 99.96/2.046 = 48.86 ksi

Th calculate effective section properties to obtain Se at stress 48.86 ksi, we assume that the webs are fully effective. Compression ~nge: A = (1.052/ 4.00) (70.62) Y48.86/29500 = 1.512>0.673 p = [1-(0.22/1.512)]/1.512 = 0.565 b = 0.565 (7.415) = 4.189 in.

Element

L Effective Length (in.)

Webs Upper qorners Lower Corners Compression Flange Tension Flange Sum

2 x 2.415 =4.830 2 x 0.377 =0.754 2 x 0.377 =0.754 4.189 2 x 0.508 = 1.016 11.543

x Distance from 1bp Fiber (in.) 1.500 0.140 2.860 0.053 2.948

(Eq. C3.1.2-11)

I'1 About

Own Lx (in. 2)

LX2 (in. a)

Axis (in. a)

7.245 0.106 2.156 0.222 2.995 12.724

10.868 0.015 6.167 0.012 8.830 25.. 892

2.347

--2.347

Examples Based on the August 19,1986 Edition of the Cold-Formed Specification

IV-93

Distance from top fiber to y-axis is Xeg = 12.724/11.543 = 1.102 in. Th check if the webs are fully effective (Section B2.3): fl = [(1.102 -0.293)/1.102] (48.91) = 35.91 ksi (compression) f2 = -[(1.898 -0.293)/1.102] (48.91) = -71.24 ksi (tension) '" = -71.24/35.91 = -1.984 k .=" 4 + 2 [1 - ( -1.984)] 3 + 2[ 1 - ( - 1.984) ] = 63.109 ~ = (1.052/Y63.109) (23.00) Y35.91/29500=0.106 0.809 in., b I + b2shall be taken as 0.809 in. This verifies the assumption that the web is fully effective.

= 25.892 + 2.347 -11.543(1.102)2 = 14.221 in. 3 Actually = 14.221(0.105) = 1.493 in.4 = Iy/xeg = 1.493/1.102 = 1.355 in. 3 = MeSe/Sr = 100.07(1.355)/2.046 = 66.27 kip-in. I'y

CEq. C3.1.2-1)

Mny shall be the smaller of 40.65 kip-in. and 66.27 kip-in. Thus = = = = =

40.65 kip-in. 1.67 Mny/Or 40.65/1.67 24.34 kip-in.

(Eq. C3.1-1)

40.65 kip-in. 1.67 40.65/1.67 24.34 kip-in.

8. Cmy = 0.6 -0.4 (M I/M2) ~ 0.4 MI/M2 = -1.00 (single curvature) 0.6 -0.4 ( -1.00) = 1.00> 0.4 Cmy = 1.00 9. Determination of 1/ ay: fie P cr Iy

= 1.92 = 11'2Ely/(~Ly)2 = 1.786 in.4 ~Ly = 1.0(16 X 12) = 192 in. Pcr = [~(29500) (1. 786)]/(192)2 = 14.11 kips l/ny = 1/[l-(OcP/ Pcr)] = 1/[1-(1.92 x 2.5/14.11)] = 1.516

= 0.660

CEq. C5-5)

(Eq. C5-4)

Examples Based on the August 19,1986 Edition of the Cold-Formed Specification

IV-94

10. Check interaction equations: (P /Pa) + (Cmy/May) x (My/a) = (2.500/7.344) + (1.00/24.34) x (5.00/0.660) = 0.340 + 0.311 = 0.651 < 1.0 OK (P/Pao ) + (My/Mayo) = (2.50/30.55) + (5.00/24.34) = 0.082 + 0.205 = 0.287 < 1.0 OK

(Eq. C5-1)

(Eq. C5-2)

Therefore the section is adequate for the applied loads. Solution:

Part (b)

1. FUll section properties are the same as previously calculated in part (a. 1). 2. P a = 7.344K (calculated in part (a»). 3. P/Pa =2.50/7.344=0.340>0.15 Therefore the following interaction equations must be satisfied. (P /Pa) + (CmxM)Maxax) + (CmyMJMayay) ~ 1. 0

(Eq. C5-1)

(P/PaJ + (Mx/Maxo) + (My/Mayo) ~ 1.0

(Eq. C5-2)

4. P ao = 30.55K (calculated in part (a) 4). 5. Determination of Mx (Section C5): The centroidal x-axis is the same for both the full and effective sections. ey = 4.000 in. Mx = Pey = (2.50) (4.000) = 10.00 kip-in. 6. Determination of Max (Section C3): Mnx shall be taken as the smaller of the ultimate moments calculated according to Sections C3.1.1 and C3.1. 2. (a) Section C3.1.1: Mnx will be calculated based on the initiation of yielding First approximation: • Assume a compressive stress of f = F y = 50 ksi in the top fiber of the section . • Assume that the web is fully effective. Compression flange:

= 2.415 in. = 2.415/0.105 = 23.00 = 1.28 v'E/f 8 = 1.28 V~29.!.....-50-0-/5-0 = 31.09 For 8/3 = 10.36 < w /t = 23.00 < S = 31.09 w w /t

= t 4399{[(w/t)/S] -0.33}3 = (0.105)4 (399) [(23.00/31.09) -0.33]3 = 0.003337 in.4

= (0.508)3 (0.105)/12 = 0.001147 in.4

Is/Ia = 0.001147/0.003337 = 0.344

= 0.800 in.

(Eq. B4-1)

(Eq. B4.2-6)

IV-95

Examples Based on the August 19,1986 Edition of the Cold-Formed Specification

D/w = 0.800 in. /2.415 in. = 0.331 w /t = 23.00 < 60 OK

[Section B1.1-(a)-(3)]

For 0.25> D/w = 0.331 3d

Check if distance between bolt hole center and edge of connecting member > 1.5d.

IV-117

Examples Based on the August 19,1986 Edition of the Cold-Formed Specification

IV-118

EXAMPLE NO. 19 FLAT SECTION wI ARC SPOT WELDED CONNECTION

I Visible Diameter of Weld, d = 3/4"

1/16

Given:

3/4" Diameter

1. Steel: F y = 50 ksi, F u = 65 ksi. 2. Total Load, F = 4.6k. 3. Detail of connection shown in sketch.

Required: Design the connection to transmit F = 4. 6k using arc spot welds having % in.

visible diameter.

Examples Based on the August 19,1986 Edition of the Cold-Formed Specification

IV-119

Solution:

1. Weld Dimensions

= 0.75 in.

d da

d-t 0.75-0.06 = 0.69 in. = 0.7d -1.5t but ~ 0.55d = 0.7 (0.75) -1.5 (0.06) = 0.44 = =

(Eq. E2.2-5)

= 0.55(0.75) = 0.41 in. 0.44> 0.41, use de = 0.41 > 3fs in. OK 0.55d

2. Determine number of arc spot welds required. Ca) P = 0.625 d~ F xx

(Eq. E2.2-1)

Using E60 electrode, F xx = 60 ksi P = 0.625(0.41)2 (60) = 6.30k/weld (b) Compute daft = 0.69/0.06 = 11.5 Compute YE/F u = Y29500/65 = 21.3 For daft = 11.5 < 0.815YE/F u = 17.4 P = 2.20 tdaF u = 2.20(0.06) (0.69) (65) = 5.92k/weld P

CEq. E2.2-2)

= 5.92k/weld controls

P a = P /!1 w = 5.92/2.50 = 2. 37k/weld

CEq. E2-1)

Number of welds = 4.6k/(2.37k/weld) = 1.94 welds, use 2. 3. Check edge distance and spacing requirements (a) F u/F y = 65/50 = 1.3> 1.15 For Fu/Fy > 1.15,!1e = 2.0 e

= P /F ut = (4.6k/2)/[ (65) (0.06)] = 0.59 in.

e min = e!1e = (0.59) (2.0) = 1.18 in. 1.25 edge distance> 1.18 OK (b) Edge distance shall not be less than 1.5d. 1.5d = 1.5(0.75) = 1.13, 1.25> 1.13 OK (c) Clear distance between weld and end of member shall not be less than 1.0d. 1.0d = 1 (0.75) = 0.75 in. Clear distance = 1.25 -0.375 = 0.875> 0.75 OK (d) Thinnest connected part, t = 0.060.028

CEq. E2.2-7)

IV-120

Examples Based on the August 19,1986 Edition of the Cold-Formed Specification

EXAMPLE NO. 20 FLAT SECTION w/ARC SEAM WELDED CONNECTION

1/2" x 1W'

--+O+------f-oIf----Widt~

of Weld, d

Examples Based on the August 19,1986 Edition of the Cold-Formed Specification

IV-121

1. Steel: F y = 50 ksi, F u = 65 ksi. 2. Total Load, F = 2.8k. 3. Detail of connection shown in above sketch.

Given:

Required: Design the connection to transmit F

= 2.8k using Arc Seam Welds. Try d = Y2 in.

