Yu W., LaBoube R.A. Cold-Formed Steel Design

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DIFFERENCES BETWEEN SPECIFICATIONS FOR CARBON STEELS AND STAINLESS STEELS 355

(annealed Types 409, 430, and 439). This speciﬁcation was

based on the LRFD concept with the ASD concept as an

alternative.

1.238,1.253,12.9,12.15

In the 1990s, additional studies have been made at Rand

Afrikaans University, University of Sydney, Glasgow Cale-

donian University, University of Strathclyde, and Univer-

sity of Liege. For details, see Refs. 2.63–2.65, 12.10–12.14,

and 12.16–12.36.

Subsequently, the ASCE Standard was updated in

2002

12.39

to supersede the 1990 Standard. The main techni-

cal revisions of design provisions are summarized by Lin,

Yu, and Galambos in Ref. 12.40. This revised document

also includes the design of structural members and connec-

tions using UNS S20400 (annealed and

hard) stainless

steels.

In the past decade, numerous studies have been

conducted by various research groups and individuals. The

research ﬁndings are reported in Ref. 1.412, 12.41–12.77,

12.79, and 12.80.

As far as the design standards are concerned, the ASCE

Standard Speciﬁcation is being updated to reﬂect the results

of additional research. Eurocode 3: Part 1.4 was published

since 1994.

12.37

In 1996, the South African Bureau of

Standards prepared the “Draf Code of Practice—Limit State

Design of Cold-Formed Stainless Steel Members.”

12.38

The

Australian/New Zealand Standard: Cold-Formed Stainless

Steel Structures was published in 2001.

12.78

12.2 DIFFERENCES BETWEEN SPECIFICATIONS

FOR CARBON STEELS AND STAINLESS STEELS

A comparison of the North American Speciﬁcation for

carbon steels

1.345

and the speciﬁcations for stainless

steels

1.160,12.9,12.39

indicates the differences for the follow-

ing aspects:

1. Inelastic buckling of ﬂat elements for compression,

shear, and bending modes

2. Safety factor, load factor, and resistance factor

3. Limitations of width-to-thickness ratio

4. Deﬂection determination

5. Anisotropy

6. Local and distortional buckling considerations

7. Design of beams

8. Column buckling

9. Connections

12.2.1 Inelastic Buckling of Flat Elements for

Compression, Shear, and Bending Modes

In order to consider inelastic buckling (i.e., when the buck-

ling stress exceeds the proportional limit), the following

plasticity reduction factors are being used in the ASCE

standard for stainless steel design to modify the design

formulas derived for elastic buckling:

Type of Buckling Stress

for Flat Elements Plasticity Reduction Factor

Compression

Unstiffened E

Stiffened



Shear G

Bending E

= initial modulus of elasticity, E

= secant modulus, E

= tangent

modulus, G

= initial shear modulus, and G

= secant shear modulus.

The initial moduli of elasticity, initial shear moduli,

secant moduli, tangent moduli, and various plasticity reduc-

tion factors are provided in the Standard for different

grades of stainless steels to be used for various design

considerations.

12.2.2 Safety Factor, Load Factor,

and Resistance Factor

In carbon steel design speciﬁcation a basic safety factor of

1.67 has been used since 1960. For stainless steel design, a

relatively large safety factor of 1.85 is retained in the ASD

speciﬁcation because of the lack of design experience and

due to the fact that in stainless steel design it is necessary to

consider the inelastic behavior at lower stresses than those

used for carbon steel. For column design, the allowable

stress used for stainless steel has also been derived on the

basis of a relatively larger safety factor than for carbon

steel.

Because the 1990 and 2002 ASCE Standard Speciﬁ-

cations were based on the LRFD method with the ASD

method as an alternate, different load factors, safety factors,

resistance factors, and nominal strength equations are given

in the Standard Speciﬁcation for the design of stainless steel

structural members and connections.

12.2.3 Limitations of Width-to-Thickness Ratio

Since pleasing appearance is one of the important consid-

erations in stainless steel design, the maximum permissible

width-to-thickness ratios of ﬂat elements have been reduced

in order to minimize the possible local distortion of ﬂat

elements.

