1. What is Beam Deflection Calculation?

Beam deflection calculation determines the vertical displacement of a beam under load. The equation provided calculates deflection at any point x along a simply supported beam with uniform distributed load.

2. How Does the Calculator Work?

The calculator uses the beam deflection equation:

Where:

• \( \delta_x \) — Deflection at point x (m)
• \( q \) — Uniform load (N/m)
• \( x \) — Distance from left support (m)
• \( L \) — Beam length (m)
• \( E \) — Modulus of elasticity (Pa)
• \( I \) — Moment of inertia (m⁴)

Explanation: This equation calculates the deflection at any point along a simply supported beam carrying a uniformly distributed load.

3. Importance of Deflection Calculation

Details: Deflection calculations are crucial for structural design to ensure beams don't deflect excessively, which could cause serviceability issues or structural failure.

4. Using the Calculator

Tips: Enter all values in consistent units. Ensure x ≤ L. All values must be positive. Moment of inertia is typically very small (e.g., 10⁻⁶ to 10⁻⁸ m⁴ for typical beams).

5. Frequently Asked Questions (FAQ)

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

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

Q3: What are typical modulus of elasticity values?
A: Steel: ~200 GPa, Concrete: ~20-30 GPa, Wood: ~8-14 GPa depending on species and grade.

Q4: How do I calculate moment of inertia?
A: Moment of inertia depends on cross-sectional shape. For rectangular sections: I = b·h³/12, where b = width, h = height.

Q5: What are acceptable deflection limits?
A: Typically L/360 for live loads and L/240 for total loads in building design, but check local building codes.