timberRoofTieLRFD

Rafter 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](/docs/calculators/us) for the current edition. ## Method & scope | Property | Detail | | -------------- | ----------------------------------------------------------------------------------------------------------------------------------------------------------- | | What it checks | Rafter geometry and horizontal thrust, Tie tension check, Rafter bending and shear checks, Deflection check, Time-effect factor and LRFD adjustment factors | #### 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 Open it from **Run calc** in the About this calculator panel above. 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). ## Common questions 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. 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. 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. 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 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. 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 Complete list of Calcs.com design calculators available for United States projects (AISC, ACI, NDS, ASCE 7, IBC, and related standards). Design wood beams to NDS 2018 (LRFD): bending, shear, bearing and deflection. An earlier code edition, kept for existing projects. NDS 2024 LRFD wood beam: bending, shear, bearing, three deflection checks with conversion and time effect factors. Multi-ply, flitch plate, inclined. Design wood columns and studs to NDS 2018 (LRFD). An earlier code edition, kept for existing projects. 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. 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.