2012.02.01 - Cold-Formed Steel Design 2007 Edition - S100

by

COLD-FORMED STEEL DESIGN:

2007 EDITION

SE University, February 2012

by

Roger LaBoube

Wei-Wen Yu Center for Cold

Missouri University of Science and Technology

by

FORMED STEEL DESIGN:

2007 EDITION – S100

1

by

LaBoube

Yu Center for Cold-Formed Steel Structures

Missouri University of Science and Technology

What are the changes in 2007?

Why is cold-formed steel

so much more

complex than hot


Or

Is it really that much different?

What are the changes in 2007?

formed steel

so much more

complex than hot-roll design?

2

Or

Is it really that much different?

SOME TYPICAL COLD

CROSS SECTIONSStuds or Joists


Other Shapes

SOME TYPICAL COLD-FORMED SHAPE

CROSS SECTIONS

3

Think about the behavior

SOME TYPICAL COLD

CROSS SECTIONS

Roof Decks

Long-Span Decks


Floor Decks

Curtain Wall Panels

Ribbed Panels

Corrugated Sheets

SOME TYPICAL COLD-FORMED PANEL

CROSS SECTIONS

4

KEY CHARACTERISTICS OF COLD

STEEL STRUCTURES

• Shapes are cold-formed from flat sheets or plates

• Original mechanical propertiesto the cold forming process


to the cold forming process

• Standardized and customized shapes are available

• Thin material (in most cases less than

• Predominant cross-section failure mode is influenced by local buckling, followed by postbuckling strength increase

KEY CHARACTERISTICS OF COLD-FORMED

STEEL STRUCTURES

formed from flat sheets or plates

mechanical properties of steel are changed due to the cold forming process

5

to the cold forming process

Standardized and customized shapes are available

(in most cases less than 0.10 inch)

section failure mode is influenced by postbuckling strength increase

Specification Applicable in North America

Canada

Mexico

United States


United States

Specification Applicable in North America

Canada

Mexico

United States

6

United States

Design Methods

United States: Allowable Strength Design and Load and

Resistance Factor Design

Canada: Limit States Design

Mexico: Allowable Strength Design and Load and


Mexico: Allowable Strength Design and Load and

Resistance Factor Design

Design Methods

Allowable Strength Design and Load and

Limit States Design


7


ASD STRENGTH REQUIREMENTS(Section A4.1.1)

R ≤ ≤ ≤ ≤ R

R = Required strength



Rn = Nominal strength

Ω = Safety Factor

Rn/Ω = Design strength (allowable strength)

STRENGTH REQUIREMENTS(Section A4.1.1)

Rn/ΩΩΩΩ


8


= Nominal strength

= Safety Factor

Design strength (allowable strength)

LRFD STRENGTH REQUIREMENTS(Section A5.1.1)

Ru ≤ φ≤ φ≤ φ≤ φ



Ru = Required strength

Rn = Nominal strength

φ = Resistance factor

φRn = Design strength (factored resistance)

STRENGTH REQUIREMENTS(Section A5.1.1)

≤ φ≤ φ≤ φ≤ φRn

= Required strength

9

= Required strength

= Nominal strength

= Resistance factor

= Design strength (factored resistance)

ORGANIZATION OF THE 2007 SPECIFICATION

(AISI S100A. General Provisions

B. Elements

C. Members

D. Structural Assemblies and Systems

E. Connections and Joints



F. Tests for Special Cases

G. Fatigue

Appendices for each country

Appendix 1 for Direct Strength Method

Appendix 2 for Second-Order Analysis

ORGANIZATION OF THE 2007 SPECIFICATION

(AISI S100-07)

D. Structural Assemblies and Systems


10


F. Tests for Special Cases

Appendices for each country

Appendix 1 for Direct Strength Method

Order Analysis

Limits of Applicability

(Section A1.2)

• Nominal strength and stiffness shall be determined by Chapters A through G and Appendices A and B.

• As an alternate:

– Determine design strength or stiffness by tests


– Determine design strength or stiffness by tests and Chapter F

– Determine design strength or stiffness by rational analysis Section A1.1

– Direct Strength Method (Appendix 1)

– Second Order Analysis (Appendix 2)

Limits of Applicability

(Section A1.2)

Nominal strength and stiffness shall be determined by Chapters A through G and Appendices A and B.

