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 was developed by H. Views Read Edit View history. 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. For example, as shown below, a pin or roller support at the beeam of the real beam provides zero displacement, but a non zero slope.
Here the conjugate beam has a free end, since at this end there is zero shear and zero moment. From the above comparisons, we can state two theorems related methd the conjugate beam: 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.
The basis conjuyate the method comes from the similarity of Eq. Below is a shear, moment, and deflection diagram. 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.
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. 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.
To show this similarity, these equations are shown below. 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.
This page was last edited on 25 Octoberat Retrieved from ” https: Corresponding real and conjugate supports are shown below. When the real beam ebam fixed supported, both the slope and displacement are zero. Upper Saddle River, NJ: The displacement of a point in the real beam is numerically equal to the moment at the corresponding point in 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.
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