Conjugate beam theory stated that the M/EI function obtained from inspecting the internal forces developed in beam, is converted to the function of distributed load acting on conjugate beam. In other words, the shape of such diagram is treated as distributed load on conjugate beam.
To use this method, we need to produce bending moment diagram for the entire beam and divide it by EI. Then, the end condition of conjugate beam is determined based on the conditions on real beam. To determine the slope of rotation at one point, we may calculate the shear force developed at that point on conjugate beam. For displacement, we need to determine the bending moment developed instead.
The following introduces the calculation of beam deflection using conjugate beam method. Watch the video above for full details.
Beam overview
Internal moment function
Bending moment diagram
Real beam and conjugate beam end condition
Shear force at fixed end for conjugate beam
Based on conjugate beam theory, shear force at one point on conjugate beam equals to the slope of that point on real beam.
Bending moment at fixed end for conjugate beam
Based on conjugate beam theory, bending moment at one point on conjugate beam equals to the displacement of that point on real beam.
Final result
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