Determine design strength or stiffness by tests

11

Determine design strength or stiffness by tests

Determine design strength or stiffness by rational analysis Section A1.1

Direct Strength Method (Appendix 1)

Second Order Analysis (Appendix 2)

STEEL MATERIALS AND PRODUCTS(Section A1.1)

The Specification Covers

• Steel:


• Steel Products:

• Members:

STEEL MATERIALS AND PRODUCTS(Section A1.1)

The Specification Covers

Carbon and low alloy

12

Sheet, strip, plate, bar

Cold formed to shape

TYPICAL APPROVED STEELS(Section A2.1)

16 Approved Steels in Section A2.1.

ASTM A653 Steel Sheet, Zinc Coated (Galvanized) or Zinc-Iron Alloy-Coated (Galvannealed) by the HotProcess


ProcessFy = 33 to 50 ksi Fu = 45 to 70 ksiFy = 80 ksi Fu = 82 ksi

ASTM A792 Steel Sheet, 55% AluminumCoated by the Hot-Dip ProcessFy = 33 to 50 ksi Fu = 45 to 70 ksiFy = 80 ksi Fu = 82 ksi


16 Approved Steels in Section A2.1.

Steel Sheet, Zinc Coated (Galvanized) or Coated (Galvannealed) by the Hot-Dip

13

= 45 to 70 ksi= 82 ksi

Steel Sheet, 55% Aluminum-Zinc Alloy-Dip Process

= 45 to 70 ksi= 82 ksi


ASTM A1011 Steel Sheet, HotStructural, High Strength LowFormability


ASTM A1003 Steel Sheet, Carbon, MetallicNonmetallic-Coated for Cold Formed Framing Members

(Replaced A653 for framing members)


Steel Sheet, Hot-Rolled, Carbon, Structural, High Strength Low-Alloy with improved

14

Steel Sheet, Carbon, Metallic- and Coated for Cold Formed Framing

(Replaced A653 for framing members)


ASTM A1039 Steel Sheet, HotCommercial and Structural, Produced by TwinCasting Process.

Grades: 40, 50, 55, 60, 70, and 80.


Grades: 40, 50, 55, 60, 70, and 80.

Steel thicknesses less than 0.064”, Fmeet ductility requirements of 10% Section A2.3.1. Thus Section A2.3.2 applies.

TYPICAL APPROVED STEELS(Section A2.1) (New in 2007)

Steel Sheet, Hot-Rolled, Carbon, Commercial and Structural, Produced by Twin-Roll

Grades: 40, 50, 55, 60, 70, and 80.

15

Grades: 40, 50, 55, 60, 70, and 80.

Steel thicknesses less than 0.064”, Fy > 55 ksi do not meet ductility requirements of 10% Section A2.3.1. Thus Section A2.3.2 applies.

OTHER STRUCTURAL QUALITY STEELS(Section A2.2)

Maximum Thickness

Published Material Specification with Specified


Published Material Specification with Specified Mechanical and Chemical Properties

Minimum Ductility Requirements of Section A2.3

OTHER STRUCTURAL QUALITY STEELS(Section A2.2)

Maximum Thickness ≤≤≤≤ 1 inch

Published Material Specification with Specified

16

Published Material Specification with Specified Mechanical and Chemical Properties

Minimum Ductility Requirements of Section A2.3

REQUIRED DUCTILITY(Section A2.3.1)

Fu/Fy ≥≥≥≥


Elongation ≥ 10% (two

≥ 7% (eight

REQUIRED DUCTILITY(Section A2.3.1)

≥≥≥≥ 1.08

17

10% (two-inch gage length)

7% (eight-inch gage length)

LOW DUCTILITY STEELS(Section A2.3.2)

ASTM A653, A792, A875 and A1008, Grade 80 material

May be used for deck and panel profiles


Limits on Fy and Fu

Alternatively, suitability shall be determined by tests.

