Wood Beam Span Calculator - Calculate Deflection in Wood Beam
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:
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:
To calculate the actual bending stress, we use this formula:
\[ f_b = \frac{M}{S} \]
Where:
The bending moment \(M\) is calculated as:
\[ M = 1/8 (\cdot w \cdot L^2) \]
Where:
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:
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 |