Beam Shear

For cases of footings whose thicknesses are small in relation to their plan dimensions, the critical section used to calculate beam shear is taken at a distance, d, from the face of the column. The shear force is taken as the sum of the forces acting in all piles that lie outside a critical perimeter d from the face of the column, for all load combinations under consideration. For a detailed description of the calculation of the concrete shear capacity please refer to Beam Shear Capacity .

Due to the nature of pile caps, in many situations the critical section for beam shear is outside of all of the piles in the pile cap. In this situation the guidelines outlined in CRSI page 13-21 are used.

When w/d ≥ 1.0

v_{c} = 1.9 \sqrt{{f^{'}}_{c}} + 0.1 \sqrt{{f^{'}}_{c}} \frac{V_{u} d}{M_{u}} \geq 2 \sqrt{{f^{'}}_{c}}

ACI 318-14 Sec R22.5.5.1

When w/d < 1.0; Limit

\frac{M_{u}}{V_{u} d} \leq 1.0

;

\infty > \frac{V_{u} d}{M_{u}} \geq 1.0

v_{c} = (\frac{d}{w}) [3.5 - 2.5 (\frac{M_{u}}{V_{u} d})] [1.9 \sqrt{{f^{'}}_{c}} + 0.1 \sqrt{{f^{'}}_{c}} \frac{V_{u} d}{M_{u}}]

CRSI 02 Eq. 13-2

v_{c} \leq 10 \sqrt{{f^{'}}_{c}}

Concrete Capacity

V_c = v_c(bd)

where

distance from face of column to center of closest pile in direction of critical section.

Note: that

v_{c} = 2 \sqrt{{f^{'}}_{c}}

(Sec 11.3.1.1) is an approximation of ACI Eq. 11-5 where

\frac{V_{u} d}{M_{u}} = 1.0

and

2, 500 ρ_{w} = 0.1 \sqrt{{f^{'}}_{c}}

per ACI 318-14 Sec R22.5.5.1

Note: For the Beam shear calculation at face of column the moment used to calculate M_u is taken as the distance from the centroid of the pile forces in the critical section + construction tolerance of the column.