Conjugate Beam Method of Slope and Deflection

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I was surfing through a Facebook page and I found that people are confused with this method, so I thought to put it on my blog. You can follow my page on Facebook:
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Back to topic, I will put this in very simple words, for details please leave a comment in the comment box.

• What is conjugate beam?

Conjugate beam is an imaginary beam which has the same length as that of the original beam and has the same supports but has different loading. Loading for the conjugate beam at any point is the bending moment diagram for the original beam divided by "EI" i.e. flexural rigidity of the beam. In short the loading for the conjugate beam is M/EI diagram of the original beam.

Conjugate Beam

• Slope at a point using conjugate beam:

Now as you have drawn the conjugate beam, to find out the slope at any point on the beam, simply find out the shear force at that point for the conjugate beam, that is it.

• Deflection at a point using conjugate beam:

Similarly to find out the deflection at a given point, you have to find out the bending moment at that point in the conjugate beam.  It is as simple as explained.

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