The threemoment equation gives us the relation between the moments between any three points in a beam and their relative vertical distances or deviations. This method is widely used in finding the reactions in a continuous beam.
Consider three points on the beam loaded as shown.
From proportions between similar triangles:
→ equation (1)
Substitute t_{1/2} and t_{3/2} to equation (1)
Multiply both sides by 6
Distribute 1/EI
Combine similar terms and rearrange
If E is constant this equation becomes,
If E and I are constant then,
For the application of threemoment equation to continuous beam, points 1, 2, and 3 are usually unsettling supports, thus h_{1} and h_{3} are zero. With E and I constants, the equation will reduce to
Factors for the threemoment equation
The table below list the value of and for different types of loading.
Type of Loading  
Concentrated load anywhere on the span.


Concentrated load at the midspan.


Uniform load over the entire span.


Increasing triangular load on the whole span.


Decreasing triangular load on the whole span.


Isosceles triangular load over the entire span.


Moment load at any point on the span.


General uniform loading.


Recent comments