Predicting the large-deflection path of tapered cantilever beams

Beam taper examples and actual vs. predicted deflection.

A mathematical model for predicting the deflection path of both non-tapered and continuously tapered cantilever beams loaded with a vertical end force is presented. It is based on the proposition that the path is a function of the ratio of the endpoints’ moments of inertia. This was verified through physical testing, comparison to solution of the Bernoulli-Euler equation, and results obtained in finite element analysis. Predicted deflections were found to be accurate within 1.8% of the actual deflection path for moment of inertia ratios varying from 1:1 to 1000:1.