12.2.4 Deﬂection Determination

Because the proportional limit of stainless steel is rela-

tively low and the stress in the extreme ﬁber may be

higher than the proportional limit under service load, special

356 12 INTRODUCTION TO STAINLESS STEEL DESIGN

provisions are included in the stainless s teel speciﬁcation

for computing deﬂections, in which a reduced modulus of

elasticity E

= (E

+ E

)/2 is used. In this expression,

is the reduced modulus of elasticity, E

is the secant

modulus corresponding to the stress in the tension ﬂange,

and E

is the secant modulus corresponding to the stress

in the compression ﬂange.

12.2.5 A nisotropy

For a ustenitic stainless steel, the stress–strain curves are

different for longitudinal tension and compression and for

transverse tension and compression, as shown in Fig. 12.2.

In the ASCE stainless steel speciﬁcation, the basic design

stresses are based on the values obtained from a statistical

analysis. This statistical analysis has been made to ensure

that there is a 90% probability that the mechanical proper-

ties will be equaled or exceeded in a random selection of

the material lot under consideration.

For ferritic stainless steels, a c omprehensive study was

made by Van der Merwe in 1987.

12.6

Figure 12.3 shows

typical stress–strain curves for Types 409 and 430 stainless

steels. It can be seen that these stress–strain relationships

are different from those of austenitic stainless steels as

shown in Fig. 12.2.

12.2.6 Local and D istortional Buckling

Considerations

Since the proportional limits for stainless steel are low

as compared with those for carbon steel and the exposed

surfaces of stainless steel are important for architectural

purposes, the design provisions for determining the permis-

sible stresses for unstiffened and stiffened compression

elements are included for two instances: (1) no local distor-

tion at design loads is permissible and (2) some slight

waving at design loads is permissible.

In the current North American Speciﬁcation for carbon

steel design, distortional buckling provisions are included

for the design of open ﬂexural and compression members

having compression ﬂanges with edge stiffeners. These

relatively new design provisions have not been included

in the ASCE Standard.

Figure 12.3 Initial portion of stress–strain curves for ferritic stainless steels.

12.6

DIFFERENCES BETWEEN SPECIFICATIONS FOR CARBON STEELS AND STAINLESS STEELS 357

12.2.7 Design of Beams

In the speciﬁcation for stainless steel, the theoretical

equation for the critical lateral–torsional buckling moment

has been generalized by utilizing a plasticity reduction

factor E

In addition, the allowable stress used in the stainless steel

ASD speciﬁcation is based on a safety factor of 1.85 instead

of 1.67 used for carbon steel design. The resistance factor

used for stainless steel design is smaller than that for carbon

steel design.

For the web crippling strength of carbon steel, the current

North American Speciﬁcation

1.345

uses the uniﬁed web

crippling equation for different types of sections. For stain-

less steel design, the ASCE Standard adopts the same

design approach used in the 1996 edition of the AISI Spec-

iﬁcation for carbon steel design.

12.2.8 Column Buckling

Since the stress–strain relationships of stainless steels are

different from those for carbon steel, the column buckling

stress for axially loaded compression members is based on

the tangent modulus theory for ﬂexural buckling, torsional

buckling, and ﬂexural–torsional buckling. The safety factor

applied in the ASD design formulas is 2.15 instead of the

1.80 used for cold-formed carbon steel design.

12.2.9 Connections

1. Welded Connections. The design provisions for

welded connections are developed on the basis of the

available research data on stainless steel connections and

the 1996 edition of the AISI Speciﬁcation for cold-formed

carbon steel design.

2. Bolted Connections. Based on a study of the strength

of bolted and welded connections in stainless steel

conducted by Errera, Tang, and Popowich,

12.5

the design

provisions for bolted connections are generalized to reﬂect

the results of research work. The design provisions are

related to the determination of edge distance, tension

stress, and bearing stress. Additional design information is

included for the shear and tension stresses for Types 201,

304, 316, and 430 stainless steel bolts.

3. Screw Connections . The ASCE Standard does not

include design provisions for screw connections due to lack

of research data at the time of developing the document.

