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Converting real beam into the conjugate beam is quite simple and can be converted with a few simple rules I have given below for you. 

Conjugate beam have the same length as the Real beam. But in load in the conjugate beam will be the bending moment of real beam divided by EI at the same point.

It is the most common and familiar method for civil engineers to analyze slope and displacement of the beam.

This method was developed by H. Müller-Breslau in 1865 A.D. It takes the same computation like another process of finding slope and deflection of the beam like moment area method.

To find the slope and deflection of the beam we require to convert the real beam into the conjugate beam. So, here I have given important rules to convert the real beam into the conjugate beam.

1) The length of real beal will be equal to the conjugate beam. I.e it will not change.

2) Loading on the conjugate beam is provided by (M/EI) diagram of the loads on the real beam where M is the moment on real beam at a different point.

3) Simple support for the real beam remains simple support for the conjugate beam.

4) A fixed end for the real beam becomes the free end for the conjugate beam.

5) Hinge at the real beam will be roller support at conjugate beam.

6) Intermediate support at real beam will be hinge at conjugate beam.

7) The point where there is zero slopes in the real beam will be zero shears for the conjugate beam.

8) The point of where there is maximum deflection for the real beam will be a maximum moment for the conjugate beam.

To Make you more simple to understand I have given below a chart of Covertion of Real beam into Conjugate beam.

How to convert real beam into conjugate beam - with example
Real beam into Conjugate beam

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