For the cantilever beam of span $$3$$ $$m$$ (shown below), a concentrated load of $$20$$ $$kN$$ applied at the free end causes a vertical displacement of $$2$$ $$mm$$ at a section located at a distance of $$1$$ $$m$$ from the fixed end. If a concentrated vertically downward load of $$10$$ $$kN$$ is applied at the section located at a distance of $$1$$ $$m$$ from the fixed end (with no other load on the beam), the maximum vertical displacement in the same beam (in $$mm$$) is ________

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

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