Exceptions: Multi-web configurations (flexural strength)

Closed box sections (compression strength)

LOW DUCTILITY STEELS(Section A2.3.2)

ASTM A653, A792, A875 and A1008, Grade 80 material

used for deck and panel profiles

18

Alternatively, suitability shall be determined by tests.

web configurations (flexural strength)

Closed box sections (compression strength)

BUCKLING MODES

(Overall & Cross Section)


BUCKLING MODES

(Overall & Cross Section)

Cold-formed vs.Hot-rolled behavior,any different?

Challenge of

19

Challenge of cold-formedsteel design is to cope with local and distortional buckling.

DISTORTIONAL BUCKLING STRENGTH

Section C3.1.4

0.673dλ ≤

0.5 0.5

1 0.22 crd crdM MM M

= −

For

Mn =My

For λd > 0.673


1 0.22 crd crdn

y y

M MM M

M M

= −

d y crdM Mλ =

My = SfyFy

Sfy = Elastic section modulus of full unreduced section

Mcrd = SfFd


Section C3.1.4 (New in 2007)

0.5 0.5

crd crdM MM M

(Eq. C3.1.4-1)

20

crd crdy

y y

M MM M

M M

(Eq. C3.1.4-2)

Elastic section modulus of full unreduced section

(Eq. C3.1.4-3)


Section C3.1.4

Distortional buckling stress:

2

d d 2

o

E tF βk

12(1 ) b

πµ

= −

0.7


β accounts for the moment gradient.

0.7

od

o

b Dsinθk 0.5 0.6 8.0

h t

= ≤ ≤

( )0.7 0.71.0 1 0.4 L/L 1 M M 1.3mβ = ≤ + − ≤


Section C3.1.4


This is the simplified equation for the buckling stress

2

o

E t

12(1 ) b

21

accounts for the moment gradient.

for the buckling stress and removed in 2010 Supplement.

( )0.7 0.7

1 21.0 1 0.4 L/L 1 M M 1.3= ≤ + − ≤


Section C3.1.4

General distortional buckling stress equation:

fe wek k kF

φ φ φβ+ +

=


fe we

d

fg wg

k k kF

k k

φ φ φ

φ φ

β+ +

=% %


Section C3.1.4


fe wek k kφ φ φ+ +

22

fe we

fg wg

k k k

k k

φ φ φ

φ φ

+ +

+% %


Section C4.2

For λd > 0.561

Pn = Py

For λd > 0.561

P =


d y crdP Pλ =

Py = AgFy

Pcrd = AgFd

Pn =


Section C4.2 (New in 2007)

(Eq. C4.2-1)

23

(Eq. C4.2-2)

(Eq. C3.1.4-3)


Section C4.2


2

d d 2

o

E tF k

12(1 ) b

πα

µ

= − 0.7


α accounts for the benefit of the unbraced length.

0.7

od

o

b Dsinθk 0.5 0.6 8.0

h t

= ≤ ≤


Section C4.2

Distortional buckling stress:2

o

E t

12(1 ) b

This is the simplified equation

for the buckling stress

24

accounts for the benefit of the unbraced length.

k 0.5 0.6 8.0

for the buckling stress and removed in 2010 Supplement.


Section C4.2


fe wek k kF

φ φ φβ+ +

=


fe we

d

fg wg

k k kF

k k

φ φ φ

φ φ

β+ +

=% %


Section C4.2


fe wek k kφ φ φ+ +

25

fe we

fg wg

k k k

k k

φ φ φ

φ φ

+ +

+% %

MAJOR COLD-FORMED STEEL DESIGN CONCEPT

Effective Design Width

• Stiffened Elements


• Stiffened Elements

• Partially Stiffened Element

• Unstiffened Elements

FORMED STEEL DESIGN CONCEPT

Effective Design Width

Stiffened Elements

26

Stiffened Elements

Partially Stiffened Element

Unstiffened Elements

STIFFENED AND UNSTIFFENED ELEMENTS:

EXAMPLES

Stiffened


Unstiffened

STIFFENED AND UNSTIFFENED ELEMENTS:

