The deflection equation and the values for maximum deflection and maximum slope for a simply supported beam are shown below. Derive the moment equations for the beam and use double integration to derive these deflection and slope values.

$v_{\text{m}\text{a}\text{x}}=-\frac{P{L}^3}{48EI}$

$atx=\frac{L}{2}$

${}_{\text{m}\text{a}\text{x}}=\frac{P{L}^2}{16EI}$

at $x=0$ or $x=L$

$v=\frac{P}{48EI}(4x^3-3L^{2}x)$

$0x\frac{L}{2}$