Beam Deflections

Deflection of Beams
The deformation of a beam is usually expressed in terms of its deflection from its original unloaded position. The deflection is measured from the original neutral surface of the beam to the neutral surface of the deformed beam. The configuration assumed by the deformed neutral surface is known as the elastic curve of the beam.

Elastic Curve of a Beam Under Load


Methods of Determining Beam Deflections
Numerous methods are available for the determination of beam deflections. These methods include:

  1. Double-integration method
  2. Area-moment method
  3. Strain-energy method (Castigliano's Theorem)
  4. Conjugate-beam method
  5. Method of superposition


Of these methods, the first two are the ones that are commonly used.