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)

Stresses in service: elastic theory 335
end, and are tensioned between external end anchorages, by which the
tension is maintained while the concrete is placed. When the concrete has
hardened sufficiently the ends of the tendons are slowly released from the
anchorages. During this operation, which is known as transfer, the force in
the tendons is transferred to the concrete by bond stress [5-7]. The length
required at each end of a member to transmit the full tendon force to the
concrete is called the transmission length and is roughly about 65 diameters
for crimped wires and 25 diameters for strands (see BS 8110: Clause 4.10
for values to use in design). In post-tensioning, the concrete member is cast
incorporating ducts for the tendons. When the concrete has hardened
sufficiently, the tendons are tensioned by jacking against one or both ends
of the member, and are then anchored by means of anchorages which bear
against the member or are embedded in it.
Pre-tensioning is more suitable for mass production of standard
members in a factory; usually straight tendons only are used. Posttensioning
is generally used on site for members cast in their final place;
within limits, tendon profiles of any shape can be used.
Prestressed concrete has several important advantages over reinforced
concrete. First, reference to the stress diagram in Fig. 9.1-1(e) shows that
the entire concrete section is effective in resisting the applied moment M,
whereas only the portion of the section above the neutral axis is fully
effective in reinforced concrete; this leads to greatly reduced deflections
under service conditions. Second, the use of curved tendon profiles (in
post-tensioning) enables part of the shear force to be carried by the
tendons. Also, as we shall see in Section 9.6, the precompression in the
concrete tends to reduce the diagonal tension. In general, the same applied
load can be carried by a lighter section in prestressed concrete; this yields
more clearance where it is required and enables longer spans to be used.
The absence or near absence of cracks under service loading is another
advantage.
9.2 Stresses in service: elastic theory
In contrast to the design of reinforced concrete members, the design of
Class 1 and Class 2 prestressed concrete members is generally governed by
the stress criteria in service or at transfer, rather than by their ultimate
strengths, though the latter must be checked. Hence the elastic theory is
very relevant in prestressed concrete design. Designs are normally based
on the conditions in service, but the stresses at transfer (see Section 9.3)
must be checked.
Consider again the simply supported beam in Fig. 9.1-1. Suppose the
prestressing force in the tendon is P at transfer. When the beam is in
service, the prestressing force will be less than P, because of loss of
prestress, which topic will be discussed in Section 9.4. In the meantime it is
sufficient to note that under service condition the effective prestressing
force will be
(9.2-1)