Calculate Deflection Of Wood Beam

Maximum Deflection Formula:

\[ \delta_{\text{max}} = \frac{P L^3}{48 E I} \]

Point Load (P):

Length (L):

Modulus of Elasticity (E):

psi

Moment of Inertia (I):

in⁴

Maximum Deflection (δ_max):

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1. What is Maximum Deflection of Wood Beam?

Maximum deflection of a wood beam refers to the greatest displacement that occurs at the center of a simply supported beam when a point load is applied. It's a critical factor in structural design to ensure beams don't deflect beyond acceptable limits.

2. How Does the Calculator Work?

The calculator uses the maximum deflection formula:

\[ \delta_{\text{max}} = \frac{P L^3}{48 E I} \]

Where:

\( \delta_{\text{max}} \) — Maximum deflection (in)
\( P \) — Point load applied at center (lb)
\( L \) — Length of the beam (in)
\( E \) — Modulus of elasticity of wood (psi)
\( I \) — Moment of inertia of beam cross-section (in⁴)

Explanation: This formula calculates the center deflection of a simply supported beam with a point load at midspan, which is the maximum deflection point.

3. Importance of Deflection Calculation

Details: Calculating maximum deflection is essential for structural integrity, ensuring beams meet building code requirements, and preventing excessive sagging that could lead to structural failure or serviceability issues.

4. Using the Calculator

Tips: Enter point load in pounds, length in inches, modulus of elasticity in psi, and moment of inertia in in⁴. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical modulus of elasticity for wood?
A: Modulus of elasticity varies by wood species. Common values range from 1,000,000 to 1,800,000 psi for structural lumber.

Q2: How do I calculate moment of inertia?
A: For rectangular beams, I = (b × h³)/12, where b is width and h is height of the beam cross-section.

Q3: What is considered acceptable deflection?
A: Building codes typically limit deflection to L/360 for live loads and L/240 for total loads, where L is span length.

Q4: Does this formula work for distributed loads?
A: No, this formula is specifically for a single point load at the center. Different formulas are used for distributed loads.

Q5: How does moisture affect wood beam deflection?
A: Moisture content affects wood's modulus of elasticity. Higher moisture content generally reduces stiffness and increases deflection.