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

Подождите немного. Документ загружается.

FRAMING STANDARDS 365

Figure 13.5 Double L-header assembly. (Courtesy of Steel Framing Alliance.)

In 2004, provisions for single L-headers (Fig. 13.5) were

added, based on work by LaBoube.

13.18

In 2007, design

provisions were included for designing inverted L-header

assemblies.

13.2.2.6 North American Standard for Cold-Formed

Steel Framing—Lateral Design, AISI S213. This

standard contains design requirements for shear walls,

diagonal strap bracing that is part of a structural wall,

and diaphragms that provide lateral support to a building

structure.

The standard includes provisions for both Type 1 and

Type 2 shear walls. Both s trength and deﬂection guidelines

are provided. Prior to development of this standard, these

requirements were scattered among various building code

provisions, design guides, technical notes, and research

reports. AISI S213 presents in one document the results of

various research studies summarized by Refs. 13.27–13.40.

In 2007, substantive changes were made to the standard and

commentary, including the addition of provisions for shear

walls with ﬁberboard sheathing and special seismic provi-

sions for diagonal strap bracing and provisions for forces

contributed by masonry and concrete walls and forces

contributed by other concrete or masonry construction. In

addition, provisions for shear walls sheathed with wood

structural panel and gypsum board sheathing were added

for use in Canada.

Reference 13.41 discusses the design for wood panel and

steel sheet sheathed cold-formed steel framed shear wall

assemblies. Design and detailing examples are provided

for both wind- and seismic force-resistant shear wall

assemblies.

13.2.2.7 North American Standard for Cold- Formed

Steel Framing—Truss Design, AISI S214. This standard

provides technical information and design provisions for

cold-formed steel truss construction and applies to cold-

formed steel trusses used for load-carrying purposes in

366 13 LIGHT-FRAME CONSTRUCTION

buildings. The standard is not just for design. It also applies

to manufacture, quality criteria, installation, and testing a s

they relate to the design of cold-formed steel trusses.

The requirements of the truss standard apply to both

generic C-section trusses as well as the various propri-

etary truss systems and were developed, in part, based

on extensive research at the University of Missouri-

Rolla, as reported by Harper,

13.16

Reiman,

13.22

Koka,

13.17

Ibrahim,

13.42

and LaBoube and Yu.

13.34

AISI S214 requires compression chord members to be

evaluated using AISI S100, but the standard stipulates

appropriate assumptions for the unbraced length, KL.For

example, when the chord is continuous over at least one

panel point and where sheathing is directly attached to the

chord, K may be taken as 0.75.

Design provisions are available for determining the axial

compressive strength of thin, ﬂat gusset plates based on the

research work of Lutz and LaBoube.

13.20

Determination of the shear strength or web crippling

strength of coped C-sections is enabled by S214.

13.2.2.8 Standard for Cold-Formed Steel Framing—

Prescriptive Method for One- and Two-Family Dwellings.

AISI S230. This standard provides prescriptive require-

ments for cold-formed steel-framed detached one- and

two-family dwellings, townhouses, attached multifamily

dwellings, and other attached single-family dwellings. It

includes numerous tables and details to allow typical resi-

dential buildings (Fig. 13.6) complying with the limitations

therein to be constructed. Alternatively such dwellings may

be designed by a design professional. In 2007, the standard

was updated to latest codes and standards and expanded

in many ways, including wind speeds up to 150 miles per

hour and seismic loads up to seismic design category E.

The allowable number of stories was increased from two

to three, and provisions were added for clip angle bearing

stiffeners, anchor bolt washers in high-wind/seismic areas,

FLOOR FRAMING(F1)

(NL1)

NON-LOAD

ROOF FRAMING

(R1)

WALL

(W1)

BEARING

WALL

FRAMING

Figure 13.6 Typical residential building.

13.8

DESIGN GUIDES 367

gable endwall framing, hip roof framing, single L-headers,

inverted L-header assemblies, and grade 50 headers and

roof rafters.

