Civil Engineering Reference
In-Depth Information
Figure 3.13
Imposed loads and imposed defl ections on a cantilever
that the end of the cantilever is displaced downwards by a load applied at the end to
a predetermined defl ection
. If the defl ection is large enough the reinforcement will
yield, but the cantilever will not fail, as it is not allowed to defl ect any further. In fact,
the end load will be sustained at that required just to maintain the defl ection. This is of
course a result of the ductility of reinforced concrete; if the cantilever had been made
of brittle material, imposing a large defl ection on it would also have caused it to fail.
There are many instances in the design and analysis of structures where such fi xed
displacements are the relevant form of loading. The structures may be damaged by
them, but as long as they have suffi cient ductility they cannot fail. However, it is
possible that the damage caused may be such as to render the structure unserviceable.
Consequently, they need to be considered differently; the ULS is not the relevant
criterion governing design.
For instance, the settlement of one pier of a bridge deck may well cause it to crack,
but if the deck respects normal design criteria and is ductile, it will not fail. It may
however be damaged to the point where it becomes unserviceable or requires repair.
Another very common occurrence of this situation is where a bridge deck is pinned
to a series of piers (
7.9
), and the piers are subject to bending due to the changes in
the length of the deck. The change in length, whether it is caused by temperature
variations or by creep and shrinkage of the concrete, is a defi ned displacement and
cannot pull the piers over, although it can damage them.
An instance where confusion may well arise is where the deck rests on the pier
through a sliding bearing. The bearing exerts a longitudinal force on the pier equal to
the vertical reaction multiplied by the friction coeffi cient. Although the action of the
bearing on the pier is often assumed to be an applied force, and the pier designed to
the ULS, in fact the movement of the bearing is limited by the length change of the
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