Question

A 4-ft concrete post is reinforced with four steel Ex-29 x 106 psi and Ec- 3.6 x 106 psi determine the normal sterss in the steel and in the concentrete when a 150-kip axial cential force P is applied to the post bars, each with a in diameter Knowing that 4 ft s in in. Fig.P2.35

Answer 1

answer) here first we have

P=Ps+Pc

so Ps+Pc=150.........1)

now we know the condition

$\delta$c=$\delta$s................2)

now we know the formula

$\delta$c=PcL/AcEc=Pc*4*12/(64-4*(pi/4)*(3/4)²)*3.6*10⁶=0.2143*10^-6Pc

$\delta$s=PsL/AsEs=Ps*4*12/(4*(pi/4)*(3/4)²*29*10⁶=0.9366*10^-6Ps

from eqn 2) we have

0.2143*10^-6Pc=0.9366*10^-6Ps

Pc=4.372Ps........3)

from eqn 1 we have

4.371Ps+Ps=150

5.371Ps=150

Ps=27.925kips

again using eqn 3

Pc=4.372*27.925=122.088kips

now putting the values

$\delta$c= -Pc/Ac=122.088/64-4*(pi/4)*(3/4)²=-1.962ksi

and $\delta$s=-Ps/As=27.925/4*pi/4*(3/4)²= -15.8 ksi