13.2.2.9 Code of Standard Practice for Cold-Formed

Steel Structural Framing. This document deﬁnes

accepted norms of good practice for fabrication and

installation of cold-formed steel structural framing. It

helps deﬁne the lines of responsibility in cold-formed steel

framing design and construction, which have previously

been vague and unclear. Among the many topics covered

are general requirements, classiﬁcation of materials, plans

and speciﬁcations, installation drawings, materials, manu-

facture and delivery, installation requirements, quality

control, and contractual relations. The document helps

deﬁne the roles of the owner’s representative, architect of

record, engineer of record, specialty engineer, manufac-

turer, framing contractor, and truss/wall panel supplier in

the design and construction of cold-formed steel-framed

structural systems. It is loosely based on similar documents

by the American Institute of Steel Construction and

Steel Joist Institute and was guided by documents by

the Structural Building Component Association (formerly

Steel Truss and Component Association) and the Council

of American Structural Engineers.

13.3 DESIGN GUIDES

To assist the design community, numerous design guides on

such topics as structural elements and systems, shear walls

and diaphragms, corrosion and durability, ﬁre, sound, and

thermal have been developed. Many of these documents

are free downloads from either the Steel Framing Alliance

(www.steelframing.org) or Cold-Formed Steel Engineers

Institute (www.cfsei.org) websites. Noteworthy references

are AISI Cold-Formed Steel Framing Design Guide

13.43

and

Steel Stud Brick Veneer Design Guide

13.44

and the CFSEI

Cold-Formed Steel Framed Wood Panel or Steel Sheathed

Shear Wall Assemblies.

13.45

CHAPTER 14

Computer-Aided Design

14.1 GENERAL REMARKS

Computers are widely used in research, structural analysis,

and design. With the adoption of the direct-strength method

for cold-formed steel design, the use of a numerical method

is explicitly permitted. In fact, a numerical method is

required in order to determine the elastic buckling load for

the member as a whole rather than an element-by-element

local buckling analysis. Numerical methods are enabled by

the use of the computer and include ﬁnite element, ﬁnite

strip, generalized beam theory, and others.

Because the research work on cold-formed steel struc-

tures usually involves studies of the structural behavior

and instability of plate components, individual members,

and/or the entire assembly, hand calculations are exces-

sively lengthy and extremely difﬁcult. Computers have been

used to great advantage in obtaining solutions for compli-

cated problems involving these structures under various

boundary and loading conditions.

As discussed in the preceding c hapters, the formulas used

for the design of cold-formed steel structural members are

quite complicated, particularly for those members having

unusual cross sections. It may be found that even the

determination of sectional properties requires burdensome

calculations, which may involve the use of successive

approximations. For this reason, various institutions and

companies have used computers to develop the data neces-

sary for the preparation of design tables and charts.

In addition, computers have also been used for the devel-

opment and design of industrialized buildings, minimum-

weight design of structural members, minimum-cost design

of structural systems, and special structures.

Section 14.2 contains a brief review of some computer

programs used for the analysis and design of cold-formed

steel members and structures in the past.

14.2 COMPUTER PROGRAMS FOR DESIGN

OF COLD-FORMED STEEL STRUCTURES

14.2.1 Sectional Properties

Computer programs have been used extensively for the

preparation of the design tables included in Ref. 1.349

and in many manufacturers’ publications. The equations

needed for the calculation of s ectional properties of angles,

channels, hat sections, I-sections, T-sections, and Z-sections

are summarized in Part I of Ref. 1.349.

Previously the calculation of the sectional properties of

various types of structural members has been included as a

subroutine in complete computer programs for the analysis

and design of cold-formed steel structures.

14.1

14.2.2 Optimum Design

The minimum-weight design of cold-formed steel members

has been studied by Seaburg and Salmon

1.247

on the basis of

the AISI speciﬁcation.

