1. What is the Beam Deflection Equation?

The beam deflection equation calculates the vertical displacement of a simply supported steel beam under a uniform load. This formula is derived from Euler-Bernoulli beam theory and is essential for structural engineering applications.

2. How Does the Calculator Work?

The calculator uses the beam deflection equation:

Where:

• \( \delta \) — Deflection at position x (m)
• \( q \) — 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 equation calculates the deflection at any point along a simply supported beam carrying a uniformly distributed load.

3. Importance of Deflection Calculation

Details: Calculating beam deflection is crucial for ensuring structural integrity, preventing excessive deformation, and meeting building code requirements for various construction projects.

4. Using the Calculator

Tips: Enter all values in the specified units. Position x must be between 0 and the beam length L. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the maximum deflection position?
A: For a simply supported beam with uniform load, maximum deflection occurs at the center (x = L/2).

Q2: What are typical values for steel modulus of elasticity?
A: For structural steel, E is typically around 200 GPa (200 × 10⁹ Pa).

Q3: How does beam deflection affect design?
A: Excessive deflection can cause serviceability issues, damage to non-structural elements, and discomfort for occupants.

Q4: Are there limitations to this equation?
A: This equation applies only to simply supported beams with uniform loading. Different support conditions or load types require different formulas.

Q5: What factors influence moment of inertia?
A: Moment of inertia depends on the cross-sectional shape and dimensions of the beam. Standard values are available for common steel sections.