Wide Flange Beam Deflection Calculator

Maximum Deflection Formula:

\[ \delta_{\text{max}} = \frac{5 w L^4}{384 E I} \]

Uniform Load (w):

N/m

Length (L):

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Maximum Deflection (δ_max):

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1. What is the Wide Flange Beam Deflection Formula?

The maximum deflection formula for a wide flange beam under uniform load calculates the center deflection of a simply supported beam. This is a fundamental calculation in structural engineering for determining beam performance under load.

2. How Does the Calculator Work?

The calculator uses the deflection formula:

\[ \delta_{\text{max}} = \frac{5 w L^4}{384 E I} \]

Where:

\( \delta_{\text{max}} \) — Maximum deflection at center (m)
\( w \) — Uniformly distributed load (N/m)
\( L \) — Length of the beam (m)
\( E \) — Modulus of elasticity of the material (Pa)
\( I \) — Moment of inertia of the cross-section (m⁴)

Explanation: This formula calculates the maximum vertical displacement at the center of a simply supported beam subjected to a uniformly distributed load.

3. Importance of Deflection Calculation

Details: Deflection calculations are crucial in structural design to ensure that beams and other structural elements don't deflect excessively under load, which could lead to serviceability issues or structural failure.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a wide flange beam?
A: A wide flange beam is an I-beam with wider flanges than standard I-beams, providing better resistance to bending in both directions.

Q2: What are typical values for modulus of elasticity?
A: For steel, E ≈ 200 GPa (200 × 10⁹ Pa); for aluminum, E ≈ 69 GPa; for wood, E varies from 8-14 GPa depending on species.

Q3: How do I find the moment of inertia for a specific beam?
A: Moment of inertia values are typically provided in beam tables or can be calculated from the beam's cross-sectional dimensions.

Q4: What are acceptable deflection limits?
A: Deflection limits vary by application, but common limits are L/360 for floors and L/240 for roofs under live load.

Q5: Does this formula work for other beam types?
A: This specific formula is for simply supported beams with uniform load. Different support conditions and load types require different formulas.