1.4

It has been found that the gradient

search method requires less time than the direct-search

method. This optimization technique has been illustrated

for the selection of the most favorable cross section of the

hat-shaped roof deck.

In 1971 a computer program, DOLGAS, was developed

by Klippstein for the design of steel trusses fabricated from

cold-formed steel members.

14.1

It provides for the selection

of minimum-weight members (channels, Z-sections, hat

sections, sigma sections, or tubular sections) to meet the

requirements of the AISI Speciﬁcation.

1.4

This program

used STRESS to compute member forces and then check

the design of members on the basis of the AISI design

criteria. The output included structural design information

and the necessary data for fabrication.

In some cases, emphasis has changed to the minimum-

cost design to consider the costs of material, fabrication,

and erection. For e xample, the minimum-cost design of

composite ﬂoor systems using cold-formed steel decking

has been conducted by Nicholls and Merovich.

14.2

In the

design, the grid search procedure has been used. This study

includes the costs of cold-formed steel decking, concrete

slab, rolled beams, shoring of decking as necessary, temper-

ature mesh in slab, and necessary ﬁreprooﬁng. In addition,

the optimization of cold-formed steel shapes is presented

by Douty in Ref. 14.3.

14.2.3 Special Structures

In Chapter 9 it was mentioned that the accurate analysis

and design of special structures subjected to unsymmetrical

loading and nonuniform support conditions can be

achieved by using computers. For example, the analysis

and design of the world’s largest cold-formed steel

369

370 14 COMPUTER-AIDED DESIGN

primary structure

1.82

have been completed by using the

ﬁnite-element method.

14.4

The hypar module as shown in

Fig. 9.24 has been analyzed under four different loading

conditions. Reference 14.4 indicates that the computer

program specially developed by Tezcan, Agrawal, and

Kostro can be used to determine the deﬂections and

stresses of a ny general multiwing hyperbolic paraboloid

shell with any type of support and beam arrangement

under any arbitrary load condition.

14.2.4 Industrialized Buildings

The conventional optimum design of industrialized

buildings is usually accomplished by repeated analysis,

modiﬁcation, and reanalysis of redeﬁned structural systems.

The use of computers increases the design ﬂexibility of

the building system and results in a minimum-weight or a

minimum-cost design.

13.5

Computers may also be used for

other operations concerning manufacturing, distribution,

and administration work.

14.2.5 Decision Table and Flow Charts

A decision table is a concise tabular display of the logical

conditions and the appropriate actions to be taken as the

result of these conditions. It is useful in preparing computer

programs which utilize the speciﬁcation provisions and

in identifying all c ombinations of factors not speciﬁcally

covered by the speciﬁcation.

The decision table formulation of the AISI Speciﬁcation

for the design of cold-formed steel structural members was

originally developed by Seaburg and modiﬁed to conform

to the 1986 edition of the speciﬁcation by Midgley–Clauer

Associates (Ref. 14.7). The decision table can be converted

directly into programming language.

The 1986 edition of the AISI Cold-Formed Steel Design

Manual contained a series of ﬂow charts. These charts

proved to be an excellent means of helping the user to

understand the design provisions and to provide a clear

picture of the items that need to be considered in design.

They were very useful guidelines for computer program-

mers. Reference 14.12 presents an overview of the 2007

edition of the North American Speciﬁcation,

1.345

the 2008

edition of the AISI Design Manual,

1.349

as well as ﬂow

charts based on Ref. 1.345 for both compression members

and ﬂexural members.

14.2.6 Computer Programs

As computer technology advances, the use of computers

for the design of cold-formed steel structures is unlim-

ited, as demonstrated by Zuehlke (Ref. 14.8) and

others.

In 1991, the American Iron and Steel Institute published

a document, Cold-Formed Steel Design Computer

Programs, which contained descriptions of 12 computer

programs using the AISI Speciﬁcation. This document w as

updated by the Center for Cold-Formed Steel Structures

in 1993 and 1996 to include 30 programs from the

United States, Canada, Australia, and South Africa.

