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 $$MPa$$ ?

The pin-jointed $$2$$-$$D$$ truss is loaded with a horizontal force of $$15$$ ݇ܰ at joint S and another $$15$$ ݇ܰ vertical force at joint $$U,$$ as shown.Find the force in member $$RS$$ (in $$kN$$ ݇ܰ) and report your answer taking tension as positive and compression as negative. _____________

A propped cantilever made of a prismatic steel beam is subjected to a concentrated load $$P$$ at mid span as shown.

If load $$P=80$$ $$kN,$$ find the reaction ܴ$$R$$ (in $$kN$$) (correct to $$1$$-decimal place)using elastic analysis ___________

A propped cantilever made of a prismatic steel beam is subjected to a concentrated load $$P$$ at mid span as shown.

If the magnitude of loadܲ is increased till collapse and the plastic moment carrying capacity of steel beam section is $$90$$ $$kN$$-$$m$$, ݇ܰ݉determine reaction ܴ$$R$$(in ݇ܰ$$kN$$)(correct to $$1$$-decimal place) using plastic analysis. ____________