MATHalino

The three-moment 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.
 

Continuous beams are those that rest over three or more supports, thereby having one or more redundant support reactions.
 

These section includes
1. Generalized form of three-moment equation
2. Factors for three-moment equation
3. Application of the three-moment equation
4. Reactions of continuous beams
5. Shear and moment diagrams of continuous beams
6. Continuous beams with fixed ends
7. Deflection determined by three-moment equation
8. Moment distribution method
 

Problem 705
Find the reaction at the simple support of the propped beam shown in Fig. P-705 and sketch the shear and moment diagrams.
 

Problem 704
Find the reactions at the supports and draw the shear and moment diagrams of the propped beam shown in Fig. P-704.
 

Superposition Method

There are 12 cases listed in the method of superposition for beam deflection.

• Cantilever beam with...
  1. concentrated load at the free end.
  2. concentrated load anywhere on the beam.
  3. uniform load over the entire span.
  4. triangular load with zero at the free end
  5. moment load at the free end.
• Simply supported beam with...
  1. concentrated load at the midspan.
  2. concentrated load anywhere on the beam span.
  3. uniform load over the entire span.
  4. triangular load which is zero at one end and full at the other end.
  5. triangular load with zero at both ends and full at the midspan.
  6. moment load at the right support.
  7. moment load at the left support.

See beam deflection by superposition method for details.