Concrete has a notable capacity against compression stresses but very little capacity against tension stresses (it cracks easily). One strategy to counteract this weakness in tension involves using wires or rods to prestress the concrete beam in regions where flexural tension can be anticipated. Consider the simply-supported beam shown, which has a rectangular cross section of 18" x 12". If concrete has specific weight of 150 pcf (pounds per cubic foot) determine the required tension in rod AB, which runs through the beam so that no tensile stress is developed in the concrete at its center section a-a. Neglect the size of the rod and any deflection of the beam. 16 in. B÷2 in. 18 in. 6 in. 6 in. - 4 ft- - 4 ft

Structural Analysis
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ISBN:9781337630931
Author:KASSIMALI, Aslam.
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Chapter2: Loads On Structures
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Problem 20.2
Concrete has a notable capacity against compression stresses but very little capacity against
tension stresses (it cracks easily). One strategy to counteract this weakness in tension involves
using wires or rods to prestress the concrete beam in regions where flexural tension can be
anticipated. Consider the simply-supported beam shown, which has a rectangular cross section
of 18" x 12". If concrete has specific weight of 150 pcf (pounds per cubic foot) determine the
required tension in rod AB, which runs through the beam so that no tensile stress is developed in
the concrete at its center section a-a. Neglect the size of the rod and any deflection of the beam.
a
16 in.
B 2 in.
18 in.
6 in. 6 in.
-4 ft-
- 4 ft
Tip: the beam's self-weight causes and internal moment at the midspan section and therefore
flexural tension stress at the bottom of the beam. When the rod is tensioned it applies both an
axial stress and a bending moment (since it is applied eccentrically on the cross-section). The
total stress from the self-weight and the tensioned rod on the concrete should be zero.
Transcribed Image Text:Problem 20.2 Concrete has a notable capacity against compression stresses but very little capacity against tension stresses (it cracks easily). One strategy to counteract this weakness in tension involves using wires or rods to prestress the concrete beam in regions where flexural tension can be anticipated. Consider the simply-supported beam shown, which has a rectangular cross section of 18" x 12". If concrete has specific weight of 150 pcf (pounds per cubic foot) determine the required tension in rod AB, which runs through the beam so that no tensile stress is developed in the concrete at its center section a-a. Neglect the size of the rod and any deflection of the beam. a 16 in. B 2 in. 18 in. 6 in. 6 in. -4 ft- - 4 ft Tip: the beam's self-weight causes and internal moment at the midspan section and therefore flexural tension stress at the bottom of the beam. When the rod is tensioned it applies both an axial stress and a bending moment (since it is applied eccentrically on the cross-section). The total stress from the self-weight and the tensioned rod on the concrete should be zero.
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