Civil Engineering Reference
In-Depth Information
term Young's modulus. If the displacement is maintained the load then gradually
drops off, with the fi nal load being related to the creep characteristics of the concrete,
Figure 3.14 (b).
The degree to which the load relaxes depends on the rate at which the displacement
is applied. For instance, if the displacement is applied quickly, in one phase, the long-
term fi nal load will typically be only 20 per cent of the initial load. It is for this reason
that it is not worth trying to alter the bending moments in a concrete beam by jacking
the supports, as is routinely done for steel bridges; the jacked-in bending moments
creep away.
If, at the other extreme, the displacement is applied very slowly, over a period of
months or years, the long-term fi nal load will typically be of the order of 40 per cent
of the load calculated on the assumption of elastic behaviour.
In most instances that affect prestressed concrete bridges, the rate of application of
the displacement is between these two extremes. For instance, piers that are pinned
to a bridge deck, as described in
7.9
, are subjected to imposed displacements by the
shortening of the deck. This shortening has an initial rapid component as the prestress
is applied to the deck, followed by a slow component as it continues to shorten under
the infl uence of creep and shrinkage.
All such calculations are approximate, and for preliminary calculations at least,
one could do worse than to assume that the fi nal load will be, for a rapidly applied
displacement, between upper and lower bounds of 20 per cent and 30 per cent of the
initial load, and for slow application of the displacement, between 40 per cent and
50 per cent of the load calculated on the assumption of elastic behaviour. The piers
will also be subjected to cyclical movements of the deck, some of which are short term,
and some seasonal. The effect of the short-term loading should be calculated using a
Young's modulus that is slightly below the value used for live loading, while the effect
of seasonal movements should be calculated with a lower
E
. A reasonable compromise
is to use an
E
of 75 per cent of the short-term value for all temperature movements.
For a more mathematical defi nition of these two extremes, see reference [8].
Alternatively, the data given in Appendix B of BS5400: 1990: Part 4 can be used as the
basis for repetitive calculations that appear to give an accurate representation of the
evolution of the forces. However, it should be borne in mind that the reliability of the
result of this calculation depends on the validity of the initial data, which is at best one
view of a very extensive body of experimental data.
3.10 Truss analogy
3.10.1 Truss analogy applied to beams
Truss analogy is very useful in providing a tool to design the shear reinforcement
for reinforced and prestressed concrete beams. The concrete beam is likened to a
truss, in which the compression boom and the inclined compression web members
are in concrete, while the tension boom and the tensile web members consist of
reinforcement.
In a reinforced concrete beam, the compressive web members are usually assumed
to be inclined at 45°, as this is the inclination of the principal compressive stress. In
a prestressed concrete member, the longitudinal compression fl attens the angle of the
principal compressive stress, and the web struts may be assumed to lie at a fl atter
