Wood Beam Design Example: NDS Bending, Shear, and Deflection Checks (Breyer 6.18)
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The foundation of clearspan is a set of structural engineering design tools. These tools are not powered by AI and are no different than other commercially available software. To verify that clearspan produces correct results, we ran a textbook beam design example through the platform and compared every check to the published solution. Clearspan matched the textbook on every check.
The example below walks through the full comparison so you can see exactly how clearspan's output lines up with the expected answer.
The Problem Setup
Source: Design of Wood Structures — ASD/LRFD, Breyer et al., 6th Edition, Example 6.18. This is the standard textbook used to teach structural wood design in university engineering programs across the country.
Given:
- Beam: 2×6 No. 1 Douglas Fir-Larch
- Span: 13.5 ft, simply supported
- Spacing: 16 in. on center
- Dead load: D = 14 psf
- Roof live load: Lr = 20 psf
- Bracing: continuous lateral support (sheathing)
- Conditions: dry service, normal temperature
Check: Bending, shear, deflection, and bearing.
Reference Design Values
Clearspan looks up the following design values from the NDS Supplement for Douglas Fir-Larch #1.
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Loads
The first calculation step is converting the area loads (psf) into line loads (plf) on the joist using the tributary width.
Tributary width
w_trib = 16 in. / 12 = 1.333 ft
Uniform line loads
The line loads determined by the clearspan beam analysis tool are:
| Load | Intensity (psf) | Tributary (ft) | Line Load (plf) |
|---|---|---|---|
| Dead (D) | 14 | 1.333 | 18.67 |
| Roof Live (Lr) | 20 | 1.333 | 26.67 |
Load combinations
The following ASD load combinations will be calculated per the governing building code (IBC and ASCE 7):
| Case | Load Duration Factor, CD | w (plf) |
|---|---|---|
| D | 0.9 | 18.67 |
| D + Lr | 1.25 | 45.33 |
Shear and Moment Demand
The clearspan beam analysis tool generates the loading diagram below and plots the shear and bending moment diagrams.
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| Load Case | V (kips) | M (kip-ft) |
|---|---|---|
| D | 0.126 | 0.425 |
| D + Lr | 0.306 | 1.033 |
The governing demands determined by the software from the D + Lr case are: M = 1,033 lb-ft and V = 306 lb.
Bending
The clearspan wood design tools will check the capacity of a 2x6 beam (Doug Fir #1). This tool follows the 2024 National Design Specification (NDS) as referenced by the International Building Code (IBC) and other codes in the United States.
Adjustment Factors
The beam is continuously braced at the top flange by sheathing so the beam stability factor (C_L) = 1.0. The clearspan tools also can calculate the beam stability factor for unbraced conditions.
A summary of the NDS adjustment factors for the bending capacity check are:
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The adjustment factors are used to check the bending capacity of the beam per the NDS provisions. The math below is pulled directly from an example pdf calculation report generated by clearspan.
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The 2x6 is adequate for bending.
Shear
The NDS provisions are used to check the shear capacity using the maximum shear demand.
The applicable adjustment factors for shear are:
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Similar to the bending calculation, the adjustment factors are used to check the capacity of the beam per the NDS provisions. The math below is pulled directly from an example pdf calculation report generated by clearspan.
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The 2x6 is adequate for shear.
Deflection
Next we check deflection against code limits. The NDS adjustment factors for the modulus of elasticity used in deflection calculations are:
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Per IBC Table 1604.3 the applicable limits for roof members supporting a gypsum board (non plaster ceiling) are:
- Live load (Lr): L/240
- Total load (D + Lr): L/180
The deflection for each load case is plotted by clearspan and summarized below.
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Deflection Summary
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The total load deflection exceeds L/180 — the No. 1 grade does not pass. Following the textbook example, upgrade to No. 1 & Btr (E = 1,800,000 psi) and recheck.
No. 1 & Btr Grade
The deflections are checked again for a 2x6 No. 1 and better grade. The textbook example does not complete this deflection. The new deflection is very close to the limit. Clearspan only considers designs with a DCR less than or equal to 1.0 to be acceptable. In this case we will follow the textbook example.
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Use 2x6 No. 1 & Better
Bearing
The bearing check evaluates compression perpendicular to grain at the supports. The applicable NDS adjustment factors are:
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Following the textbook example we will check a minimum bearing length. In a real world design a rafter should be given a larger bearing length than this.
l_b = 0.33 in
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The 2x6 is adequate for bearing.
Summary
Clearspan's results matched the textbook solution on every design check. The table below summarizes the comparison.
| Check | Textbook Result | Clearspan Result | Match |
|---|---|---|---|
| Bending | Adequate | Adequate | ✅ |
| Shear | Adequate | Adequate | ✅ |
| Deflection (No. 1) | Fails L/180 | Fails L/180 | ✅ |
| Bearing | Adequate | Adequate | ✅ |
Clearspan correctly identified that the No. 1 grade 2×6 does not meet the total-load deflection limit.
Want to see how this beam is entered step by step in the clearspan tool? Follow along in the Beam design walkthrough.
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