A cantilever beam OP is connected to another beam PQ with a pin joint as shown in figure. A load of $$10$$ kN is applied at the mid-point of PQ. The magnitude of bending moment (in kN-m) at fixed end $$O$$ is

A simply supported beam of length $$L$$ is subjected to a varying distributed load $$\sin \left( {3\pi x/L} \right)N{m^{ - 1}},$$ where the distance $$x$$ is measured from the left support. The magnitude of the vertical reaction force in $$N$$ at the left support is

In a simply-supported beam loaded as shown below, the maximum bending moment in N-m is

A beam is made up of two identical bars AB and BC, by hinging them together at B. The end A is built-in (cantilevered) and the end C is simply supported. With the load P acting as shown, the bending moment at A is