Answer:
so length is 8.27 in
Explanation:
Given data
cross section = 1 in × 2 in
modulus of elasticity E = 30,000,000 psi
maximum allowable stress = 30,000 psi
to find out
minimum length
solution
we know the Eular Formula i.e
allowable stress = [tex]\pi ^{2} E I_(min) / length^{2}[/tex] ................1
here I(min)/area = r² min
I min = 2 × 1³/12 = 0.166 and area = 2×1 = 2 in²
r (min ) = 0.166/2 = 0.083333 in²
so put all value in equation 1 we get length
allowable stress = [tex]\pi ^{2} E I_(min) / length^{2}[/tex]
30,000 = [tex]\pi ^{2} 30000000( 0.08333²) / length^{2}[/tex]
length^{2} = [tex]\pi ^{2} 30000000( 0.08333²) / 30000
length = 8.27 in
so length is 8.27 in
