Conjugate beam method

Summary

The conjugate beam method computes slopes and deflections of a beam by statics alone. One loads an imaginary beam of the same length, the conjugate beam, with the bending moment diagram of the real beam divided by $EI$. The shear force of the conjugate beam is then the slope of the real beam. Its bending moment is the deflection of the real beam. It works because deflection and moment satisfy differential equations of the same form, $w'' = -M/EI$ and $M'' = -q$.