**INTRODUCTION:**

Inflection points are where the function changes concavity.

When either, or both, of the end couples in Figure 7.9 is reversed in direction, there is at least one section of the beam where the bendmg moment is zero.

Fig 1: Single point of inflection in a beam

In Fig 1 the end couple MB is applied in an anticlockwise direction; the bending moment at a distance z from B is

The distance PB is the relevant root of this quadratic equation. When the end couple M, is also reversed in direction, Figure 7.1 1, there are two points, P and Q, in the beam at which the bending moment is zero. The distances P and Q from B are given by the roots of the equation