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

A three-span continuous beam has an internal hinge at $$B.$$ Section $$B$$ is at the mid-span of $$A.C.$$ Section $$E$$ is at the mid-span of $$CG$$. The $$20$$ $$kN$$ load is applied at section $$B$$ whereas $$10$$ $$kN$$ loads are applied at sections $$D$$ and $$F$$ as shown in the figure. Span $$GH$$ is subjected to uniformly distributed load of magnitude $$5$$ $$kN/m$$. For the loading shown, shear force immediate to the right of section $$E$$ is $$9.84$$ $$kN$$ upwards and the sagging moment at section $$E$$ is $$10.31$$ $$kN$$-$$m.$$

The magnitude of the shear force immediate to the left and immediate to the right of section $$B$$ are, respectively

A three-span continuous beam has an internal hinge at $$B.$$ Section $$B$$ is at the mid-span of $$A.C.$$ Section $$E$$ is at the mid-span of $$CG$$. The $$20$$ $$kN$$ load is applied at section $$B$$ whereas $$10$$ $$kN$$ loads are applied at sections $$D$$ and $$F$$ as shown in the figure. Span $$GH$$ is subjected to uniformly distributed load of magnitude $$5$$ $$kN/m$$. For the loading shown, shear force immediate to the right of section $$E$$ is $$9.84$$ $$kN$$ upwards and the sagging moment at section $$E$$ is $$10.31$$ $$kN$$-$$m.$$

The vertical reaction at support $$H$$ is

A homogeneous, simply supported prismatic beam of width $$B,$$ depth $$D$$ and span $$L$$ is subjected to a concentrated load of magnitude $$P.$$ The load can be placed anywhere along the span of the beams. The maximum flexural stress developed in beam is