Solve the example problem in lecture notes page $82.$

b

Figure $1.$

A rigid$-$perfectly plastic beam of the length $l$ and cross section $ba$ is subjected to a uniform load $q_0.$ The beam is fully clamped at one end and simply supported at the other as shown in Figure $6.$

$($a$)$ Solve the reaction force at the roller support $($the right hand side$).$

$($b$)$ Calculate the maximum bending moment and its location.