EXAMPLES

27

POST-BUCKLING STRESS DISTRIBUTION


BUCKLING STRESS DISTRIBUTION

28

EFFECTIVE WIDTH CONCEPT


o

w

fdx = b∫

EFFECTIVE WIDTH CONCEPT

29

fdx = bfmax

CLASSIC EFFECTIVE WIDTH EXPRESSION

cr yf = F = 12(1-

∴ b = 1.9t


b = 0.95t kE

f 1 - 0.208

max

also, b = 1.9t

CLASSIC EFFECTIVE WIDTH EXPRESSION

1

2

2

2 2

4 E

12(1- )(b/t)

π

µ

= 1.9t E/Fy

30

3

41 - 0.208 (t

w)

kE

f

max

= 1.9t E/fmax

BASIC EFFECTIVE WIDTH EXPRESSION(Section B2.1)

b = w when

w when = b ρ

0.22

SE University, February 2012Used in all cases of effective width considerations

= λ

0.22 - (1 = ρ

12(1 k = F cr

BASIC EFFECTIVE WIDTH EXPRESSION(Section B2.1)

Eq.B2.1-1

Eq.B2.1-2

hen 0.673λ ≤

0.673 > w when λ

0.22

31

Eq.B2.1-3

Eq.B2.1-4

Eq.B2.1-5

Used in all cases of effective width considerations

f/Fcr

)/0.22

λλ

))(w/t-12(1

E22

2

µπ

EFFECT OF LOCAL BUCKLING ON

COLUMN SECTION

σult



COLUMN SECTION

IneffecitveAreas

32

f = Fy

Aeff

Effective Section

Areas

NOMINAL AXIAL STRENGTH, P

a) For locally stable compression members

Pn = AgFn

No local buckling will occur before the nominal compressive stress reaches the column buckling stress or the yield stress. Hence, the gross area of the section is used.

b) For locally unstable compression members


b) For locally unstable compression members

Pn = AeFn

Local buckling will occur and the effective cross sectional area is used and is calculated at the nominal compressive buckling stress.

NOMINAL AXIAL STRENGTH, Pn

For locally stable compression members

No local buckling will occur before the nominal compressive stress reaches the column buckling stress or the yield stress. Hence, the gross area of the section is used.

For locally unstable compression members

33

For locally unstable compression members

Eq.C4-1

Local buckling will occur and the effective cross sectional area is used and is calculated at the nominal compressive buckling

NOMINAL AXIAL BUCKLING STRESS, F(Section C4(a))

The nominal axial buckling stress is calculated as follows.

For λc ≤ 1.5 :

For λ > 1.5 : F =

0 877.F

( )Fn = 0 6582

. λc Fy


For λc > 1.5 :

Where

and Fe is the least of the elastic flexuralflexural buckling stresses.

Fn =

0 8772

.

λ c

yF

λ c

y

e

F

F=

NOMINAL AXIAL BUCKLING STRESS, Fn(Section C4(a))

The nominal axial buckling stress is calculated as follows.

(inelastic buckling) Eq.C4-2

(elastic buckling) Eq.C4-3

34

(elastic buckling) Eq.C4-3

Eq.C4-4

flexural, torsional and torsional-

OPEN CROSS SECTION FLEXURAL MEMBERS (Section C3.1.2.1)

• Laterally Unsupported Members



Laterally Unsupported Members

35

OPEN CROSS SECTION FLEXURAL MEMBERS(Section C3.1.2.1)

Lateral Buckling Strength

Elastic Lateral-Torsional Buckling

IC)L

E( + GJIE

LS = F yw

2

yf

e

ππ


or

where

S

A r = F tey

f

oe σσ

ey

2

2y

to2 =

E

(KL/ r ) ; =

1

Ar GJ + σ

πσ


Torsional Buckling

1

36

2

2

w

t

2GJ + EC

(KL)

π

Inelastic Lateral-Torsional Buckling

Not subject to L-T buckling when F

use Section C3.1.1(a)

When 2.78Fy > Fe > 0.56Fy



For Fe ≤ 0.56Fy

Fc = Fe

F36

F10 - 1 F

9

10 = F

e

yyc

Torsional Buckling

T buckling when Fe ≥ 2.78Fy,


37

Eq.C3.1.2.1-2

e Eq.C3.1.2.1-3




38


BENDING STIFFNESS

b = wb/2

CN.A.

ycg ycg

T


ycg

M3

M2

M1

M


BENDING STIFFNESS

b/2f = Fy

C

T

C

T

N.A.N.A.

ycg

b/2b/2

Ineffective

39

M2 M1

M3 M2M1

B.M.