14.9

Information pertaining to several of the computer programs

is available on the Center’s website.

14.10

Reference 14.13,

developed by the Cold-Formed Steel Engineers Institute

(CFSEI), is a summary of 13 available computer programs

for cold-formed steel design.

Dr. Helen Chen developed a set of MathCAD computer

programs on the basis of the 1996 edition of the AISI Spec-

iﬁcation. The example problems deal with (a) beam lateral

buckling strength, (b) shear strength of the stiffened web,

cylindrical tubes, (f) brace force for C- and Z-sections,

(g) welded c onnections, (h) bolted connections, and

(i) screw connections.

14 11

These programs can be found

on the AISI website at www.steel.org.

CHAPTER 15

Direct-Strength Method

15.1 GENERAL REMARKS

Chapters 3–6 of this book deal mainly with the traditional

design of cold-formed steel structural members using the

effective width approach. For this method, the effective

widths of individual elements are determined in accordance

with the main speciﬁcation.

1.345

From Eq. (3.39), it can

be seen that the reduction factor ρ, used for calculating

the effective width of a given element, is a function of

the critical local buckling stress f

and the maximum

compressive stress applied in the element. The premise

of the direct-strength method (DSM) is that this idea for

elements can be extended to entire members. The DSM

provides expressions to determine the strength as a function

of elastic buckling for a local-plate mode similar to the

effective width but also for distortional and global modes.

It extends the design expression for effective width to all

modes.

The DSM was developed in the early 2000s under

the supervision of the AISI Subcommittee on Element

Behavior.

15.13

A new Appendix 1, Design of Cold-Formed

Steel Structural Members Using the Direct Strength

Method, was added to the 2001 edition of the North Amer-

ican Speciﬁcation in the AISI Supplement 2004.

1.343, 1.344

The Direct Strength Method (DSM ) Design Guide was

prepared by Schafer in 2006.

1.383

Appendix 1 of the speciﬁcation provides alternative

design procedures for several sections of the main Spec-

iﬁcation. The provisions are applicable for determining

the nominal axial strengths (P

) for columns and ﬂex-

ural strengths (M

) for beams. It is permitted to substitute

the nominal strengths, safety factors, and resistance factors

from Appendix 1 for the corresponding values in the main

Speciﬁcation.

As stated in the Design Guide, the practical advantages

of the DSM are (a) no effective width calculations, (b) no

interactions are required, and (c) gross cross-sectional prop-

erties are used. The theoretical advantages are (1) explicit

design method for distortional buckling, (b) includes inter-

action of elements, and (c) explores and includes all

stability limit states. However, this method is currently

limited only to the determination of nominal strengths for

columns and beams under prequaliﬁcations. Other advan-

tages and limitations are discussed in the Design Guide.

This chapter covers only the general information on the

DSM. For the reasoning behind and justiﬁcation for the

DSM expressions, the reader is referred to Section 13.4 of

the SSRC Guide,

1.412

the Commentary,

1.346

and the Design

Guide.

1.383

Additional information can also be found from

Refs. 15.14–15.26.

15.2 NORTH AMERICAN DSM PROVISIONS

Appendix 1 of the North American Speciﬁcation contains

two major sections for the design of cold-formed steel struc-

tural members using the DSM. Section 1.1 covers general

provisions dealing with (a) applicability, (b) geometric and

material limitations for prequaliﬁed columns and beams,

Section 1.2 provides member design requirements.

On the basis of Section 1.1.1.1 of Appendix 1, unperfo-

rated columns and beams that fall within the geometric and

material limitations given in Tables 1.1.1-1 and 1.1.1-2 of

Appendix 1, respectively, shall be permitted to be designed

using Sections 1.2.1 and 1.2.2 of Appendix 1, respec-

tively. For members including perforations, the new design

methods have been developed from Moen and Schafer’s

research work.

