Structural Concrete - Hassoun

Problems 783
27. Y. Guyon. Prestressed Concrete. Wiley, New York, 1960.
28. P. Zia, H. K. Peterson, N. L. Scott, and E. B. Workman. “Estimating Prestress Losses.” Concrete International
1 (June 1979).
PROBLEMS
19.1 A 60-ft-span of a simply supported pretensioned beam has the section shown in Fig. 19.12. The beam
is prestressed by a force F i = 395 K at transfer (after the elastic loss). The prestress force after all losses
is F = 320, f c
′ (compressive stress after all losses) =6ksiandf ′ = 4 ksi. For the midspan section and
ci
using the ACI Code allowable stresses, (a) calculate the extreme fiber stresses due to the prestressing
force plus dead load and (b) calculate the allowable uniform live load on the beam.
Figure 19.12 Problem 19.1.
19.2 For the beam of Problem 19.1 (Fig. 19.12), calculate the elastic loss and all time-dependent losses
using the following data: F i = 405 K, A ps = 2.39 in. 2 located at 6.5 in. from the base, f c ′ = 4ksi, and f c ′ =
6ksi. E c = 57, 000 √ f c ′ ,andE s = 28, 000 ksi. The profile of the tendon is parabolic, and the eccentricity
at the supports is 0.
19.3 The cross section of a 56-ft-span simply supported posttensioned girder that is prestressed by 30 cables
7
16
in. diameter (area of one cable is 0.1089) is shown in Fig. 19.13. The cables are made of seven-wire
stress-relieved strands. The profile of the cables is parabolic with the centroid of the prestressing steel
(CGS) located at 9.6 in. from the base at the midspan section and located at the centroid of the concrete
section (e = 0) at the ends. Calculate the elastic loss of prestress and all other losses. Given: f c ′ = 6ksi,
f ′ ci = 4ksi, E c = 57, 000√ f c ′ , E s = 28, 000 ksi, f pu = 250 ksi, F 0 = 175 ksi, DL = 1.0K∕ft (excluding
self-weight), and LL = 1.6 K/ft.
19.4 For the girder of Problem 19.3,
a. Determine the location of the upper and lower limits of the tendon profile for the section at midspan
and for at least two other sections between midspan and support. (Choose sections at 12, 18, and
25 ft from support.)
b. Check if the parabolic profile satisfies these limits.
19.5 For the girder of Problem 19.3, check the limiting values of the prestressing force at transfer F i .