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E.13 Moving Load Analysis in Simply Supported Beam

E.13.1 Moving Load

As shown in the figure, a moving load analysis was performed for a simply supported beam. The analysis was carried out using ten 2-node beam elements and 4-node shell elements, and the results were compared with the analytical solution.

Figure E.12.1 Moving Load Verificatgion Example

In some cases, a simplified analysis using beam elements, as shown in Figure E.12.2, may be required. In such cases, an offset load from the beam centroid can be represented by selecting a vertical load and a rotational moment as moving loads. To move a moment along a beam, the BeamMoving load should be used. If the moment component is absent, BeamMoving load is equivalent to LineMoving load, but it must be applied only to beam elements. In contrast, LineMoving load can move along the edges of elements, including beams.

Figure E.12.2 Simplified analysis using beam

Input file

  • LineMovingLoad.inp : Beam + LineMoving
  • ShellMovingLoad.inp : Shell + SurfaceModving
  • ShellMoving-HHT.inp : SHELL + SurfaceMoving, but HHT time integration is used
  • ShellMoving-Modal.inp : SHELL + SurfaceMoving, but modal analsyis is .
  • BeamMovingLoad.inp : Beam + BeamMoving
  • BeamMoving-HHT.inp : Beam + BeamMoving, but HHT time integration is used
  • BeamMoving-Modal.inp : Beam + BeamMoving, but modal analsyis is .

E.13.2 Moving SDF System (under construction)

Figure E.12.3 Moving SDF System

[To be supplemented]

  • Use Biggs’ solution to obtain the exact solution for comparison. The current example is unrealistic, particularly making it difficult to compare beam and shell elements.
  • Verify that the SDF represents an overdamped system.
  • Confirm that the damping ratio of the SDF has little effect on the bridge response.
  • When rolling a very heavy SDF, damping may actually increase the bridge response.
  • In some cases, the bridge response increases when damping is applied — this also needs investigation (in this example, partial modal analysis does not operate properly).

Input file

  • sbeam.inp : B2D2H
  • sbeam-Modal.inp : B2D2H, but model analysis is used
  • sbeam3d.inp : B3D2H
  • sbeam3d-Modal.inp : B3D2H, but model analysis is used
  • ssurface.inp : S4F
  • ssurface-Modal.inp : S4F, but modal analysis is used.