W Beam Deflection Calculator

Maximum Deflection Formula:

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

Uniform Load (w):

N/m

Beam Length (L):

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Maximum Deflection (δ_max):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is W Beam Maximum Deflection?

The maximum deflection formula calculates the center deflection of a simply supported W-beam under uniform load. This is important for structural engineering to ensure beams don't deflect beyond acceptable limits.

2. How Does the Calculator Work?

The calculator uses the maximum deflection formula:

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

Where:

\( \delta_{max} \) — 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 beam cross-section (m⁴)

Explanation: This formula calculates the maximum deflection at the center of a simply supported beam carrying a uniformly distributed load.

3. Importance of Deflection Calculation

Details: Calculating beam deflection is crucial for structural design to ensure that beams don't sag excessively under load, which could affect functionality, cause cracking in supported elements, or lead to structural failure.

4. Using the Calculator

Tips: Enter uniform load in N/m, beam 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 typical acceptable deflection limit?
A: For most beams, deflection is limited to L/360 for live loads and L/240 for total loads, where L is the span length.

Q2: Does this formula work for all beam types?
A: This specific formula applies only to simply supported beams with uniformly distributed loads. Other support conditions and load types require different formulas.

Q3: How do I find the moment of inertia for a W-beam?
A: Moment of inertia values for standard W-beam sections are published in steel manuals and can be found in engineering reference tables.

Q4: What is a typical modulus of elasticity for steel?
A: For structural steel, the modulus of elasticity is typically 200 GPa (200 × 10⁹ Pa).

Q5: Can this calculator be used for other materials?
A: Yes, as long as you use the correct modulus of elasticity for the specific material (e.g., 70 GPa for aluminum, 10-30 GPa for wood depending on species).