For discontinuous uniformly distributed load and point loads at various points in a beam, a single equation of Mx will not be sufficient to determine the slope and deflection everywhere in the beam.
In such situation’s Mecaulay’s method may be used. In Mecaulay’s method, a single equation of moment is formed for all loads on the beam in such a way that the constants of integration apply equally to all positions of the beam.
For example, let us consider a simply supported beam of span l which carries point loads W1 and W2 at a′ and b′ from the supports as shown in Figure 8.18.
Let RA and RB be the reactions ...