Application of Effective Widths

The curves of Fig. 8.7 were plotted from values of Eqs. (8.8) and (8.9). They may be used to determine b/ t for different values of w/ t and unit stresses ƒ. The effective width b is dependent on the actual stress ƒ, which in turn is determined by reducedsection properties that are a function of effective width. Employment of successive approximations consequently may be necessary in using these equations and curves.
A direct solution for the correct value of b/ t can be obtained from the formulas, however, when ƒ is known or is held to a specified maximum allowable value for deflection determination (20 ksi for Fy  33 ksi, for example). This is true, though, only when compression controls; for example, for symmetrical channels and Z and I sections used as flexural members bending about their major axis (Fig. 8.1e, f, k and n) or for unsymmetrical channels and Z and I sections with neutral axis closer to the tension flange than to the compression flange. If w/ t of the compression flange does not exceed about 60, little error will result in assuming that ƒ  0.60  33  20 ksi for Fy  33 ksi. This is so even though the neutral axis is above the geometric centerline. For wide, inverted, pan-shaped sections, such as deck and panel sections, a somewhat more accurate determination using successive approximations will prove necessary.
For computation of moment of inertia for deflection or stiffness calculations, properties of the full unreduced section can be used without significant error when w/ t of the compression elements does not exceed 60. For greater accuracy, use Eqs. (8.8) and (8.9) to obtain appropriate effective widths.
Example. As an example of effective-width determination, consider the hat section of Fig. 8.8. The section is to be made of steel with a specified minimum yield strength Fy  33 ksi. It is to be used as a simply supported beam with the top flange in compression, at a basic working stress of 20 ksi. Safe load-carrying