Problem $3.$

A beam with a circular cross$-$section is subjected to the loading as shown below. There is a uniform

distributed load, q$=1000($N$)/($m$)$ applied over the entire beam length, L$=10$m and a concentrated load,

P$=50$kN applied at a distance a$=3$ meter from support A $.$ The allowable bending stress of the

material is $\backslash$sigma $\_($all $)=7\mathrm{.}0$MPa and the allowable shear stress $\backslash$tau $\_($all$)=0\mathrm{.}6$MPa.

$($i$)$ Draw the free body diagram and determine the reaction force at A and B$.$

$($i$)$ Determine the minimum required diameter, d$,$ of the beam.

c$=(\backslash$lambda $)/(2)$