Solution:

1. Load shall not exceed either p =[(d~/4)+(Lde/3)]2.5Fxx

(Eq. E2.3-1)

Try E60 electrode, F xx = 60 ksi L = 1.5, or maximum 3d, 3(0.5) = 1.5 in.

da = 0.5 -0.06 = 0.44 in.

(Eq. E2.3-3)

de =0.7d-1.5t = 0.7(0.5)-1.5(0.06) = 0.260 in.

(Eq. E2.3-5)

P = {[(0.26)2/4] + [1.5(0.26)/3]}2.5(60) = 22.0k

OR P = 2.5tF u (0.25L + 0.96d a ) = 2.5 (0.06) (65) [0.25 (1.5) + 0.96 (0.44)] = 7.77k

(Eq. E2.3-2)

U sing the lesser P = 7. 77k Pa =7.77/2.5=3.11k>2.8kreq'd

(Eq. E2-1)

2. Determine minimum edge distance in line of force. (a) F u/F y = 65/50 = 1.3> 1.15

= P /F ut = 2.8k/[ (65) (0.06)] = 0.72 in. emin = e!le = (0.72 x 2.0) = 1.44 in.

1.5 edge distance> 1.44 in.

(b) Edge distance shall not be less than 1.5d. 1.5d = 1.5(0.5) = 0.75, 1.5> 0.75 in.

(c) Clear distance between weld and end of member shall not be less than 1.0d 1.0d = 1.0(0.5) = 0.5 in. Clear distance = 1.5 -0.25 = 1.25> 0.5 in.

3. Use arc seam welded connection per sketch with E60 electrode and d = 1/2 in.

(Eq. E2.2-7)

IV-122

Examples Based on the August 19,1986 Edition of the Cold-Formed Specification

EXAMPLE NO. 21 FLAT SECTION wI LAP FILLET WELDED CONNECTION

Ixxxxxxxxxxxxxxxxx

t=0.06"

F=4.0 k

•

Given:

1. Steel: F y = 50 ksi, F u = 65 ksi. 2. Thtal Load, F = 4.0k. 3. Detail of connection shown above in sketch.

Required: Check to see if longitudinal fillet welded connection is adequate to transmit F =4.0k. Solution: 1. L/t = 2/0.06 = 33.33 > 25

For L/t~25, P = 0.75tLFu =0.75(0.06)(2)(65) = 5.85k

(Eq. E2.4-2)

2. Note: t = 0.064.0k OK

(Eq. E2-1)

Examples Based on the August 19,1986 Edition of the Cold-Formed Specification

IV-l23

EXAMPLE NO. 22 FLAT SECTION w/SINGLE FLARE BEVEL GROOVE WELDED CONNECTION

1/8

3.5

1. Steel: F y = 50 ksi, F u = 65 ksi. Total Load, F = 4.0 kips. 2. Detail of connection shown in above sketch. 3. Transverse loading.

Given:

Required: Design the welded connection to transfer F = 4.0 kips. Solution:

1. Solve for P using P a = P /flw = F P

(Eq. E2-1)

= (4.0k) (2.5) = 10.Ok

2. For flare-bevel groove welds, transverse loading, the load P shall not exceed P

0.S33tLF u

Solve for L L = P/0.833tF u = 10.Ok/[O.833 (0.06) (65)] L = 3.0S in. 3. Use 3.5 in. long flare bevel groove weld per sketch. 4. Size of weld 1/8" (1/16 min)

(Eq. E2.5-1)

Examples Based on the August 19,1986 Edition of the Cold-Formed Specification

IV-124

EXAMPLE NO. 23 C·SECTION BRACING UNDER GRAVITY LOADING

30'

-IGiven:

1. 2. 3. 4. 5.

30'

-I·

Steel: F v = 50 ksi. 60 ft. wide building, 20 ft. bays, simply supported purlins on 5-foot centers. Roof slope 1: 12. Same channel as in ex. # 15. Dead and live load: 17.6 psf

Required: Design of bracings of the roof system under gravity loads, using D3.2.1 of Specification. Solution: P = 0.05W W = 17.6 x 30 x 20 = 10560 lbs. P = 0.05 (10560) = 528lbs.

A total restraint force of 528 lbs. must be supplied in each bay. It is up to the designer to decide what devices can be used to supply this force.

Examples Based on the August 19,1986 Edition of the Cold-Fonned Specification

IV-125

EXAMPLE NO. 24

Same roof system as Example 23, with Z-section instead of channel. Z-section is the one used in Example 4.

Given:

Required: Design of bracings of the roof system under gravity loads, using D3.2.1 of

Specification. Solution:

b d t np 9 W

= 1.689 in. = 6.000 in. = 0.060 in. = 7 = 4.76°, tan 9 = 0.083 = 17.6 x 30 x 20 = 10560 lbs.

1. Single span system with restraints at supports. 0.220b1.5 ] P L =0.5 [ npo.72do.9to.6 -tan9 W

(Eq. D3.2.1-1)

] 0.22(1.689)1.5 P L = 0.5 [ 70.72 x 6.0000. 9 X 0.0600.6 -0.0833 10560 P L =2381bs. 2. Single span system with third point restraints: 0.474b1.22 ] P L = 0.5 [ n O. 57 dO. H9 t o.aa -tan9 W

(Eq. D3.2.1-2)

] 0.474 (1.689 )1.22 P L = 0.5 [ 70.57 x 6.0000.H9 x 0.0600.;~~ -0.0833 10560 PI. =3651bs. 3. Single span system with midspan restraint: P L =0.5 [ n

0.224bu2 ] O. 65 d0.H:~ t o.5O -tan9 W

0.224 (1.689)U2 ] PI, = 0.5 [ 70.65 X 6.0000. H;{ X 0.0600.50 -0.0833 10560 P L =3541bs. Each brace will be designed to resist one of the P L forces, determined above, depending on the restraint condition of the span.

(Eq. D3.2.1-3)

IV-126

Examples Based on the August 19,1986 Edition of the Cold-Formed Specification

EXAMPLE NO. 25 WALL PANEL

R=1/8" (TYP)

3.000"

2.000"

14.000"

1. Steel: F y = 50 ksi. 2. Section: as shown in the sketches.

Given:

Required: Section properties for positive and negative bending. Solution:

1. Linear Properties. Refer to Part III, Section 1. Elements ® and @> 90° corners, r = R + t/2 = 0.125 + 0.030/2 = 0.140 in. Length of arc, U = 1.57r = 1.57 x 0.140 = 0.220 in. Distance of c.g. from center of radius, c l = 0.637r = 0.637 x 0.140 = 0.089 in.

