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 :

A fixed end beam is subjected to a load, W at $$1/3rd$$ span from the left support as shown in the figure. The collapse load of the beam is