1. What is the Beam Deflection Formula?

The Beam Deflection Formula calculates the deflection at position x for a simply supported beam under uniform load. It provides the vertical displacement of the beam at any point along its length.

2. How Does the Calculator Work?

The calculator uses the beam deflection formula:

Where:

• \( \delta \) — Deflection at position x (m)
• \( w \) — Uniform load (N/m)
• \( x \) — Position along the beam (m)
• \( L \) — Length of the beam (m)
• \( E \) — Modulus of elasticity (Pa)
• \( I \) — Moment of inertia (m⁴)

Explanation: The formula accounts for the beam's material properties, geometry, and loading conditions to determine deflection.

3. Importance of Deflection Calculation

Details: Accurate deflection calculation is crucial for structural design, ensuring beams meet serviceability requirements and don't deflect excessively under load.

4. Using the Calculator

Tips: Enter uniform load in N/m, position and length in meters, modulus of elasticity in Pa, and moment of inertia in m⁴. All values must be positive and position must not exceed beam length.

5. Frequently Asked Questions (FAQ)

Q1: What types of beams does this formula apply to?
A: This formula applies to simply supported beams with uniform distributed load across the entire span.

Q2: Where is maximum deflection typically located?
A: For simply supported beams with uniform load, maximum deflection occurs at the center (x = L/2).

Q3: What are typical deflection limits?
A: Deflection limits vary by application but are often L/240 to L/360 for floor beams and L/180 to L/240 for roof beams.

Q4: How does material affect deflection?
A: Materials with higher modulus of elasticity (stiffer materials) will have less deflection under the same loading conditions.

Q5: Can this formula be used for other loading conditions?
A: No, this specific formula is only for uniform load. Different formulas exist for point loads, varying loads, and other support conditions.