$8\mathrm{.}3-12$ The beam shown in the figure has a guided sup$-$

port at A and a spring support at $B.$ The guided support

permits vertical movement but no rotation. Derive the

equation of the deflection curve and determine the deflec$-$

tion ${}_B$ at end $B$ due to the uniform load of intensity $q.$

$($Note: Use the second$-$order differential equation of the

deflection curve.$)|$

PROB. $8\mathrm{.}3-12$