EI

IneffectiveAreas


Ωb = 1.67 φb = 0.90

(a) For Singly-, Doubly-, and Point

Where for (A) & (B)

S

ArC = F tey

obe σσ

ccn FSM =


Eq.C3.1.2.1-4

and for (C)

S

= F teyf

e σσ

2S

Ar C = F tey

f

obe σσ


= 0.90 Eq.C3.1.2.1-1

, and Point-Symmetric Sections

40

SHEAR STRENGTH(Section C3.2.1)

Nominal Shear Strength, VnVn = AwFv

(a) For

(b) For

yv F/Ekt/h ≤

yv F60.0F =

yv Ek51.1t/hF/Ek ≤<


(b) For

(c) For

yv Ek51.1t/hF/Ek ≤<

)t/h(

FEk60.0F

yvv =

yv F/Ek51.1t/h >

22v

2

vh(

904.0

)t/h)(µ1(12

EkπF =

−=

SHEAR STRENGTH(Section C3.2.1)

Eq.C3.2.1-1

Eq.C3.2.1-2

yv F/Ek

41

Eq.C3.2.1-3

Eq.C3.2.1-4

yv F/Ek

2v

)t/h

Ek904

WEB CRIPPLING (Section C3.4)

Basic Web Crippling Equation

+

−=

t

NC1

t

RC1sinFCtP NRy

2n θ


Web crippling coefficients C, CR, Cappropriate tables for fastened or unfastened

R/t = inside bend radius ratio N/t = bearing length ratio h/t = web slenderness ratio


Eq.C3.4.1-1

−

t

hC1

t

Nh

42

, CN, and Ch are given in the unfastened to the support.

R/t = inside bend radius ratio N/t = bearing length ratio


• Alternatively, for end-one-flange loading condition on a C

Pnc = α Pn

α is a function of the overhang length, purlin depth, and purlin thickness.


WEB CRIPPLING (Section C3.4) (New in 2007)

flange loading condition on a C- or Z-section,

Eq. C3.4.1-2

is a function of the overhang length, purlin depth, and purlin thickness.

43

COMBINED BENDING AND TORSIONAL LOADING (Section C3.6)

For laterally unrestrained flexural members subject to both bending and torsional loading, Mn computed in accordance with Section C3.1.1(a) shall be reduced by a reduction


n

C3.1.1(a) shall be reduced by a reduction factor.

bending

bending torsion

fR

f f= ≤

+

COMBINED BENDING AND TORSIONAL LOADING (Section C3.6) (New in 2007)

For laterally unrestrained flexural members subject to both bending and torsional loading,

computed in accordance with Section C3.1.1(a) shall be reduced by a reduction

44

C3.1.1(a) shall be reduced by a reduction

1bending torsion

= ≤

MEMBER BRACING(Section D3.3) (New in 2007)

BRACING OF AXIALLY LOADED COMPRESSION MEMBERS

Design considerations:


• Strength,

• Stiffness,

P P

β

MEMBER BRACING(New in 2007)

BRACING OF AXIALLY LOADED COMPRESSION MEMBERS

Design considerations:

45

,1 0.01br nP P=

,1

2[4 (2 / )] nbr

b

n P

Lβ

−=

Standards for Cold

Light-Frame Construction

COLD-FORMED STEEL LIGHT

(Section D4)


Light-Frame Construction

Standards for Cold-Formed Steel

Frame Construction

FORMED STEEL LIGHT-FRAME CONSTRUCTION

(Section D4) (New in 2007)

46

Frame Construction

AISI COFS Mission

• To eliminate regulatory barriers and increase the reliability and cost competitiveness of cold-formed steel framing in residential and light commercial building construction through improved design and installation standards.


