Cantilever Deflection Calculation

Cantilever 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 Deflection?

Cantilever deflection refers to the displacement of a cantilever beam's free end when subjected to an external load. It's a critical parameter in structural engineering for ensuring beams don't deflect beyond acceptable limits.

2. How Does the Calculator Work?

The calculator uses the cantilever deflection formula:

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

Where:

\( \delta \) — Deflection at the free end (m)
\( F \) — Applied force at the free end (N)
\( L \) — Length of the cantilever beam (m)
\( E \) — Elastic modulus of the material (Pa)
\( I \) — Area moment of inertia (m⁴)

Explanation: The formula calculates the maximum deflection of a cantilever beam with a concentrated load at its free end, assuming linear elastic material behavior.

3. Importance of Deflection Calculation

Details: Accurate deflection calculation is crucial for structural design to ensure safety, serviceability, and compliance with building codes. Excessive deflection can lead to structural failure or functional issues.

4. Using the Calculator

Tips: Enter force in newtons (N), length in meters (m), elastic modulus in pascals (Pa), and moment of inertia in meters to the fourth power (m⁴). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is a cantilever beam?
A: A cantilever beam is fixed at one end and free at the other, commonly used in construction for elements like balconies, diving boards, and aircraft wings.

Q2: What are typical deflection limits?
A: Deflection limits vary by application but are often L/180 to L/360 for live loads, where L is the span length.

Q3: Does this formula work for distributed loads?
A: No, this specific formula is for a concentrated load at the free end. Different formulas exist for distributed loads.

Q4: What affects moment of inertia?
A: Moment of inertia depends on the cross-sectional shape and dimensions. It's a measure of a beam's resistance to bending.

Q5: Are there limitations to this formula?
A: This formula assumes small deflections, linear elastic material, and a concentrated load at the free end. It may not be accurate for large deflections or complex loading conditions.