List of top Solid Mechanics Questions on Euler buckling

Which one of the following vertical columns, of circular cross-section, sustains the highest load without buckling?

A vertical column fixed at one end is subjected to a compressive axial load at the free end. The column’s section modulus, \(EI = 9.82 \times 10^5 \, \text{Nm}^2\), and the cross-sectional area is \(A = 7.85 \times 10^{-3} \, \text{m}^2\). The length of the column is \(L = 2 \, m\). The yield stress of the material is \(145 \, \text{MPa}\). If the column can fail either in buckling or by Tresca’s criterion, the maximum load that the structure can safely sustain is ............... kN (rounded off to one decimal place).

A block of mass $m = 10 \, kg$ is lying on an inclined plane $PQ$ at $30^\circ$. The mass is restrained from sliding down by a force $F$ applied up the plane. The coefficient of friction is $\mu = 0.3$. Take $g = 10 \, m/s^2$. The smallest force $F$ (in N) required to prevent the block from sliding down is ............ (rounded off to one decimal place).

A cylinder made of rubber (length $= L$ and diameter $= d$) is inserted in a rigid container as shown in the figure. The rubber cylinder fits snugly in the rigid container. There is no wall friction. The modulus of elasticity of the rubber is $E$ and its Poisson’s ratio is $\nu$. The cylinder is subjected to a small uniform pressure $p$ as shown in the figure. The resulting axial strain ($\varepsilon_{zz}$) is: