2x6 Wood Beam Span Calculator - Deflection and Load Analysis
2x6 Wood Beam Overview
2x6 Wood Beam is a versatile and commonly used lumber size for various construction and DIY projects. Below are its key details:
- Nominal Size: 2 inches × 6 inches
- Actual Size: Typically 1.5 inches × 5.5 inches (38mm × 140mm)
- Materials: Made from softwood (e.g., pine, cedar) or hardwood (e.g., oak, maple).
- Applications:
- Wall framing and studs
- Decking and fence rails
- Roof framing and light structural supports
- Furniture and shelving projects
- Advantages: Lightweight, easy to work with, and suitable for a range of projects.
- Limitations: Limited load-bearing capacity for larger or heavy-duty structures.
2x6 wood beams are a practical choice for many small to medium construction projects due to their balance of strength, size, and ease of handling.
Deflection of a Wood Beam Formula
To calculate the deflection of a wood beam with a rectangular cross-section, use the following formula:
\[ \delta = \frac{5 \cdot w \cdot L^4}{384 \cdot E \cdot I} \]
Where:
- \(\delta\) (Deflection):
- The deflection at the midspan of the wood beam in inches.
- \(w\) (Uniform Load):
- The uniformly distributed linear load applied to the beam, in pound-force per inch (lbf/in).
- \(L\) (Beam Span):
- The span or unbraced length of the beam in inches.
- \(E\) (Modulus of Elasticity):
- The modulus of elasticity of the wood species used, in pounds per square inch (psi).
- \(I\) (Moment of Inertia):
- The area moment of inertia of the beam's cross-section, in inches to the fourth power (in\(^4\)).
We calculate the area moment of inertia (\(I\)) of the beam's cross-section using this formula:
\[ I = \frac{b \cdot d^3}{12} \]
Where:
- \(I\):Area moment of inertia in inches to the fourth power (in\(^4\)).
- \(b\):Actual base width or thickness of the lumber in inches.
- \(d\):Actual height of the lumber in inches.
To calculate the actual bending stress, we use this formula:
\[ f_b = \frac{M}{S} \]
Where:
- \(f_b\):Bending stress in pounds per square inch (psi).
- \(M\):Bending moment in pound-force inches (lbf·in).
- \(S\):Section modulus in cubic inches (in\(^3\)).
The bending moment \(M\) is calculated as:
\[ M = 1/8 (\cdot w \cdot L^2) \]
Where:
- \(w\):Uniformly distributed load in pound-force per inch (lbf/in).
- \(L\):Beam span or unbraced length in inches.
The shear force \(V\) is calculated as:
\[ V = \cdot w \cdot L / 2 \]
We calculate the actual shear stress (\(f_v\)) by dividing the shear force by the cross-sectional area of the beam:
\[ f_v = \frac{V}{A} \]
Where:
- \(f_v\):Shear stress in pounds per square inch (psi).
- \(V\):Shear force in pound-force (lbf).
- \(A\):Cross-sectional area of the beam in square inches (in\(^2\)).
Wood Species - Modulus of Elasticity (E ×106 psi)
Species | No. 1 | No. 2 | No. 3 | Stud | Const. | Standard | Utility |
---|---|---|---|---|---|---|---|
Alaska Cedar | 1.3 | 1.2 | 1.1 | 1.1 | 1.2 | 1.1 | 1.0 |
Alaska Spruce | 1.5 | 1.4 | 1.3 | 1.3 | 1.3 | 1.2 | 1.1 |
Alaska Yellow Cedar | 1.4 | 1.3 | 1.2 | 1.2 | 1.3 | 1.1 | 1.1 |
Beech-Birch-Hickory | 1.6 | 1.5 | 1.3 | 1.3 | 1.4 | 1.3 | 1.2 |
Coast Sitka Spruce | 1.5 | 1.5 | 1.4 | 1.4 | 1.4 | 1.3 | 1.2 |
Douglas Fir-Larch | 1.7 | 1.6 | 1.4 | 1.4 | 1.5 | 1.4 | 1.3 |
Douglas Fir-Larch (North) | 1.8 | 1.6 | 1.4 | 1.4 | 1.5 | 1.4 | 1.3 |
Douglas Fir-South | 1.3 | 1.2 | 1.1 | 1.1 | 1.2 | 1.1 | 1.0 |
Eastern Hemlock-Balsam Fir | 1.1 | 1.1 | 0.9 | 0.9 | 1.0 | 0.9 | 0.8 |
Eastern White Pine | 1.1 | 1.1 | 0.9 | 0.9 | 1.0 | 0.9 | 0.8 |
Hem-Fir | 1.5 | 1.5 | 1.3 | 1.2 | 1.3 | 1.2 | 1.1 |
Hem-Fir (North) | 1.7 | 1.6 | 1.4 | 1.4 | 1.5 | 1.4 | 1.3 |
Mixed Maple | 1.2 | 1.1 | 1.0 | 1.0 | 1.1 | 1.0 | 0.9 |
Mixed Oak | 1.0 | 0.9 | 0.8 | 0.8 | 0.9 | 0.8 | 0.8 |
Mixed Southern Pine | 1.5 | 1.4 | 1.2 | 1.2 | 1.3 | 1.2 | 1.1 |
Northern Red Oak | 1.4 | 1.3 | 1.2 | 1.2 | 1.2 | 1.1 | 1.0 |
Northern White Cedar | 0.7 | 0.7 | 0.6 | 0.6 | 0.7 | 0.6 | 0.6 |
Norway Spruce (North) | 1.3 | 1.3 | 1.2 | 1.2 | 1.2 | 1.1 | 1.1 |
Red Maple | 1.6 | 1.5 | 1.3 | 1.3 | 1.4 | 1.3 | 1.2 |
Red Oak | 1.3 | 1.2 | 1.1 | 1.1 | 1.2 | 1.1 | 1.0 |
Redwood | 1.3 | 1.2 | 1.1 | 0.9 | 0.9 | 0.9 | 0.8 |
Southern Pine | 1.6 | 1.4 | 1.3 | 1.3 | 1.4 | 1.2 | 1.2 |
Spruce-Pine-Fir | 1.4 | 1.4 | 1.2 | 1.2 | 1.3 | 1.2 | 1.1 |
Spruce-Pine-Fir (South) | 1.2 | 1.1 | 1.0 | 1.0 | 1.0 | 0.9 | 0.9 |
Western Cedars | 1.0 | 1.0 | 0.9 | 0.9 | 0.9 | 0.8 | 0.8 |
White Oak | 1.0 | 0.9 | 0.8 | 0.8 | 0.9 | 0.8 | 0.8 |
Yellow Cedar | 1.4 | 1.4 | 1.2 | 1.2 | 1.3 | 1.2 | 1.1 |