0.350"

Element

0.932"

Element® r = 0.140 in. 9 = 45° = 0.785 rad. c l = r sin 9/9 = 0.140 x 0.707/0.785 = 0.126 in. n = 0.350 -2 x 0.140 (I-cos 45°) = 0.350 -0.082 = 0.268 in. lb = 0.268/sin 45° = 0.379 in. la = 9r = 0.785 x 0.140 = 0.110 in. I' (straight portions) = 2 x 1/12 X lb x n2= 2 x 1/12 x 0.379 x 0.2682 = 0.0045 in. 3 I' (Arcs) == 4 x 0.110 x (0.350/2 -0.140 + 0.126)2 = 0.0114in.3 I' = I' (straight portions) + I' (Arcs) = 0.0045 + 0.0114 = 0.0159 in. 3 I = l't == 0.0159 x 0.030 = 0.000477 in.4 Check adequacy of intermediate stiffener according to Section B5. For wit == (3.000 -0.140 -0.932/2)/0.030 = 79.8 (Element@) I min = [3.66t4 V(w /t)2 -4000/F Yo] but not less than (18.4t4) = 0.000015 in. 4 I min = [3.66 X (0.030)4 V(79.8)2 -4000/50] = 0.000235 in.4 < 0.00477 in.4 satisfactory Let = 4la + 2lb = 0.440 + 0.758 == 1.198 in.

(Eq. B5-1)

Examples Based on the August 19,1986 Edition of the Cold-Formed Specification

IV-127

R = 1/8"

Element®

L Length (in.) 90° Corner Straight Segments Semi-Circle Sum

0.220 0.500 0.440 1.160

Y Distance from Center of Top Flange (in.) 0.140 -0.089 = 0.051 0.265 0.390 + 0.089 = 0.479

l'1 About Own Axis (in. 3)

Ly (in. 2)

Ly2 (in. 3 )

0.011 0.133 0.211 0.355

0.035 0.101 -0.136

0.003 -

0.003

Ycg = 0.355/1.160 = 0.306 in. I~ = I~ + Ly2 - LY~g = 0.003 + 0.136 -1.160 x 0.306 2= 0.139 -0.109 = 0.030 in. 3 Ix = I~t = 0.030 x 0.030 = 0.00090 in.4 2. Section Modulus for Load Determination-Positive Bending Since the neutral axis will be below the center of the cross section, the compression stress will govern. Element ® from Section B3.1 (a) since stress gradient is in opposite direction w k f ~ p

= = = = = =

0.25 in. 0.43 F y [see B2.1a(1)] (1.052/Y0.43) (0.25/0.030) Y50/29500 = 0.550

(Eq. B2.1-4)

Ifor~$0.673

(Eq. B2.1-1)

w=0.25 in.

Element@ from Section B4.2 (a) wit = [3 -3(0.140)]/0.030 = 86 f= Fy S = 1.28 VE/f= 1.28 V29500/0.6(50) =40.138 D/w = [0.25 + 2(0.125) + 1.5(0.030)]/[3 -3(0.140)] = 0.211 =1/3 forw/t>S n Ia = (0.030)4 [115(86/40.138) + 5] = 0.000204

(Eq. B4-1)

(Eq. B4.2-13)

= I~ =

= 3.57(0.003/0.000204)113 + 0.43 = 9.176 >4

(Eq. B4.2-10)

= (1.052/v4) (86) V50/29500 = 1.862

(Eq. B2.1-4)

= (1-0.22/1.862) (1/1.862) = 0.474

(Eq. B2.1-3)

= pw = 0.474[3 -3(0.140)] = 1.233 in.

CEq. B2.1-2)

= A~ = 0.348

CEq. B4.2-12)

0.003

in. 2

for Is ~ Ia

IV-I28

Examples Based on the August 19,1986 Edition of the Cold-Formed Specification

Element ® from Section B3.2 (a) w = 0.415 -0.030 -0.125 = 0.26 in. k = 0.43 f< Fy ~

p b

Use F y as conservative value.

= (1.052/V0.43) (0.26/0.030) Vr-50--:/--29-50-0 = 0.572 = 1for~!S0.673 = w = 0.26 in.

(Eq. B2.1-4) (Eq. B2.1-1)

Element @ from Section B4.2 (a) wit =[2-2(0.140)]/0.030=57.333 . f=F y [see B2.1a(1)] S = 1.28 VE/f= 1.28 V29500/0.6(50) = 40.138 D/w = [0.415 -0.5(0.030)]/[2 -2(0.140)] = 0.233 for w/t>S n = 1/3 Ia = (0.030)4 [(57.333/40.138) (115) + 5] = 0.000137 for w /t ~ S Is = (1/12) bh3= (1/12) (0.030) (0.415 -0.125 -0.030)3 = 0.000044 k = 3.57 (O.~0044/0.000137)1I3 + 0.43 = 2.875 < 4 ~ = (1.052/ 2.875) (57.333) V50/29500 = 1.464 p = [1-(0.22/1.464)] (1/1.464) = 0.580 b = pw = 0.580[2 -2(0.140)] = 0.998 in. d s = (Is/Ia)d~ = (0.000044/0.000137) (0.26) = 0.084 in.

(Eq. B4-1)

(Eq. B4.2-13) (Eq. B4.2-10) (Eq. B2.1-4) (Eq. B2.1-3) (Eq. B4.2-11)

Element

Ly2

I'1

1 2 3 4 5 6 7 8 9 10

1.160 1.233 0.998 0.660 3.440 4.788 2.396 2.068 0.260 0.440 17.443

0.321 0.015 0.015 0.066 1.015 2.015 1.840 2.015 0.285 1.964

0.372 0.018 0.015 0.044 3.490 9.650 4.410 4.170 0.074 0.864 -23.107

0.120

0.030

0.003 3.550 19.440 8.110 8.400 0.021 1.700 -41.344

0.849 -

-0.879

= 23.107/17.443= 1.325 in. = 41.344 + 0.879 -17.443(1.325)2 = 11.600 in. 3 Ix = I~t = 11.600(0.030) = 0.348 in.4 Sx = Ix/Y cg = 0.163/1.325 = 0.123 in. 3

Ycg

Mn = SeFy = 0.123(50) = 6.150 kip-in. Ma = Mn/Or= 6.150/1.67 = 3.683 kip-in.

(Eq. C3.1-1)

Element @ from Section B2.3 (a) Ycg = 1.325 in. fl = [(1.325 -0.125 -0.030)/1.325] (50) = 44.199 f2 = -[(2.030 -0.125 -0.030 -1.325)/1.325] (50) = 20.755

= f2/fl = -20.755/44.199= -0.470 = 4 + 2(1 + 0.470)3 + 2(1 + 0.470) = 13.293 >4

(Eq. B2.3-4)

= (1.052/Y13.293) {[2.030 -2 (0. 155)]/0.030} V44.151/29500 = 1.640

(Eq. B2.1-4)

= (1-0.22/1.640) (1/1.640) = 1.025

(Eq. B2.1-3)

= pw = 1.025(1. 720) = 1. 763, use 1. 72 = w

(Eq. B2.1-2)

Thus element @ is fully effective so properties above are correct. If be < 1. 72 then properties should be recomputed for an exact solution.

Examples Based on the August 19,1986 Edition of the Cold-Fonned Specification

IV-129

= 0.947 in. = 1.370 -0.030 -0.125 = 1.215

hI + b2

Revise section properties for loss of (1.215 -0.947) (0.030) (2) = 0.0161 in. 2 for element

@ if greater accuracy is required. 3. Moment of Inertia for Deflection Determination-Positive Bending Element@ from Section B4.2 (h) f = F y/1.67 = 30 ksi w = 3 -3(0.140) = 2.580 in. ~e = 0.256 + 0.328(2.580/0.030) v'50/29500 = 1.417 k =4 ~ = (1.052/\14) (2.580/0.030) v'30/29500= 1.443 p

(Eq. B2.1-10) (Eq. B2.1-4)

[0.41 + 0.59 Y50/30 - (0.22/1.443)] (1/1.443) = 0.706

(Eq. B2.1-9)

= pw = 0.706(2.580) = 1.821 in. As = A~ = 0.348 in. 2 b

(Eq. B2.1-2) (Eq. B4.2-12)

Element@ from Section 4.2 (b) f = 50/1.67 = 30 ksi w = 2 -2(0.140) = 1.720 in. ~e = 0.256 + 0.328(1. 720/0.030) Y50/29500 = 1.030 k = 2.875 ~ = (1.052/Y2.875) (1. 720/0.030) v'30/29500 = 1.134

(Eq. B2.1-10) (Eq. B2.1-4)

= [0.41 + 0.59 Y50/30 -(0.22/1.134)] (1/1.134) = 0.862

(Eq. B2.1-9)

b = pw = 0.862 (1. 720) = 1.483 in.

