A mass less beam has a loading pattern as shown in figure. The beam is rectangular cross-section with a width of 30 mm and height of 100 mm.

The maximum bending moment occurs at

The two shafts $$AB$$ and $$BC$$, of equal length and diameters $$d$$ and $$2d$$, are made of the same material. They are joined at $$B$$ through a shaft coupling, while the ends $$A$$ and $$C$$ are built-in (cantilevered). A twisting moment $$T$$ is applied to the coupling. If $${T_A}$$ and $${T_C}$$ represent the twisting moments at the ends $$A$$ and $$C,$$ respectively, then

Two identical cantilever beams are supported as shown, with their free ends in contact through a rigid roller. After the load P is applied, the free ends will have

The number of degrees of freedom of a planar linkage with 8 links and 9 simple revolute joints is