Maximum Value of Bending Moment:

If the BM diagram is a continuous curve, where dM/ dx = 0, the SF shall be zero, and BM shall be maximum positive or maximum negative. For maximum value of bending moment,

                                                                       δM / δx = 0

In other terms, for maximum bending moment, the shear force is zero. But in real practice, the bending moment might be maximum where shear force changes sign. Though, the above relation is extremely important to get the maximum value of bending moment over the beam.

Equating the shear force at a distance of x from the support to zero, we obtain the point where the maximum bending moment shall occur. Taking the moments at that section, maximum bending moment might be obtained.