## 63 Design Bases

For cold-formed steel design, three design approaches are being used in the North American Specification [7]. They are (1) ASD, (2) LRFD, and (3) LSD. The ASD and LRFD methods are used in the United States and Mexico, while the LSD method is used in Canada. The unit systems used in the North American Specification are (1) U.S. customary units (force in kip and length in inches), (2) SI units (force in newtons and length in millimeters), and (3) MKS units (force in kilograms and length in centimeters).

6.3.1 Allowable Strength Design (United States and Mexico)

In the ASD approach, the required allowable strengths (moments, axial forces, and shear forces) in structural members are computed by accepted methods of structural analysis for all applicable load combinations of nominal loads as stipulated by the applicable building code. In the absence of an applicable building code, the nominal loads and load combinations should be those stipulated in the American Society of Civil Engineers (ASCE) Standard ASCE 7 [38].

The required allowable strengths should not exceed the allowable design strengths permitted by the applicable design standard. The allowable design strength is determined by dividing the nominal strength by a factor of safety as follows:

where Ra is the allowable design strength, Rn is the nominal strength, and Q is the factor of safety. For the design of cold-formed steel structural members using the AISI ASD method, the factors of safety are given in Table 6.1. For details, see the AISI Specification [7].

6.3.2 Load and Resistance Factor Design (United States and Mexico)

Two types of limit states are considered in the LRFD method. They are (1) the limit state of strength required to resist the extreme loads during its life and (2) the limit state of serviceability for a structure to perform its intended function.

For the limit state of strength, the general format of the LRFD method is expressed by the following equation:

where Ru = Y1 giQi is the required strength, f Rn is the design strength, gi is the load factor, Qi is the load effect, f is the resistance factor, and Rn is the nominal strength.

The structure and its components should be designed so that the design strengths, f Rn, are equal to or greater than the required strengths, giQi, which are computed on the basis of the factored nominal loads and load combinations as stipulated by the applicable building code or, in the absence of an applicable code, as stipulated in ASCE 7 [38].

In addition, the following LRFD criteria can be used for roof and floor composite construction using cold-formed steel:

where Ds is the weight of the steel deck, Cw is the weight of wet concrete during construction, and C is the construction load, including equipment, workmen, and formwork, but excluding the weight of the wet concrete. Table 6.1 lists the f factors, which are used for the LRFD and LSD methods for the design of cold-formed steel members and connections. For details, see the AISI Specification [7].

The methodology for the LSD method is the same as for the LRFD method, except that the load factors, load combinations, target reliability indices, and assumed live-to-dead ratio used in the development of the design criteria are different. In addition, a few different terms are used in the LSD method.

Like the LRFD method, the LSD method specifies that the structural members and connections should be designed to have factored resistance equal to or greater than the effect of factored loads as follows:

where Rf is the effect of factored loads, Rn is the nominal resistance, f is the resistance factor, and f Rn is the factored resistance.

For the LSD method, the load factors and load combinations used for the design of cold-formed steel structures are based on the National Building Code of Canada. For details, see appendix B of the North American Specification [7]. The resistance factors are also listed in Table 6.1.

TABLE 6.1 Factors of Safety, O, and Resistance Factors, f, used in the North American Specification [7]

Type of strength

ASD factor of safety, O

LRFD resistance factor, f

LSD resistance factor, f

Tension members For yielding

For fracture away from the connection For fracture at the connection (see connections) Flexural members Bending strength

For sections with stiffened or partially stiffened compression flanges For sections with unstiffened compression flanges Laterally unbraced beams

Beams having one-flange through fastened-to-deck or sheathing

(C- or Z-sections) Beams having one-flange fastened to a standing seam roof system Web design Shear strength Web crippling Built-up sections

Single-web channel and C-sections Single-web Z-sections Single-hat sections Multiweb deck sections Stiffeners

Transverse stiffeners Concentrically loaded compression members Combined axial load and bending For tension For compression For bending Closed cylindrical tubular members Bending strength Axial compression Wall studs and wall assemblies Wall studs in compression Wall studs in bending Diaphragm construction Welded connections Groove welds

Tension or compression Shear (welds) Shear (base metal) Arc spot welds Welds

Connected part Minimum edge distance Tension Arc seam welds Welds

Connected part Fillet welds