Concave Up Or Concave Down in Bending Moment Diagram

In Structural Analysis when a member of a frame or a single beam is analyse on which a shear force ( Force perpendicular to axis of beam) is acting. In that we make shear force and bending moment diagram which tell us about how beam will react? or how will it  bend?

When drawing a bending moment diagram for beam or a member which is under a U.D.L (Uniform Distributed Loading) there  comes a curve between two points, between the starting and ending points of UDL. The question arises, how to join the two points?

Yes by a curve, but which curve?

Either from concave up or concave down?

To solve this query there is a simple maths rule of relative maxima and relative minima.

Steps by which you can find easily either to joint the points by concave up or concave down;

1. Differentiate the equation of Bending moment diagram and find the value of ‘x’, by equating it to 0.

2. Differentiate equation second time and put the value of ‘x’ in it.

3. If the answer is ‘+’ than joint the points as concave up.

4. If the answer is ‘-‘ than joint the points as concave down.

Also for finding the maximum and minimum value of curve, put the value of the ‘x’ which you find, in Bending moment equation, where you will find the maximum or minimum value of Bending moment.

Note: The Derivative of Bending moment is equal to shear force.

Hence by a simple math technique, a concept of bending moment diagram will  be cleared easily.

Want to ask anything about?

Comment here! 🙂


2 thoughts on “Concave Up Or Concave Down in Bending Moment Diagram”

  1. Thank you for that. I have a question regarding the shear diagram. When we have a triangular load the shear diagram will be a second-degree curve, how can I make sure about the concavity of shear diagram between two particular points?

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