haunched beams, and framed bents may be computed by a procedure. I. LETAL. *See H. M. Westergaard, “Deflection of Beams by the Conjugate Beam Method.

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The conjugate-beam method conjutate developed by H. Here the conjugate beam has a free end, since at this end there is zero shear and zero moment.

Retrieved 20 November The slope at a point in the real beam is numerically equal to the shear at the corresponding point in the conjugate beam. Conjugate beam is defined as the imaginary beam with the same dimensions length as that of the original beam but load at any point on the conjugate beam is equal to the bending moment at that point divided by EI.

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Conjugate beam method – Wikipedia

When the conjguate beam is fixed supported, both the slope and displacement are zero. To make use of this comparison we will now consider a beam having the same length as the real beam, but referred here as the “conjugate beam. The following procedure provides a method that may be used to determine the displacement and deflection at a point on the elastic curve of a beam using the conjugate-beam method.


From the above comparisons, we can state two theorems related to the conjugate beam: From Wikipedia, the free encyclopedia. When drawing the conjugate beam it is important that the shear and moment developed at the supports of the conjugate beam account for the corresponding slope and displacement of the real beam at its supports, a consequence of Theorems 1 and 2.

NPTEL :: Civil Engineering – Structural Analysis I

Note that, as a rule, neglecting axial forces, statically determinate real beams have statically determinate conjugate beams; and statically indeterminate real beams have unstable conjugate beams. To show this similarity, these equations are shown below. The displacement of a point in the real beam is numerically equal to the moment at the corresponding point in the conjugate beam.

Essentially, it requires the same amount of computation as the moment-area theorems to determine a beam’s slope or deflection; however, this method relies only on the principles of statics, so its application will be more familiar.


For example, as shown below, a pin or roller support at the end jptel the real beam provides zero displacement, but a non zero slope. Below is a shear, moment, and deflection diagram.

Conjugate beam method

Consequently, from Theorems 1 and 2, the conjugate beam must be supported by a pin or a roller, since this support has zero moment but has a shear or end reaction. This page was last edited on 25 Octoberat The basis for the method comes from the similarity of Eq.

Corresponding real and conjugate supports are shown below.

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