Wood Beam Span Calculator

A wood beam span calculator is a tool for determining the proper size of a wood beam to be used, given its span and the load that it must bear. It determines the strength of the beam to ensure that the weight is safe without bending or breaking. Inputting the length of the span, the type of load, and the type of wood gives the appropriate beam size and material. It is usually implemented in construction with the objective of safe, cost-effective, and efficient selection of beams with respect to building code and safety compliance.

If you want to know accurately the amount of wood needed for your beam spans, integrating with timber quantification is a reliable option. This way, you will have the right amount of materials needed for your project, hence saving you from material shortage and errors, saving you both time and costs and ensuring your beams are just the right size for stability.

Step-by-Step Calculation Procedure

Calculating the right size of a wood beam is essential in ensuring the safety and stability of a structure. The process basically involves determining the span, load, and material specifications of the beam to ascertain whether it would be able to carry the given weight without collapsing or excessive deflection. All the formulas with examples are hereby provided for a step-by-step breakdown of the procedure.

Step 1: Determine the Load Requirements

The first step of finding the span of the wood beam is to calculate the load it will carry. The load is divided into two types:

Dead Load: The weight of the beam itself and other permanent structures like floors, ceilings, or roofs.

Live Load: This is the weight that comes from items that periodically change, such as furniture, people, and other movable items.

For instance, when a beam supports a floor, the dead load could be 10 PSF, while the live load would be 30 PSF.

Total Load Formula

Total Load = Dead Load + Live Load

Example Calculation

• Dead Load = 10 PSF
• Live Load = 30 PSF
• Total Load = 10 + 30 = 40 PSF

We already know the fact that the total load is 40 pounds per square foot. So we would definitely need it further down in the next step.

Step 2: Specify Beam Span

The beam span is the distance between two supports of a beam; this is usually walls or columns. The larger the span is, the more massive the beam has to be in order not to bend and break. Normally, the span is measured in feet.

Example: For instance, if the supports are 12 feet apart, placing the beam in between, the span would then be 12 feet.

Step 3: Choose Beam Size

For this example, let us assume that we are using a 2×8 nominal beam, so the actual size of the beam would be:

• b = 1.5 inches
• h = 7.25 inches

Nominal sizes are what most standard 2×8 beams have, although actual sizes do vary slightly according to the actual manufacturer

Step 4: Choosing the species and Grade of wood

The strength and stiffness of the beam are dependent on the wood species and grade. Different species of wood have different load-bearing capabilities, and the grade affects the overall performance of the beam. For example, the most common species of wood for beams is Douglas Fir, and it comes in different grades, such as No. 1 and No. 2.

For each wood species, one would determine E and Fb. The further computations for the ability of the selected beam to carry the load safety would be based on these values.

Example Material Selection: For calculation purposes, we are going to use Douglas Fir-Larch which is widely applied for structural purposes. Typical values for this species:

• Allowable Bending Stress (Fb​) = 1,200 psi
• Modulus of Elasticity (E) = 1.6 x 10(8) psi

Let’s work an example with Douglas Fir – No. 2 grade for this illustration. The modulus of elasticity for the wood is on the order of 1,600,000 psi, and the allowable bending stress is around 1,200 psi.

Step 5: Determine the Moment of Inertia (I)

The Moment of Inertia (I) measures a beam’s ability to resist bending. A larger moment of inertia indicates a stronger beam that is less likely to bend. The formula for calculating the moment of inertia for a rectangular beam is:

• I = 12b⋅h3​

Where

• b = width of the beam (1.5 inches)
• h = height of the beam (7.25 inches)

Substitute the Known Values:

I = 1.5 / (7.25)3 / 12

First, Determine the Cube of The Height

(7.25)3 = 382.76

Now, Find the Moment of Inertia

I = 1.5 / 382.76 / 12 = 574.14 / 12 = 47.85 

Step 6: Determine the Maximum Bending Moment (M)

The maximum bending moment (MMM) of a beam under a uniform load occurs at the midpoint of the beam. The expression for maximum bending moment is given as:

• M= w⋅L2 / 8M = M=8w⋅L2​

Where

• w = load per linear foot (45 plf)
• L = span of the beam (let’s assume a span of 12 feet)

Substitute the Values Into the Equation

M=45⋅(12) 28= 45 x 144/ 8 =6480 / 8 = 810 foot-pounds 

Now, convert this value to inch-pounds (since our other calculations use inches):

