Analysis of flexural behavior of a simple supported thin beam under concentrated multiloads using trigonometric series method

For accurately predicting the local stresses around the loading points, a stress function in the form of trigonometric series (TS) was applied to obtain the displacements and stresses for simply supported thin beams under concentrated multiloads. The convergences of TS solutions were testified for both displacements and stresses, where the convergence criteria were established and the proper iteration numbers were given. Besides, the accuracy of TS solutions was verified by finite element analysis, where the stress concentration effect is obvious for the shear stresses around the loading sections, not following the parabolic distribution proposed in literatures. Finally, taking thin beams under multi-wheels loads as an example, parameter studies were then performed to examine the effects of wheels' numbers, distances and locations on the flexural response of beams. Numerical results were summarized into a series of curves indicating the distribution of displacements and stresses for various parameters.