The strain energy stored in member $$'AB'$$ of the pin jointed truss shown aside when $$'E'$$ and $$'A'$$ are same for all members is

The stiffness matrix of a beam element is given as $${{2EI} \over L}\left[ {\matrix{ 2 & { + 1} \cr { + 1} & 2 \cr } } \right].$$ Then the flexibility matrix is

The steel portal frame shown in figure is subjected to an imposed service load of $$15$$ $$kN$$. Compute the required plastic moment capacity of the members. All the members are of the same cross-section. Draw the collapse load.

A three hinged arch shown in Figure is quarter of a circle. If the vertical and horizontal components of reaction at $$A$$ are equal, the value of $$\theta $$ is