Consider a propped cantilever $$ABC$$ under two loads of magnitude $$P$$ each as shown in figure below. Flexural rigidity of the beam is $$EI$$.

The rotation at $$B$$ is

A thin-walled long cylindrical tank of inside radius $$'r'$$ is subjected simultaneously to internal gas pressure $$P$$ and axial compressive force $$F$$ at its ends. In order to produce 'pure shear' state of stress in the wall of the cylinder, $$F$$ should be equal to

Consider the beam $$AB$$ shown in the figure below. Part $$AC$$ of the beam is rigid while Part $$CB$$ has the flexural rigidity $$EI$$. Identify the correct combination of deflection at end $$B$$ and bending moment at end $$A,$$ respectively.

A beam with cross-section given below is subjected to a positive bending moment (causing compression at the top) of $$16$$ $$kN$$-$$m$$ acting around the horizontal axis. The tensile force acting on the hatched area of the cross-section is