Conjugate beam method – with Numerical Example

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Converting the real beam into the conjugate beam is quite simple and can be converted with a few simple rules I have given below for you. Here I have mentioned some numerical to find slop and deflection of the beam by conjugate beam method which will make you a clear understanding of this topic.

The Conjugate beam has 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.

Before numerical for the Conjugate beam method let us see how 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.

How to convert Real beam into conjugate beam?

  1. The length of the 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 the 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 the conjugate beam.
  6. Intermediate support at the real beam will be hinge at the conjugate beam.
  7. The point where there are 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.

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

Conjugate beam method

Numerical problem for conjugate beam method.

Q) Determine the slop at A and the direction of B of the beam shown in Figure below using the conjugate beam method.

Conjugate beam method
Conjugate beam method

So, guys in this way you can calculate the slope and deflection by the conjugate beam method. I Hope friends, you understood. please comment below if you have any questions.

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