Footing Design

The circular column is treated as a square of same area (ACI 318-05 15.3). First, determine net pressure on the bottom of the footing.

$h_{col}=sqrt{0.25 pi d^2}=sqrt{0.25*pi*26^2}=$ 23 in

$h_{col} <= h <= 1.6h_{col} right 23 <= h <= 37$ Try h = 24 in

$P_{foot}=0.150*2=$ 0.300 ksf

$P_{soil}=0.120*3=$ 0.360 ksf

$P_{floor}=0.150*{4/12}+0.075=$ 0.125 ksf

$P_{net}=4-0.3-0.36-0.125=$ 3.215 ksf

Estimate dimensions.

$A_{req}={P_D + P_L}/P_{net} = {74+11}/3.215=$ 26.439 sf

L=B= 6 ft = 72 in A=LB= 36 sf

$P_{u,net}={1.2*74+1.6*11}/36$ =2.956 ksf

d approx 24-3-1= 20 in

$B=h_{col}+d=23+20$ =43 in = 3.583 ft

$V_u = P_{u,net}(A-B^2)=3.215*(36-3.583^2)=$ 74.47 kip

beta_c=1, alpha_s=40, b_0=4B=172

$V_c=min[2+4/{beta_c} , {alpha_s d}/{b_0} +2, 4 ]sqrt{f prime_c} b_0 d=$ min[2+4/{1} , {40*20}/{172} +2, 4 ]*sqrt{4000}*172*20= min[6 , 6.651, 4 ]*217.6= 870.3 kip

phi V_n=phi V_c=0.75*870.3= 652.7 kip > V_u✔

$G= {L/2} -{h_{col}/2}-d = {6/2} - {23/12*2} - {20/12}=3-0.9583-1.667=$ 0.375 ft

$V_u = P_{u,net} B G = 2.956*6*0.375=$ 6.651 kip

$phi V_c = phi 2 srt{f prime_c} L d = 0.75*2*sqrt{4000}*72*20=$ 136.6 kip > V_u✔

Footing^6' x 6' x 2'|

Determine reinforcement.

$F={L/2}-{h_{col}/2}={72/2}-{23/2}=$ 24.5 in = 2.042 ft

$M_u={P_{u,net} B F^2}/2 = {2.956*6*2.042^2}/2 =$ 36.97 ft-kip = 443.6 in-kip

$A_s approx M_u/{phi A_s f_y (0.95d)} = 443.6/{0.9*60*0.95*20}=$ 0.4323 in²

$A_{s,min}=0.0018 B h=0.0018*72*24=$ 3.11 in² Controls → φ=0.9

Try 6#7 = 3.60 in²

d=24-3-{7/8}= 20.13

$a={A_s f_y}/{0.85 f prime_c B} = {3.6*60}/{0.85*4*72}=$ 0.8824 in

$phi M_n = phi A_s f_y (d - {a/2}) = 0.9*3.6*60*(20.13-{0.8824/2})=$ 3828 in-kip > 443.6✔

Footing Reinforcement	6#7

Place reinforcement uniformly across the bottom in both directions.

Check development length.

Length Available= {{72-23}/2} -3= 21.5 in

c=min[3+{7/16},11/2,]= min[3.437,5.5] = 3.437

${c+k_{tr}}/d_b = {3.437+0}/0.4375 =$ 7.857 > 2.5 → Use 2.5

$l_d = {d_b 3 fy psi_t psi_e psi_s lambda}/{40 sqrt{f prime_c} ({{c+k_{tr}}/d_b}) }=$ {0.4375* 3 *60000*1.0*1.0*1.0*1.0}/{40*sqrt{4000}*2.5 }= 12.45 in < 21.5✔