AW$25032\mathrm{.}7$ structural steel $E=200$GPa wideflange shape is loaded and supported as shown. A uniformly distributed load of $w=18k\frac{N}{m}$ is applied to the beam, causing the roller support at $B$ to settle downward $($i$.$e$.,$ displace downward$)$ by $11$ mm $.$ Determine:

$($a$)$ the reactions at supports $A,B,$ and $C.$

$($b$)$ the maximum bending stress ${}_{\text{m}\text{a}\text{x}}$ in the beam.

Assume $L_{AB}=3\mathrm{.}8m,L_{BC}=4\mathrm{.}9m.$

Answers:

$($a$)A=kN,B=$ i $kN,C=$

$$ kN $.$

$($b$){}_{\text{m}\text{a}\text{x}}=$ MPa.p