User:Floquenbeam/SE Workbench/Conjugate beam method
The conjugate beam method is a structural analysis method for determining deformations in statically determinate and indeterminate beams developed by Otto Mohr (or possibly Harold M. Westergaard?). It was published in XXXX in XXXX?[1] The method only accounts for flexural effects and ignores axial and shear effects. While other classical structural analysis methods are usually more convenient when determining reactions, this method is useful in hand calculation of deflections.
Introduction
[edit]The basis for the conjugate beam method is the analogous mapping between the basic differential equations governing shears and moments, and the basic differential equations governing slopes and deflections. A conjugate beam can be created with shear and moment boundary conditions corresponding to the actual beam's slope and deflection boundary conditions. When loads analogous to the original beam's shears and moments are applied to the conjugate beam, the resulting shears and moments in the conjugate beam correspond to the slopes and deflections in the actual beam. Since most people are more familiar with analysis of shears and moments, this can make the determination of beam deflections much more intuitive, even though the underlying mathematics is existentially the same.
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add equations described above here
Implementation
[edit]To apply the conjugate beam method, the following steps are taken.
Determine shears and moments
[edit]If statically indeterminate, it's OK to write shears and moments in terms of unknowns
Conjugate beam
[edit]A conjugate beam is created who's shear and moment boundary conditions correspond to the actual beam's slope and deflection boundary conditions.
discuss boundary condition mapping
Apply analogous loads to conjugate beam
[edit]text goes here
Determine shears and moments in conjugate beam
[edit]text goes here
Correlate to slopes and deflections in actual beam
[edit]text goes here
Example
[edit]The statically indeterminate beam shown in the figure is to be analyzed.
Result
[edit]Notes
[edit]- ^ need authoritative cite for developer: Mohr or Westergaard
References
[edit]- XXX, XXX (XXX). XXX (3rd ed.). XXX. pp. XXX. ISBN XXX.
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