$${U_1}$$ and $${U_2}$$ are the strain energies stored in a prismatic bar due to axial tensile forces $${P_1}$$ and $${P_2},$$ respectively. The strain energy $$U$$ stored in the same bar due to combined action of $${P_1}$$ and $${P_2}$$ will be

For the linear elastic beam shown in the figure, the flexural rigidity, $$EI$$ is $$781250\,\,kN$$ - $${m^2}.$$ When $$w=10$$ $$kN/m,$$ the vertical reaction $${R_A}$$ at $$A$$ is $$50$$ $$kN.$$ The value of $${R_A}$$ for $$w = 100\,kN/m$$ is

For the plane frame with an overhang as shown below, assuming negligible axial deformation, the degree of static indeterminacy, $$d,$$ and the degree of kinematic indeterminacy, $$k,$$ are

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 beam. The maximum flexural stress developed in beam is