$1.$ A beam of solid rectangular section, breadth $\backslash ($ B $\backslash )$ and depth $\backslash ($ D $\backslash ),$ is bent about an axis parallel to the sides of breadth $\backslash ($ B $\backslash )(\backslash ($ x$-$x $\backslash )$ axis$).$ If the bending moment $\backslash ($ M $\backslash )$ is steadily increased to $0\mathrm{.}88$ Mp $,$ find the depth of elastic core. If $\backslash ($ M $\backslash )$ is then reduced to zero, find the residual stress, assuming elastic behavior on unloading.