A $$450$$ $$mm$$ long plain concrete prism is subjected to the concentrated vertical loads as shown in the figure. Cross section of the prism is given as $$150\,\,mm\,\, \times \,\,150\,\,mm.$$ Considering linear stress distribution across the cross-section, the modulus of rupture (expressed in $$MPa$$) is ______________

The beam of an overall depth $$250$$ $$mm$$ (shown below) is used in a building subjected to two different thermal environments. The temperatures at the top and bottom surfaces of the beam are $${36^ \circ }C$$ and $${72^ \circ }C$$ respectively. Considering coefficient of thermal expansion $$\left( \alpha \right)$$ as $$1.50 \times {10^{ - 5}}\,\,$$ per$${}^ \circ C,$$ the vertical deflection of the beam (in $$mm$$) at its mid-span due to temperature gradient is ______________

A beam with cross-section given below is subjected to a positive bending moment (causing compression at the top) of $$16$$ $$kN$$-$$m$$ acting around the horizontal axis. The tensile force acting on the hatched area of the cross-section is

A simply supported beam of uniform rectangular cross-section of width $$b$$ and depth $$h$$ is subjected to linear temperature gradient, $${0^ \circ }$$ at the top $${T^ \circ }$$ at the bottom, as shown in the figure. The coefficient of linear expansion of the beam material is $$\alpha .$$ This resulting vertical deflection at the mid-span of the beam is