Bending calculation of multi-span beam under arbitrary boundary conditions and engineering application thereof

Abstract

[Objectives] To find the worst-case of a deck structure under patch loading quickly.[Methods] For the bending of a multi-span beam under arbitrary boundary conditions,an Improved Fourier Series Method(IFSM)is used to describe the displacement functions of the multi-span beam,list the boundary equations that the displacement functions need to meet and solve such equations to obtain the relational expressions of coefficients;and then an energy control equation is obtained on the basis of the Hamilton principle,the displacement functions of beam structure satisfying the boundary conditions is acquired with the Galerkin method,and the functions are compared with the finite element results by means of example analysis. Finally,this method is applied to the calculation of the worst-case analysis of multi-span beam under patch loading.[Results] The results show that the error between the result of this paper and the finite element analysis is less than 0.05%,indicating good accuracy.[Conclusions] Compared with finite element method,the speed of solving the worst-case of the multi-span beam is greatly reduced by using this method,and a more accurate location to which the worst-case of patching loading is applied is obtained by combining the genetic algorithms.

Keywords

• multi-span beam
• patch loading
• bending
• arbitrary boundary conditions
• Hamilton principle
• worst-case analysis