## 65 Element Strength

For cold-formed steel members, the width to thickness ratios of individual elements are usually large. These thin elements may buckle locally at a stress level lower than the yield point of steel when they are

subjected to compression in flexural bending and axial compression as shown in Figure 6.6. Therefore, for the design of such thin-walled sections, local buckling and postbuckling strength of thin elements have often been the major design considerations. In addition, shear buckling and web crippling should also be considered in the design of beams.

### 6.5.1 Maximum Flat Width to Thickness Ratios

In cold-formed steel design, the maximum flat width to thickness ratio, w/t, for flanges is limited to the following values in the AISI Specification [7]:

1. Stiffened compression element having one longitudinal edge connected to a web or flange element, the other stiffened by

• Any other kind of adequate stiffener — 90

2. Stiffened compression element with both longitudinal edges connected to other stiffened element — 500

3. Unstiffened compression element — 60

For the design of beams, the maximum depth to thickness ratio, h/t, for webs is:

2. Webs that are provided with transverse stiffeners:

• Using bearing stiffeners and intermediate stiffeners, (h/t)max = 300

### 6.5.2 Stiffened Elements under Uniform Compression

The strength of a stiffened compression element such as the compression flange of a hat section is governed by yielding if its w/t ratio is relatively small. It may be governed by local buckling as shown in Figure 6.7 at a stress level less than the yield point if its w/t ratio is relatively large.

FIGURE 6.8 Postbuckling strength model (courtesy of Yu, W.W. 1991).

The elastic local buckling stress, Fcr, of simply supported square plates and long plates can be determined as follows:

kn2 E

where k is the local buckling coefficient, E is the modulus of elasticity of steel = 29.5 x 103 ksi (203 GPa or 2.07 x 106 kg/cm2), w is the width of the plate, t is the thickness of the plate, and m is the Poisson's ratio = 0.3.

It is well known that stiffened compression elements will not collapse when the local buckling stress is reached. An additional load can be carried by the element after buckling by means of a redistribution of stress. This phenomenon is known as postbuckling strength and is most pronounced for elements with large w/t ratios.

The mechanism of the postbuckling action can easily be visualized from a square plate model as shown in Figure 6.8 [39]. It represents the portion abcd of the compression flange of the hat section illustrated in Figure 6.7. As soon as the plate starts to buckle, the horizontal bars in the grid of the model will act as tie rods to counteract the increasing deflection of the longitudinal struts.

In the plate, the stress distribution is uniform prior to its buckling. After buckling, a portion of the prebuckling load of the center strip transfers to the edge portion of the plate. As a result, a nonuniform stress distribution is developed, as shown in Figure 6.9. The redistribution of stress continues until the stress at the edge reaches the yield point of steel and then the plate begins to fail.

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