Problem $3$

The beam of flexural rigidity $EI$ in Fig. $3$ is clamped at end $A,$ supported at $C,$ and loaded by the couple at $B$ together with the load uniformly distributed over the region $BC.$ The cross$-$section of the beam is double$-$T$-$iron $27,$ the yield stress of the steel is $240$ MPa $,$ the recommended coefficient of safety is $2.$ Determine allowable value of $"q"$ if $l=0\mathrm{.}5m.$

Fig$\mathrm{.}3.$a

Fig. $3.$b