 M=810 ft x lb× 12= 9720 in-lb

Step 7: Calculate Section Modulus (S)

The section modulus (S) is a geometric property that tells about the strength of a beam in bending. It can be computed with the following formula:

• S = I / c 

Where

• I = moment of inertia (47.85 in4)
• c = distance from the neutral axis to the outermost fiber (half of the beam height, c = h / 2 = 3.625  inches)

Now, calculate the section modulus

S = 47.85 / 3.625 = 13.19 in3

Step 8: Calculate the Bending Stress (Fb)

Bending stress, Fb will indicate if the beam will bend or break when subjected to load. To find the bending stress, the following formula is applied:

• Fb = M / S 

Where

• M = Maximum bending moment calculated in the next step
• S = Section modulus calculated in the previous step

Example: Since the maximum moment (M) derived from the above is 1800 foot-pounds, converted to inch-pounds: 1800 × 12 = 21,600 inch-pounds, the bending stress would be

• Fb = 21,600 / 144 = 150 psi

Now we compare this bending stress value to the allowable bending stress of the wood species and grade. If it is less than the allowable bending stress, in this case, 1,200 psi for Douglas Fir No. 2, then the beam is okay.

Step 9: Calculate load per foot of beam

From the span, we will convert the total load from per square foot to pounds per foot based on the beam spacing.

• Formula: w = Total load x beam spacing /12
• Example: w = 50/ per square foot x 16in/ 12 = 66.67 / lb / ft

Step 10: Calculate Beam Deflection 

Deflection is how much the beam bends under the applied load. The deflection should not be greater than specified limits in the building codes. For this beam, the maximum allowable deflection is:

• L/360 =12 / 360 =0.0333 feet

We now have the following formula to find the actual deflection for a simply supported beam under a uniform load.

• 5 x w x L4 / 384 x E x I

Here:

• w = load per foot (45 plf)
• L = span (12 feet)
• E = modulus of elasticity (1.6 x 10⁶ psi)
• I = moment of inertia (47.85 in⁴)

Now, let us do step by step the calculations.

Numerator first

5 x w x L4 = 5x 45 x 124 = 5 x 45x 20736 =4,663,6805 

Calculate the denominator now:

384 x E x I = 384 x1.6 x106 x 47.85 = 2.94 ×10(10)

Now divide the numerator by the denominator to determine the deflection.

4,663,680 / 2.94 × 10(10) ≈0.16 inches

Because the calculated deflection (0.16 inches) is less than the allowable deflection (0.4 inches), this beam meets the deflection requirement.

Step 11: Determine the Right Beam Size

You can now compute all the steps above and compare them to the allowed limits. The beam size may be determined when the bending stress, deflection, and moment fall within the allowed limits. The size of the beam can now be chosen when all the parameters fall within acceptable limits. Confirm the beam size using wood beam span calculators. Input the height, width, and the distance between the beams of the beam, for example, 16 or 24 inches at the center. For example, Let a 2×10 beam with 16-inch center-to-centre spacing.

Wood Beam Span Table 

The following table provides the maximum recommended span for different wood species beam sizes and grades based on typical live load and dead load values. The live load is assumed to be 40 psf, and the dead load is assumed to be 10 psf, with the beams spaced 16 inches apart. These are standard conditions for most residential projects

Beam Size	Wood Species	Grade	Live Load (psf)	Dead Load(psf)	Beam Spacing(inches)	Max Span(ft)
2×6	Douglas Fir	No. 1	40	10	16	7.6.
2×6	Southern Pine	No. 2	40	10	16	6.4
2×8	Douglas Fir	No. 2	40	10	16	8.5
2×8	Spruce-Pine-Fir	No. 1	40	10	16	8.0
2×10	Douglas Fir	No.1	40	10	16	12.0
2×10	Southern Pine	No. 2	40	10	16	10.8
2×12	Douglas Fir	No. 2	40	10	16	13.5
2×12	Hem-Fir	No. 1	40	10	16	13.5
3-2×10	Douglas Fir	No. 2	40	10	16	17.2

Choosing the right wood beam size is very crucial in building a deck, framing a house, or erecting a shed; knowing how to calculate beam size, type, and material will help you save time, money, and effort while ensuring that you are safe and comply with all building codes.