Question

A pinned-pinned steel column has a rectangular cross section 1 in by 2 in. The modulus of elasticity E is 30,000,000 psi and the maximum allowable stress for the column is 30,000 psi. Determine the minimum length L for Eular Formula to be applicable

Answer 1

so length is 8.27 in

Step-by-step 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 =
`\pi ^(2)  E I_(min) / length^(2)` ................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 =
`\pi ^(2)  E I_(min) / length^(2)`

30,000 =
`\pi ^(2) 30000000( 0.08333²) / length^(2)`

length^{2} = [tex]\pi ^{2} 30000000( 0.08333²) / 30000

length = 8.27 in

so length is 8.27 in