A steel bar is held by two fixed supports as shown in the figure and is subjected to an increases of temperature $$\Delta T = {100^ \circ }C.$$ If the coefficient of thermal expansion and Young's modulus of elasticity of steel are $$11 \times {10^{ - 6}}/{}^ \circ C$$ and $$200$$GPa, respectively, the magnitude of thermal stress (in MPa) induced in the bar is __________.

The state of stress at a point is $${\sigma _x} = {\sigma _y} = {\sigma _z} = {\tau _{xz}} = {\tau _{zx}} = {\tau _{yz}} = {\tau _{zy}} = 0$$ and $${\tau _{xy}} = {\tau _{yx}} = 50$$MPa. The maximum normal stress (in MPa) at the point is _________.

For a loaded cantilever beam of uniform cross-section, the bending moment (in N-mm) along the length is M(x) = 5x²+10x, where x is the distance (in mm) measured from the free end of the beam. The magnitude of shear force (in N) in the cross-section at x=10mm is _________.

A cantilever beam of length $$L$$ and flexural modulus $$EI$$ is subjected to a point load $$P$$ at the free end. The elastic strain energy stored in the beam due to bending (neglecting transverse shear) is