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 displacement of a point in the real beam is numerically equal to the moment at the corresponding point in the conjugate beam.

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

Conjugate beam method

To show this similarity, these equations are shown below. For example, as shown below, a pin or roller support at the end of the real beam provides zero displacement, but a non zero slope.

From the above comparisons, we can state two theorems related to 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. This page was last edited on 25 Octoberat Corresponding real and conjugate supports are shown below.


Below is a shear, moment, and deflection diagram.

When the real beam is fixed supported, both the slope and displacement are zero. Conjugate beam is defined as the imaginary beam with the same dimensions length as conjugatf 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.

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. To make use of this comparison we will now consider a beam having the same length as the real beam, but conjugzte here as the “conjugate beam.

NPTEL :: Civil Engineering – Structural Analysis I

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.

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. 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 bewm of statics, so its application will be more familiar.


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. The basis for the method comes from the similarity of Eq. From Wikipedia, the free encyclopedia.