A box of weight 100 kN shown in the figure is to be lifted without swinging. If all forces are coplanar, the magnitude and direction ($$\theta$$) of the force (F) with respect to x-axis should be

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

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

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