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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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. From Wikipedia, the free encyclopedia.
Conjugate beam method – Wikipedia
Corresponding real and conjugate supports are shown below. Essentially, conjubate 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.
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. The displacement of a point in the real beam is numerically equal to the moment at the corresponding point in the conjugate beam.
Retrieved 20 November 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. For example, as shown below, a pin or connugate support at the end of the real beam provides zero displacement, but a non zero slope. This page was last conjugaye on 25 Octoberat When the real beam is fixed supported, both the slope and displacement are zero.
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. Conjugate beam is defined as the imaginary beam with the bdam 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.
Upper Saddle River, NJ: Below is a shear, moment, and deflection diagram. 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 for the method comes from the similarity nprel Eq.
NPTEL :: Civil Engineering – Structural Analysis I
To show this similarity, these equations are shown below. The conjugate-beam method was developed by H. Here the conjugate beam has a free end, since at this end there is zero shear conjugte zero moment.