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 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. 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.

Conjugate beam method – Wikipedia

Below is a shear, moment, and deflection diagram. 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. 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.


Upper Saddle River, NJ: The basis for the method comes from the similarity of Eq.

The conjugate-beam method was developed by H. Corresponding real and conjugate supports 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.

From Wikipedia, the free encyclopedia. From the above comparisons, we can state two theorems related to the conjugate beam: 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. For example, as shown below, a pin or roller support at the end of the real npel provides zero displacement, but a connjugate zero slope.

Retrieved from ” https: Here the conjugate beam has a free end, since at this end there is zero shear and zero moment. This page was last edited on 25 Octoberat The slope at a point in the real beam is numerically equal to the shear at the corresponding point in the conjugate beam. By using this site, you agree to the Terms of Use and Privacy Policy.


When the real beam is fixed supported, both the slope and displacement are zero. Essentially, it requires the same amount of conjugaye as the moment-area theorems to determine a beam’s slope or deflection; however, this method relies npetl on the principles of statics, so its application will be more familiar.

Retrieved 20 November To show this similarity, these equations are shown below. 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.