Structural Concrete - Hassoun

730 Chapter 19 Introduction to Prestressed Concrete
Increase the live load now to L 3 = 2733 lb/ft. The stresses due to the live load, L 3 ,are
2.733 ×(24)2
M LL = = 196.8K⋅ ft
8
6(196.8 × 12, 000)
σ L3
= =±2050 psi
12(24) 2
The final stresses at the top and bottom fibers due to the dead load, live load (L 3 ), and the
prestressing force are 1825 psi and 0, respectively (Fig. 19.2). Note that the final stresses are
about the same as those in the previous cases, yet the live load has been increased to 2733 lb/ft.
A tensile stress of 225 psi is developed when the prestressing force is applied on the beam. This
stress is less than the modulus of rupture of concrete, f r = 503 psi; hence, cracks will not develop
in the beam.
5. The maximum live load when the eccentric force P acts at e = 6 in. is determined as follows. In the
previous case, the final compressive stress is equal to 1825 psi, which is less than the allowable
stress of 2050 psi. Therefore, the live load may be increased to L 4 = 3033 lb/ft.
Notes:
3.033 ×(24)2
M LL =
8
6(218.4 × 12, 000)
σ L4
= =±2275 psi
12(24) 2
Final stresses due to the dead load, live load (L 4 ), and the prestressing force are −2050 psi and
± 225 psi (Fig. 19.2). The compressive stress is equal to the allowable stress of 2050 psi, and the
tensile stress is less than the modulus of rupture of concrete of 503 psi. In this case, the uniform
live load of 3033 lb/ft has been calculated as follows: Add the maximum allowable compressive
stress of 2050 psi to the initial tensile stress at the top fibers of 225 psi to get 2275 psi. The moment
that will produce a stress at the top fibers of 2275 psi is equal to
( )
bh
2
M = σ
6
= 2.275
6 (12)(24)2 = 2620.8K⋅ in. = 218.4K⋅ ft
M = W L L2
8
and W L = 8 × 218.4
(24) 2 = 3.033 K∕ft
a. The entire concrete section is active in resisting the external loads.
b. The final tensile stress in the section is less than the modulus of rupture of concrete, which indicates
that a crackless concrete section can be achieved under full load.
c. The allowable load on the beam has been increased appreciably due to the application of the
prestressing force.
d. An increase in the eccentricity of the prestressing force will increase the allowable applied load,
provided that the allowable stresses on the section are not exceeded.
19.1.2 Partial Prestressing
A partially prestressed concrete member can be defined as one in which (1) there have been introduced
internal stresses to counteract part of the stresses resulting from external loadings, (2) tensile
stresses are developed in the concrete under working loads, and (3) nonprestressed reinforcement