problem $3(25$ pts $)$

Version C

The beam is supported by a pin at A and a roller at $B.$

Let $M_C=8kN*m,w_1=8k\frac{N}{m},$ and $w_2=4k\frac{N}{m}.$ Using discontinuity functions, derive an expression for the elastic curve, $v(x),$ for the beam if $EI$ is constant. Compute the deflection $v(4)$ at $x=4m,$ using $EI=1\mathrm{.}0{10}^{5}kN*m^2.$ Hint: $A_y=16kN$ and $B_y=24kN$