Wood Beam Deflection Calculator Point Load

Point Load Deflection Formula:

\[ \delta = \frac{P b^2 (3 a L - 3 a b - b^2)}{6 E I L} \]

Point Load (P):

Distance b:

Distance a:

Beam Length (L):

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Deflection (δ):

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1. What is Wood Beam Deflection?

Wood beam deflection refers to the displacement of a beam under load. For a point load applied at a specific location along the beam, this calculator determines the maximum deflection using the standard engineering formula.

2. How Does the Calculator Work?

The calculator uses the point load deflection formula:

\[ \delta = \frac{P b^2 (3 a L - 3 a b - b^2)}{6 E I L} \]

Where:

\( \delta \) — Deflection (m)
\( P \) — Point load (N)
\( b \) — Distance from support to load point (m)
\( a \) — Distance from opposite support to load point (m)
\( L \) — Total beam length (m)
\( E \) — Modulus of elasticity (Pa)
\( I \) — Moment of inertia (m⁴)

Explanation: This formula calculates the deflection at the point where the load is applied, considering the beam's material properties and geometry.

3. Importance of Deflection Calculation

Details: Calculating deflection is crucial in structural design to ensure beams don't sag excessively under load, which could affect functionality, aesthetics, or even lead to structural failure.

4. Using the Calculator

Tips: Enter all values in the specified units. Ensure distances a and b sum to the total beam length L. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical modulus of elasticity for wood?
A: Values range from 8-14 GPa (8-14 × 10⁹ Pa) for common construction woods, with higher values for harder woods.

Q2: How do I calculate moment of inertia?
A: For rectangular beams, I = (b × h³)/12, where b is width and h is height. Values are typically in m⁴.

Q3: What is an acceptable deflection limit?
A: Building codes typically limit deflection to L/240 to L/360 for floor joists, where L is the span length.

Q4: Does this formula work for all beam types?
A: This specific formula applies to simply supported beams with a single point load. Different support conditions require different formulas.

Q5: How does moisture affect wood deflection?
A: Wood's modulus of elasticity decreases with increasing moisture content, potentially increasing deflection under the same load.