1. What is the Beam Deflection Formula?

The beam deflection formula calculates the maximum deflection of a simply supported beam with a uniformly distributed load. It's derived from the Euler-Bernoulli beam theory and is widely used in structural engineering.

2. How Does the Calculator Work?

The calculator uses the deflection formula:

Where:

• \( \delta \) — Maximum deflection (inches)
• \( w \) — Uniformly distributed load (pounds per inch)
• \( L \) — Length of beam (inches)
• \( E \) — Modulus of elasticity (psi)
• \( I \) — Moment of inertia (inches⁴)

Explanation: The formula shows that deflection increases with load and length (especially to the 4th power), and decreases with stiffer materials (higher E) and larger cross-sections (higher I).

3. Importance of Deflection Calculation

Details: Calculating beam deflection is crucial for ensuring structural integrity, preventing excessive sagging that could affect functionality, and meeting building code requirements.

4. Using the Calculator

Tips: Enter all values in consistent units (inches and pounds). Ensure inputs are positive numbers. Typical values for E: 29,000,000 psi for steel; 1,800,000 psi for wood.

5. Frequently Asked Questions (FAQ)

Q1: What types of beams does this formula apply to?
A: This formula is for simply supported beams with uniformly distributed loads. Different formulas exist for other support conditions or load types.

Q2: What are typical deflection limits?
A: Building codes often limit deflection to L/360 for live loads and L/240 for total loads, where L is span length.

Q3: How does material affect deflection?
A: Stiffer materials (higher E) deflect less. Steel deflects less than wood for the same dimensions and load.

Q4: What if my beam isn't simply supported?
A: Different support conditions (fixed, cantilever, etc.) require different deflection formulas.

Q5: How accurate is this calculation?
A: It's accurate for linear elastic materials and small deflections (where the beam's slope remains small).