DL 50 k LL 30 k W 20 k existing ground 5 soil 3 24 x 24 a

DL = 50 k, LL = 30 k W 20 k existing ground 5\' soil 3\' 24\" x 24\" a) Calculate the minimum plan dimensions of the footing b) Calculate the minimum thickness of the footing c) Determine the required reinforcement for the footing and pedestal Assumptions: f\'c = 3,000 psi fy 60 ksi Allowable bearing pressure -2,000 psf coefficient of sliding friction = 0.2

Solution

a) size of the footing

Alowable bearing pressure=2000psf= 2ksf

ignoring the self weight of footing

Area of footing= (DL+LL+W)/ Allowable bearing pressure

=(50+30+20)/2 = 50 sq.ft

assume footing will be a square footing

so size of the footing = 7.1 X 7.1 ft size

minimun plan size should be 7.1 X 7.1 ft

b) thickness of the footing(d)

assume renforcement of the column be 0.75 \'\'

q_u= (1.2 DL + 1.6 LL + 1.6 W)1000/144 psi = 16.95 psi

d = q_u {(B/2)-(C/2)}/{ (2? ? f\'c^(1/2))+q_u} =16.95 {(85.2/2)-(24/2)}/{ (2* 0.75 *1 * 3000 ^(1/2))+16.95} = 5.23\'\'

c) Maximum bending moment (M_u?)= q_u * {(B/2)-(C/2)}² * B/2=676.117 k.ft

R_u = M_u / bd² = 290.12 psi

?= 0.85 f\'c/fy { 1-{ 1-(2R_u/(? 0.85 f\'c))}^(1/2)}= 0.007028

As=  ?bd= 3.13 in²

provide 6 numbers of .6in² bars