How To Calculate Cantilever Size

Cantilever Size Formula:

\[ Size = \sqrt{\frac{Load \times L^3}{3 \times E \times Deflection}} \]

Load (N):

Length (L):

Modulus (E):

Deflection:

Cantilever Size (Height for Rectangular):

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1. What is Cantilever Size Calculation?

The cantilever size calculation determines the required height (for rectangular cross-section) of a cantilever beam based on load, length, modulus of elasticity, and maximum allowable deflection. This ensures structural integrity and performance under specified conditions.

2. How Does the Calculator Work?

The calculator uses the cantilever size formula:

\[ Size = \sqrt{\frac{Load \times L^3}{3 \times E \times Deflection}} \]

Where:

\( Load \) — Applied force in Newtons (N)
\( L \) — Length of the cantilever in meters (m)
\( E \) — Modulus of elasticity in Pascals (Pa)
\( Deflection \) — Maximum allowable deflection in meters (m)

Explanation: This formula calculates the minimum required size (height for rectangular cross-section) to ensure the cantilever beam does not exceed the specified deflection under the given load.

3. Importance of Cantilever Size Calculation

Details: Proper cantilever sizing is essential for structural safety, preventing excessive deflection that could lead to failure, and ensuring the beam meets design requirements while maintaining efficiency.

4. Using the Calculator

Tips: Enter load in Newtons, length in meters, modulus in Pascals, and deflection in meters. All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a cantilever beam?
A: A cantilever beam is a rigid structural element supported at one end and free at the other, commonly used in bridges, buildings, and various mechanical applications.

Q2: Why is deflection important in cantilever design?
A: Excessive deflection can affect functionality, cause discomfort, or lead to structural failure, making it a critical parameter in design.

Q3: What materials are commonly used for cantilevers?
A: Common materials include steel, aluminum, wood, and composites, each with different modulus of elasticity values.

Q4: Can this formula be used for non-rectangular cross-sections?
A: This specific formula calculates height for rectangular cross-sections. Other cross-sections require different formulas based on their moment of inertia.

Q5: How does length affect the cantilever size?
A: Longer cantilevers require larger sizes to resist deflection, as deflection increases with the cube of the length.