timberRoofTieLRFD
Run the calcRafter loads link from upstream calculations directly, change span or loading and both the tie tension and all rafter checks update automatically. Designs wood collar ties and rafter ties to NDS 2018 LRFD, checking factored tension (Pu / φTn ≤ 1.0) and all phi-factor limit states for the rafter.
This calculator uses an earlier code edition (NDS 2018 (LRFD)). It stays available for existing projects. For new designs, check the Calculator Library for the current edition.
Method & scope
Calculation method
Rafter geometry and horizontal thrust
The calculator resolves the pitched rafter geometry from the horizontal span and roof pitch. For a rafter spanning from the ridge to the wall plate, the horizontal outward thrust at the wall plate that the tie must resist is derived from the tributary load and pitch angle: H = (w × L / 2) / tan(θ) where w is the total factored load per unit length of the rafter (dead plus live or snow under the governing ASCE 7 LRFD combination), L is the horizontal rafter span, and θ is the pitch angle. For a collar tie positioned at height y above the wall plate, the tie tension is amplified by the ratio of the full rafter height h to the tie height y: Pu = H × (h / y)Tie tension check
The factored tensile resistance of the tie member per NDS 2018 LRFD: φTn = φ_t × K_F,t × F_t × λ × C_M × C_t × C_F × A_n where φ_t = 0.80 for tension parallel to grain, K_F,t is the format conversion factor, λ is the time-effect factor for the governing load combination (0.8 for occupancy live, 1.15 for roof live or snow, 1.0 for wind), and A_n is the net cross-sectional area at connections. The utilization ratio Pu / φTn must be ≤ 1.0.Rafter bending and shear checks
The rafter is modeled as a simply supported inclined member loaded by self-weight and the applied gravity load. The governing factored bending moment Mu occurs at or near mid-span, and the critical shear Vu is taken at the face of the support. φMn = φ_b × K_F,b × F_b × λ × C_M × C_t × C_F × C_r × C_L × S φVn = φ_v × K_F,v × F_v × λ × C_M × C_t × (2/3 × A) where φ_b = 0.85 for bending and φ_v = 0.75 for shear. The beam stability factor C_L is computed from the slenderness ratio R_B based on the lateral bracing condition of the rafter. Both Mu / φMn and Vu / φVn must be ≤ 1.0.Deflection check
Rafter mid-span deflection under serviceability load combinations is computed using beam bending theory for the inclined span. The calculator checks against a user-specified span-to-deflection ratio (default L/240 for total load). Long-term deflection includes the NDS creep multiplier for the sustained dead load component.Time-effect factor and LRFD adjustment factors
All resistance values are adjusted by the time-effect factor λ, which parallels the ASD load duration factor C_D. For the governing load combination, λ takes values of 0.6 for permanent dead load only, 0.8 for occupancy live, 1.15 for roof live or snow, and 1.0 for wind. The calculator automatically selects the governing combination and applies the corresponding λ to each capacity term, along with the format conversion factor K_F and the applicable wet service, temperature, and size factors.How to use it
1
Open the calculator
Open it from Run calc in the About this calculator panel above.
2
Enter your inputs
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.
3
Review the results and export
Check the utilization of each governing check in the summary, then export a PDF report. See Views and Export.
Common questions
What does this calculator design?
What does this calculator design?
Wood collar ties and rafter ties per NDS 2018 LRFD. It checks factored tension in the tie member and all rafter limit states (bending, shear, deflection) using LRFD phi-factors and ASCE 7 factored load combinations.
What are the key inputs?
What are the key inputs?
Roof pitch, rafter span (horizontal run), rafter spacing, tie position, wood species and grade, section sizes for tie and rafter, and factored load combinations (dead, live, snow) per ASCE 7.
What does it check and output?
What does it check and output?
Factored tension in the tie (Pu / φTn ≤ 1.0), factored rafter bending (Mu / φMn ≤ 1.0), factored rafter shear (Vu / φVn ≤ 1.0), and rafter deflection. Outputs include the derived horizontal thrust, tie tension force, and utilization ratios.
How does this differ from the ASD version?
How does this differ from the ASD version?
Same geometry and checks, but uses LRFD load factors and resistance factors instead of ASD allowable stresses. Use the LRFD version when your project uses ASCE 7 factored load combinations or when wind or seismic loads are significant contributors to the rafter loading.
When do I need a structural ridge beam instead of a tie?
When do I need a structural ridge beam instead of a tie?
When architectural requirements prohibit a tie (e.g. vaulted ceilings), the outward thrust must be resisted by a structural ridge beam carrying compression rather than relying on a tie in tension. In that case, use the wood beam calculator for the ridge. This calculator is specifically for rafter-and-tie systems.
Does this calculator support load linking with connected calculations?
Does this calculator support load linking with connected calculations?
Yes. Dead and live loads applied to the rafters can be linked directly from upstream calculations in the same project, gravity loads from a floor or roof load calculator update the rafter and tie design automatically. Rafter reactions at the wall plate link downstream to stud or wall calculations, keeping the full vertical load path connected without manual re-entry.
Next steps
Calculator Library
Complete list of Calcs.com design calculators available for United States projects (AISC, ACI, NDS, ASCE 7, IBC, and related standards).
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Design a Wood Column (LRFD) to NDS 2024
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