3.243–3.246, 3.251

It is expected that new provi-

sions will soon be available for the design of perforated

members.

According to Section 1.1.2 of Appendix 1 for elastic

buckling, analysis shall be used for the determination

of elastic buckling loads and for moments used in this

appendix. For columns, this includes the local, distor-

tional, and overall buckling loads (P

crl

, P

crd

,andP

cre

of Section 1.2.1). For beams, this includes the local,

distortional, and overall buckling moments (M

crl

, M

crd

and M

cre

of Section 1.2.2).

Based on Section 1.1.3 of Appendix 1 for serviceability

determination, the bending deﬂection at any moment, M ,

due to nominal loads shall be permitted to be determined

by reducing the gross moment of inertia, I

, to an effective

moment of inertia for deﬂection as given in Eq. (15.1):

eff

= I





≤ I

(15.1)

371

372 15 DIRECT-STRENGTH METHOD

where M

= nominal ﬂexural strength (resistance) M

deﬁned in Section 1.2.2 of the speciﬁcation,

but with M

replaced by M in all equations

of Section 1.2.2 of the speciﬁcation

M = moment due to nominal loads (speciﬁed

loads) on member to be considered

(M ≤ M

)

The following excerpts for strength determinations of

columns and beams are adapted from Appendix 1 of the

North American speciﬁcation

1.345

1.2 Members

1.2.1 Column Design

The nominal axial strength [resistance], P

, shall be the

minimum of P

, P

,andP

as given in Sections 1.2.1.1–

1.2.1.3 of the speciﬁcation. For columns meeting the geometric

and material criteria of Section 1.1.1.1 of the speciﬁcation, 

and φ

shall be as follows:



= 1.80 (ASD)



0.85 (LRF D)

0.80 (LSD)

For all other columns,  and φ of the main Speciﬁcation,

Section A1.2(b), shall apply. The available strength [factored

resistance] shall be determined in accordance with applicable

method in Section A4, A5, or A6 of the main Speciﬁcation.

1.2.1.1 Flexural, Torsional, or Flexural–Torsional Buckling

The nominal axial strength [resistance], P

, for ﬂexural,

torsional, or ﬂexural–torsional buckling shall be calculated in

accordance with the following:

(a) For λ

≤ 1.5



0.658



(15.2)

(b) For λ

> 1.5



0.877



(15.3)

where



cre

(15.4)

where

= A

(15.5)

and P

cre

is the minimum of the critical elastic column buck-

ling load in ﬂexural, torsional ,orﬂexural–torsional buckling

determined by analysis in accordance with Section 1.1.2 of the

speciﬁcation.

1.2.1.2 Local Buckling

The nominal axial strength [resistance], P

,forlocal buckling

shall be calculated in accordance with the following:

(a) For λ

≤ 0.776

= P

(15.6)

(b) For λ

> 0.776



1 −0.15



crl



0.4





crl



0.4

(15.7)

where



crl

(15.8)

and P

= value as deﬁned in Section 1.2.1.1 of the

speciﬁcation

crl

= critical elastic local column buckling load

determined by analysis in accordance with

Section 1.1.2 of the speciﬁcation

1.2.1.3 Distortional Buckling

The nominal axial strength [resistance], P

,fordistortional

buckling shall be calculated in accordance with the following:

(a) For λ

≤ 0.561

= P

(15.9)

(b) For λ

> 0.561



1 −0.25



crd



0.6





crd



0.6

(15.10)

where



crd

(15.11)

where P

= value as given in Eq. (15.5)

crd

= critical elastic distortional column buckling

load determined by analysis in accordance

with Section 1.1.2 of the Speciﬁcation

1.2.2 Beam Design

The nominal ﬂexural strength [resistance], M

, shall be the

minimum of M

, M

,andM

as given in Sections 1.2.2.1–

1.2.2.3 of the Speciﬁcation. For beams meeting the geometric

and material criteria of Section 1.1.1.2 of the Speciﬁcation, 

and φ

shall be as follows:



= 1.67 (ASD)



0.90 (LRFD)

0.85 (LSD)

COMMENTARY ON APPENDIX 1 (DSM) 373

For all other beams,  and φ of the main Speciﬁcation,

Section A1.2 (b), shall apply. The available strength [factored

resistance] shall be determined in accordance with applicable

method in Section A4, A5, or A6 of the main Speciﬁcation.

