## 66 Member Design

This chapter deals with the design of the following cold-formed steel structural members: (1) tension members, (2) flexwral members, (3) concentrically loaded compression members, (4) combined axial load and bending, and (5) closed cylindrical tubular members. The nominal strength equations with factors of safety (Q) and resistance factors (f) are provided in the Specification [7] for the given limit states.

### 6.6.1 Sectional Properties

The sectional properties of a member such as area, moment of inertia, section modulus, and radius of gyration are calculated by using the conventional methods of structural design. These properties are based on full cross-section dimensions, effective widths, or net section, as applicable.

For the design of tension members, the nominal tensile strength is presently based on the gross and net sections. However, for flexural members and axially loaded compression members, the full dimensions are used when calculating the critical moment or load, while the effective dimensions, evaluated at the stress corresponding to the critical moment or load, are used to calculate the nominal strength.

6.6.2 Linear Method for Computing Sectional Properties

Because the thickness of cold-formed steel members is usually uniform, the computation of sectional properties can be simplified by using a ''linear'' or "midline" method. In this method, the material of each element is considered to be concentrated along the centerline or midline of the steel sheet and the area elements are replaced by straight or curved ''line elements.'' The thickness dimension t is introduced after the linear computations have been completed. Thus, the total area A = Lt, and the moment of inertia of the section I = /t, where L is the total length of all line elements and I' is the moment of inertia

of the centerline of the steel sheet. The moments of inertia of straight line elements and circular line elements are shown in Figure 6.17.

### 6.6.3 Tension Members

In the United States and Mexico, the nominal tensile strength of axially loaded cold-formed steel tension members is determined by the following equations:

1. For yielding:

2. For fracture away from connection:

where Tn is the nominal strength of the member when loaded in tension, Ag is the gross area of cross-section, An is the net area of cross-section, Fy is the design yield point of steel, and Fu is the tensile strength of steel.

3. For fracture at connection: The nominal tensile strength is also limited by sections E2.7, E3, and E4 of the North American Specification [7] for tension members using welded connections, bolted connections, and screw connections. For details, see chapter E of the Specification under the title ''Connections and Joints.''

In Canada, the design of tension members is based on appendix B of the AISI North American Specification [7].

### 6.6.4 Flexural Members

For the design of flexural members, consideration should be given to several design features: (1) bending strength and deflection, (2) shear strength of webs and combined bending and shear, (3) web crippling strength and combined bending and web crippling, and (4) bracing requirements. For some cases, special considerations should also be given to shear lag and flange curling due to the use of thin materials.

### 6.6.4.1 Bending Strength

Bending strengths of flexural members are differentiated according to whether or not the member is laterally braced. If such members are fully supported laterally, they are designed according to the nominal section strength. Otherwise, if they are laterally unbraced, then the bending strength may be governed by the lateral-torsional buckling strength. Section 6.9 discusses the flange distortional buckling. For C- or Z-sections with tension flange attached to deck or sheathing and with compression flange laterally unbraced, the nominal bending strength may be reduced according to the AISI Specification.

### 6.6.4.1.1 Nominal Section Strength

Two design procedures are now used in the AISI Specification for determining the nominal section strength. They are (1) initiation of yielding and (2) inelastic reserve capacity.

According to procedure I on the basis of initiation of yielding, the nominal moment, Mn, of the cross-section is the effective yield moment, My, determined for the effective areas of flanges and the beam web. The effective width of the compression flange and the effective depth of the web can be computed from the design equations given in Section 6.5 on Element Strength. The yield moment of a cold-formed steel flexural member is defined by the moment at which an outer fiber (tension, compression, or both) first attains the yield point of the steel. Figure 6.18 shows three types of stress distribution for yield moment based on different locations of the neutral axis. Accordingly, the nominal section strength for initiation of yielding can be computed as follows:

where Se is the elastic section modulus of the effective section calculated with the extreme compression or tension fiber at Fy and Fy is the design yield stress.

For cold-formed steel design, Se is usually computed by using one of the following two cases:

1. If the neutral axis is closer to the tension than to the compression flange (case c of Figure 6.18), the maximum stress occurs in the compression flange, and therefore the plate slenderness factor l (Equation 6.9) and the effective width of the compression flange are determined by the w/t ratio and f= Fy. This procedure is also applicable to those beams for which the neutral axis is located at the mid-depth of the section (case a).

2. If the neutral axis is closer to the compression than to the tension flange (case b), the maximum stress of Fy occurs in the tension flange. The stress in the compression flange depends on the location of the neutral axis, which is determined by the effective area of the section. The latter cannot be determined unless the compressive stress is known. The closed-form solution of this type of design is possible but would be a very tedious and complex procedure. It is, therefore, customary to determine the sectional properties of the section by successive approximation.

See Examples 6.2 and 6.3 for the calculation of nominal bending strengths. EXAMPLE 6.2

Use the ASD and LRFD methods to check the adequacy of the I-section with unstiffened flanges as shown in Figure 6.19. The nominal moment is based on the initiation of yielding using Fy = 50 ksi.

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