Differences between Euler-Bernoulli and Timoshenko beam formulations for calculating the effects of moving loads on a periodically supported beam

Abstract It is generally considered that a Timoshenko beam is superior to an Euler-Bernoulli beam for determining the dynamic response of beams at higher frequencies but that they are equivalent at low frequencies. Here, the case is considered of the parametric excitation caused by spatial variations in stiffness on a periodically supported beam such as a railway track excited by a moving load. It is shown that large differences exist between the results obtained using Timoshenko and Euler-Bernoulli beams for a railway track with typical parameters; the Euler-Bernoulli beam model underestimates this parametric excitation by around a factor of 3. This difference is shown to be due to shear deformation in the rail, which is significant for span lengths less than about 2 m. A 2.5D finite element model of the rail is used as a reference. This gives a deflection that is closer to the Timoshenko beam model. However, the displacement profile obtained from the Timoshenko beam model has a discontinuity of gradient at the support points, whereas neither the Euler-Bernoulli beam nor the 2.5D finite element model contains the discontinuity of gradient. Finally, the moving load is introduced explicitly in the various periodically supported models. The results for a moving constant load, expressed as an equivalent roughness, are not strongly affected by the load speed until the sleeper passing frequency approaches the vertical track resonance at which the track mass bounces on the support stiffness. Consequently, a quasi-static model gives satisfactory results for moderate load speeds.