Clapeyron and Cross methods for the analysis of beams with variable inertia
DOI:
https://doi.org/10.21501/21454086.3987Keywords:
Cross, Clapeyron, Three Moments, Constant inertia, Variable inertiaAbstract
In the academic world, the global analysis of structures with beams considered to have constant inertia I is frequently considered. This is attested by the multiple teaching bibliography. In spite of this, there are also cases where this is considered as variable I(x). This casuistry could be extrapolated to the case of real structures. Many of them have beams with constant depth, although some of them, for various reasons, have variable depth. This fact has considerably complicated the formulation and resolution of the structural problem in the classical methods.
This paper presents a historical approach to this problem, presenting two of these methods for solving hyperstatic structures (Clapeyron’s method, also known as the Three Moments method and Cross’s method), as well as their formulation and solution for the case of continuous beams with constant I and variable I(x) inertia.
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