Gugul Conjugate beam method — Wikipedia metthod Retrieved 20 November Upper Saddle River, NJ: 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 conjugate-beam method was developed by H. By using this site, you agree to the Terms of Use and Privacy Policy. The displacement of a point in the real beam is numerically equal to the moment at the corresponding point in the conjugate beam. 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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Gugul Conjugate beam method — Wikipedia metthod Retrieved 20 November Upper Saddle River, NJ: 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 conjugate-beam method was developed by H. By using this site, you agree to the Terms of Use and Privacy Policy. The displacement of a point in the real beam is numerically equal to the moment at the corresponding point in the conjugate beam.

The slope at a point in the real beam is numerically equal to the shear at the corresponding point in the conjugate beam. This page was last edited on 25 Octoberat Here the conjugate beam has a free end, since at this end there is zero shear and zero moment. When the real beam is fixed supported, both the slope and displacement are zero. 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.

Views Read Edit View history. 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 the above comparisons, we can state two theorems related to the conjugate beam: To show this similarity, these equations are shown below. Corresponding real and conjugate supports are shown below. From Wikipedia, the free encyclopedia. Conjugate beam is defined as comjugate 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.

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. 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. TOP 10 Related.

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## 5.5 The Conjugate Beam Method

Resources 5. This figure suggests that, if we could somehow treat the curvature diagram as if it was a loading diagram, then we could determine slope and deflection using graphical integration, the same method that we currently can use to find the shears and moments. This could potentially be an easy way to find the slopes and deflections. Figure 5. It sounds easy, but there is one problem: if in this beam the shears represent slopes and the moments represent deflections, then we also need to convert our boundary conditions so that they have the same effect on the shear and moment in the conjugate beam as the boundary conditions had on the slope and deflection in the real beam. Therefore, for the equivalent conjugate support we need a support that has zero shear equivalent to zero rotation in the real beam and zero moment equivalent to zero deflection in the real beam.

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## Conjugate beam method

Malalkis The conjugate-beam method was developed by H. Views Read Edit View history. 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. 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. 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.

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## CONJUGATE BEAM METHOD NPTEL PDF

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