Civil Engineering Reference
In-Depth Information
5.17.5 Elastic shortening of the concrete
As the stressing force is applied to the concrete it shortens. If the prestress force is
applied with just one tendon, this shortening would not cause any loss of prestress.
However, if the prestress consists of more than one tendon, those that have already
been anchored will shorten with the concrete under the effect of the stressing of
subsequent tendons.
5.17.6 Creep
The delayed shortening of concrete due to the compression induced by prestress will
affect all the tendons. It is the compression at the level of the tendons that creates the
loss. Consequently, for a tendon that is not at the neutral axis, the stress under which
the concrete creeps is affected by bending in the beam. The loss should be assessed
under the long-term dead load condition of the deck. If the cables are bonded to the
concrete, the loss due to creep will be local to a particular concrete section, and will
not be averaged out along their length. If the tendons are unbonded, the creep loss will
be averaged out over the length of the tendon.
The total amount of creep will be affected by the same factors that affect the total
amount of shrinkage. However, creep is also strongly affected by the age at which the
concrete is fi rst loaded, being less for older concrete. Consequently, when stressing
tendons early to allow a rapid turn-round of falsework and a short construction cycle,
it is important to stress as few tendons as possible in the fi rst phase, delaying the
stressing of the remainder to as late as possible in the cycle.
5.17.7 Relaxation of the steel
Most modern strand has a relaxation that does not exceed 2.5 per cent of the initial
stressing force at 1,000 hours, and that is taken as the total relaxation. However, some
bars and strand may lose up to 7-8 per cent of their stress due to relaxation.
5.18 The concept of equivalent load
There is yet another method of explaining and understanding prestressing. Consider
the cable in tension subjected to a concentrated force at its mid-point, as shown in
Figure 5.16 (a). For equilibrium, the cable must be defl ected into a 'V' shape. If the
cable force is
P
, the central load
W
and the cable is defl ected by an angle
.
The cable is applying an upwards force that is equal and opposite to the downwards
load.
Consider now the prestressed concrete beam of rectangular cross section shown
in Figure 5.16 (b) of length 2
l
. The prestressing cable with a force
P
is anchored
at the neutral axis at the ends of the beam, and is defl ected in a 'V' shape, with a
defl ected angle of
α
,
W
=2
P
sin
α
and an eccentricity at mid-span of
e
c
. The effect on the beam is of
a compressive force at its neutral axis of
P
cos
α
, a downwards vertical force at its ends
of
P
sinα, and an upwards vertical force at mid-span of 2
P
sin
α
, Figure 5.16 (c).
As in most prestressed beams the angle of the prestressing cables with respect to
the beam neutral axis is usually less than 10°, it is assumed that cos
α
α
=1, and that
