Structural Concrete - Hassoun

756 Chapter 19 Introduction to Prestressed Concrete
Elastic loss is 381 − 358 = 23 K = 6.1%. This value is greater than the assumed elastic loss
of 4%.
Elastic loss per unit steel area = 23
2.178 = 10.6ksi
c. Time-dependent losses:
F i per unit steel area = 358
2.178 = 164.4ksi
Loss due to shrinkage is 8.7ksi (as before). Loss due to creep ∶
Elastic strain =
Let C c = 1.5. Then
F i 358
=
= 0.240 × 10−3
A c E c 372 × 4000
Δf s = C c (ε cr E s )
Δf s = 1.5(0.24 × 10 −3 × 29, 000) =10.4ksi
Percent loss = 10.4
164.4 = 6.3%
Loss due to relaxation of steel is 7 ksi (as before). Time-dependent losses equal
8.7 + 10.4 + 7 = 26.1 ksi, for a percentage loss of 26.1/164.4 = 15.8%, which is very close to
the previously estimated value of 15.7%.
F = ηF i =(1 − 0.158)F i = 0.842F i
η = 0.842
19.5 DESIGN OF FLEXURAL MEMBERS
19.5.1 General
The previous section emphasized that the stresses at the top and bottom fibers of the critical
sections of a prestressed concrete member must not exceed the allowable stresses for all cases or
stages of loading. In addition to these conditions, a prestressed concrete member must be designed
with an adequate factor of safety against failure. The ACI Code requires that the moment due to
the factored service loads, M u , must not exceed φM n , the flexural strength of the designed cross
section.
For the case of a tension-controlled, prestressed concrete beam, failure begins when the steel
stress exceeds the yield strength of steel used in the concrete section. The high-tensile prestressing
steel will not exhibit a definite yield point, such as that of the ordinary mild steel bars used in
reinforced concrete. But under additional increments of load, the strain in the steel increases at an
accelerated rate, and failure occurs when the maximum compressive strain in the concrete reaches
a value of 0.003 (Fig. 19.7).
The limits for reinforcement of prestressed concrete flexural members according to the ACI
Code, Sections 7.6.2, 8.6.2, and 9.6.2, is based on the net tensile strain for tension-controlled,
transition, or compression-controlled sections in accordance with the ACI Code, Section 21.2.2.2,
as was explained here in this textbook, Section 3.5. The strength reduction factor, φ, was given
earlier in Section 3.7 of this textbook based on the ACI Code, Section 21.2.1.