For the truss shown below, the member $$PQ$$ is short by $$3$$ $$mm.$$ The magnitude of vertical displacement of joint $$R$$ (in $$mm$$) is ______________________

The ultimate collapse load $$(P)$$ in terms of plastic moment $${M_P}$$ by kinematic approach for a propped cantilever of length $$L$$ with $$P$$ acting at its mid-span as shown in the figure, would be

Match the information given in Group $$-$$ $${\rm I}$$ with those in Group $$-$$ $${\rm II}.$$

Mathematical idealization of a crane has three bars with their vertices arranged as shown in the figure with a load of $$80$$ $$kN$$ hanging vertically. The coordinates of the vertices are given in parentheses. The force in the member $$QR,\,\,{F_{QR}}$$ will be