Solved Problems

Problem: A W200x46 steel column ($E = 200$ GPa) has a length of 6 m. It is pinned at both ends. Determine the critical buckling load. Properties of W200x46: $I_x = 45.5 \times 10^6$ mm$^4$, $I_y = 15.3 \times 10^6$ mm$^4$.

Problem: A hollow aluminum tube acts as a flagpole fixed at the base and free at the top. The length is 4 m. The outer diameter is 100 mm and the thickness is 5 mm. $E = 70$ GPa. Determine the critical load.

Problem: A solid circular steel rod ($E = 200$ GPa, Yield Stress $\sigma_y = 250$ MPa) is used as a column pinned at both ends. Determine the smallest slenderness ratio ($L/r$) for which Euler's Formula is valid (i.e., buckling occurs before yielding).

Problem: A rectangular wooden column has cross-sectional dimensions of $100 \text{ mm} \times 200 \text{ mm}$ and a length of $3 \text{ m}$. It is pinned at both ends. Determine the critical buckling load ($P_{cr}$) if it is free to buckle in any direction. Assume $E = 12 \text{ GPa}$. Then, determine the critical buckling load if the column is laterally braced at its mid-height against buckling about the weak axis.