A rigid bar $$GH$$ of length $$L$$ is supported by a hinge and a spring of stiffness $$K$$ as shown in the figure below. The buckling load, $${P_{cr}}'$$ for the bar will be

The stepped cantilever is subjected to moments, $$M$$ as shown in the figure below. The vertical deflection at the free end (neglecting the self weight) is

Cross-section of a column consisting of two steel strips, each of thickness $$t$$ and width $$b$$ is shown in the figure below. The critical loads of the column with perfect bond and without bond between the strips are $$P$$ and $${P_0}$$ respectively. The ratio $$P/{P_0}$$ is

A mild steel specimen is under uniaxial tensile stress. Young's modulus and yield stress for mild steel are $$2 \times {10^5}\,\,MPa$$ and $$250$$ $$MPa$$ respectively. The maximum amount of strain energy per unit volume that can be stored in this specimen without permanent set is