Cantilever Beam Deflection Calculator

Cantilever Beam Deflection Formula:

\[ \delta_{\text{max}} = \frac{w L^4}{8 E I} \]

Uniform Load (w):

N/m

Length (L):

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Maximum Deflection (δ_max):

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1. What is Cantilever Beam Deflection?

Cantilever beam deflection refers to the maximum displacement of a beam that is fixed at one end and free at the other under a uniformly distributed load. This calculation is crucial in structural engineering to ensure beams don't deflect beyond acceptable limits.

2. How Does the Calculator Work?

The calculator uses the cantilever beam deflection formula:

\[ \delta_{\text{max}} = \frac{w L^4}{8 E I} \]

Where:

\( \delta_{\text{max}} \) — Maximum deflection (m)
\( w \) — Uniformly distributed load (N/m)
\( L \) — Length of the beam (m)
\( E \) — Modulus of elasticity (Pa)
\( I \) — Moment of inertia (m⁴)

Explanation: The formula calculates the maximum vertical displacement at the free end of a cantilever beam under uniform loading conditions.

3. Importance of Deflection Calculation

Details: Calculating beam deflection is essential for structural integrity, ensuring that beams don't sag excessively under load, which could lead to structural failure or serviceability issues.

4. Using the Calculator

Tips: Enter all values in consistent units (N/m for load, m for length, Pa for modulus, m⁴ for moment of inertia). All values must be positive and non-zero.

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, buildings, and aircraft structures.

Q2: What affects beam deflection the most?
A: Beam length has the greatest impact on deflection, as deflection increases with the fourth power of length (L⁴).

Q3: What are typical deflection limits?
A: Deflection limits vary by application, but generally range from L/180 to L/360 of the span length for different structural requirements.

Q4: Can this formula be used for point loads?
A: No, this specific formula is for uniformly distributed loads. Different formulas exist for point loads and other loading conditions.

Q5: What is moment of inertia (I)?
A: Moment of inertia is a geometric property that measures a beam's resistance to bending, depending on its cross-sectional shape and dimensions.