(Eq. B2.1-2)

ds = 0.084 in. Element

1 2 3 4 5 6 7 8 9 10

1.160 1.821 1.483 0.660 3.440 4.788 2.396 2.068 0.260 0.440 18.516

0.321 0.015 0.015 0.066 1.015 2.015 1.840 2.015 0.285 1.964

0.372 0.027 0.022 0.044 3.490 9.650 4.410 4.170 0.074 0.864 -23.123

Ly2

I'1

0.120

0.030

0.003 3.550 19.440 8.110 8.400 0.021 1.700 -41.344

0.849 -

-0.879

= 23.123/18.516= 1.249 in. = 41.344 + 0.879 -18.516 (1.249)2 = 13.338 in. 3 Ix = I~t = 13.338(0.030) = 0.400 in.4

Yeg I~

4. Section Modulus for Load Determination-Negative Bending Since the N.A. may be closer to the compression flange than to the tension flange, the compression stress is unknown, and therefore the effective width of the compression flange and section properties must be determined by an iterative method. Elements (!), @, @, @, @, ® and ~ do not vary with stress level.

Examples Based on the August 19,1986 Edition of the Cold-Formed Specification

IV-130

Element

L (in.)

1 2 3 4 5 9 10 Sum

1.160 2.580 1.720 3 x 0.220 = 0.660 2 x 1. 720 = 3.440 0.260 2 x 0.220 = 0.440 10.260

Y Distance from Top Fiber (in.) 0.321 0.015 0.015 0.066 1.015 0.285 1.964

I'1 Ly (in. 2)

Ly2 (in. 3)

0.372 0.039 0.026 0.044 3.490 0.074 0.864 -4.909

0.119 0.001 -

0.003 3.550 0.021 1.700 5.394

About Own Axis (in. 3) 0.030 -

0.849 -

-0.879

Element ® from Section B5 (d) Assume Ycg= 1.300 in. = [(2.030 -1.300)/1.300] (50) = 28.077 ksi f wit = [3 -0.140 -0.5(0.932)]/0.030 = 79.8 k=4 ~ = (1.052/\/'4) (79.8) Y28.077/29500= 1.295

(Eq. B2.1-4)

= (1-0.22/1.295) (1/1.295) = 0.641

(Eq. B2.1-3)

= pw = 0.641 (2.394) = 1.535 in.

(Eq. B2.1-2)

= 0.030[(1.535/0.030) -0.10(79.8 -60)] = 1.476 in.

(Eq. B5-3)

Element ® from Section B5 (d) 60r~ Z , I I

•

-----,H

_ _~_ _- L______________~~_ _~I________~__~~________~ _ _ _

' - Flange of C-shaped Section ~------~----------------~~------------------------~--Fastener "Panel Support

w -{a) Elevation

jBeam

jPanel

I i'

/ Connectors

------

.........

I I I

1--1 f::1

I I "I I

Support

I /

Panel Rib (if any) ~

I I --j ---I

I I ~/ ~ I %- - %

(b) Plan

Figure 3 Test Specimen and Horizontal Test Setup

2.7 Rotational-Lateral Stiffness-The rotational-lateral stiffness, K, is equal to the total lateral load applied on the unattached flange of the test beam, divided by the length dimension of the beam, LR (Figure 3b), and divided by the lateral deflection of the unattached flange of the beam at that load level. Thus, the units of K are: kips of lateral load per inch of beam length per inch of deflection, or klin.lin. 3. Materials 3.1 Components of the test specimen(s) shall be measured, and the component suppliers shall be identified. 3.2 Physical and material properties of the panel and beam shall be determined according to the latest edition of Specification ASTM E370 or other applicable standards.

4. Test Specimens 4.1 The overall panel width, W (Figure 3), of the specimen shall be such that the dial-gage support and the specimen support are each separated from the beam by a distance, WI' not less than the largest of the following distances: .(a) 1.5 times the overall panel depth PD' (b) the overall width of the attached beam flange WF , and (c) the fastener spacing along the flange of the beam, F s. For ribbed panels, WI shall also exceed two times the width of the attached flat of the panel.

Test Procedures for use with the August 19,1986 Edition of the Cold-Formed Specification

VII-9

4.2 The clamped width of the specimen, Wc' shall be at least equal to two times the panel depth, but not less than 2 inches. 4.3 The end dimension, WE' shall be long enough to conveniently attach a dial gage or an extenso meter to the end of the panel. 4.4 The minimum overall panel width shall be equal to: W=WE +2W 1 +W F +WC

(1)

4.5 The minimum beam and panel length, L B , of the test specimen shall not be less than the largest of (a) two times the maximum connector spacing, F s, used in actual field installations, or (b) the nominal coverage width of the panel. The specimen shall contain at least two fasteners in each line of connections along the beam. 4.6 Each specimen shall be assembled under the supervision of a representative of the testing laboratory, either at the manufacturer's facilities or at the testing laboratory. 4.7 Each specimen shall be assembled from new material; i. e., materials not used in previous test specimens, and in accordance with manufacturer's specifications. 4.8 The fabrication and field installation procedures specified for the overall assembly, and the tools used, shall also ~e used in the specimen construction as much as possible. 4.9 Drilled or punched pilot holes in the panels or beams shall be the same as those used in field installations. 5. Test Setup

5.1 The test specimens may be tested in a horizontal or vertical position (Figure 3 and Figure 4, respectively). The zero-load readings of the deflection-measuring device(s) shall be recorded.

Panel~

Load, P,

I I figure 4 VertIcal Teat Setup

'---suPPOrt

VII-lO

Test Procedures for use with the August 19,1986 Edition of the Cold-Formed Specification

5.2 The clamped end of the panel shall be the only support of the test specimen. 5.3 When the test specimen panel is a hollow-core, corrugated, or trapezoidal panel, voids of the clamped regions shall be filled with filler materials such as wood, gypsum, or similar filler materials to ensure that the clamped overall depth of the panel is reasonably maintained. For foam-filled sandwich panels, if necessary, the filler material over the distance We may be replaced with wood, gypsum, or similar filler materials. 5.4 Loads applied to the unattached flange shall be introduced as close as possible to the extreme fiber of the beam, or at the intersection of the outer faces of the unattached flange and the web. 5.5 If the beam does not have a flat face perpendicular to the panel at the locations where the load is to be applied and the lateral displacement is to be measured, brackets are to be mechanically attached to the beam web to provide a nat surface. Figure 5 shows a typical application of a load bracket and/or dial gage bracket. The attachment of either bracket shall be accomplished such that the bracket does not stiffen the beam, or reduce its distortion. 5.6 The total lateral load applied, P, shall be distributed over several locations, if necessary, to reduce variations in the lateral deflection along the length of the unattached flange. 5.7 The load application shall be accomplished by chain or wire, and the necessary precautions shall be taken to ensure that the direction of the applied load remains essentially parallel to the original plane of the panel (Figure 5).

Bracket, Detail A Load, P (Parallel to Original Panel Position)

[==============--=~~----~~~ Original Panel Position

P Load

Detail A

Figure 5 Dial Gage and Load Bracket

Test Procedures for use with the August 19,1986 Edition of the Cold-Formed Specification

5.8 One or more dial gages or displacement transducers shall be used to measure the lateral displacements during loading. The gages shall be arranged symmetrically about the midwidth point, and have graduations at not greater than O.OOl-inch intervals. 6. Test Procedures 6.1 The dial-gage height, H D , and load height, H L , as shown in Figure 3, shall be arranged such as to equal as close as possible the overall beam depth, H. Prior to loading the test specimen, the dimensions HD and H L , and the dial-gage readings shall be recorded.

