If the moment diagram is known, will it be easy to construct the elastic curve? how?Give an example?

Concept of elastic curve:

Suppose there is a simply supported beam of length L as shown in figure:

Since, the beam is unloaded, hence the central or longitudinal axis is a straight line. Now apply some loads on this simply supported beam, say W at different positions, then the straight central axis takes the shape of elastic curve due to loading, which is shown in figure below:

So, when a beam is loaded, then its central axis or longitudinal axis becomes a curved line is known as ELASTIC CURVE.

Yes, if the Bending Moment diagram is known, it will be easy to construct the elastic curve. The concept of drawing an elastic curve through Bending Moment diagram is that when the Bending moment diagram is positive then the shape of elastic curve will be concave up and when the Bending Moment diagram is negative, then the shape of elastic curve will be concave down.

If the moment diagram is positive, then the shape of the elastic curve is:

If the moment diagram is negative, then the shape of the elastic curve is:

The reason behind this concept is that the Bending Moment Diagram indicates the resistance of Bending Moment (internally) by the beam section throughout the length of the beam, whereas elastic curve indicates the elastic shape of central axis of beam after load is applied. Elastic curve is somehow similar to deflection curve that is how the beam is deflecting which is an external behavior of beam, whereas the Bending moment diagram indicates the internal behavior. So, both the terms are opposite. We can easily indicate the shape of elastic curve through the Moment diagram.