The conjugate beam method is a structural analysis method to determine slopes and deflections of a beam. It was developed by Christian O. Mohr. In essence, it requires the same amount of calculation as moment-of-area theorems to determine a beam's slope or deflection; Even so, this method applies only the principles of statics "Statics (mechanical)"), so its application may be more familiar.[1]​ The conjugate beam is defined as an imaginary beam with the same dimensions (length) as the original beam, but a load at any point on the conjugate beam is equal to the bending moment at that point on the original beam divided by EI.[2]​.

The basis for the method comes from the similarity of equations 1 and 2 to those 3 and 4. To show this similarity, these equations are shown below.

Integrating, the equations look like this:

Here the shear V is compared to the slope θ, the moment M is compared to the deflection v, and the external load w is compared to the M/EI diagram. The figure shows a shear, moment diagram and another deflection diagram. The M/EI diagram is a moment diagram divided by the product of the Young's modulus of the beam and its moment of inertia.

To make use of this comparison we will now consider a beam that has the same length as the real beam, but called here as the "conjugate beam." The conjugate beam is "loaded" with the M/EI diagram derived from the load on the real beam. With these comparisons, we can state two theorems related to the conjugate beam:

When drawing the conjugate beam, it is important that the shear and moment developed at the supports of the conjugate beam consider the slope and deflection of the real beam at its supports, as a consequence of Theorems 1 and 2. For example, as shown below, in a hinge or a roller at one end of the real beam there is no deflection, but there is a slope. Consequently, from theorems 1 and 2, the conjugate beam must be supported on a joint or a roller, since these supports do not have a moment but do have a shear or reaction. When the actual beam is embedded, both the slope and deflection are zero. The corresponding conjugate beam has a free end at this point, since there both the moment and the shear are zero. In the tables below, the supports corresponding to a conjugate beam are shown from those of a real beam. It is noted that, as a general rule, neglecting axial forces, isostatic beams have isostatic conjugate beams, while hyperstatic beams have unstable conjugate beams. Even if this occurs, the M/EI load provides the "balance" necessary for the conjugate beam to be stable.[1]​.