Optimum Geometry of Stepped-Taper Beams,
CALIFORNIA STATE UNIV NORTHRIDGE
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An application of the parametric load index approach is presented which yields a general least weight formulation for stepped taper beams optimized for any prescribed number of stepped segments. The method provides for treating all cross-sectional dimensions dependent on the step lengths as the only independent variables. Results for both cantilevered and simply supported uniform loading demonstrate that only a two or three segment stepped beam can realize about one half of the maximum weight reduction obtainable through a continuous taper. For example, a two segment cantilever is shown to yield a 30 weight reduction with the continuous taper representing a maximum of 57 weight reduction, both being compared to a uniform cross section. For each prescribed number of steps, comparisons are made between optimized step lengths as opposed to equal length divisions. For the cases considered, it is found that optimizing individual step lengths realizes only small benefit compared to equal length steps.