Simplified Approach to AISC Bending Formulas

In Section 1.5.1.4.6a of the AISC Specification1 there are three equations for determining the allowable bending stress in a beam, and the equations to be used depend on the l/rT limits of the beam in question. However, where Cb is greater than one, or for other steel strengths, these equations must be used to determine Fb. In looking at Formulas (1.5-6a) and (1.5-6b) and at their corresponding l/rT limits, it can be noted that all numerical constants are 510 x 103, or multiples thereof. Further, these same expressions contain the variables Fy and Cb, except for Formula (1.5-6b) which is independent of steel strength. Thus, with all of these common terms it would appear that there exists a procedure wherein the mathematics involved could be simplified. To develop that procedure is the intent of this paper.