$${\rm I}$$-section of a beam is formed by gluing wooden planks as shown in the figure below. If this beam transmits a constant vertical shear force of $$3000$$ $$N$$, the glue at any of the four joints will be subjected to a shear force (in $$kN$$ per meter length ) of

A long shaft of diameter $$d$$ is subjected to twisting moment $$T$$ at its ends. The maximum normal stress acting at its cross-section is equal to

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

The buckling load $$P = {P_{cr}}$$ for the column $$AB$$ in figure, as $${K_T}$$ approaches infinity, becomes $$\alpha {{{\pi ^2}E{\rm I}} \over {{L^2}}}$$

Where $$\alpha $$ is equal to