For the linear elastic beam shown in the figure, the flexural rigidity, $$EI$$ is $$781250\,\,kN$$ - $${m^2}.$$ When $$w=10$$ $$kN/m,$$ the vertical reaction $${R_A}$$ at $$A$$ is $$50$$ $$kN.$$ The value of $${R_A}$$ for $$w = 100\,kN/m$$ is

$${U_1}$$ and $${U_2}$$ are the strain energies stored in a prismatic bar due to axial tensile forces $${P_1}$$ and $${P_2},$$ respectively. The strain energy $$U$$ stored in the same bar due to combined action of $${P_1}$$ and $${P_2}$$ will be

If principle stresses in two-dimensional case are $$\left( - \right)\,\,10\,MPa$$ and $$20$$ $$MPa$$ respectively, then maximum shear stress at the point is

In a two dimensional analysis, the state of stress at a point is shown below.

If $$\sigma = 120\,\,MPa$$ and $${\tau _{xy}} = 70\,\,MPa,\,\,{\sigma _x}$$ and $${\sigma _y},$$ are respectively