Further insights into moving load problem on inclined beam based on semi-analytical solution

D. S. Yang, Chien Ming Wang, W. H. Pan

Research output: Contribution to journalArticleResearchpeer-review

16 Citations (Scopus)


This paper presents the semi-analytical solutions for a vertical load moving on an inclined simply supported beam. By adopting the energy approach along with the Fourier sine series for the beam deflection shape, the governing equation of motion is obtained as an easy-to-solve ordinary differential equation. The frequencies of the inclined beam excited by the moving load can be expressed in analytical form which elucidates the intrinsic and fundamental features of the solution. The moving load problems solved herein show that the dynamic responses (deflections) at any point on the inclined beam with respect to the moving load position are smaller with increasing angle of inclination. For more insights into the axial load effect on the beam stiffness, the exciting frequencies are found to decrease as the load moves up the inclined beam. Interestingly, while the moving load is traversing over a certain portion of the beam, the frequencies stay constant rather than decrease monotonically; in other word, the stiffness of the inclined beam remains virtually unaffected when the moving load passes in this portion of the inclined beam. The stability issues of the inclined beam with a moving load are discussed by examining the determinant of the global stiffness matrix of the beam. Moreover, the maximum magnitude of moving load with allowable deflection is obtained to provide design recommendations.

Original languageEnglish
Pages (from-to)247-256
Number of pages10
Publication statusPublished - Aug 2020
Externally publishedYes


  • Energy approach
  • Fourier sine series
  • Inclined beam
  • Moving load
  • Structural stability

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