Structural Concrete - Hassoun

778 Chapter 19 Introduction to Prestressed Concrete
where
f ps = stresses in prestressed reinforcement at nominal strength (psi)
f se = effective stress in prestressed reinforcement after all losses (psi)
d b = nominal diameter of wire or strand (in.)
If bonding of the strand does not extend to end of members, and design includes tension
at service loads in the precompressed tension zone l d calculated by equation 19.65 shall be
doubled.
In pretensioned members, high tensile stresses exist at the end zones, for which special reinforcement
must be provided. Such reinforcement in the form of vertical stirrups is uniformly distributed
within a distance h/5 measured from the end of the beam. The first stirrup is usually placed at 1 to
3 in. from the beam end or as close as possible. It is a common practice to add nominal reinforcement
for a distance d measured from the end of the beam. The area of the vertical stirrups, A v ,to
be used at the end zone can be calculated approximately from the following expression:
A v = 0.021 F ih
f se l t
(19.66)
where f se is allowable stress in the stirrups (usually 20 ksi) and l t is equal to 50 tendon diameters.
Example 19.8
Determine the necessary stirrup reinforcement required at the end zone of the beam given in
Example 19.4.
Solution
F i = 365.9K h = 40 in. f s = 20 ksi l t = 50 × 7 = 22 in.
16
(pro-
Therefore,
365.9 × 40
A v = 0.021 × = 0.7in. 2
20 × 22
h
2 = 40 5 = 8in.
Use four no. 3 closed stirrups within the first 8 in. distance from the support; A v
vided) = 4 × 0.22 = 0.88 in. 2 .
19.10.2 Posttensioned Members
In posttensioned concrete members, the prestressing force is transferred from the tendons to the
concrete, for both bonded and unbonded tendons, at the ends of the member by special anchorage
devices. Within an anchorage zone at the end of the member, very high compressive stresses and
transverse tensile stresses develop, as shown in Fig. 19.10. In practice, it is found that the length of
the anchorage zone does not exceed the depth of the end of the member; nevertheless, the state of
stress within this zone is extremely complex.
The stress distribution due to one tendon within the anchorage zone is shown in Fig. 19.11.
At a distance h from the end section, the stress distribution is assumed uniform all over the section.
Considering the lines of force (trajectories) as individual elements acting as curved struts, the trajectories
tend to deflect laterally toward the centerline of the beam in zone A, inducing compressive
stresses. In zone B, the curvature is reversed in direction and the struts deflect outward, inducing
tensile stresses. In zone C, struts are approximately straight, inducing uniform stress distribution.