Checking Column Punching Shear

Consider a perimeter d/2 from column face, where 10 of the 12 piles in the group lie outside this perimeter,

V_{u} = 160 (10) - 0.9 [\frac{138 (102) - (20 + 46.3) (16 + 46.3)}{12^{3}}] 57 \frac{150}{1, 000} = 1, 556 kips

ϕ V_{n} = ϕ 4 \sqrt{{f^{'}}_{c}} b_{o} d

(ACI 318-14 Sec. 22.6.5.2)

where

b_o

2(c1 + c2 + 2d) = 2(20 + 16 + 2·46.3) = 257"

ϕ V_{n} = 0.75 (4) \sqrt{3, 000} (257) (46.3) = 1, 955 kips > 1, 556 kips, OK

Check Pile Punching Shear

In General,

V_u = 160 kips

ϕ V_{n} = ϕ 4 \sqrt{{f^{'}}_{c}} b_{o} d

Single Corner Pile,

b_{o} = 2 E + \frac{π}{2} (d_{p} + d)

ϕ V_{n} = 0.75 (4) \sqrt{3, 000} [2 (15) + \frac{π}{2} (8 + 46.3)] (46.3) = 552 kips, OK

Single Edge Pile,

ϕVn = 877 kips, OK

Single Interior Pile,

b_{o} = π (d_{p} + d)

ϕ V_{n} = 0.75 (4) \sqrt{3, 000} π (8 + 46.3) (46.3) = 1, 298 kips, OK

Two-Pile Corner Condition,

b_{o} = 2 e_{p} + s_{p} + \frac{π}{4} (d_{p} + d)

ϕ V_{n} = 0.75 (4) \sqrt{3, 000} [2 (15) + 36 + \frac{π}{4} (8 + 46.3)] (46.3) = 827 kips, OK

Two-Pile Interior Condition,

b_{o} = 2 s_{p} + π (d_{p} + d)

ϕ V_{n} = 0.75 (4) \sqrt{3, 000} [2 (36) + π (8 + 46.3)] (46.3) = 1, 846 kips, OK