1. What Is The Beam Deflection Formula?

The general deflection formula for a simply supported beam with uniform load calculates the maximum deflection at the center of the beam. This formula is derived from beam theory and is widely used in structural engineering.

2. How Does The Calculator Work?

The calculator uses the beam deflection formula:

Where:

• \( \delta \) — Maximum deflection (m)
• \( q \) — Uniform 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 center of a simply supported beam subjected to a uniformly distributed load.

3. Importance Of Deflection Calculation

Details: Deflection calculation is crucial in structural design to ensure that beams and other structural elements meet serviceability requirements and don't deflect beyond acceptable limits.

4. Using The Calculator

Tips: Enter uniform load in N/m, length in meters, modulus of elasticity in Pascals, and moment of inertia in m⁴. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a simply supported beam?
A: A beam supported at both ends, free to rotate and deflect vertically, but not horizontally.

Q2: What is uniform load?
A: A load that is evenly distributed along the entire length of the beam.

Q3: What are typical deflection limits?
A: Deflection limits vary by application, but common limits are L/360 for live loads and L/240 for total loads in building design.

Q4: Does this formula work for other support conditions?
A: No, this specific formula is only for simply supported beams with uniform load. Other support conditions require different formulas.

Q5: What affects beam deflection the most?
A: Length has the greatest effect (L⁴ term), followed by moment of inertia, modulus of elasticity, and load magnitude.