Example of Effective Section Calculation

A 5.5 in deep by 1.25 in wide by 0.057 in thick C-section without lips is shown in Fig. 10.11a. The specified yield stress for the material is 33 ksi. It is required to determine the effective section modulus, Se, for a maximum bending stress equal to the yield stress. First, determine the effective width of the compression (top) flange (Art. 10.8.1 and 10.9.2). The radius to midthickness of the bend is

The next step is to determine whether the web is fully effective. To do this, first determine the location of the neutral axis. Because the top flange is not fully effective, the neutral axis will be located below the centroidal axis of the gross cross section. Table 10.13 shows the calculations to determine the distance of the neutral axis from the top fiber, y, and the moment of inertia of the effective section, Ix. The web is treated as a stiffened element with a stress gradient (Art. 10.8.2). With a stress of 33 ksi in the top flange, the stresses at the edges of the flat web, Æ’1 and Æ’2 (Fig 10.1b) can be readily determined from similar triangles.
The other calculations follow from Art. 10.8.2.

Based on the assumption of a fully effective web, the width that is in compression, Fig. 10.11b, is 2.819 - 0.057/2 - 0.216 = 2.575 in. Because this is less than 3.776 in, the web is fully effective and no further iteration is required. If the web had not been fully effective,

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