A W$53092$ structural steel wide$-$flange shape $E=200$GPa;$I=554{10}^{6}m{m}^4$ is loaded and supported as shown. Determine:

$($a$)$ the force and moment reactions at supports A and $C($positive force is up$,$ positive moment is counterclockwise$).$

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

$($c$)$ the deflection $v_B$ of the beam at $B.$

Assume $L_{AB}=5\mathrm{.}4m,L_{BC}=4\mathrm{.}1m,P=141kN.$

Answers:

$($a$)A=$

i$.$

$kN,M_A=$

i

$kN,M_A=ikN-m.$

$kN-m,C=$

$kN,M_C=$

$kN-m.$

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

i

MPa.

$($c$)v_B=$

$mm.$