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

A rigid rod $$AB$$ of length $$L$$ is hinged at $$A$$ and is maintained in its vertical position by two springs with spring constants $$K$$ attached at end $$B.$$ The system is under stable equilibrium under the action of load $$P$$ when $$P < \,{P_{Cr}}$$. The system will be in unstable equilibrium when $$P$$ attains a value greater than