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A Simplified Technique for the Analysis of Multi-Stepped Beams

The availability of software packages that enable algebraic manipulation of equations enables the reconsideration of analytical methods for design optimization which have fallen into disuse because of the difficulty of automating the analysis. Here, the analysis of multistepped beams is simplified by replacing the multi-stepped geometry by a beam of uniform cross-section. A general formula is established to define the induced forces and moments that replace the steps. This enables the singularity function method, which is usually restricted to the analysis of uniform beams, to be easily applied to determine shearing forces and bending moments, and thus simplifies the analysis.