Applying the generalized step-function to solve the bending problems of nonuniform beams with variable cross section |
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Authors: | Lin Xin-san Xu Bao-yuan Xiong Huan-guo |
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Institution: | Shanghai Part-time Institute of Technology |
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Abstract: | The bending problems of nonuniform beams with variable cross-section can be approximated by that of a step beam under sectionally uniform load (including both concentrated forces and couples). In this paper, the concept of Heaviside function {x–a}0 will be generalized, and a new function {x–a}n,n=0, 1, 2..., will be defined, which may be named as a generalized step function. The rules of operation will also be given to {x–a}n{x–b}0. The reciprocal of the flexural of rigidity 1/EJ and the bending momentM(x) can all be expressed in terms of {x–a}n, and substituted into the differential equation of the elastic curve of the beam respectively. Thus we may establish a set of unified method to solve various types of bending problems of straight beams. The general solution of the deflection equation will be given. |
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Keywords: | reliability growth Duane model AMSAA model AMSAA-BISE model |
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