If a beam of rectangular cross-section is subjected to a vertical shear force $$V,$$ the shear force carried by the upper one-third of the cross-section is

A circular shaft shown in the figure is subject to torsion $$T$$ at two points $$A$$ and $$B.$$ The torsional rigidity of portions $$CA$$ and $$BD$$ is $$G{J_1}$$ and that portion $$AB$$ is $$G{J_2}$$. The rotations of shaft at points $$A$$ and $$B$$ are $${\theta _1}$$ and $${\theta _2}$$. The rotation $${\theta _1}$$ is

The maximum tensile stress at the section $$X$$ - $$X$$ shown in the figure below is

The symmetry of stress tensor at a point in the body under equilibrium is obtained from