When part of a beam is bent one way and part the other way, the place where the curvature changes from one to the other is called a point of contraflexure. It is like the middle part of the letter "S". At this point the bending moment falls to zero. A good idea of what this is like can be seen by laying a thin lath across a support, so that both ends drop downwards, and then lifting one end till it bends the other way, i.e. one part is curved upwards. When a continuous beam passes over a support it is concave downwards, whereas between supports it is concave upwards. Points of contraflexure occur where the concavity changes from upwards to downwards. Since there is no bending effect at points of contraflexure, pins could be fitted there without loss of strength.
You can see the drawing.