The possible location of shear center of the channel section, shown below, is

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

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

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