CHAPTER 13

Light-Frame Construction

13.1 GENERAL REMARKS

Cold-formed steel structural members have been used for

residential and commercial light-frame construction for

many years (Fig. 13.1). The primary advantages of cold-

formed steel are light weight, high strength and stiffness,

ductility, uniform quality, dimensional stability, ease of

prefabrication and mass production, economy in transporta-

tion and handling, ease and speed of installation, noncom-

bustibility, and the fact that it is termite proof and rot proof.

The major structural components used for light-frame

construction are wall studs, ﬂoor and ceiling joists, roof

rafters, roof and ﬂoor trusses, decking, and panels. Since

1960, numerous research and development projects have

concentrated on cold-formed steel light-frame construction

(see Refs. 1.21, 1.24–1.28, 1.30, 1.39, 1.72, 1.113, 1.114,

1.282–1.285, 1.297–1.301, 5.107, 5.138, 5.139, 8.88, and

13.1–13.46). These projects represent a signiﬁcant invest-

ment by the industry to eliminate barriers to the increased

use of cold-formed steel in light-frame construction.

The industry also recognized that the lack of prescrip-

tive building code requirements prevented cold-formed steel

from gaining wider acceptance among builders and code

ofﬁcials. To remedy this situation, a four-year project was

conducted by the National Association of Home Builders

Research Center to develop a prescriptive method for resi-

dential cold-formed steel framing.

1.280

This project was

sponsored by the American Iron and Steel Institute, the U.S.

Department of Housing and Urban Development (HUD),

and the National Association of H ome Builders (NAHB).

In 1997, provisions of the prescriptive method were ﬁrst

adopted by the International Code Council (ICC) for its

One- and Two-Family Dwelling Code. This prescriptive

method is now an ANSI-approved standard, as discussed

in Section 13.2.2.8.

13.2 FRAMING STANDARDS

Starting in the mid-1990s, there began an increased interest

in cold-formed steel for residential and light commer-

cial framing in the United States and worldwide. These

applications include wall, ﬂoor, and roof framing in a

number of building types. Although the AISI North Amer-

ican speciﬁcation

1.345

had gained acceptance and was in

widespread use, a number of framing-speciﬁc design issues

were not adequately addressed for this emerging market.

As AISI considered the needs of the light framing

industry, it assessed the scope, limitations, and complexity

of its speciﬁcation and noted that the emphasis was on

member design, primarily for traditional C- and Z-shapes.

However, within typical light framing applications there

were many applications where the members would be used

in systems not explicitly addressed by the AISI North

American Speciﬁcation, such as built-up header assemblies

(Fig. 13.2), roof trusses, and shear walls. New design rules

were needed to recognize the efﬁciencies inherent to these

assemblies.

Also, cold-formed steel truss assemblies were emerging

with complex chord shapes (Fig. 13.3) that were devel-

oped to better optimize the combination of material,

fabrication, transportation, and installation cost. Unfortu-

nately, these shapes were not explicitly addressed by the

Speciﬁcation.

1.345

In addition, to facilitate the needs of

homebuilders, an industry consensus prescriptive method

was needed to allow builders to have standard construction

details and easy-to-use tables to select appropriate member

sizes.

AISI extended its standards development activity to

support the growing needs of the cold-formed steel framing

industry. However, rather than add to the complexity of the

AISI North American Speciﬁcation, it was decided that a

new family of standards should be developed.

It seemed logical to accommodate this activity under the

existing AISI structure. However, it was decided that a

new committee should be formed, called the Committee

on Framing Standards. The Committee on Speciﬁcations

would retain responsibility for the Speciﬁcation, as well its

test procedures, design manuals, and design guides. The

Committee on Framing Standards would take on the new

standards needed for cold-formed steel framing.

13.1–13.8

13.2.1 The Committee on Framing Standards

The AISI Committee on Framing Standards (COFS) was

formed in 1997 and operates under the same procedures

as the AISI Committee on Speciﬁcations. These proce-

dures earned AISI the approval of ANSI as a recognized

consensus standards organization. Speciﬁc requirements are

met in order to accommodate balance between producer,

359

360 13 LIGHT-FRAME CONSTRUCTION

Figure 13.1 Cold-formed steel framing. (Courtesy of ITW Building Components Group.)

