Two steel columns $$P$$ (Length $$L$$ and yield strength $${f_y} = 250\,\,MPa$$) and $$Q$$ (length $$2L$$ and yield strength $${f_y} = 500\,\,MPa$$) have the same cross-sections and end-conditions. The ratio of buckling load of column $$P$$ to that of column $$Q$$ is:

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 $$MPa$$ ?

Two steel columns $$P$$ (Length $$L$$ and yield strength $${f_y} = 250\,\,MPa)$$ and $$Q$$ (length $$2L$$ and yield strength $${f_y} = 500\,\,MPa$$) have the same cross-sections and end-conditions. The ratio of buckling load of column $$P$$ to that of column $$Q$$ is

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 __________.