The state of $$2D$$-stress at a point is given by the following matrix of stresses: $$$\left[ {\matrix{ {{\sigma _{xx}}} & {{\sigma _{xy}}} \cr {{\sigma _{xy}}} & {{\sigma _{yy}}} \cr } } \right] = \left[ {\matrix{ {100} & {30} \cr {30} & {20} \cr } } \right]MPa$$$

What is the magnitude of maximum shear stress in $$MPa$$ ?

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

The state of two dimensional stresses acting on a concrete lamina consists of a direct tensile stress, $${\sigma _x} = 1.5\,\,N/m{m^2},$$ and shear stress, $$\tau = 1.20\,N/m{m^2},$$ which cause cracking of concrete. Then the tensile strength of the concrete in $$N/m{m^2}$$ is