Question

A simply supported Aluminium column of length 1 m and rectangular cross-section \( w \times t \) with \( t \leq w \), is subjected to axial compressive loading.
Young’s modulus is 70 GPa. Yield stress under uniaxial compression is 120 MPa.
The value of \( t \) at which the failure load for yielding and buckling coincide is _________ mm.

Hint:

For columns under axial compression, equate the buckling load and yield load to determine the size at which both failure modes coincide.

Answer 1

Correct Answer: 43

For a column under axial load, the failure load occurs when the yield stress due to axial compression is equal to the critical buckling load. The Euler’s buckling load for a column with a simply supported condition is: \[ P_{\text{cr}} = \frac{\pi^2EI}{L^2}. \] The axial compressive failure load due to yielding is: \[ P_{\text{yield}} = \sigma_{\text{yield}} A = 120 \times w \times t. \] At the point of failure, \( P_{\text{cr}} = P_{\text{yield}} \). Substituting the values and solving for \( t \): \[ \frac{\pi^2EI}{L^2} = 120 \times w \times t. \] By calculating the critical value of \( t \), we get: \[ t \approx 43 \, \text{mm}. \] Thus, the value of \( t \) at which the failure load for yielding and buckling coincide is approximately \( 43 \, \text{mm} \).