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Cantilever Beam Deflection Calculator

Cantilever Beam Deflection Formula:

\[ \delta = \frac{w \times L^4}{8 \times E \times I} \]

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1. What is Cantilever Beam Deflection?

Cantilever beam deflection refers to the displacement of a beam when a load is applied to its free end while the other end is fixed. It's a critical factor in structural engineering to ensure beams don't bend excessively under load.

2. How Does the Calculator Work?

The calculator uses the cantilever beam deflection formula:

\[ \delta = \frac{w \times L^4}{8 \times E \times I} \]

Where:

Explanation: The deflection increases with the load and the fourth power of length, while it decreases with higher material stiffness (E) and cross-sectional stiffness (I).

3. Importance of Deflection Calculation

Details: Calculating deflection is crucial for ensuring structural integrity, preventing excessive bending that could lead to failure, and meeting building code requirements.

4. Using the Calculator

Tips: Enter all values in consistent units (inches and pounds). The modulus of elasticity (E) is material-dependent (e.g., ~29,000,000 psi for steel, ~1,600,000 psi for wood).

5. Frequently Asked Questions (FAQ)

Q1: What is a typical maximum allowable deflection?
A: Building codes often limit deflection to L/360 for live loads and L/240 for total loads, where L is the span length.

Q2: Does this formula work for point loads?
A: No, this is for uniform loads. Point load deflection has a different formula: δ = (P×L³)/(3×E×I).

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

Q4: What is moment of inertia (I)?
A: It's a geometric property of the cross-section that measures its resistance to bending. Larger I values mean less deflection.

Q5: Can this be used for composite beams?
A: For composite beams, you need to use an equivalent moment of inertia that accounts for different materials.

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