Structural Concrete - Hassoun

19.1 Prestressed Concrete 733
Figure 19.3 Load–deflection curves of concrete beams with different prestressing.
The cracking load is W cr
.
reaches its yield strength or proof stress. The beam has small deflection and undergoes brittle failure.
The underreinforced beam fails by the steel reaching its yield or ultimate strength. It shows
appreciable deflection and cracking due to elongation of the steel before the gradual crushing of
the concrete and the collapse of the beam.
Between curves a and e is a wide range of concrete beams with varying amounts of reinforcement
and subjected to varying amounts of prestress. The beam with little prestressing is closer to
curve a, while the beam with a large prestress is closer to curve e. Depending upon the allowable
concrete stress, deflection, and maximum crack width, a suitable combination of prestressed and
nonprestressed reinforcement may be chosen for the required design.
Curve b represents a beam that will crack under full working load. If only part of the live load
L 1 occurs frequently on the structure, then W 1 represents the total dead load and that part of the live
load L 1 .
Curve c represents a beam that starts cracking at working load. The maximum tensile stress
in the concrete = 7.5 √ f ′ c.
Curve d represents a beam with limited prestress. The critical section of the beam will not
crack under full working load, but it will have a maximum tensile stress of 0 < f t < 7.5 √ f ′ c.The
maximum tensile stress in concrete allowed by the current ACI Code is 6 √ f ′ c.
Curves e and e ′ represent fully prestressed concrete beams with no tensile stress under working
loads. (See Fig. 19.4.)