1. What is Beam Deflection?

Beam deflection refers to the displacement of a beam under load. For a simply supported beam with a central point load, the maximum deflection occurs at the center of the beam and is calculated using the formula δ_max = PL³/(48EI).

2. How Does the Calculator Work?

The calculator uses the beam deflection formula:

Where:

• \( P \) — Point load applied at the center (N)
• \( L \) — Length of the beam (m)
• \( E \) — Modulus of elasticity of the beam material (Pa)
• \( I \) — Moment of inertia of the beam cross-section (m⁴)

Explanation: This formula calculates the maximum deflection at the center of a simply supported beam with a point load applied at the midpoint.

3. Importance of Deflection Calculation

Details: Calculating beam deflection is crucial in structural engineering to ensure that beams will not deflect excessively under load, which could lead to structural failure or serviceability issues.

4. Using the Calculator

Tips: Enter the point load in newtons, beam length in meters, modulus of elasticity in pascals, and moment of inertia in meters to the fourth power. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is a simply supported beam?
A: A simply supported beam is supported at both ends, with one support allowing rotation and the other allowing both rotation and horizontal movement.

Q2: What are typical values for modulus of elasticity?
A: Steel has E ≈ 200 GPa, aluminum ≈ 70 GPa, and wood varies from 8-14 GPa depending on species and grade.

Q3: How do I calculate moment of inertia?
A: Moment of inertia depends on the cross-sectional shape. For a rectangle, I = bh³/12; for a circle, I = πd⁴/64.

Q4: Does this formula work for distributed loads?
A: No, this formula is specifically for a central point load. Different formulas exist for distributed loads.

Q5: What is considered acceptable deflection?
A: Deflection limits vary by application, but a common rule is to limit deflection to L/360 for floors and L/240 for roofs under live loads.