All members in the rigid-jointed frame shown are prismatic and have the same flexural stiffness $$EI$$. Find the magnitude of the bending moment at $$Q$$ (in ݇ܰ݉$$kN$$-$$m$$) due to the given loading _______________

A uniform beam ($$EI=$$ constant) $$PQ$$ in the form of a quarter-circle of radius $$R$$ is fixed at end $$P$$ and free at the end $$Q,$$ where a load $$W$$ is applied as shown. The vertical downward displacement, $${\delta _q},$$ at the loaded point $$Q$$ is given by : $${\delta _q} = \beta \left( {{{W{R^3}} \over {EI}}} \right).$$

Find the value of $$\beta $$(correct to $$4-$$decimal places). _____________________

Beam $$PQRS$$ has internal hinges in span $$PQ$$ and $$RS$$ as shown. The beam may be subjected to a moving distributed vertical load of maximum intensity $$4$$ $$kN/m$$ of any length anywhere on the beam. The maximum absolute value of the shear force (in $$kN$$) that can occur due to this loading just to the right of support $$Q$$ shall be: