Problem $5\mathrm{.}22($Circular beam: screwer, diagrams$)$:

A beam with median plane xOy, of constant cross$-$section $S,$ has a semi$-$circular median line of radius $R,$ Figure $5\mathrm{.}24.$ The beam lies in a vertical plane $(Oy$ being the ascending vertical$),$ is subjected to its own weight $P=Rp$ and is simply supported, as shown.

Calculate on the current cross$-$section, located at angle $,$ the normal force $N,$ the transverse shear $V=V_Y$ and the bending moment $M=M_Z.2.$ Draw the corresponding diagrams.

Figure $5\mathrm{.}24$: Doubly supported circular Figure $5\mathrm{.}25$: Gantry subjected to a unibeam under its own weight. form distributed load.