Concept: Net weight of the UDL = wL = W RA + RB = wL Due to symmetry, ${RA} = \frac{{wL}}{2};{RB} = \frac{{wL}}{2}$ Taking a moment about B $M = {RA}x - \frac{{w{x^2}}}{{2}} = \frac{{wL}}{2}x - \frac{{w{x^2}}}{2}$ For maximum B.M, $\frac{{dM}}{{dx}} = 0\;i.e.\;\frac{{wL}}{2} - \frac{{w.2x}}{2} = 0$ $x = \frac{L}{2}$ ${M{max}} = \frac{{wL}}{2} \times \frac{L}{2} - \frac{{w{L^2}}}{8} = \frac{{w{L^2}}}{8}$