1. What is the Maximum Deflection Equation?

The maximum deflection equation for a simply supported beam with uniform load calculates the maximum vertical displacement at the center of the beam. This is crucial for structural engineering applications to ensure beams meet deflection requirements.

2. How Does the Calculator Work?

The calculator uses the maximum deflection equation:

Where:

• \( \delta_{max} \) — 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 equation calculates the maximum deflection at the center of a simply supported beam subjected to a uniformly distributed load.

3. Importance of Deflection Calculation

Details: Calculating maximum deflection is essential for structural design to ensure that beams and structural members meet serviceability requirements and don't deflect excessively under load.

4. Using the Calculator

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

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 are typical deflection limits?
A: Deflection limits vary by application, but common limits are L/360 for floors and L/240 for roofs under live load.

Q3: How does moment of inertia affect deflection?
A: Deflection is inversely proportional to moment of inertia. Higher moment of inertia means less deflection.

Q4: What materials have different modulus of elasticity?
A: Steel has E ≈ 200 GPa, aluminum ≈ 69 GPa, wood varies by species (typically 8-14 GPa).

Q5: Are there other load cases with different deflection equations?
A: Yes, different equations exist for point loads, cantilever beams, and other support conditions.