1. What is the Beam Deflection Formula?

The beam deflection formula calculates the maximum deflection of a simply supported beam under a uniform load. This is a fundamental calculation in structural engineering to ensure beams meet design requirements for stiffness and serviceability.

2. How Does the Calculator Work?

The calculator uses the beam deflection formula:

Where:

• \( \delta_{max} \) — Maximum deflection (m)
• \( q \) — Uniform load (N/m)
• \( L \) — Length of beam (m)
• \( E \) — Modulus of elasticity (Pa)
• \( I \) — Moment of inertia (m⁴)

Explanation: This formula calculates the maximum deflection at the center of a simply supported beam carrying a uniformly distributed load.

3. Importance of Deflection Calculation

Details: Calculating beam deflection is crucial for structural design to ensure that beams don't deflect excessively under load, which could cause serviceability issues or damage to supported elements.

4. Using the Calculator

Tips: Enter all values in the correct units. The uniform load should be in N/m, length in meters, modulus of elasticity in Pascals, and moment of inertia in m⁴. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What types of beams does this formula apply to?
A: This formula applies specifically to simply supported beams with a uniformly distributed load along the entire length.

Q2: What are typical deflection limits?
A: Deflection limits vary by application but are often L/360 for live loads and L/240 for total loads in building design, where L is the span length.

Q3: How does material affect deflection?
A: Materials with higher modulus of elasticity (E) will deflect less under the same loading conditions.

Q4: What if the load is not uniform?
A: Different formulas are needed for concentrated loads, partial uniform loads, or other loading conditions.

Q5: How does beam shape affect deflection?
A: The moment of inertia (I) depends on the cross-sectional shape and dimensions. Beams with higher I values (deeper sections) deflect less.