$\dfrac{y}{x} = \dfrac{w_o}{L}$
$y = \dfrac{w_o}{L}x$
$F_x = \frac{1}{2}xy$
$F_x = \dfrac{1}{2}x \left( \dfrac{w_o}{L}x \right)$
$F_x = \dfrac{w_o}{2L}x^2$
Shear equation:
$V = -\dfrac{w_o}{2L}x^2$
Moment equation:
$M = -\frac{1}{3}x F_x = -\dfrac{1}{3}x \left( \dfrac{w_o}{2L}x^2 \right)$
$M = -\dfrac{w_o}{6L}x^3$
To draw the Shear Diagram:
- V = - wo x2 / 2L is a second degree curve; at x = 0, V = 0; at x = L, V = -½ woL.
To draw the Moment Diagram:
- M = - wo x3 / 6L is a third degree curve; at x = 0, M = 0; at x = L, M = - 1/6 woL2.