A beam $($length$,$ L $=6$m$)$ is constructed out as a truss system, as shown on figure $1.$ The hollow,

circular longitudinal beams have an outer diameter equal to $32$ mm and a wall thickness of $2$ mm$.$ They are

made out of Aluminum $($E $=70$ GPa and maximal allowable normal stress $\backslash$sigma max $=100$ MPa$).$ The centerline of

these horizontal beams is located on distance of $200$mm between each other. The influence of the

connecting $($i$.$e$.$ non$-$horizontal beams$)$ on the moment of inertia can be neglected $($figure $2).$ The beam can

be considered as simply supported and is subjected to two equal loads G which occur at a distance of L$/3$

from each support, as indicated on figure $3.$

a$)$ Draw the shear force and bending moment diagrams for this beam and give a formula for each

relevant point in these diagrams?

b$)$ What is the maximum allowable value of G$?$

c$)$ Where does the maximum deformation occur in this beams? How large is this deformation if G

equals $500$N$?$fig. $1$

fig. $2$

Fig. $3$