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Successive differentiation of deflection equation discloses the following:

= Deflection

= Slope

= Moment = M

= Shear = V =

= Load =

From the above, we can see that treating clip_image016 diagram as a fictitious loading, computing the shear and moment at any point caused by this loading gives slopes and deflections in the beam at corresponding points.

This technique is known as the Conjugate Beam Method and sometimes as the method of elastic weights.

  1. The actual slope = the fictitious shear and
  2. The actual deflection = the fictitious moment.

This method is especially useful for simply supported beams. For other beams, such as cantilevers or overhanging beams, artificial constraints must be applied.

Solved Example

To find the Deflection at the centre of the given beam by conjugate beam method

Conjugate Beam Method of Structural Analysis

For the conjugate beam,