6.2 No preload is to be used. The load shall be applied in a direction which is critical for the intended use of the results. 6.3 The applied load shall be increased in five or more equal increments to the maximum expected value, in order to produce deflection increments of not more than 5 percent of the beam depth. 6.4 If the specimen includes fiberglass insulation or other non-metallic elements in the joint between panel and beam, the load shall be held at each increment for 5 minutes before reading the lateral movement. 6.5 After each load increment is added, and the deflection has stabilized, the load and lateral movement of the unattached flange shall be measured and recorded. 6.6 A test shall be terminated at failure (fastener pullout, fastener failure, panel buckling, panel failure, beam failure, etc.) and the mode of failure recorded, unless the design engineer has determined that the application of the rotational-lateral stiffness, K, occurs at lower load or displacement levels and that the test may be terminated earlier. 7. Number of Tests

7.1 The minimum number of tests for one set of parameters shall be three. For parametric studies using multiple values of one or more parameters a smaller number of tests may be used. 7.2 If used as part of a series of at least three tests, one test is sufficient for a specific condition of an all-metallic mechanically-fastened specimen using the same basic components, but using unique geometrical or physical-property differences such as fastener spacings, different beam or panel yield strengths, etc. 7.3 Three tests are required for any specific condition of welded or adhesively-bonded specimens, or for specimens using non-metallic materials. 7.4 When the rotational-lateral stiffness for three or more panel or beam thicknesses with otherwise identical parameters is to be determined, at least two specimens each with the minimum and the maximum thickness shall be tested. For a ratio of maximum-to-minimum thicknesses greater than 2.5, additional specimens with intermediate thicknesses must be tested. One test of every thickness may be used in accordance with Section 7.2. 7.5 When the rotational-lateral stiffness for a range of screw spacings is to be determined, the minimum number of specimens shall be as follows: For a ratio of maximum-to-minimum screw spacings equal to or less than 2, at least two specimens each with the minimum and the maximum screw spacing shall be tested. For a range of five or more different screw spacings, or for a ratio of maximum-to-minimum screw spacings greater than 2, additional specimens with intermediate spacings must be tested. One test of every screw spacing may be used in accordance with Section 7.2 7.6 Where the rotational-lateral stiffness for a range of other panel parameters-such as

VII-ll

VII-12

Test Procedures for use with the August 19,1986 Edition of the Cold-Formed Specification

yield or ultimate strength, changes in geometry, etc.-are to be determined, a number of tests similar to the requirements under Sections 7.2 through 7.5 shall be performed. 7.7 For un symmetric or staggered fastener arrays and/or beams unsymmetric about a plane parallel to the web, duplicate tests may be required by the design engineer using new specimens with the beam orientation, or the force direction, reversed. 8. Test Evaluation Procedure

8.1 Typical load-displacement curves (P vs. D) obtained from the tests are as shown in Figure 6. For multiple tests of one set of test parameters, the curve resulting in the lowest value of~, as defined in Section 8.2, shall be used for the test evaluation procedure. * P (Load)

Pu~---------------------------------------------== O.8Pu PNr-------------------~ PNr---------------------------------~

~------------~------------

(Displacement)

~--------------------------------------~--------~D

(a)

(b)

DN=O. 8Du

--~------------------------------------------------~~--------------D DN~

O.80 u

(c)

Figure 6 ~plcal L08ck1laplacement Curves

*The test stiffness, Kt. includes the stiffness effects of the beam, Ke. and the beam-~panel connection, ~, but excludes the effects of the bending stiffness oftbe panel, Ke, and follows the relationship Kt = (11K. + 1/~)-1.

Test Procedures for use with the August 19,1986 Edition of the Cold-Formed Specification

VII-13

8.2 The test stiffness, ~, at any load level is detennined by ~=P/D/LB

(2)

8.3 The nominal test stiffness. K N, shall be detennined by

(3) where P Nand DN shall be detennined for a point, N, such that either P Nshall be equal to 0.8 times the ultimate load, P u' for load-displacement curves as shown in Figure 6(a), or the displacement DN shall be equal to 0.8 times the ultimate displacement, Du, for loaddisplacement curves as shown in Figure 6(b), or by a tangent drawn from the origin to the P-D curve as shown in Figure 6(c), resulting in P N:S 0.8P uand DN :s 0.8Du'

8.4 When the design engineer specifies in advance a desired maximum lateral displacement limit of D NL , the test may be discontinued when DNL is reached, and KN may be detennined from P Nat D NL , as long as the limits under Section 8.3 are observed and DNL is not exceeded in actual design applications.

8.5 Where either HD or HL are not equal to the overall beam height, H, corrected by the factor HDHdH2.

and KN shall be

8.6 In addition,~ and KN shall be adjusted by the stiffness contributions of the panel, Kc' derived from the linear-elastic displacement analysis representing the actual design applications, unless such an analysis shows that these contributions are insignificant. Alternately, the panel stiffness may be included by using the alternate test method under Section 10. 8.7 For subassemblies such as shown in Figure 2, the applied lateral test loads cause a bending moment distribution in the panel similar to that shown in Figure 7, and a lateral displacement of the unattached flange of the beam, Dc, equal to

(4) where W s is the width of the subassembly (Figure 2 and Figure 7), E is the modulus of elasticity of the panel material, and I is the effective moment of inertia of the panel cross section (obtained from deflection detennination calculations for cold-fonned metal deck panels). The panel stiffness is equal to

(5) 8.8 The overall rotational-lateral stiffness of the subassembly shall be detennined as

(7) 8.9 When tests covering ranges of parameters (thickness, yield strengths, screw spacings, etc.) are conducted according to Section 7, a linear interpolation may be used to detennine intennediate K values.

9. Test Report

9.1 The test report shall consist of a description of all specimen components, including drawings defining the actual and nominal geometry, material specifications, material properties test results describing the actual physical properties of each component, and the sources of supply. Differences between the actual and the nominal dimensions and material properties shall be noted in the report.

VII-14

Test Procedures for use with the August 19,1986 Edition of the Cold-Formed Specification

~~ V;,___

~;;.....---------+---------~

Moment Diagram D= PH2W g 12EI

Figure 7 Bending Moment Diagram for Panel with an Interior Beam

9.2 In addition, the test report shall contain a sketch or photograph of the test setup, the latest calibration date and accuracy of the equipment used, the signature of the person responsible for the tests, and a tabulation of all raw and evaluated test data.

9.3 All graphs resulting from the test evaluation procedure shall be included in the test report. 9.4 A summary statement, or tabulation, shall be included in the summary of the report to define the actual and nominal rotational-lateral stiffness derived from the tests conducted, including all limitations. 10. Alternate Rotational-Lateral Stiffness Test* 10.1 Th include the panel-stiffness contribution in the test, rather than by linear-elastic analysis, the design engineer may request a test specimen and setup as shown in Figure 8 and Figure 9, respectively. 10.2 The test specimens shall be as described under Section 4 except as follows. 10.2.1 The minimum overall panel width of the specimen, W (Figure 8), shall be

(6) 10.2.2 The minimum end dimension, WE' shall equal the width of the attached beam flange plus 4 inches to allow the development of local deformation patterns around the fasteners as they would develop in a real structure.

*This method is conservative as compared to the basic methods which analytically account for the stiffness of the

panel.

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Test Procedures for use with the August 19,1986 Edition of the Cold-Formed Specification

10.2.3 For specimens representing interior-beam subassemblies, as shown in Figures 1 and 2, the dimension WI of the test specimen (Figure 8) shall be equal to Y12 of the subassembly width, Ws (Figures 1 and 2), to assure that the overall rotational-lateral stiffness contribution of the test-specimen panel is the same as that of the subassembly. 10.2.4 For other subassembly conditions, WI shall be determined to represent the actual conditions. 10.3 The test-setup shall be as described under Section 5 except as follows. 10.3.1 The clamped support as shown in Figures 8 and 9 shall be sufficiently rigid to minimize the rotation and translation of the test specimen at the support. 10.3.2 The lateral-displacement measuring device shall be located on a support fixed relative to the clamped support of the test panel, as shown in Figure 9.

