Ex $1$

A beam with constant cross$-$section $A=bh,$ Young's modulus $E$ is loaded by a concentrated couple, whose moment is $M,$ applied at the beam end. Compute and represent the diagrams of the bending moment, the curvature, and the vertical displacement.

$L=1m$

$M=3kNm$;

$E=200e9Pa$;

$b=5cm,h=5cm$