Question

A 24 in. x 16 in. column on the second floor of a multi-story building is to be designed to carry a live load of 500,000 lb, and a dead load that is 75 % of the live load (includes self weight). The nominal moment is calculated to be 5,769 kip.in. Use the interaction diagrams with γ = 0.8 to design the column reinforcement for a concrete strength of 4000 psi and a steel strength of 60000 psi. Include the detail of the ties in your design.

Answer 1

Step 1:

L.L=500 kips

D.L=500x0.75=375 kips

Pu=1.2(375)+1.6(500)=1250 kips

Step 2:

Mu=5769 in-kips

e=Mu/Pu=5769/1250

e=4.61 in

Step 3:

Pn=1250/0.65=1923 kips

Kn=Pn/fcAg

Kn=1923/(4x24x16)

Kn=1.25

Step 4:

Rn=Pne/(fcAgh)

Rn=1250x4.61/(4x24x16x24)

Rn=0.1563

Now from the interaction charts

=0.8

Step 5:

=0.05

Ast=0.043x16x24=16.512 in2

Provide bar no 14, 8 in number

Step 5:

Now check for lateral ties:

Assuming #3 bars

(a) Spacing=48x3/8=18 in

(b) 16x14/18=12.44 in

(c) L.L.D=16 in

Provide #3 ties with spacing of 12.4 in