.. p

Panel

==:J ~~

W1 =Ws/12

I I

Figure 8 Panel Width for Alternate Test Procedure

~ Load/Gage Bracket

• p

C=====:=== __ =~~~__~~J

Specimen Support

Figure 9 Te.t Setup For Alternate Te.t

VII-16

Test Procedures for use with the August 19,1986 Edition of the Cold-Formed Specification

10.4 Test procedures shall be the same as described under Section 6. 10.5 The number of tests shall be determined as described in Section 7. 10.6 The test-evaluation procedure shall follow the underlying principles used. to develop Section 8. The test stiffness at any load level shall be determined according to Equation 2 and the nominal test stiffness shall be determined according to Equation 3. No further adjustments are needed. 10.7 For other interior-beam spacings, for exterior-beam conditions, or for other geometrical conditions, the measured displacements shall be adjusted by a linear-elastic analysis to represent the actual field conditions, unless such an analysis shows that these displacements and their effect on K are insignificant.

STUB-COLUMN TEST METHOD(1) FOR EFFECTIVE AREA OF COLD-FORMED STEEL COLUMNS 1. Scope

1.1 This test method covers the determination of the effective cross-sectional area of coldformed steel columns. It primarily considers the effects of local buckling and residual stresses and applies to solid or perforated columns that have holes (or hole patterns) in the flat and/or curved elements of the cross section (1).2

1.2 The effective area is used to determine the allowable axial loads of cold-formed column sections in accordance with the AISI Specification For The Design Of Cold-Formed Steel Structural Members, hereafter called AISI Specification . .J

1.3 The effective area is a variable section property of columns. It reflects the effects oflocal buckling in relatively thin area elements caused by axial stresses, or loads. When the axial load is zero, the effective area is equal to the gross cross-sectional area; however, when an axial load is applied, the effective area may be less than the gross area. In such a case, the effective area will reduce with increasing load. 1.4 Local buckling reduces the axial load-carrying capacity that would otherwise be limited only by general yielding or overall column buckling. The amount of the reduction depends on the width-to-thickness ratio of the flat elements of the column cross section, the yield strength of the steel sheet from which the column is formed, and the size and frequency of holes or hole patterns, if present. 2. Applicable Documents

2.1 ASTM Standards: A370-Tensile Test Method For Steel Sheets E4-Verification of Testing Machines 2.2 AISI Specification for the Design of Cold-Formed Steel Structural Members, 1986 Edition. lThis test and evaluation method will be proposed to the appropriate ASTM Committee for review and adoption. 2Numbers in parentheses refer to references at the end of this test method.

Test Procedures for use with the August 19,1986 Edition of the Cold-Formed Specification

3. Terminology 3.1 ASTM Definitions Standards: E6-Definitions of Terms Relating to Methods of Mechanical Testing. E380-Standard for Metric Practice. 3.2 Description of terms specific to this standard: Elements = Straight or curved portions of the cross section ofa column or stub column. Local Buckling = The local buckling mode of a flat element of a column cross section, which influences the overall column-buckling behavior. Overall Buckling = Buckling of a column as a function of its overall length. Stub-Column = An axial compression member of the same cross section and material as the column for which the strength needs to be determined, but of sufficiently short length to preclude overall column buckling, ifpossible. 3.3 Symbols: A

= the gross cross-sectional area of a column without holes or perforations, or the minimum gross cross-sectional area of a column with holes or perforations.

= the average of all gross cross-sectional areas of the stub columns in a test unit, or the average of gross cross-sectional areas of a stub column.

Ae = the effective cross-sectional area of a stub column at a load less than the ultimate test load, or the effective area of a full-length column. Aei = the effective cross-sectional area of a stub column at load Pi. Aeu = the nominal effective cross-sectional area at ultimate load adjusted to the nominal thickness and the minimum specified yield strength. Aeua = the average effective cross-sectional area of a test unit of stub columns at the ultimate axial load. Aeul = the effective cross-sectional area of a stub column with parameters of Test Unit 1 at ultimate load. Aeu2 = the effective cross-sectional area of a stub column with parameters of Test Unit 2 at ultimate load. Al = the minimum gross cross-sectional area of a stub column with parameters of Test Unit 1 at ultimate load. A2 = the minimum gross cross-sectional area of a stub column with parameters of Test Unit 2 at ultimate load. D

= the axial shortening of a stub column at load P.

= the axial shortening of a stub column at load Pi.

= the axial shortening of a stub column at load P u.

= the average axial stress assumed to be uniformly distributed over the effective

cross-sectional area, Ae. ~

= the average axial stress assumed to be uniformly distributed over the effective

cross-sectional area, Aei at load Pi.

VII-17

VII-18

Test Procedures for use with the August 19,1986 Edition of the Cold-Fonned Specification

= the average axial stress assumed to be uniformly distributed over the effective cross-sectional area, Ae, above which the section is not fully effective.

F n = the nominal ultimate stress, assumed to be uniformly distributed over the effective cross section of a column as calculated from Section C4 of the AISI Specification, at which flexural, torsional, torsional-flexural, or local buckling, and/or yielding, may occur. Fu

= the ultimate stress, assumed to be uniformly distributed, at which local failure occurs in a tested stub column.

F y = the minimum specified elastic limit or yield stress of column or stub-column material. Fya = the average elastic limit or yield stress of the sheet steel for a given test unit. Fyi = the individual elastic limit or yield stress of the sheet-steel specimens in a test unit. =

load-displacement-reading number for a particular stub-column test (load displacement Di at load Pi).

total number of load-displacement readings taken for a particular stub-column test.

the length of the stub-column test specimen.

Lp = the pitch of a repeating pattern of perforations along the longitudinal column axis. n

the ratio of the effective cross-sectional area at the ultimate load to the full crosssectional area, AeulA.

the applied axial compression force (column load).

the applied load at load-increment i.

P n = the nominal failure load of a column. P u = the ultimate stub-column load at which local failure occurs. P ua = the average of all ultimate stub-column loads within a test unit. r

= the minimum radius of gyration of the cross-sectional area, A.

the nominal base-steel thickness exclusive of coating.

the average of all base-steel thicknesses within a test unit, exclusive of coating.

= the greatest overall width of the cross section including corner(s).

4. Slgnlflcance

4.1 This test method provides requirements for testing, and equations to determine, the effective area of a cold-formed column section at ultimate load, Aeu' and the load- or stressdependent effective area, Ae. These properties are used in the AISI Specification to determine the ultimate and less-than-ultimate column strengths. The ultimate column strength, P u' is the product of the minimum specified yield stress, F Y' or the buckling stress F n' and the corresponding effective cross-sectional area at that stress, Aeuo At an applied column strength of P less than P u' the corresponding effective cross-sectional area shall be Ae o

Test Procedures for use with the August 19,1986 Edition of the Cold-Formed Specification

4.2 The test method also provides a means to observe, measure, and account for local buckling deformations when the appearance of a column section under stress must be determined. 4.3 An inherent assumption of the test method is that true stub-column behavior (which considers local buckling effects only) is achieved when overall column-buckling effects are eliminated. For this condition the ultimate test load on a stub column, Pu' equals the product of the effective cross-sectional area at ultimate load, Aeu' times the stress that causes local buckling, or times the yield stress of the virgin steel sheet. In case overall buckling cannot be avoided because of geometrical constraints, the critical column-buckling stress must be used. 4.4 The determination of Ae may be conducted by either one of the two following methods: (1) The basic, more simple, and conservative method:

This method is embodied in the main part of this document and is based on the measured test loads of stub columns and their measured and tested physical and mechanical properties. (2) An alternate and less conservative method:

This method is based on the shortening of stub columns which occurs during testing. Also, this evaluation method requires more calculations. The results of this method lead to more accurate results for Ae, and to higher allowable axial loads at lower-thanultimate stress levels. The evaluation procedure for this method is described in Appendix A.

5. Apparatus 5.1 The tests shall be conducted on a testing machine that complies with the requirements of ASTME4.

5.2 Linear displacement devices for measuring lateral displacements shall have a O.OOI-inch least-reading capability. 5.3 Measuring devices for determination of the actual geometry of a test specimen shall have a O.OOI-inch least-reading capability. 5.4 If axial shortening is recorded, the measuring device shall have.a O.OOOI-inch leastreading capability.

