Structural Concrete - Hassoun

5.2 Shear Stresses in Concrete Beams 189
Figure 5.1
Bending moment and shearing force diagrams for a simple beam.
Figure 5.2
theory.
Bending and shear stresses in a homogeneous beam according to elastic
formula f = Mc/I, whereas the shear stress at any point is calculated by the shear formula of Eq. 5.1.
The maximum shear stress is at the neutral axis and is equal to 1.5v a (average shear), where
v a = V/bh. The shear stress curve is parabolic.
For a singly reinforced concrete beam, the distribution of shear stress above the neutral
axis is a parabolic curve. Below the neutral axis, the maximum shear stress is maintained down
to the level of the tension steel, because there is no change in the tensile force down to this
point and the concrete in tension is neglected. The shear stress below the tension steel is zero
(Fig. 5.3). For doubly reinforced and T-sections, the distribution of shear stresses is as shown
in Fig. 5.3.