Consider a beam of uniform flexural stiffness EI and length L, which is simply-supported at its ends C and G.
The beam carries a concentrated lateral load W at a distance a from C. Then the reactions at C and G are
Now consider a section of the beam a distance z from C; if z < a, the bending moment at the section is
In these equations A, B, A' and B' are arbitrary constants. Now for z = a the values of v are equal, and the slopes are
also equal, as there is continuity of the deflected form of the beam through the point D. Then