6. Test Unit 6.1 A test unit shall include a minimum of three identicat stub-column specimens and a minimum of two corresponding sheet-type tensile specimens. 6.2 The specimens within a unit shall represent one type of cold-formed steel section with the same specified geometrical, physical, and chemical properties. The specimens may be taken from the same column or from different production runs provided the source of the specimens is properly identified and recorded. 6.3 If stub-column specimens are taken from different production runs, at least two corresponding sheet-type specimens must be taken and tested from each production run. 6.4 The stub-column test specimens shall be used to determine: (1) The actual geometry of each specimen.

(2) The ultimate stub-column test load.

VII-19

VII-20

Test Procedures for use with the August 19,1986 Edition of the Cold-Formed Specification

(3) Axial shortenings at each load level if the alternate test-evaluation method described in Appendix A is used. (4) Lateral displacements of the specimen at locations of interest (if desired). 6.5 The tensile test specimens shall be used to define the yield stress of each stub-column specimen acording to the requirements described in ASTM A370. 6.6 For each test specimen and test unit, the measured geometrical and tested physical properties of the individual specimens shall meet the requirements stated by the fabricator and material producer, respectively. 6.7 If the average area, thickness, or yield strength of a test miit varies by more than 20 percent from the respective nominal or specified-minimum value, the test unit is considered to be non-representative of the column section, and further evaluations of the effective area are considered to be invalid. 7. Stub-Column Specimens The stub-column specimens shall meet length and end-flatness requirements as follows, depending on whether or not unconnected or welded end plates are used.

7.1 Stub-Column Length-The length requirements of the stub-column test specimen, L, as shown in Figures 1 and 2, are that it be (1) sufficiently short to eliminate overall column buckling effects, and (2) sufficiently long to minimize the end effects during loading, which means that its center portion be representative of the repetitive hole pattern in the full column. 7.1.1 To eliminate overall column-buckling effects, the stub-column length shall not exceed twenty times the minimum radius of gyration, r, of the cross section, A, except where necessary to meet the requirements of Sections 7.1.2 through 7.1.5. 7.1.2 For unperforated columns (Figure la) the stub-column length shall not be less than three times the greatest overall width of the cross section, W. 7.1.3 For perforated columns in which the pitch (gage length) of the perforation pattern, Lp ' for a single hole or a group of holes, is smaller than, or equal to, the greatest over~ll width, W, of the cross section (Figures lb and 19), or for a single hole pattern with a gage length larger than the greatest overall width (Figure lc), the specimen length shall not be less than three times the greatest overall width of the cross section, W. For widely spaced hole patterns (Figure lc) the significant hole or hole pattern shall be located at or near the midlength of the stub column. 7.1.4 For perforated columns in which the pitch of the perforation pattern, Lp ' is greater than the widest side, W, of the cross section (Figures ld, Ie, If, and lh), the specimen length shall not be less than three times the pitch of the perforation pattern. 7.1.5 For perforated sections in which the specimen end planes must pass through the normal perforation pattern (Figure Ii), a special section (Figure lj) may be fabricated to obtain full cross-sectional surfaces at the specimen ends. 7.2 Stub-Column End Surface Preparation-The end planes of the stub-column test specimens shall be carefully cut to a flatness tolerance of plus or minus 0.002 inches. When the required flatness can be achieved, welding of the stub-column ends to the endplates is not required. However, when this flatness cannot be achieved, steel endplates shall be continuously welded to both ends of the specimen so that there shall be no gap between the ends of the stub column and the end plates. 7.3 Stub-Column Specimen Source-Stub-column test specimens may be cut from the commercially fabricated column product. Alternatively, stub columns may be specially

Test Procedures for use with the August 19, 1986 Edition of the Cold-Forrt:led Specification

__ J.. __

--'--- - ..... I

VII-21

~ I

...J

III

...J

.9t") III ...J

--t--

I-i..-

~ VI

.9'W

(8)

(b)

(c)

(e)

(d)

--_1--

.9t")

III ...J

...J ~

_ _ _ _ _I _ L -

(j)

--,-(f)

~ VI

.9-

(g)

,(h)

(I)

figure 1 Hypothetlclll Perfondlon Patterns And Suggested Stub Column Lengtha NOTES: (1) Perforations shown 81'8 In a flat portion of a member with width W (2) L = Length of Stub Column , (3) L" = PItCh Length of Perforation Pattern

VU-22

Test Procedures for use with the August 19,1986 Edition of the Cold-Formed Specification

fabricated provided care is taken not to exceed the cold work of forming expected in the commercial product; however, subsequent proof tests using specimens from commerically produced columns are recommended. 7.4 Tensile Specimen Source-Longitudinal tensile specimens shall be cut from the center of the widest flat of a formed section from which the stub-column specimens have been taken. If perforations are large and frequent in all flats of the formed section, the tensile specimens may be taken from the sheet or coil material used for the fabrication of the stubcolumn specimens. The tensile specimens shall not be taken from parts of a previously tested stub column. 7.5 Endplate Requirements-Steel endplates shall be at least 0.5 inch thick and have a flatness tolerance of plus or minus 0.002 inches. 8. Stub-Column Test Procedure

8.1 Vertical alignment of the stub column is essential to ensure that th~ applied load is uniformly distributed over the specimen end surfaces. Care should also be taken to center the specimen on the axis of the test machine. 8.1.1 Steel end plates shall be used to transfer the test loads uniformly into the stub columns (Figure 2). P

