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Wood Beam Span Calculator - Calculate Deflection in Wood Beam


Wood Beam Span Calculator



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\(^4\)).
Area Moment of Inertia (I)

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.
Bending Stress (\(f_b\))

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\(^3\)).
Bending Moment (\(M\))

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.
Shear Force (\(V\))

The shear force \(V\) is calculated as:

\[ V = \cdot w \cdot L / 2 \]

Shear Stress (\(f_v\))

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 Cedar1.31.21.11.11.21.11.0
Alaska Spruce1.51.41.31.31.31.21.1
Alaska Yellow Cedar1.41.31.21.21.31.11.1
Beech-Birch-Hickory1.61.51.31.31.41.31.2
Coast Sitka Spruce1.51.51.41.41.41.31.2
Douglas Fir-Larch1.71.61.41.41.51.41.3
Douglas Fir-Larch (North)1.81.61.41.41.51.41.3
Douglas Fir-South1.31.21.11.11.21.11.0
Eastern Hemlock-Balsam Fir1.11.10.90.91.00.90.8
Eastern White Pine1.11.10.90.91.00.90.8
Hem-Fir1.51.51.31.21.31.21.1
Hem-Fir (North)1.71.61.41.41.51.41.3
Mixed Maple1.21.11.01.01.11.00.9
Mixed Oak1.00.90.80.80.90.80.8
Mixed Southern Pine1.51.41.21.21.31.21.1
Northern Red Oak1.41.31.21.21.21.11.0
Northern White Cedar0.70.70.60.60.70.60.6
Norway Spruce (North)1.31.31.21.21.21.11.1
Red Maple1.61.51.31.31.41.31.2
Red Oak1.31.21.11.11.21.11.0
Redwood1.31.21.10.90.90.90.8
Southern Pine1.61.41.31.31.41.21.2
Spruce-Pine-Fir1.41.41.21.21.31.21.1
Spruce-Pine-Fir (South)1.21.11.01.01.00.90.9
Western Cedars1.01.00.90.90.90.80.8
White Oak1.00.90.80.80.90.80.8
Yellow Cedar1.41.41.21.21.31.21.1
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