# What is the significance of hinge in the internal structure of the beam?

I had come across a question on shear force and bending moment diagram where a cantilever beam with a roller support at point C is given and the portion beyond point C in overhang. Does this hinge act as a internal release point in the structure? If yes then the does this mean bending moment about point B is zero.

A hinge is a point where there is no restriction on rotation. For other points on a beam, the rotation to the left of a point must be equal to the rotation to the right of that same point; that is, there can't be a discontinuity in the rotations along a beam.

Hinges, however, don't have this restriction and therefore allow for discontinuities of rotation. And since bending moment is generated by a beam trying to resist changes to its curvature, we can conclude that there is no internal bending moment at a hinge.

does this mean bending moment about point B is zero

To be clear, a stable structure will have zero bending moment about any imaginable point. We tend to perform our $$\sum M = 0$$ calculations around supports because it eliminates some variables, but that equilibrium equation is valid about any point in the universe.

But if that's the case, how do we obtain non-zero bending moments along a beam? Well, that's because what we're calculating there is internal bending moment. And internal bending moment is calculated as the sum of bending moments to one side of the relevant point.

So, at midspan in a beam, for example, you calculate the bending moment generated by all the loads to the left (or right) of the beam, which will (usually) result in a non-zero value, representing the beam's internal reaction to the curvature being felt at that point.

But hinges don't resist rotation, so we know that the internal bending moment at the hinge is zero. Therefore, the bending moment to either side of the hinge is zero. That's what makes hinges different from other points on a beam. Any other point has a guaranteed null external bending moment (sum of all loads throughout the structure), but only hinges have guaranteed null internal bending moments (sum of all loads to the left of the hinge equal to zero).

• Thanks a lot for the answer. – Ashish Mutekar Jun 30 at 8:58
• @AshishMutekar if this answered your question, feel free to click the checkmark to the left to mark it as the accepted answer. – Wasabi Jun 30 at 12:04

If yes then the does this mean bending moment about point B (the hinge) is zero.