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 $$MPa$$ ?

A uniform beam weighing $$1800$$ $$N$$ is supported at $$E$$ and $$F$$ by cable $$ABCD$$. Determine the tension (in $$N$$) in segment $$AB$$ of this cable (correct to $$1$$-decimal place). Assume the cables $$ABCD$$, $$BE$$ and $$CF$$ to be weightless ________

A symmetric $${\rm I}$$-section (with width of each flange $$=50mm$$, thickness of each flange $$=10mm,$$ depth of web $$=100mm,$$ and thickness of web $$=10mm$$) of steel is subjected to a shear force of $$100$$ $$kN.$$ Find the magnitude of the shear stress (in $$N/m{m^2}$$) in the web at its junction with top flange __________.

The ‘'plane section remains plane’' assumption in bending theory implies: