For the beam and loading shown, use the double$-$integration method to determine $($a$)$ the equation of the elastic curve for segment $AB$ of the beam, $($b$)$ the deflection at $B,$ and $($c$)$ the slope at A$.$ Assume that $El$ is constant for the beam. Let $P=30kN,L=5\mathrm{.}0m,E=185$ GPa, and $I=125{10}^{6}m{m}^4.$

Part $1$

Cut a cross$-$section through the beam between points A and $B$ and draw a free body diagram. Determine the internal bending moment $M(x).$ The diagram shows $M(x)$ in its positive direction. Your answer may be negative. Check your equation by solving for $M$ at $x=1\mathrm{.}3m.$

Answer: