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# Design a Wood Roof Tie (LRFD) to NDS 2024
> NDS 2024 LRFD roof tie. Factored tie tension and rafter limit states - bending, shear, bearing, deflection - with φt, φb, KF, λ. Load linking.
United StatesNDS 2024 (LRFD)
The easy to use online Calcs.com Wood Roof Tie LRFD Calculator to NDS 2024 enables you to do quick and powerful design and analysis for wood collar ties and rafter ties. Choose from our library of thousands of common wood sections, or create your own and get instant results with our easy to understand traffic light checks for tension in the ties and all limit states for the rafters.
## Method & scope
| Property | Detail |
| ---------------- | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| Design standards | NDS 2024 (LRFD) |
| Regions | United States |
| Presets | Collar Tie, Rafter Tie, Collar & Rafter Tie |
| What it checks | LRFD adjustment framework, Roof geometry and horizontal thrust, Factored tie tension check, Rafter bending check, Rafter shear check, Rafter bearing check, Deflection checks, Time effect factor and load combinations, NDS 2024 vs. NDS 2018 |
#### Calculation method
The Wood Roof Tie (LRFD, NDS 2024) calculator designs collar ties and rafter ties as a coupled rafter-and-tie assembly under the Load and Resistance Factor Design provisions of the 2024 National Design Specification for Wood Construction. Pitched rafters generate an outward horizontal thrust at the wall plate; the tie must resist that thrust in tension to prevent wall spreading. The calculator solves this geometry simultaneously, computing the tie tension and the rafter moment diagram as a function of roof pitch, rafter span, and tie height.
##### LRFD adjustment framework
NDS LRFD converts reference design values, tabulated on an ASD basis in the NDS 2024 Supplement, into the LRFD resistance space using the format conversion factor **KF**. Each adjusted resistance is then multiplied by the applicable resistance factor **φ** and the time effect factor **λ**, which accounts for the duration of the governing load:
* **λ = 0.8** for occupancy live loads
* **λ = 1.0** for snow (short duration) and impact
* **λ = 1.25** for wind and seismic
The general form of a factored LRFD resistance is:
**φRn = φ × KF × λ × (reference design value) × (applicable adjustment factors)**
All adjustment factors, wet service CM, temperature Ct, size CF, flat use Cfu, incising Ci, repetitive member Cr, and beam stability CL, are applied consistently across the tie tension and rafter limit states as appropriate for each member.
##### Roof geometry and horizontal thrust
The horizontal outward thrust from the pitched rafter is derived from the slope angle and the tributary load. For a symmetric gable with pitch angle α:
**H = (w × Lh) / (2 × tan(α)) × (1 / cos(α))**
Where w is the tributary load per unit of rafter slope length and Lh is the horizontal rafter run. The horizontal thrust H equals the tie tension when the tie is at plate level. Placing the tie higher (collar tie configuration) reduces the tie force because the lower rafter segment carries its own horizontal component, but it increases the unbraced rafter span above the tie, raising bending demand. The calculator assumes symmetrical geometry, applied loads and framing are equal on both sides of the ridge.
##### Factored tie tension check
The factored tensile resistance of the tie member is:
**φtTn = φt × KF,t × λ × Ft × CM × Ct × CF × Ci × Anet**
Where:
* **φt = 0.80** is the NDS LRFD tension resistance factor
* **KF,t = 2.70** is the format conversion factor for tension parallel to grain (from NDS 2024 Table N1)
* **λ** is the time effect factor for the governing load combination
* **Ft** is the tabulated reference tensile design value from the NDS 2024 Supplement
* **CM, Ct, CF, Ci** are the wet service, temperature, size, and incising adjustment factors
The tension utilization check is:
**Tu / φtTn ≤ 1.0**
Connection design, nails, bolts, or metal straps at the tie-to-rafter interface, is the responsibility of the engineer and is not checked by this calculator.
##### Rafter bending check
The factored moment resistance is:
**φbMn = φb × KF,b × λ × Fb × CM × Ct × CF × Cfu × Ci × Cr × CL × S**
Where:
* **φb = 0.85** is the NDS LRFD flexure resistance factor
* **KF,b = 2.54** is the format conversion factor for bending (from NDS 2024 Table N1)
* **CL** is the beam stability factor for lateral-torsional buckling, the rafter top face is assumed to be continuously braced by roof sheathing, which suppresses LTB on the compression face and permits CL = 1.0 for standard framing with adequate sheathing attachment
* **Cr = 1.15** applies when three or more rafters at 24 in. spacing or less share a load-distributing element
The bending check is:
**Mu / φbMn ≤ 1.0**
##### Rafter shear check
The factored shear resistance is:
**φvVn = φv × KF,v × λ × Fv × CM × Ct × Ci × (2/3) × A**
Where **φv = 0.75** is the shear resistance factor and **KF,v = 2.88** is the format conversion factor for shear (from NDS 2024 Table N1). The check is:
**Vu / φvVn ≤ 1.0**
##### Rafter bearing check
At the wall plate, the rafter bears perpendicular to grain. The factored bearing resistance is:
**φcRn = φc × KF,c⊥ × Fc⊥ × CM × Ct × Ci × Cb × Abearing**
Where **φc = 0.90** is the compression resistance factor for bearing and **Cb** is the bearing area factor from NDS 2024 §3.10.4. The bearing check is:
**Ru / φcRn ≤ 1.0**
##### Deflection checks
Two deflection limit states are verified using unfactored (service-level) loads, consistent with NDS LRFD practice for serviceability:
* **Short-term (ST):** instantaneous elastic deflection under the specified live or snow load combination, checked against the user-defined span-ratio limit (default L/360).
* **Long-term (LT):** total deflection including creep, computed as the ST deflection amplified by the applicable creep factor for the in-service moisture condition, checked against the user-defined limit (default L/240).
##### Time effect factor and load combinations
For each ASCE 7 factored load combination, the calculator identifies the shortest-duration load type that contributes meaningfully to the demand and applies the corresponding λ. This means a snow-governed combination (e.g. 1.2D + 1.6S) applies λ = 1.0, while a wind-governed combination (e.g. 0.9D + 1.0W) applies λ = 1.25. The governing combination, the one producing the highest utilization ratio after accounting for both the factored demand and the factored resistance, is reported for each limit state.
##### NDS 2024 vs. NDS 2018
This calculator applies reference design values and KF values from the 2024 edition of the NDS and the 2024 NDS Supplement. For some species and grade combinations, tabulated Fb, Ft, Fv, Fc⊥, and E values differ between the 2018 and 2024 Supplements. If your jurisdiction still references NDS 2018, use the timberRoofTieLRFD calculator instead.
## How to use it
Open it from **Run calc** in the About this calculator panel above. To start from a typical setup, choose one of the presets listed there.
Work through the input sections from top to bottom. Click any input label to see its reference explanation, clause, conditions and assumptions. See [Checks, References, Conditions and Assumptions](/docs/running-calculations/checking-results/checks-references-conditions-assumptions).
Check the utilization of each governing check in the summary, then export a PDF report. See [Views and Export](/docs/running-calculations/exporting-reports/views-and-export).
## Available presets
Each preset opens the calculator with a typical setup already entered.
| Preset | Open in Calcs.com |
| ------------------------------------------------ | ------------------------------------------------------------------------------------------------------- |
| Collar Tie | [Run with preset](https://app.calcs.com/new/sheet/timberRoofTieLRFDNDS-2024?presetCode=collarTie) |
| Rafter Tie | [Run with preset](https://app.calcs.com/new/sheet/timberRoofTieLRFDNDS-2024?presetCode=rafterTie) |
| Collar & Rafter Tie | [Run with preset](https://app.calcs.com/new/sheet/timberRoofTieLRFDNDS-2024?presetCode=collarRafterTie) |
## Common questions
This calculator implements Load and Resistance Factor Design (LRFD) per the 2024 National Design Specification for Wood Construction (NDS 2024). Factored resistances for tie tension and rafter limit states use the tension resistance factor φt = 0.80 and the flexure resistance factor φb = 0.85, together with format conversion factors KF and time effect factors λ sourced from the 2024 NDS Supplement. Use this version when your jurisdiction has adopted NDS 2024 or the 2024 IBC and your project load combinations follow ASCE 7 factored format.
Key inputs include roof pitch (entered as a slope angle or rise-to-run ratio), rafter horizontal span, rafter spacing, tie height measured vertically from the bearing plate, member species and grade, section sizes for both the rafter and the tie, and applied loads by type (dead, live, snow). Service conditions, wet or dry use, temperature range, and incising treatment, are specified for each member.
The calculator checks factored tie tension utilization (Tu / φTn ≤ 1.0) and all rafter LRFD strength limit states: bending (Mu / φMn ≤ 1.0), shear (Vu / φVn ≤ 1.0), and bearing at the wall plate (Ru / φRn ≤ 1.0). Deflection checks for short-term and long-term limits remain serviceability-based and use unfactored loads. Each check shows the governing load combination, the applicable NDS 2024 adjustment factors, and the utilization ratio.
Use LRFD when your project uses ASCE 7 factored load combinations throughout, this avoids converting factored loads back to unfactored ASD values and keeps the load path consistent. LRFD is also preferred when wind or seismic loads make a significant contribution to rafter loading, since the time effect factor λ = 1.25 for wind and seismic provides a direct advantage over ASD load duration factors. For projects using ASD load combinations, use the timberRoofTieASDNDS-2024 calculator instead.
Set the tie height input to represent each configuration, collar ties near the upper third of the rafter and rafter ties at or near the wall plate. Rafter ties carry the full horizontal thrust but minimize the rafter span above the tie, reducing bending demand. Collar ties carry a smaller tension force because the lower rafter segment spans to the wall independently, but they leave a longer unbraced rafter span above, increasing bending demand. Compare the LRFD utilization ratios for both configurations to find the combination of member sizes and structural efficiency that best suits your project.
Yes. Dead load, live load, and rafter member reactions can be linked directly from connected rafter or beam calculations in the same Calcs.com project. When the upstream rafter changes span, section, or loading, the linked values update automatically in this roof tie calculation, no manual re-entry needed. This keeps the full load path from roof cladding through rafters and ties to the wall plate consistent and eliminates the risk of stale values when the design is revised.
## Next steps
Design wood collar ties, rafter ties and ridge straps for gable roofs to NDS 2024 (ASD), with tie tension and all rafter limit state checks.
Complete list of Calcs.com design calculators available for United States projects (AISC, ACI, NDS, ASCE 7, IBC, and related standards).
NDS 2024 LRFD wood beam: bending, shear, bearing, three deflection checks with conversion and time effect factors. Multi-ply, flitch plate, inclined.
NDS 2024 LRFD wood column. Stability (Cp), combined bending and axial (NDS 3.9), and bearing with φc, KF, λ. Load reactions link from connected beams.
Validation examples for wood beams (ASD and LRFD) to NDS 2018: Calcs.com moment, shear and deflection results compared with textbook results.