Figure 13.2 Built-up header assembly. (Courtesy of Steel Framing Alliance.)

FRAMING STANDARDS 361

Figure 13.3 Complex shapes for truss chords.

user and general interest categories, voting, including the

resolution of negatives, and public review, interpretations,

and appeals.

The COFS established as its mission, “To eliminate regu-

latory barriers and increase the reliability and cost competi-

tiveness of cold-formed steel framing in residential and light

commercial building construction through improved design

and installation standards.”

The committee established as its primary objective, “To

develop and maintain consensus standards for cold-formed

steel framing, manufactured from carbon or low alloy ﬂat

rolled steel, that describe reliable and economical design

and installation practices for compliance with building code

requirements.”

In 2001 the COFS completed three design stan-

dards, namely Standard for Cold-Formed Steel

Framing—General Provisions, Standard for Cold-

Formed Steel Framing—Truss Design, and Standard for

Cold-Formed Steel Framing—Header Design as well as

ﬁnalizing a ﬁrst edition of Standard for Cold-Formed Steel

Framing—Prescriptive Method for One and Two Family

Dwellings. In 2002, a commentary with design examples

to the prescriptive method was completed.

In 2004, the COFS completed updates to the existing

standards and added Standard for Cold-Formed Steel

Framing—Lateral Design and Standard for Cold-Formed

Steel Framing—Wall Stud Design.

In 2005, the C OFS completed an industry Code of Stan-

dard Practice for Cold-Formed Steel Structural Framing.

In 2006, the COFS updated this document and added a

commentary.

In 2007, the COFS completed updates to the existing

standards and added North American Standard for Cold-

Formed Steel Framing—Product Data and North American

Standard for Cold-Formed Steel Framing—Floor and Roof

System Design.

13.2.2 2007 Edition Framing Standards

In 2007 it was the ﬁrst time that the standards were specif-

ically for North America, that is, intended for adoption and

use in the United States as well as Canada and Mexico. In

addition, a new numeric designation system was introduced

to better reference the documents in codes and speciﬁca-

tions. For example, AISI S100-07 was the new designation

for North American Speciﬁcation for the Design of Cold-

Formed Steel Structural Members.

13.2.2.1 North American Standard for Cold-Formed

Steel Framing—General Provisions, AISI S200-07.

This standard addresses those design aspects that are

common to engineered and prescriptive design and applies

to the design, construction, and installation of structural

and nonstructural cold-formed steel framing members

where the speciﬁed minimum base metal thickness is

from 18 mils (0.0179 in.) to 118 mils (0.1180 in.). S200

provides general requirements that are not addressed

in the AISI North American speciﬁcation for material,

corrosion protection, products, member design, member

condition, installation, and connections. In 2001, based on

work by Sokol, LaBoube, a nd Yu,

13.23

provisions were

added to address screw connections where the screws are

installed closer than permitted by the AISI North American

speciﬁcation or are stripped. In 2004, based on work by

Fox,

13.13

alignment framing tolerances where adjusted

for the case where the bearing stiffener is located on the

backside of the ﬂoor joist. In 2007, the deﬁnitions for

terms and commentary language were centralized in this

standard to provide better guidance and assure consistency

across the framing standards.

13.2.2.2 North American Standard for Cold-Formed

Steel Framing—Product Data, AISI S201. This stan-

dard is intended to establish and encourage the production

and use of standardized products (Fig. 13.4). It provides

criteria for cold-formed steel utilized in structural and

nonstructural framing applications and deﬁnes standard

material grades and speciﬁcations, minimum base steel and

design thickness, and coatings for corrosion protection.

362 13 LIGHT-FRAME CONSTRUCTION

Figure 13.4 Standard framing member types.

13.2

13.2.2.3 North American Standard for Cold-Formed

Steel Framing—Floor and Roof System Design, A ISI

S210. This standard is intended for the design and instal-

lation of cold-formed steel framing for ﬂoor and roof

systems in buildings. The standard provides a methodology

for continuously braced design, that is, considering the

structural contribution of attached sheathing or deck. For

continuously braced design Section B4 of S210 states:

Bracing members shall be designed in accordance with Section

D3 of AISI S100, unless bracing is provided that satisﬁes the

following requirements:

1. In continuously braced design, the sheathing or deck shall

consist of a minimum of

inch wood structural sheathing

that complies with DOC PS 1, DOC PS 2, CSA 0437 or

CSA 0325, or steel deck with a minimum proﬁle depth of



and a minimum thickness of 0.0269



. The sheathing

or deck shall be attached with minimum No. 8 screws at

a maximum 12 inches on center.

