Civil Engineering Reference
In-Depth Information
while retaining adequate strength to resist the longitudinal external forces applied to
the deck, and stiffness to control its longitudinal displacement. This is an excellent test
of the skill of a designer.
As the bending moments in the two anchor piers due to the deck shortening are of
opposite sign, at the SLS external longitudinal loads applied to the deck will increase
the bending on one of the two anchor piers and relieve it on the other.
At the ultimate limit state it must be remembered that the deck shortening consists
of imposed strains, not loads. Consequently if the anchor piers become over-stressed
by the deck shortening at the ULS, they would release the bending moments, either
by hinging at their base, or by rotation and sway of the foundation. For this to be a
safe assumption, the substructure must have a ductile mode of failure. The piers and
any piles must be adequately reinforced in shear. Piles must not be allowed to fail in
direct compression; either the pile shafts should be stronger than the ground, so over-
stressing would cause settlement rather than concrete failure, or the foundation should
be designed to withstand the ultimate vertical loads.
Under normal circumstances, foundation systems are adequately ductile. However,
if necessary, the ductility may be improved, for instance by designing the base of the
pier or the connection of the piles with the pile cap for plastic rotation. If the piers/
foundations are ductile, at the ULS both piers may be assumed to resist the external
longitudinal forces and the internal forces resulting from deck shortening may be
ignored.
7.9.6 Longitudinal fi xity on more than two piers
If the bridge deck rests on tall slender piers, it is quite possible to fi x the deck on
several of them. In fact, with design friction coeffi cients of the order of 5 per cent,
sliding bearings on piers near the null point may, in theory, never slide. Fixed bearings
are cheaper than sliding bearings and need less maintenance, so there is every incentive
to use them on as many piers as possible.
7.9.7 Null point
When a bridge deck is pinned to a single pier, it provides the fi xed point about which
the deck changes length. However, when the deck is pinned to two or more piers, the
position of the point of zero movement, or null point, needs to be calculated in order
to estimate the forces on the piers, the sliding movement at each of the bearings, and
the travel of the roadway expansion joints.
For a symmetrical deck with a symmetrical substructure pinned to two identical
piers, the null point for expansion and contraction will be mid-way between them,
Figure 7.14 (a). On the other hand, if for instance one pier is longer than the other, the
null point will be displaced towards the stiffer pier, Figure 7.14 (b). If the substructure
constituted an elastic system, as described in
7.10
, the position of the null point could
be readily calculated, as the sums of the horizontal bearing forces either side of it must
be equal and opposite.
Unfortunately, a substructure that includes sliding bearings is not an elastic system.
The exact friction coeffi cient in each bearing is not known. Furthermore, sliding bearings
will not slide until the horizontal force overcomes the static friction. Thus as the deck
