Structural Model

Owned by Becca Alford (Unlicensed)
Jun 20, 2020
2 min read

The method of analysis is the displacement or stiffness method.  The structure is represented by a matrix consisting of member stiffnesses.  These are derived for three possible movements at the ends of members:  vertical, horizontal, and rotational.  The following boundary conditions are then applied to the matrix for a box culvert:

  • No vertical displacement at the outside ends of the bottom slab.

  • No lateral displacement at the right end of the bottom slab.

For a three sided culvert the following boundary conditions are applied to the matrix:

  • No vertical or lateral displacement at the bottom of both walls.

  • An optional roller (which allows lateral displacement only) may be placed at the bottom of the left wall.

 Below are the structural idealization models for a box culvert and three-sided culvert:

Through matrix manipulation, the true displacements at the ends of each member are computed for each given loading condition.  Then the exact end moments and forces are determined using the computed displacements.  These moments and forces are used to develop stresses, proportion reinforcement, or alter member depth.  If member depth is altered, its effect is reevaluated in the above manner.

 The length of each member for analysis purposes will be from centerline to centerline of the supporting members.  Moments at the geometric centers of members, moments at faces of support or moments within and at the ends of fillets (haunches) built monolithic with the member and support may be selected for member design.

 It is assumed that loading applied to the top slab will be uniformly distributed over the whole bottom slab.  This is a reasonable assumption since a mat of granular material is usually placed beneath the bottom slab for the culvert to lay on.  More refined assumption appears impractical due to the lack of precise soil information for each site.

 Analysis results are reported for the each member at 10th points along the member, measured from centerline of supporting member to centerline of supporting member.  Eriksson Culvert provides two methods of presenting numerical results: graphs and text reports.