What is Cantilever Beam Deflection?

In structural engineering, a cantilever beam is a rigid structural element supported at only one end. When a load is applied to the free end or along the span of the beam, the beam bends, and the vertical displacement at any point is known as deflection. The maximum deflection typically occurs at the free end of the cantilever.

How to Use This Calculator

To calculate the deflection of a cantilever beam, you need to provide four primary values: the applied load (either a point load or a uniform load), the length of the beam, the Modulus of Elasticity (Young's Modulus) of the material, and the Area Moment of Inertia of the beam's cross-section.

Ensure that your units are consistent. This tool uses Newtons (N) for force, meters (m) for length, GigaPascals (GPa) for Young's Modulus, and cm⁴ for the Moment of Inertia. The result is conveniently provided in millimeters (mm) for better readability in engineering designs.

Key Engineering Formulas

The deflection is calculated using standard Euler-Bernoulli beam theory formulas:

• Point Load at Free End: δ = (P × L³) / (3 × E × I)
• Uniformly Distributed Load (UDL): δ = (w × L⁴) / (8 × E × I)

Factors Affecting Deflection

Several factors influence how much a beam will bend. Increasing the Length (L) of the beam has the most dramatic effect, as deflection increases with the third or fourth power of the length. On the other hand, increasing the Moment of Inertia (I)—by using a deeper beam—or using a stiffer material with a higher Young's Modulus (E) will significantly reduce the deflection.

Frequently Asked Questions

Q: What is a typical Young's Modulus for steel?
A: Most structural steel has a Young's Modulus of approximately 200-210 GPa.

Q: Why is my deflection so high?
A: Check your units. A common mistake is mixing meters and millimeters or neglecting the conversion of GPa and cm⁴ to standard SI units before calculation.