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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This page was last edited on 25 Octoberat 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 ntpel is equal to the bending moment at that point divided by EI. Here the conjugate beam has a free end, since at this end there is zero shear and zero moment.
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. Views Read Edit View history.
To show this similarity, these equations are shown below.
Conjugate beam method
Retrieved from ” https: The basis for the method comes from npttel similarity of Eq. 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. Upper Saddle River, NJ: Retrieved 20 November The conjugate-beam method was developed by H.
From Wikipedia, the free encyclopedia. From the above comparisons, we can state two theorems related to the conjugate beam: Consequently, from Theorems 1 and 2, the conjugate beam must be supported by a pin or npel roller, since this support has zero moment but has a shear or end reaction.
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.
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.
Conjugate beam method – Wikipedia
To make use of this comparison we will now ocnjugate a beam having the same length as the real beam, but referred here as the “conjugate beam. The displacement of a point in the real beam is numerically equal to the moment at the corresponding point in the conjugate beam. When the real beam is fixed supported, both the slope and displacement are zero.
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.
The following procedure provides a method that may be used to determine the displacement and deflection at a point on the elastic curve nptell a beam using the conjugate-beam method.