1.2.2.1 Lateral–Torsional Buckling

The nominal ﬂexural strength [resistance], M

, for lateral–

orsional buckling shall be calculated in accordance with the

following:

(a) For M

cre

< 0.56M

= M

cre

(15.12)

(b) For 2.78M

≥ M

cre

≥ 0.56M



1 −

10M

36M

cre



(15.13)

cre

> 2.78M

= M

(15.14)

where M

cre

= critical elastic lateral–torsional buckling

moment determined by analysis in accordance

with Section 1.1.2 of the speciﬁcation

and

= S

(15.15)

where S

= gross section modulus referenced to the extreme

ﬁber in ﬁrst yield

1.2.2.2 Local Buckling

The nominal ﬂexural strength [resistance], M

,forlocal buck-

ling shall be calculated in accordance with the following:

(a) For λ

≤ 0.776

= M

(15.16)

(b) For λ

> 0.776



1 −0.15



crl



0.4





crl



0.4

(15.17)

where



crl

(15.18)

and M

= value deﬁned in Section 1.2.2.1 of the

Speciﬁcation

crl

= critical elastic local buckling moment determined

by analysis in accordance with Section 1.1.2 of

the Speciﬁcation

1.2.2.3 Distortional Buckling

The nominal ﬂexural strength [resistance], M

,fordistortional

buckling shall be calculated in accordance with the following:

(a) For λ

≤ 0.673

= M

(15.19)

(b) For λ

> 0.673



1 −0.22



crd



0.5





crd



0.5

(15.20)

where



crd

(15.21)

and M

= value as given in Eq. (15.15)

crd

= critical elastic distortional buckling moment

determined by analysis in accordance with Section

1.1.2 of the Speciﬁcation.

15.3 COMMENTARY ON APPENDIX 1 (DSM)

The background information and the reasoning behind

various DSM design equations and the elastic buckling

analysis used for the determination of the nominal strengths

of members for overall, local, and distortional buckling

are discussed in the Commentary on Appendix 1.

1.346

For

the compression and bending elastic buckling analysis

using the ﬁnite-strip method, examples are presented in the

Commentary and the Design Guide for C-section, Z-shape,

angle, hat section, and other shapes by using the computer

program CUFSM.

For column design using a C-section (9CS 2.5 ×059),

Fig. 15.1 shows the ratios of (a) the critical elastic

local buckling load to the yield load (P

crl

), (b) the

critical elastic distortional buckling load to the yield load

crd

), and (c) the elastic ﬂexural buckling load to the

yield load (P

cre

). For beam design, using the same C-

section, Fig. 15.2 shows the ratios of (a) the critical elastic

local buckling moment to the yield moment (M

crl

(b) the critical elastic distortional buckling moment to

the yield moment (M

crd

), and (c) the critical elastic

lateral–torsional buckling to the yield moment (M

cre

Based on these computed results, the nominal axial

strengths for columns can be computed from Eqs. (15.2)–

(15.11). Similarly, the nominal ﬂexural strengths for

beams can be computed from Eqs. (15.12)–(15.21). Good

agreements between the available test data and the member

strengths calculated from DSM are shown in Fig. 15.3 for

columns and in Fig. 15.4 for beams.

374 15 DIRECT-STRENGTH METHOD

Figure 15.1 Compression elastic buckling analysis of C-section (9CS 2.5 ×059) with ﬁnite-strip

method.

1.346

Figure 15.2 Bending elastic buckling analysis of C-section (9CS 2.5 ×059) with ﬁnite-strip

method.

1.346