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

A steel column, pinned at both ends, has a buckling load of $$200$$ $$kN.$$ If the column is restrained against lateral movement at its mid-height, its buckling load will be

The buckling load $$P = {P_{cr}}$$ for the column $$AB$$ in figure, as $${K_T}$$ approaches infinity, becomes $$\alpha {{{\pi ^2}E{\rm I}} \over {{L^2}}}$$

Where $$\alpha $$ is equal to

The maximum tensile stress at the section $$X$$ - $$X$$ shown in the figure below is