QUESTION $1[$ Composite Beams$][25$ points$]$

A simply supported composite beam with a $3\mathrm{.}6m$ span supports a triangularly distributed load of peak intensity $q_0$ at mid$-$span $($see Figure Q$1$ part a$).$ The beam is constructed of two wood joists, each $50mm280mm,$ fastened to two steel plates, one of dimensions $6mm80mm$ and the lower plate of dimensions $6mm120mm($see Figure Q$1$ part b$).$ The modulus of elasticity for the wood is $11$GPa and for the steel is $210$GPa. If the allowable stresses are $7$MPa for the wood and $120$MPa for the steel,

a$)$ Find the allowable peak load intensity $q_{0,\text{m}\text{a}\text{x}}$ when the beam is bent about the $z$ axis. Neglect the weight of the beam.

$25$

$2024/05/2711$:$30$

$($a$)$

$($b$)$

Figure Q$1$: Composite Beam.