Cantilever Beam Deflection Calculator

Cantilever Beam Deflection Formula:

\[ \delta = \frac{F L^3}{3 E I} \]

Force (F):

Length (L):

Elastic Modulus (E):

Moment of Inertia (I):

m⁴

Deflection (δ):

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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 safety and performance.

2. How Does the Calculator Work?

The calculator uses the cantilever beam deflection formula:

\[ \delta = \frac{F L^3}{3 E I} \]

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 subjected to a point load at the free end.

3. Importance of Deflection Calculation

Details: Accurate deflection calculation is crucial for structural design, ensuring beams don't deflect beyond acceptable limits which could lead to structural failure or serviceability issues.

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 that is fixed at one end and free at the other, commonly used in bridges, balconies, and aircraft wings.

Q2: What are typical deflection limits?
A: Deflection limits vary by application but typically range from L/180 to L/480 for live loads, where L is the span length.

Q3: How does material affect deflection?
A: Materials with higher elastic modulus (like steel) deflect less than materials with lower modulus (like wood) under the same load.

Q4: What is moment of inertia?
A: Moment of inertia is a geometric property that measures how a cross-section resists bending. It depends on the shape and size of the cross-section.

Q5: Can this formula be used for distributed loads?
A: No, this specific formula is for point loads at the free end. Different formulas apply for uniformly distributed loads or multiple point loads.