Conjugate Beam Method for slope and deflection of beam
Conjugate beam is an imaginary beam used to determine the slope and deflection of a beam. The method of conjugate beam was developed by Westergaard in 1921. It was inspired by the works of Otto Mohr and Muller-Breslau related to Moment-Area theorems.
Conjugate beam has the following relationship with the real beam.
Supports of conjugate beam are related to real beam as (i) simple support at the end of real beam becomes simple support at the end of conjugate beam (ii) fixed support of real beam becomes free end of conjugate beam (iii) free end of real beam becomes fixed support of conjugate beam (iv) simple support at the end of real beam remains as simple supports at the end of conjugate beam (v) intermediate simple support of a real beam becomes internal pin of the conjugate beam, (vi) internal pin of real beam becomes simple support of the conjugate beam. An example showing conversion of supports from real beam to conjugate beam is given below in the following figure.
See the Solved Example 7-7 on application of conjugate beam to determine the slope and deflection of a beam.
Conjugate beam method has the advantage over the other analytical methods for slope and deflection calculation as it can be easily applied for structures with neutral equilibrium also.
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