Beam Deflection Calculator Wood

Maximum Deflection Equation:

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

Uniform Load per Unit Length (w):

lb/in

Length (L):

Modulus of Elasticity (E):

psi

Moment of Inertia (I):

in⁴

Maximum Deflection (δ_max):

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1. What is the Maximum Deflection Equation?

The maximum deflection equation calculates the maximum deflection for a wood beam simply supported with uniform load. This is a fundamental calculation in structural engineering to ensure beams meet deflection requirements under load.

2. How Does the Calculator Work?

The calculator uses the maximum deflection equation:

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

Where:

\( \delta_{\text{max}} \) — Maximum deflection (in)
\( w \) — Uniform load per unit length (lb/in)
\( L \) — Length of the beam (in)
\( E \) — Modulus of elasticity (psi)
\( I \) — Moment of inertia (in⁴)

Explanation: This equation calculates the maximum deflection at the center of a simply supported beam under uniformly distributed load. The deflection is proportional to the load and the fourth power of the length, and inversely proportional to the stiffness (E × I).

3. Importance of Maximum Deflection Calculation

Details: Calculating maximum deflection is crucial for structural design to ensure that beams and other structural elements do not deflect excessively under load, which could lead to serviceability issues or structural failure.

4. Using the Calculator

Tips: Enter uniform load per unit length in lb/in, 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 simply supported beam?
A: A simply supported beam is supported at both ends, with one end typically having a pinned support and the other having a roller support, allowing rotation but preventing vertical movement.

Q2: What are typical modulus of elasticity values for wood?
A: Modulus of elasticity for wood varies by species. Common values range from 1,000,000 to 2,000,000 psi for most structural lumber.

Q3: How do I calculate moment of inertia for different beam shapes?
A: Moment of inertia depends on the cross-sectional shape. For rectangular beams, I = (b × h³)/12, where b is width and h is height.

Q4: 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 the span length.

Q5: Does this equation account for shear deflection?
A: No, this equation only calculates bending deflection. For deep beams or certain materials, shear deflection may need to be considered separately.