For a compound column section, the moment of inertia in the X-X direction (IXX) = 25,000 cm4 and the moment of inertia about the Y-Y direction (IYY) = 16,000 cm4. Find the least radius of gyration if the cross-sectional area is 1,000 cm2.

A column is subjected to Euler's crippling load Ph of flexural rigidity EI having both ends of the column hinged. If the same length of column is fixed at one end and free at the other end, and subjected to Euler's crippling load Pf with flexural rigidity 4EI, what is the relation between the two critical loads Ph and Pf?

A fixed beam of span 4 m carries a central point load of 40 kN. Calculate the magnitude of the fixed end moments.