The maximum shear stress in a solid shaft of circular cross-section having diameter subjected to a torque $$T$$ is $$\tau $$ . If the torque is increased by four times and the diameter of the shaft is increased by two times, the maximum shear stress in the shaft will be

Beam $$GHI$$ is supported by these pontoons as shown in the figure below. The horizontal cross sectional area of each pontoon is $$8\,\,{m^2},$$ the flexural rigidity of the beam is $$10000$$ $$kN$$-$${m^2}$$ and the unit weight of water is $$10$$ $$kN$$/$${m^3}$$.

When the middle pontoon is brought back to its position as shown in the figure above, the reaction at $$H$$ will be

The span$$(s)$$ to be loaded uniformly for maximum positive (upward) reaction at support $$P,$$ as shown in the figure below, is $$(are)$$

The members $$EJ$$ and $$IJ$$ of a steel truss shown in the figure below are subjected to a temperature rise of $${30^ \circ }C.$$ The coefficient of thermal expansion of steel is $$0.000012$$ per $${^ \circ }C.$$ per unit length. The displacement ($$mm$$) of joint $$E$$ relative to joint $$H$$ along the direction $$HE$$ of truss, is