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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
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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
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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.
Other Grillage
modelling issues
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