Question

A rectangular steel bar 37.5 mm wide and 50 mm thick is pinned at each end and subjected to axial compression. The bar has a length of 1.75 m. The modulus of elasticity is 200 Gpa. What is the critical buckling load

Answer 1

The critical buckling load is
`\mathbf{P_o = 141.61 \ kN}`

Step-by-step explanation:

Given that:

the width of the rectangular steel = 37.5 mm = 0.0375 m

the thickness = 50 mm = 0.05 m

the length = 1.75 m

modulus of elasticity = 200 Gpa = 200 10⁹ × Mpa

We are to calculate the critical buckling load
`P_o`

Using the formula:

`P_o = (\pi ^2 E I)/(L^2)`

where;

`I = (0.0375^3*0.05)/(12)`

`I = 2.197 * 10^(-7)`

`P_o = (\pi ^2 *200*10^9 * 2.197*10^(-7))/(1.75^2)`

`P_o = 141606.66 \ N`

`\mathbf{P_o = 141.61 \ kN}`

The critical buckling load is
`\mathbf{P_o = 141.61 \ kN}`