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)

336 Prestressed concrete simple beams
--------. ,-Level2
Centroidal +
axis -
Fig. 9.2-1
-t-
T
es
01
0_1_
_1Level1
where Pis the prestressing force at transfer, and a is the loss ratio, a = 0.8
being a typical value.
For clarity, Fig. 9.1-1(b) is redrawn in Fig. 9.2-1. Under service
conditions. we have for the typical section:
f - Pe +Pees
(9.2-2)
f
1 - A Z1
- Pe- Pees
2 - A z2
(9.2-3)
where (see notation and sign convention in Section 9.1)
f = the compressive prestress in the concrete;
A = the concrete section area (usually taken as the nominal area of
the cross-section);
Z = the elastic section modulus;
es = the eccentricity of the prestressing force Pe;
subscript 1 refers to the bottom fibre and
subscript 2 refers to the top fibre.
Note that where only one tendon is used, the eccentricity es of the
prestressing force is that of the tendon; where more than one tendon is
used, es is the eccentricity of the centroid of the tendons. For simplicity, es
will be referred to as the tendon eccentricity; also, where several tendons
are used they are often collectively referred to as the tendon. In posttensioned
beams, es usually varies along the beam; however, the
inclination of the tendon to the beam axis is sufficiently small in practice for
the horizontal component of the tendon force to be taken as equal to the
tendon force itself. Hence in eqns (9.2-2) and (9.2-3), and all equations
to follow, no distinction need be made between the tendon force and its
horizontal component.
Still considering the typical section in Fig. 9.2-1, let us introduce
symbols as follows:
Md =
sagging moment due to dead load
Mimax(Mimin) = maximum (minimum) sagging moment
due to imposed load
Mr = the moment range Mimax -
Mimin