2. In continuously braced design, ﬂoor joists, ceiling joists

and roof rafters with simple or continous spans that

exceed 8 feet shall have the tension ﬂanges laterally

braced. Each intermediate brace shall be spaced at 8 feet

maximum and shall be designed to resist a required lateral

force, P

, determined in accordance with the following:

a. For uniform loads:

= 1.5(m/d)F

where m = distance from shear center to midplane

of web

d = depth of C-shape section

F = wa

w = uniform design load

a = distance between centerline of braces

b. For concentrated loads:

If x = 0.3a

= 1.0





If x<x<1 .0 a

= 1.4





1 −



where F = concentrated design load

x = distance from concentrated load to brace

FRAMING STANDARDS 363

3. In continuously braced design, ﬂoor joists, ceiling joists

and roof rafters that are continuous over an intermediate

support shall be designed in accordance with AISI S100.

The standard also includes provisions for clip angle

bearing stiffeners, based on a recent testing program by

Fox.

13.14

13.2.2.4 North American Standard for Cold-Formed

Steel Framing—Wall Stud Design, AISI S211. This

standard provides technical information and speciﬁcations

for designing wall studs made from cold-formed steel.

It addresses items not presently covered by the AISI

North American speciﬁcation, including load combina-

tions speciﬁc to wall studs and a rational approach for

sheathing braced design based on engineering judgment

and research studies by Miller

13.21

and Lee.

13.19

Method-

ologies are included to evaluate stud-to-track connections

based on work by Fox and Schuster,

13.12

Bolte,

13.9

and

Daudet

13.10

and deﬂection track connections based on work

by Gerloff, Huttelmaier, and Ford.

13.15

In 2007, the stan-

dard was revised to recognize the Canadian limits states

design (LSD) method.

As noted above, AISI S211 provides a rational design

method for sheathing braced wall studs. Section 9.3.2

presented a general discussion of diaphragm-braced wall

studs. In AISI S211 sheathing braced design is based on

rational analysis assuming that the sheathing braces the stud

at the location of each sheathing-to-stud fastener location.

The axial capacity of the wall stud is determined based

on the strength of the unbraced length of the stud and the

sheathing-to-wall connection.

For major-axis buckling the unbraced length is the

distance between the end supports. For minor-axis buck-

ling and torsion the unbraced length is taken as twice

the distance between the sheathing connectors. Twice the

distance is conservatively assumed in order to account for

the potential that an occasional attachment is defective to a

degree that it is completely inoperative.

To prevent failure of the sheathing-to-wall stud connec-

tion, the maximum axial load is limited by AISI S211. This

maximum axial load is based on the bracing principles as

deﬁned by Winter

13.26

as discussed in Ref. 13.4.

Example 13.1 Use the ASD and LRFD methods to

compute the allowable axial load for the C-section shown

in Fig. 9.12 if it is to be used as wall studs having a length

of 12 ft. Assume that the studs are spaced at every 12 in.

and that

-in.-thick gypsum boards are attached to both

ﬂanges of the stud. All fasteners are No. 6, type S-12, self-

drilling drywall screws at 12-in. spacing. Use F

= 33 ksi.

Assume that the dead load–live load ratio is

. The design

assumptions and design data are the same as Example 9.2.

SOLUTION

A. ASD Method

1. Sectional Properties. Using the methods discussed in

Chapters 4 and 5 and the A ISI Design Manual, the

following sectional properties can be computed on the

basis of the full area of the given C-section:

A = 0.651in.

= 2.823 in.

= 0.209 in.

= 2.08 in. r

= 0.566 in.

J = 0.00109 in.

= 1.34 in.

= 1.071 in. r

= 2.41 in.

