Structural Concrete - Hassoun

5.4 Moment Effect on Shear Strength 193
To avoid a shear failure before a bending failure, a greater factor of safety must be provided against
a shear failure. The ACI Code specifies a capacity reduction factor, φ, of 0.75 for shear.
Shear resistance in reinforced concrete members is developed by a combination of the
following mechanisms [2] (Fig. 5.5):
• Shear resistance of the uncracked concrete, V z [3].
• Interface shear transfer, V a , due to aggregate interlock tangentially along the rough surfaces
of the crack [3].
• Arch action [4].
• Dowel action, V d , due to the resistance of the longitudinal bars to the transverse shearing
force [5].
In addition to these forces, shear reinforcement increases the shear resistance V s ,which
depends on the diameter and spacing of stirrups used in the concrete member. If shear reinforcement
is not provided in a rectangular beam, the proportions of the shear resisted by the various
mechanisms are 20 to 40% by V z , 35 to 50% by V a , and 15 to 25% by V d [6].
5.4 MOMENT EFFECT ON SHEAR STRENGTH
In simply supported beams under uniformly distributed load, the midspan section is subjected to
a large bending moment and zero or small shear, whereas sections near the ends are subjected to
large shear and small bending moments (Fig. 5.1). The shear and moment values are both high
near the intermediate supports of a continuous beam. At a location of large shear force and small
bending moment, there will be little flexural cracking, and an average stress v is equal to V/bd.
The diagonal tensile stresses are inclined at about 45 ∘ (Fig. 5.4c). Diagonal cracks can be expected
when the diagonal tensile stress in the vicinity of the neutral axis reaches or exceeds the tensile
strength of concrete. In general, the factored shear strength varies between 3.5 √ f c ′ and 5 √ f c.After
′
completing a large number of beam tests on shear and diagonal tension [1], it was found that in
regions with large shear and small moment, diagonal tension cracks were formed at an average shear
force of
V c = 3.5 √ f cb ′ w d (5.3)
where b w is the width of the web in a T-section or the width of a rectangular section and d is the
effective depth of the beam.
In locations where shear forces and bending moments are high, flexural cracks are formed
first. At a later stage, some cracks bend in a diagonal direction when the diagonal tension stress
at the upper end of such cracks exceeds the tensile strength of concrete. Given the presence of
large moments on a beam, for which adequate reinforcement is provided, the nominal shear force
at which diagonal tension cracks develop is given by
V c = 1.9λ √ f cb ′ w d (5.4)
This value is a little more than half the value in Eq. 5.3 when bending moment is very small.
This means that large bending moments reduce the value of shear stress for which cracking occurs.
The following equation has been suggested to predict the nominal shear stress at which a diagonal
crack is expected [1]:
v c =
V (
b w d = 1.9λ √ f c ′ + 2500ρ Vd )
≤ 3.5λ √ f c ′ (5.5)
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