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Earthquakes and Structures Volume 5, Number 5, November 2013 , pages 589-605 DOI: https://doi.org/10.12989/eas.2013.5.5.589 |
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Effects of dead loads on dynamic analyses of beams subject to moving loads |
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Hideo Takabatake
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| Abstract | ||
| The effect of dead loads on dynamic responses of a uniform elastic beam subjected to moving loads is examined by means of a governing equation which takes into account initial bending stresses due to dead loads. First, the governing equation of beams which includes the effect of dead loads is briefly presented from the author's paper (1990, 1991, 2010). The effect of dead loads is considered by a strain energy produced by conservative initial stresses caused by the dead loads. Second, the effect of dead loads on dynamical responses produced by moving loads in simply supported beams is confirmed by the results of numerical computations using the Galerkin method and Wilson-method. It is shown that the dynamical responses by moving loads are decreased remarkably on a heavyweight beam when the effect of dead loads is included. Third, an approximate solution of dynamic deflections including the effect of dead loads for a uniform beam subjected to moving loads is presented in a closed-form for the case without the additional mass due to moving loads. The proposed solution shows a good agreement with results of numerical computations with the Galerkin method and Wilson-method. Finally it is clarified that the effect of dead loads on elastic uniform beams subjected to moving loads acts on the restraint of the transverse vibration for the both cases without and with the additional mass due to moving loads. | ||
| Key Words | ||
| beams; dead load; initial stress; vibration; dynamic analysis; Galerkin equation; linear and nonlinear; live load; moving load; safety | ||
| Address | ||
| Hideo Takabatake: Department of Architecture, Kanazawa Institute of Technology, Institute of Disaster and Environmental Science, 3-1, Yatsukaho, Hakusan City, Ishikawa 924-0838, Japan | ||