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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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. 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.
When bexm 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 that of the original beam conjugats load at any point on the conjugate beam is equal to the bending moment at that point divided by EI.
When drawing the conjugate beam it is important that the shear and moment developed at the supports of the conjugate beam account for the metho slope and displacement of the real beam at its supports, a consequence of Theorems 1 and 2. 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.
From Wikipedia, the free encyclopedia. The metho of a point in the real beam is numerically equal to the moment at the corresponding point in the conjugate beam.
The basis for the method comes from the similarity of Eq. Retrieved 20 November The conjugate-beam method was developed by H.
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Retrieved from ” https: This page was last edited on 25 Octoberat Views Read Edit View history. Here the conjugate beam has a free end, since at this end there is zero shear and zero moment. To show this similarity, these equations are shown below.
Essentially, it requires the same amount of computation as the moment-area theorems methoc determine a beam’s slope or deflection; however, this method relies only on the principles of statics, so its application will be more familiar.
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.
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Upper Saddle River, NJ: From the above comparisons, we can state two theorems related to the conjugate beam: Corresponding real and conjugate supports are shown below.
The slope at a point in the real beam is numerically equal to the shear at the corresponding point in the conjugate beam.