A concrete dam $20$ m high, $1\mathrm{.}5$ m wide at top, and $4$m wide at the base has its front face vertical and retains water to a depth of $15$ m$.$ Find the maximum and minimum stress intensities at the base. The density of water is $10$~kN$/$m$^\{3\}$ and that of masonry is $24$~kN$/$m$^\{3\}.$ Check for stability of dam against tension at base, overturning and sliding $($coefficient of friction is $0\mathrm{.}6)$