Structural Concrete - Hassoun

780 Chapter 19 Introduction to Prestressed Concrete
SUMMARY
Section 19.1
The main objective of prestressing is to offset or counteract all or most of the tensile stresses in a
structural member produced by external loadings, thus giving some advantages over a reinforced
concrete member. A concrete member may be pretensioned or posttensioned. Nonprestressed reinforcement
may also be added to the concrete member to increase its ultimate strength.
Section 19.2
1. The allowable stresses in concrete at transfer are
Maximum compressive stress = 0.6 f ′ ci
Maximum compressive stress at end of simply supported beam = 0.7 f ′ ci
√
Maximum tensile stress = 3 f ′ ci
√
Maximum tensile stress at end of simply supported beam = 6
The allowable stresses after all losses are 0.45 f ′ c for compression and 6 f ′ c for tension.
2. The allowable stress in a pretensioned tendon at transfer is the smaller of 0.74 f pu or 0.82
f py . The maximum stress due to the tendon jacking force must not exceed 0.85 f pu or 0.94
f py ; and the maximum stress in a posttensioned tendon after the tendon is anchored is
0.70 f pu .
Section 19.3
The sources of prestress loss are the elastic shortening, shrinkage, and creep of concrete; relaxation
of steel tendons; and friction. An approximate lump-sum loss is 35 ksi for pretensioned members
and 25 ksi for posttensioned members (friction is not included).
Loss due to elastic shortening = nF i
A c
(Eq. 19.1)
Loss due to shrinkage = ε sh E s (Eq. 19.6)
Loss due to creep = C c (ε c E s ) (Eq. 19.7)
Loss due to relaxation of steel varies between 2.5 and 12%. Loss due to friction in posttensioned
members stems from the curvature and wobbling of the tendon.
{
P
P px = pj e −(kl px+μ p α px )
(Eq.19.10)
P pj (1 + Kl px + μ p α px ) −1
(Eq.19.11)
Section 19.4
Elastic stresses in a flexural member due to loaded and unloaded conditions are given by Eqs.
19.13 through 19.16. The limiting values of the eccentricity, e, are given by Eqs. 19.20, 19.22,
19.24, and 19.26. The minimum and maximum values of F i are given by Eqs. 19.31 and Eqs.
19.32, respectively.
f ′ ci