Structural Concrete - Hassoun

452 Chapter 13 Footings
Figure 13.11
One-way shear.
13.4.3 Two-Way Shear (Punching Shear) (V u2
)
Two-way shear is a measure of the diagonal tension caused by the effect of the column load
on the footing. Inclined cracks may occur in the footing at a distance d/2 from the face of the
column on all sides. The footing will fail as the column tries to punch out part of the footing
(Fig. 13.12).
The ACI Code, Section 22.6.5.2, allows a shear strength, V c , in footings without shear reinforcement
for two-way shear action, the smallest of
V c1
= 4λ √ f cb ′ 0 d (13.6)
(
V c2
= 2 + 4 )
λ √ f ′
β
cb 0 d (13.7)
( )
αs d
V c3
= + 2 λ √ f
b
cb ′ 0 d (13.8)
0
where
β = ratio of long side to short side of column
b 0 = perimeter of critical section taken at d/2 from loaded area (column section) (see Fig. 13.12)
d = effective depth of footing
λ = modification factor for type of concrete (ACI Code, Section 8.6.1)
λ = 1.0 for normal-weight concrete
λ = 0.85 for sand-lightweight concrete
λ = 0.75 for all-lightweight concrete