F. K. Kong MA, MSc, PhD, CEng, FICE, FIStructE, R. H. Evans CBE, DSc, D ès Sc, DTech, PhD, CEng, FICE, FIMechE, FIStructE (auth.)-Reinforced and Prestressed Concrete-Springer US (1987)

348 Prestressed concrete simple beams
Fig. 9.3-l
Lower limit for service condition
Lower limit for stresses at transfer
Hence, from eqns (9.3-5) and (9.3-6),
~ + ~s :S 21.82
P- Pes> -3 89
A Zz- .
With P = 1046 kN and A, Z 1 and Z 2 as in Example 9.2-2, we have e 5 :S
238 mm from the first condition (and, less critically, e 5 :S 262 mm from the
second).
Similarly, the reader should verify that, at transfer,
es :S 233 mm at 3 m from support
es :S 217 mm at 1 m from support
es :S 205 mm at support
Figure 9. 3-1 shows the permissible tendon zone which satisfies the stress
conditions both in service and at transfer. To increase the depth of the zone
at midspan, a lower effective prestressing force than Pe = 837 kN has to be
used.
9.4 Loss of prestress
Design calculations for the loss of prestress are usually straightforward;
simple practical procedures are given in BS 8110: Clauses 4.8 and 4.9.
In general, allowance should be made for losses of prestress resulting
from:
(a)
(b)
Relaxation of the steel comprising the tendons: Typically this
produces a loss of about 5%.
Elastic deformation of the concrete: In a pre-tensioned beam there is
an immediate loss of prestress at transfer, resulting from the elastic
shortening of the beam. In post-tensioning, the elastic shortening of
the concrete occurs when the tendons are actually being tensioned;