A $$3$$ $$m$$ long simply supported beam of uniform cross section is subjected to a uniformly distributed load of $$w = 20$$ $$kN/m$$ in the central $$1$$ $$m$$ as shown in the figure.

If the flexural rrigidity $$(EI)$$ of the beam is $$30 \times {10^6}\,\,N$$ - $${m^2},$$ the maximum slope (expressed in radians) of the deformed beam 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 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 ________

A simply supported beam is subjected to a uniformly distributed load of intensity $$w$$ per unit length. On half of the span from one end. The length of the span and the flexural stiffness are denoted as/and $$EI$$, respectively. The deflection at mid-span of the beam is