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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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.
To show this similarity, these equations are shown below. When the real beam is fixed supported, both the slope and displacement are zero. Upper Saddle River, NJ: Here the conjugate beam has a free end, since at this end there is zero shear and zero moment.
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. Retrieved 20 November Corresponding real and conjugate supports are shown below.
Views Read Edit View history. 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 method
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 conjugatte.
Note that, as a rule, neglecting axial forces, statically determinate real beams have statically determinate conjugate beams; and statically indeterminate cpnjugate beams have unstable conjugate beams.
The basis for the method comes from the similarity of Eq. Retrieved from ” https: 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 conmugate.
The slope at a point in the real beam is numerically equal to the shear at the corresponding point in the conjugate beam.
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Below is a shear, moment, and deflection diagram. From Wikipedia, the free encyclopedia. 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.
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.
The displacement of a point in the real beam is numerically equal to the moment at the corresponding point in the conjugate beam.