In a system, two connected rigid bars $$AC$$ and $$BC$$ are of identical length $$L$$ with pin supports at $$A$$ and $$B.$$ The bars are interconnected at $$C$$ by a frictionless hinge. The rotation of the hinge is restrained by a rotational spring of stiffness, $$k.$$ The system initially assumes a straight line configuration, $$ACB.$$ Assuming both the bars as weightless, the rotation at supports, $$A$$ and $$B,$$ due to a transverse load, $$P$$ applied at $$C$$ is:

A simply supported reinforced concrete beam of length $$10$$ $$m$$ sags while undergoing shrinkage. Assuming a uniform curvature of $$0.004\,\,{m^{ - 1}}$$ along the span, the maximum deflection (in $$m$$) of the beam at mid-span is ________

For the plane stress situation shown in the figure, the maximum shear stress and the plane on which it acts are:

A guided support as shown in the figure below is represented by three springs (horizontal, vertical and rotational) with stiffness $${k_x},\,\,{k_y}$$ and $${k_\theta }$$ respectively. The limiting values of $${k_x},\,\,{k_y}$$ and $${k_\theta }$$ are :