The state of stress at a point on an element is shown in figure (a). The same state of stress is shownin another coordinate system in figure (b).

The components $$\left( {{\tau _{xx,}}{\tau _{yy,}}{\tau _{xy}}} \right)$$ are given by

The cross-sections of two solid bars made of the same material are shown in the figure. The square cross-section has flexural (bending) rigidity $${{\rm I}_1}$$ while the circular cross-section has flexural rigidity $${{\rm I}_2}$$. Both sections have the same cross-sectional area. The ratio $${{\rm I}_1}$$/$${{\rm I}_2}$$ is

Two circular shafts made of same material, one solid $$(S)$$ and one hollow $$(H)$$, have the same length and polar moment of inertia. Both are subjected to same torque. Here. $${\theta _S}$$ is the twist and $${\tau _S}$$ is the maximum shear stress in the solid shaft, whereas $${\theta _H}$$ is the twist and $${\tau _H}$$ is the maximum shear stress in the hollow shaft. Which one of the following is TRUE?

A beam of length $$L$$ is carrying a uniformly distributed load $$w$$ per unit length. The flexural rigidity of the beam is $$EI$$. The reaction at the simple support at the right end is