Enter the force applied, length of the beam, elastic modulus, and moment of inertia into the calculator to determine the deflection of the beam.

Beam Deflection Formula

The following formula is used to calculate the deflection of a beam under a central point load. 

δ = (F * L^3) / (3 * E * I)

Variables:

  • δ is the deflection of the beam (meters)
  • F is the force applied to the beam (newtons)
  • L is the length of the beam (meters)
  • E is the elastic modulus of the beam material (pascals)
  • I is the moment of inertia of the beam’s cross-section (meters to the fourth power)

To calculate the deflection of a beam, multiply the force applied to the beam by the cube of the length of the beam, and then divide the product by three times the product of the elastic modulus and the moment of inertia of the beam’s cross-section.

What is Beam Deflection?

Beam deflection is the vertical displacement of a point on a loaded beam. It is a critical factor in structural engineering, as excessive deflection can compromise the structural integrity of a building or structure. The deflection depends on the beam’s material properties, the shape and size of its cross-section, the length of the beam, and the type and magnitude of the load applied.

How to Calculate Beam Deflection?

The following steps outline how to calculate the Beam Deflection.

  1. First, determine the force applied to the beam (F) in newtons.
  2. Next, determine the length of the beam (L) in meters.
  3. Next, determine the elastic modulus of the beam material (E) in pascals.
  4. Next, determine the moment of inertia of the beam’s cross-section (I) in meters to the fourth power.
  5. Next, gather the formula from above = δ = (F * L^3) / (3 * E * I).
  6. Finally, calculate the Beam Deflection (δ) in meters.
  7. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Force applied to the beam (F) = 500 N

Length of the beam (L) = 2 m

Elastic modulus of the beam material (E) = 200 GPa

Moment of inertia of the beam’s cross-section (I) = 0.0001 m^4