AISI COFS Mission

To eliminate regulatory barriers and increase the reliability and formed steel framing in residential

and light commercial building construction through improved standards.

47

AISI Framing StandardsReferenced by S100

• General Information:

– AISI S200-07: General Provisions

– AISI S201-07: Product Standard

– Code of Standard Practice

• Design Standards:


– AISI S210-07: Floor and Roof System Design

– AISI S211-07: Wall Stud Design

– AISI S212-07: Header Design

– AISI S213-07: Lateral Design

– AISI S214-07: Truss Design

• Prescriptive Methods:

– AISI S230-07: Prescriptive Method for One and Two Family Dwellings

AISI Framing StandardsReferenced by S100

: General Provisions

07: Product Standard

Code of Standard Practice

48

: Floor and Roof System Design

: Wall Stud Design

: Header Design

: Lateral Design

: Truss Design

07: Prescriptive Method for One and Two

SYSTEM BRACING AND ANCHORAGE

(Section D6.3.1)

∑=

=

p

i

j

N

1i total

j,ieffiLK

KPP

Anchorage Device Equation:

Each anchorage device must resist P


⋅−θ⋅α

+⋅+⋅⋅⋅= 4Ccos

d

t)b25.0m(3C

dI

LI

1000

2CW1CP

2x

xypi i

( ) sys

N

1jj,iefftotal KKK

a

i += ∑

=

2

2

psysd

ELtN

1000

5CK ⋅⋅=

1

p

p

aeff

ELA6C

d

K

1K

j,i

ji,

−

⋅+=

Effective lateral stiffness of all elements resisting P

Lateral stiffness of roof system, neglecting anchoragedevice (purlin to rafter & panel to purlin connections)

Effective lateral stiffness of anchorage device

SYSTEM BRACING AND ANCHORAGE

(Section D6.3.1) (New in 2007)

Each anchorage device must resist PL

Anchorage force at each purlin

49

θsin

Effective lateral stiffness of all elements resisting Pi

Lateral stiffness of roof system, neglecting anchoragedevice (purlin to rafter & panel to purlin connections)

Effective lateral stiffness of anchorage device

Anchorage force at each purlinwhen every purlin is anchoredby a rigid anchor

DESIGN SHEAR STRENGTH OF ARC SPOT WELDS(Section E2.2.1.3)

• Shear Strength - Sheet-to-Sheet Connections:

• Pn = 1.65 tdaFu


• Ω = 2.20

• Φ = 0.70

DESIGN SHEAR STRENGTH OF ARC SPOT WELDS(Section E2.2.1.3) (New in 2007)

Sheet Connections:

50

COMBINED SHEAR AND PULL(Section E4.3.2)

•ASD Method:

•Q/Pns+ 0.71 T/Pnov ≤ 1.10/Ω


•LRFD Method:

•QU/Pns+ 0.71 Tu/Pnov ≤ 1.10Φ

•Pns = 2.7 t1dFu1

•Pnov = 1.5 t1dwFu1

Note the limitations on the equations

COMBINED SHEAR AND PULL-OVER(Section E4.3.2) (New in 2007)

Eq.E4.5.1-1

51

Eq.E4.5.2-1

Note the limitations on the equations

Cold-Formed Steel Design, 4th Edition

The book expanded on to reflect:2007 North American 2007 North American Framing Standards


and other newly published standards and documents.

Ordering information:www.ccfssonline.org

Price: $110 plus shipping

Formed Steel Design, 4th Edition

he book has been thoroughly updated andexpanded on to reflect:

North American Specification2007 North American Framing Standards

52

other newly published standards documents.

Ordering information:www.ccfssonline.org

Price: $110 plus shipping

Wei-Wen Yu

Center for Cold-Formed Steel Structure


Center for Cold-Formed Steel Structure

[email protected], 573

Wen Yu

Formed Steel Structure

53

Formed Steel Structure

[email protected], 573-341-4481

QUESTIONS?


QUESTIONS?

54

2012.02.01 - Cold-Formed Steel Design 2007 Edition - S100

Documents

Transcript of 2012.02.01 - Cold-Formed Steel Design 2007 Edition - S100