Wood Beam Deflection Calculator

Maximum Deflection Formula:

\[ \delta = \frac{5wL^4}{384EI} \]

Uniform Load (w):

lb/in

Length (L):

Modulus of Elasticity (E):

psi

Moment of Inertia (I):

in⁴

Maximum Deflection (δ):

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1. What is the Maximum Deflection Formula?

The maximum deflection formula calculates the maximum vertical displacement of a simply supported wood beam under a uniform load. This is important for structural design to ensure beams don't deflect beyond acceptable limits.

2. How Does the Calculator Work?

The calculator uses the deflection formula:

\[ \delta = \frac{5wL^4}{384EI} \]

Where:

\( \delta \) — Maximum deflection (in)
\( w \) — Uniform load (lb/in)
\( L \) — Length of beam (in)
\( E \) — Modulus of elasticity (psi)
\( I \) — Moment of inertia (in⁴)

Explanation: The 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 safety, serviceability, and compliance with building codes. Excessive deflection can cause cracking, vibration issues, and user discomfort.

4. Using the Calculator

Tips: Enter all values in consistent units (lb/in for load, inches for length, psi for modulus, in⁴ for moment of inertia). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical acceptable deflection limit?
A: For wood beams, deflection is typically limited to L/240 to L/360 of the span length, depending on the application and building codes.

Q2: Does this formula work for other materials?
A: Yes, the formula applies to any homogeneous, isotropic material behaving elastically, but the modulus of elasticity (E) will vary by material.

Q3: What affects the modulus of elasticity for wood?
A: Wood species, moisture content, grade, and duration of load all affect the modulus of elasticity. Consult wood design specifications for appropriate values.

Q4: How do I calculate moment of inertia?
A: Moment of inertia depends on the cross-sectional shape. For rectangular sections, I = (b × h³)/12, where b is width and h is height.

Q5: When is this formula not applicable?
A: This formula is for simply supported beams with uniform loads. Different support conditions or load patterns require different formulas.