A beam of length 𝐿 is loaded in the 𝑥𝑦 −plane by a uniformly distributed load, and by a concentrated tip load parallel to the 𝑧 −axis, as shown in the figure. The resulting bending moment distributions about the 𝑦 and the 𝑧 axes are denoted by 𝑀_𝑦 and 𝑀_𝑧 , respectively.

Which one of the options given depicts qualitatively CORRECT variations of 𝑀_𝑦 and 𝑀_𝑧 along the length of the beam?

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

For the overhanging beam shown in figure, the magnitude of maximum bending moment (in kN-m) 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