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)

Loss of prestress 349
therefore where there is only one tendon, there is no loss due to
elastic deformation. But if there are several tendons, then the
tensioning of each tendon will cause a loss in those tendons that have
already been tensioned. Very roughly, the loss of pretress due to
elastic deformation is about 5-10% for pretensioned beams and 2 or
3% for post-tensioned beams.
(c) Shrinkage and creep of the concrete: Typically, these produce a
10-20% loss.
(d) Slip of the tendons during anchoring: This loss is important where the
tendons are short, e.g. in some post-tensioned beams.
(e) Friction between tendon and duct in post-tensioned beams: Varies
from 1 to 2% in simple beams, with a fairly flat tendon profile, to
over 10% in continuous beams.
Example 9.4-l
For the prestressed concrete section in Fig. 9.4-1, determine the loss of
prestress due to a steel relaxation fr (N/mm 2 ).
Section data :
Area- A
2nd moment of area - I
Yaung'• 1110duli : Es , Ec
Tendon fully bonded.
Fig. 9.4-1
SOLUTION
Let Ofs = loss of prestress in the tendon due to steel relaxation;
Ofc = the corresponding reduction of the concrete compressive stress
at tendon level.
In the hypothetical case of zero change in the length of the tendon, the loss
of prestress in the tendon will by definition be fr. Therefore if the actual
loss of prestress is Ofs, then there must have been a unit extension of the
tendon of (/r - Ofs)l Es.
Hence the compatibility condition is
fr- Ofs Ofc
Es = Ec
The equilibrium condition is, by statics,
M = O/sAps[1 + e;]
:Jc A e
where k = ~(1/A) is the radius of gyration.
Eliminating ofc from the compatibility and equilibrium conditions,