2. Allowable Axial Load. According to Section B1.2 of

AISI S211,

13.4

the allowable axial load for the given

stud having identical sheathing attached to both ﬂanges

shall be determined with consideration given to the axial

strength of the wall stud and the sheathing-to-wall-stud

connection.

a. To prevent column buckling of the stud between

fasteners in the plane of the wall, consideration

should be given to ﬂexural buckling of the singly

symmetric C-section. In the calculation of the

elastic buckling stress a s discussed in Chapter 5,

the unbraced length KL is taken to be two times the

distance between fasteners,

KL = 2 × spacing of screws

= 2 × 12 = 24 in.

= 42.40

(KL/r)

(29,500)

(42.40)

= 161.95 ksi





161.95

= 0.451 < 1.5

From Eq. (5.54),

= (0.658

0.451

)(33)

= 30.31 ksi

364 13 LIGHT-FRAME CONSTRUCTION

Using the effective width method as calculated

in accordance with Chapter B of AISI S100 and

discussed in Chapter 3,

= 0.535 in.

= A

= (0.535)(30.31) = 16.22 kips



16.22

1.80

= 9.01 kips

b. To prevent ﬂexural and/or torsional–ﬂexural overall

column buckling, the theoretical elastic buckling

stress F

should be the smaller of the two values

computed for the singly symmetric C-section as

follows. When calculating the elastic buckling stress

as discussed in Chapter 5, the unbraced length with

respect to the major axis shall be taken as the

distance between the end supports. The unbraced

length with respect to the minor axis and torsion shall

be taken as twice the distance between the sheathing

connectors:

2β

[(σ

+ σ

) −



(σ

+ σ

)

− 4βσ

]

= 55.54 ksi

(KL/r

)

(29,500)

(12 × 12/2.08)

= 60.75 ksi



GJ +



0.651(2.41)



11,300 × 0.00109

(29,500)(1.34)

(2 × 12)



= 168.03 ksi





55.54

= 0.771 < 1.5

= (0.658

0.771

)(33)

= 25.74 ksi

Using the effective width method as calculated

in accordance with Chapter B of AISI S100 and

discussed in Chapter 3,

= 0.550 in.

= A

= (0.550)(25.74) = 14.16 kips



14.16

1.80

= 7.87 kips

c. To prevent failure of the sheathing-to-wall-stud

connection, the maximum nominal load, that is,

the building code–speciﬁed load, shall not exceed

the values given in Table B1-1 of AISI S211. For

-in.-thick gypsum sheathing attached by No. 6

screws, the maximum nominal axial load in the stud

must not exceed 5.8 kips.

d. Determination of P

. From items (a), (b), and (c), the

following three values of allowable axial load were

computed for the different design considerations:

i. P

= 9.01 kips

ii. P

= 7.87 kips

iii. P

= 5.80 kips (controls)

From Example 9.2, P

= 5.73 kips.

B. LRFD Method. For the LRFD method, the design

strength is

= (0.85)(14.16) = 12.04 kips

Based on the load combinations given in Section 3.3.2.2,

the governing required axial load is

= 1.2P

+ 1.6P

= 1.2P

+ 1.6(5P

) = 9.2P

Using P

= φ

12.04

9.2

= 1.31 kips

= 5P

= 6.54 kips

The allowable axial load is

= P

+ P

= 7.85 kips

For LRFD, the allowable load is also governed by the

sheathing-to-wall-stud connection. Thus, ASD and LRFD

give the same allowable load.

13.2.2.5 North American Standard for Cold-Formed

Steel Framing—Header Design, AISI S212. This stan-

dard provides general, design, and installation requirements

for headers fabricated from cold-formed steel members for

use over door and window openings. The standard covers

box and back-to-back headers and double and single L-

headers used in single-span conditions for load-carrying

purposes in buildings.

The design methodologies are based on testing at the

NAHB Research Center, the University of Missouri-Rolla,

and industry, as reported by Elhajj and LaBoube,

13.11

Stephens and LaBoube,

13.24

and Stephens.

13.25

The design

methodologies consider the synergy of the header compo-

nents, C-sections, and track and address the design of the

header for bending, shear, web crippling, and combina-

tions of bending and shear and bending and web crippling.