Beam Deflection Calculator

Beam Deflection – Definition

Beam deflection refers to the vertical displacement of a structural beam when it is subjected to a load. In engineering design, controlling deflection is crucial to ensure safety, serviceability, and structural performance. Excessive deflection can cause cracking, vibration, misalignment, or even structural failure.

Background Theory

Beam deflection is governed by the principles of Euler–Bernoulli beam theory, which relates load, material stiffness, and geometry to the resulting deformation.
The deflection of a beam primarily depends on:

• Load (P or w): magnitude and type (point load or distributed load)

• Span length (L): distance between supports

• Young’s modulus (E): material stiffness

• Area moment of inertia (I): cross-sectional stiffness

• Boundary conditions: support type (simply supported, cantilever, etc.)

Different boundary conditions produce different bending moment distributions, which lead to different deflection formulas.

How This Calculator Works

This calculator computes the maximum vertical deflection of a beam by:

1. Allowing you to choose the beam constraint/support condition

2. Asking for material and geometric inputs: Load, Length, Young’s Modulus, and Moment of Inertia

3. Selecting the appropriate Euler–Bernoulli formula based on your chosen constraint

4. Calculating the deflection and displaying the result instantly

It provides a fast and reliable way to estimate beam deflection without doing manual calculations, making it useful for quick checks during engineering design.