Simplified Procedure to Determine Maximum Beam Deflection

The maximum deflection of a beam occupies an important role in discussions concerning structural design. Building codes such as ACI-63 and the AISC Specification limit the deflection caused by a live load to 1/360 of the beam span. Beam design calculations to meet the specifications usually involve tedious and lengthy computations. In this paper, the following simplified procedure is proposed: For any beam of variable moment of inertia, subject to end moments and lateral loads, first use matrix multiplication to determine a segment where maximum deflection will occur. Then, using boundary conditions of the segment, repeat matrix multiplication to obtain the maximum deflection.