1. What Is Cantilever Beam Deflection?

Cantilever beam deflection refers to the displacement of a beam that is fixed at one end and free at the other when subjected to external loads. This calculation is essential in structural engineering for ensuring beam integrity and safety.

2. How Does The Calculator Work?

The calculator uses the standard cantilever beam deflection formula:

Where:

• \( \delta \) — Deflection (m)
• \( F \) — Applied force (N)
• \( L \) — Length of the beam (m)
• \( E \) — Elastic modulus of the material (Pa)
• \( I \) — Moment of inertia of the cross-section (m⁴)

Explanation: The formula calculates the maximum deflection at the free end of a cantilever beam under a concentrated load at the free end.

3. Importance Of Deflection Calculation

Details: Accurate deflection calculation is crucial for structural design, ensuring beams meet serviceability requirements and preventing excessive deformation that could compromise structural integrity.

4. Using The Calculator

Tips: Enter force in newtons, length in meters, elastic modulus in pascals, and moment of inertia in meters to the fourth power. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a cantilever beam?
A: A cantilever beam is a structural element fixed at one end and free at the other, commonly used in bridges, balconies, and aircraft wings.

Q2: What are typical elastic modulus values?
A: Steel: ~200 GPa, Aluminum: ~70 GPa, Concrete: ~20-30 GPa, Wood: ~10 GPa (varies by species and direction).

Q3: How do I calculate moment of inertia?
A: For common shapes: Rectangle (bh³/12), Circle (πd⁴/64), I-beam (use standard tables or CAD software).

Q4: Does this formula work for distributed loads?
A: No, this formula is for concentrated loads at the free end. Distributed loads require different deflection formulas.

Q5: What is acceptable deflection in structural design?
A: Typically L/360 to L/240 for live loads, but specific requirements depend on building codes and application.