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.

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 reaction at $$C$$ is

Vertical reaction developed at $$B$$ in the frame below due to the applied load of $$100$$ $$kN$$ (with $$150,000$$ $$m{m^2}$$ cross- sectional area and $$3.125 \times {10^9}$$ $$m{m^4}$$ moment of inertia for both members) is