A Mathematical Moment-Area Technique for Simply Supported Beams

Abstract

Slope and Deflection in beams has a key role to play in determining the quality of a beam and they are thus paramount in conducting beam design. Moment-Area method of beam design is a versatile method of determining slope and deflection in beams as it can determine them in beams of varying cross-section unlike most mathematical methods of determining slope and deflection. This paper presents a novel Moment-Area method of determining slope and deflection in beams by analyzing various case scenarios of loading on a simply supported beam. The results of this novel method are validated using Macaulay’s method of slope and beam deflection and are shown to be in unison.

Keywords: Bending Moment Diagram (BMD), Breakpoint, Deflection, Moment-Area, Turning Point

DOI: 10.7176/ISDE/15-04

Publication date: September 30^th 2025