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Shear near supports on a grillage

The misreporting of shear near supports is an inaccuracy inherent to grillage analysis. Where "discrete" loads fall in a grillage bay these are distributed to the nodes in that bay. Where the bay has one or more support nodes, load is assigned directly to the support and is therefore not reported in shear results. Thus the summation of shear force each side of a support will add to less than the reaction at that support.

The issue of shear forces adjacent to supports in grillage analyses is raised in "Bridge Deck Analysis" Eugene J. O'Brien and Damien L. Keogh (E&FN SPON, 1999) section 5.3.6

The authors describe that the modelling of bridge supports in a grillage assumes an effective size dependant on the density of the grillage mesh. It follows that the mesh density should be considered, to ensure that 

  • The spacing of longitudinal members is such that the effective width assumed is not disproportionate to the size of the bearings with due consideration of shear enhancement, load spreading etc

  • The spacing of transverse members is such that the shear forces are reported close to the supports. The authors also make reference to shear enhancement and suggest "the designer would design for the shear force calculated at a deck depth from the support. Greater shear forces at points closer to the support would be ignored on the basis that load would be carried by direct compression rather than shear mechanisms".

In the normal way, grillage bays should be short enough that shear enhancement applies and this is regarded by some bridge engineers to negate the need for thorough checks. Other engineers use an additional loadcase where the HB vehicle is moved out of the end bay in order to obtain a worst shear result as distinct from a worst reaction. At abutments, the reaction may be used as a shear result as the figures are generally very close.

Plate or shell models also offer an alternative approach to bridge deck modelling and are not subject to this particular modelling problem, although clearly mesh refinement must still be checked, as in any FE analysis.

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