Two-Way Shear in Spread Footings

Two-way shear, or punching shear, is calculated for a section that is a distance of d/2 from the edge of the concrete column or modified base plate.

The shear capacity is calculated using the smaller of the values calculated according to ACI 318-14 Table 22.6.5.2:

V_{c} = 4 λ \sqrt{{f^{'}}_{c}}

(a)

V_{c} = (2 + \frac{4}{β_{c}}) λ \sqrt{{f^{'}}_{c}}

(b)

V_{c} = (2 + \frac{α_{s} d}{b_{o}}) λ \sqrt{{f^{'}}_{c}}

(c)

where

β_c	=	Ratio of the long side to the short side of the concrete column or modified base plate.
α_s	=	40 for interior columns, 30 for edge columns, and 20 for corner columns. Note: Currently all checks are made assuming interior columns.
λ	=	Modification factor to reflect the reduced mechanical properties of lightweight concrete relative to normal weight concrete of the same compressive strength. Note: The program uses the value provided by ACI 318-14 section 19.2.4.2 of λ = 1 for normal weight concrete.
b_o	=	Perimeter of critical section for two-way shear in footing.

In this case, d is calculated from the average reinforcement depth for the reinforcement parallel to the major and minor axes of the footing.

Two-Way Shear Critical Section

The ultimate shear, V_u, on the critical section is calculated as follows:

v_{u} = \frac{P_{u}}{A_{c}} + \frac{γ_{v maj} M_{u maj} C_{maj}}{J_{maj}} + \frac{γ_{v min} M_{u maj} C_{min}}{J_{min}}

Equation 4-13

V_{u_2WayShear} = v_{u} b_{o} d - P_{u_Soil}

Equation 4-14

Note: Equation 4‑14 is derived from the commentary for ACI 318-95 Section 11.12.6.2. Also see Figures below.

γ_{v} = 1 - γ_{f}

Equation ACI 318-14 8.4.4.2.2

γ_{f maj} = \frac{1}{1 + (\frac{2}{3}) \sqrt{\frac{b_{2}}{b_{1}}}}

Equation ACI 318-14 8.4.2.3.2

γ_{f min} = \frac{1}{1 + (\frac{2}{3}) \sqrt{\frac{b_{1}}{b_{2}}}}

Equation ACI 318-14 8.4.2.3.2

J_{maj} = \frac{d {(C_{L} + d)}^{3}}{6} + \frac{(C_{L} + d) d^{3}}{6} + \frac{d (C_{L} + d) {(C_{W} + d)}^{2}}{2}

Equation 4-15

J_{min} = \frac{d {(C_{W} + d)}^{3}}{6} + \frac{(C_{W} + d) d^{3}}{6} + \frac{d (C_{L} + d) {(C_{W} + d)}^{2}}{2}

Equation 4-16

where

P_{u_Soil}	=	Total soil force underneath critical area for two-way shear.
C_L	=	Column dimension parallel to the footing local major axis.
C_W	=	Column dimension parallel to the footing local minor axis.
b₁	=	Width of critical section measured in the direction of the span for which moments are determined (in units).
b₂	=	Width of critical section defined in the direction perpendicular to .

Note: Equation 4‑14 and Equation 4‑13 are derived from the commentary for ACI 318-14 Section 8.4.4.2.3.

The footing is taken to be acceptable in two-way shear if ACI 318-14 14.5.1.1(c) is satisfied.

Note: Currently only the two-way shear using α_s = 40 is used. If the supported column is close enough to the footing edge or corner, the user will need to do supplemental checks to confirm that the footing capacity is acceptable if the assumption for α_s is not valid.

RAM Structural System Help

Two-Way Shear in Spread Footings

Two-Way Shear Critical Section

Two-Way Shear Critical Section Dimensions

Stress Distribution Around Critical Section