Steel End Plate

Stub Column Linear Displacement Measuring Device

Steel End Plate

~:,.;..:,.:;.+;.~~;..,:.,..;:~~~~- Y2-lnch-Thick Grout Layer, Min. ~~-

Base of Testing Machine

~~~~~'~~4M

1 P

Figure 2 Test Setup

Test Procedures for use with the August 19,1986 Edition of the Cold-Formed Specification

8.1.2 A Y2-inch-thick layer of grout, similar to gypsum-based concrete capping compound used for fast setting, shall be placed between the stub-column endplates and the machine heads to facilitate aligning the test specimen (Figure 2). 8.2 When an axial compression load is applied to the test specimen as a result of grout expansion during curing, or if a small preload is purposely applied to ensure proper contact between the stub-column endplates and the machine heads, the load shall be treated as part of the applied test load. 8.3 The load increments applied during the test shall not exceed 10 percent of the estimated ultimate test load. 8.4 The maximum loading rate between load increments shall not exceed a corresponding applied stress rate of 3 kips per square inch of cross-sectional area per minute. 8.5 When axial shortening values are recorded, the following procedures shall be required: (1) The change in the vertical distance between the inside surfaces of the endplates (Figure 2) shall be measured to the nearest O.OOOl-inch at each load increment for each

specimen. (2) The load increments applied during the test shall be the same for each specimen within a

test unit, with a variation not to exceed one percent.

9. Calculations 9.1 For a given test unit, all individual ultimate loads, P u' derived from the stub-column tests shall be used to calculate the average ultimate load, P ua. Similarly, all individual yield strengths, Fyi, derived from the tensile tests of the same unit shall be used to calculate the average yield stress of the same test unit, F ya. 9.2 The effective areas Aeua' Aeu' and Ae shall be calculated as specified in Sections 9.3 through 9.6; however, the final value of these effective areas shall not exceed that of the minimum gross cross-sectional area, A. 9.3 For tests in which the length of the stub column does not exceed twenty times the minimum radius of gyration of the cross section, r, the average effective area at the ultimate load, Aeua, for a given test unit shall be calculated as Aeua = P ua/ F ya 9.4 For tests in which the length of the stub column exceeds twenty times the minimum radius of gyration of the cross section, the average effective area at the ultimate load shall be detennined by iteration of the following equations:

where Aa is the average minimum gross area of the stub columns in the test unit, and F n is the flexural or torsional-flexural buckling stress derived from Section C4 of the AISI Specification with K = 0.5 (using the average cross-sectional properties of the test unit). The exponent n is detennined as follows:

Assuming an initial value for n equal to less than 1.0, Aeua can be calculated from the first equation. Using this Aeua in the second equation will provide a new value for n. Repeating this process will lead to convergence of the above equations and an acceptable value of Aeua for one specific test unit.

VII-23

V11-24

Test Procedures for use with the August 19,1986 Edition of the Cold-Formed Specification

9.5 The value of Aeua for a specific test unit shall be adjusted to Aeu' which is the effective cross-sectional area of a column at ultimate load with a nominal cross section of A and a specified minimum yield strength of F y. The adjustment shall be performed in one or two steps as follows.

9.5.1 If the average area of the stub columns in the test unit, Aa, or the average base steel thickness, t a , are diferent from the nominal area or thickness, respectively, the effective cross-sectional area at ultimate load shall be calculated as follows:

9.5.2 If the average yield strength of all stub columns in a test unit, F ya' is different from the nominal yield strength, F y' the effective cross-sectional area at ultimate load shall be the lower of the two values calculated as follows:

9.5.3. If the average area and the minimum specified yield strength are different from the nominal values ofa test unit, Aeu derived from the equation in Section 9.5.1 shall be used as Aeua in the equations of Section 9.5.2, which will lead to an acceptable value of Aeu. 9.6 The effective area at any working stress level, Ae, may be determined by

9.7 For a series of sections, such as in a parameter study during which only one parameter (thickness, depth, width, yield strength, etc.) is changed, interpolations between test units, or extrapolations beyond test units, shall be acceptable a~ described in Appendix B.

9.8 Extrapolations beyond 20 percent of the extreme parameters tested shall not be permitted.

Test Procedures for use with the August 19,1986 Edition of the Cold-Formed Specification

10. Report 10.1 Documentation-The report shall include a complete record of the sources and loca-

tions of all stub-column and tensile-test specimens and shall describe whether the specimens were taken from one or several columns, one or several production runs, coil stock, or other sources. 10.2 The documentation shall include all measurements taken for each stub-column test

specimen, including (1) cross-section dimensions, (2) uncoated sheet thickness, (3) longitudinal yield strength, (4) end preparation procedure, (5) applicable material specification, and (6) test and evaluation procedure used. 10.3 The determination of the selected stub-column length shall be fully documented with

appropriate calculations. 10.4 A description of the test setup-including the endplates, the grout layer used for

alignment, and the instrumentation used to measure laterial displacements and axial shortening-shall be included. 10.5 The report shall include the load increments, rate of loading, and intermediate and

ultimate loads for each stub column tested. 10.6 The report shall include complete calculations and results of the effective area, Aeu' for

each test unit and calculations of Ae , if requested. 11. Precision

11.1 The following criteria shall be used to judge the acceptability of the test results. 11.1.1 Repeatability-Individual stub-column test results shall be considered suspect if they differ by more than 10 percent from the mean value for a test unit with at least three specimens. 11.1.2 Reproducability-The results of tests on stub-columns conducted at two or more laboratories should agree within ten (10) percent when adjusted for differences in cross sectional dimensions and yield strength.

REFERENCES

(1) T. Pekoz, "Development of a Unified Approach to the Design of Cold-Formed Steel Members, Committee of Sheet Steel Producers, American Iron and Steel Institute, 1000 16th Street, NW, Washington, DC 20036, 1986.

VII-25

VII-26

Test Procedures for use with the August 19,1986 Edition of the Cold-Formed Specification

APPENDIX A

Use Of Axial Shortening Measurements In Design A-1 Axial shortening measurements as part of thin-walled cold-formed steel stub-column tests may be used as an alternative method of determining the effective area of a column, A e, at a certain design load or stress. This method provides a more accurate and less conservative alternative to design engineers to determine the effective area ofa column section, Ae' A-2 The calculations by this method shall be made separately for each stub-column specimen within a test unit. This shall result in a total of j calculations as a result of a total of j loaddisplacement tests for each test unit. A-3 For a given specimen the effective area at ultimate load, Aeu' shall be calculated from Section 9.3 or 9.4 letting Aeua = Aeu' Aa = A, F ya = F y' and P ua = P u' A-3.1 Calculations at each load-displacement reading, i, shall be conducted according to the following procedure; however, at zero load, the effective area, A e , shall be equal to the minimum gross cross-sectional area, A. This provides results for the effective area at each load point: (1) Starting with the lowest load-displacement reading, the effective area, ~, and the

assumed uniformly distributed stress fi' shall be calculated for each reading, i, from: and

A.= PiDu el F y D.1

where Di an Du are the axial shortening at loads Pi and P u' respectively. (2) If Aei calculated is greater than A, Aei shall be set equal to A.

(3) If Aei calculated is less than A, Aei shall be as calculated, and fo' the stress above which the section is not fully effective, shall be set equal to fi_l , as calculated for the previous load-displacement reading. A.3.2 For specimens within a test unit, the lowest Aei values shall be used for further evaluations.

A-4 For any load that causes a stress f higher than fo' an exponential equation may be developed as follows.: Ac = A[1-(1- Aeu/ A) (f -fo)/F y -fo)]b j

where

I (Xi) (Y) -(a) I (X) i=)

i=)

.I (X)2 1=

and

X = In[(fi -fo)/(Fy -fo)] Yi = In(1-A'eJ A) a = In(1- Aeul A)

and In designates the natural logarithm. A·S If the effective areas for a section with specified dimensions and minimum yield strength are desired, which are different from the tested specimens, the Aeu and Aei values calculated under Section A-3 shall be normalized to the specified parameters according to Section 9.5 before the curve-fitting procedure of Section A-4 is employed.

A-6 All calculations pertaining to this procedure shall be included in the report, as discussed in Section 10.

Test Procedures for use with the August 19,1986 Edition of the Cold-Formed Specification

APPENDIX 8

Parametric Studies 8-1 For parametric studies intended to develop the effective area for a series of sections with the same basic cross section (either C, U, H, or any other shape) and the same hole pattern, but with one or more changing parameters, the required number of test units may be less than the sum of all sections with different geometries and yield strengths. 8-1.1 For a series of sections with three different values for one parameter only (dimension or nominal yield strength), at least two test units shall be chosen to include the minimum and the maximum value of the changing parameter. For the third value, Aeu may be interpolated according to Section B-2. 8-1.2 If more than three different values for one parameter are included in a series of sections, additional units with intermediate values shall be tested such that the ratio of the changing values in adjacent units is not greater than 1.5 or be less than 0.67. For intermediate values of the changing parameter, Aeu may be interpolated according to Section B-2. 8-1.3 For a series of sections with the same basic cross section that includes different values for several parameters (dimensions and/or yield strength), an appropriate factorial of test units shall be established by the responsible professional engineer in accordance with the guidelines for changes in an individual parameter, and in compliance with responsible code authorities. Interpolations and extrapolations may be made as mutually agreeable, following the general guidelines set forth in Section B-2 for changes of one parameter only. 8-1.4 For a section that falls outside a series of tested members with the same basic cross section, Aeu may be extrapolated provided the changing parameter does not exceed a value of 20 percent below or above the respective minimum or maximum values tested in the series.

8-2 Interpolations and extrapolations are allowed as part of a parametric study, and as defined under B-l. 8-2.1 For a section with a thickness different from the thicknesses tested, but with identical overall nominal cross-sectional dimensions and minimum specified yield strength, Aeu for a thickness t and an area A may be calculated provided t does not exceed the limits described under Section B-1.2 and B-1.4. Under these conditions, Aeu may be determined by interpolation or extrapolation from the results of the nearest two test units with thicknesses tl and t 2 , respectively:

where Al and A;. are the minimum gross cross-sectional areas, and Aeul and Aeu2 are the nominal effective cross-sectional areas for Test Units 1 and 2, respectively.

8-2.2. For a section with a yield strength different from the yield strengths tested, but with identical cross-sectional dimensions, Aeu for a yield strength F y may be calculated provided Fy does not exceed the limits described under Section B-1.2 and B-l.4. Under these conditions, Aeu may be determined by interpolation or extrapolation from the results of the nearest two test units with yield strengths FYI and F y2' and with effective areas Aeul and Aeu2 , respectively:

VII-27

Cold-formed Steel Design Manual 290.pdf - PDFCOFFEE.COM (2024)

References