Comparison of response of rayleigh beams to moving loads for calculated and arbitrary values of rotary inertia correction factor

Abstract

The effects of calculated and arbitrary values of rotary inertia correction factor (r⁰) on the dynamic response of a simply supported Rayleigh beam is investigated when the beam is subjected to distributed and concentrated loads respectively. The analysis was carried out for four beam types; Steel, Copper, Aluminum and Concrete. The governing equations for both the distributed and concentrated loads were tackled using Finite Fourier Sine transform and the solutions obtained were plotted against time for arbitrary values of r⁰ = 0.1, 0.2, 0.3, 0.4 and for calculated value r⁰ = 0.0133. For both load problems, the graphs for arbitrary r⁰ and calculated r⁰  were compared. Results show that for all the four beam types considered when under the action of concentrated load, the deflection of the beam are the same whether r⁰ is arbitrary or calculated. However, for the distributed loading, there is a noticeable effect on the deflection of the beams for both calculated and arbitrary values. It is established that the calculated value gives the actual deflection of the beam and thus, depending on deflection obtained for arbitrary value could be misleading.