A stepped steel shaft shown below is subjected to $$10$$ $$N$$-$$m$$ torque. If the modulus of rigidity is $$80$$ $$GPa,$$ the strain energy in the shaft in $$N$$-$$mm$$ is

A truss, as shown in the figure, is carrying $$180$$ $$kN$$ load at node $${L_2}.$$ The force in the diagonal member $${M_2}{U_4}$$ will be

The stiffness $$K$$ of a beam deflecting in a symmetric mode, as shown in the figure, is _______

In a redundant joint model, three bar members are pin connected at $$Q$$ as shown in the figure. Under some load placed at $$Q$$, the elongation of the members $$MQ$$ and $$OQ$$ are found to be $$48$$ $$mm$$ and $$35$$ $$mm$$ respectively. Then the horizontal displacement $$'u'$$ and the vertical displacement $$'v'$$ of the node $$Q,$$ in $$mm,$$ will be respectively,