Wood Roof Tie (ASD, NDS 2024)

How it calculates

Design methodology

The calculator implements Allowable Stress Design (ASD) as defined in the 2024 National Design Specification for Wood Construction (NDS 2024). A pitched-rafter-and-tie assembly is a coupled structural system: the rafters generate an outward horizontal thrust at the wall plate, and the tie - whether a rafter tie at plate level or a collar tie higher on the rafter - 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.

For every limit state, the design check takes the form:

demand / adjusted allowable ≤ 1.0

where the adjusted allowable is the tabulated reference design value multiplied by all applicable NDS 2024 adjustment factors. Reference design values are from the NDS 2024 Supplement.

Roof geometry and tie tension

The horizontal outward thrust from the pitched rafter is derived from the slope angle and the applied tributary load. For a symmetric gable with pitch angle α:

H = (w × L_h) / (2 × tan(α)) × (1 / cos(α))

where w is the tributary load per unit of rafter slope length and L_h is the horizontal rafter run. The tie tension equals this horizontal thrust. The tie height (D_Y) acts as a lever arm: placing the tie lower - closer to the plate - produces the same thrust but a shorter lever arm, resulting in a larger tie force for the same applied load. Placing the tie higher (collar tie configuration) reduces the tie force but increases the unbraced rafter span below the tie, raising the rafter bending demand.

The calculator assumes symmetrical geometry - applied loads and framing are equal on both sides of the ridge. Rafter axial load is treated as negligible in the rafter bending checks (bending governs), but tie members are designed for tension as the primary limit state.

Tie tension check

The adjusted allowable tensile capacity of the tie member is:

F't = Ft × CD × CM × Ct × CF × Ci

• CD (load duration): the highest CD among all simultaneously acting loads governs - 1.6 for wind/seismic, 1.25 for construction, 1.15 for snow, 1.0 for occupancy live load, 0.9 for permanent dead load.
• CM (wet service): reduces allowable stress when in-service moisture content exceeds 19%.
• Ct (temperature): applied when sustained service temperature exceeds 100°F.
• CF (size factor): adjusts for member cross-section dimension per NDS 2024 Supplement Table 4A.
• Ci (incising): reduces design values for preservative-treated incised members.

The tension utilization check is:

T / T' ≤ 1.0, where T' = F't × A_net

Net area accounts for the connection geometry at each end of the tie. Connection design - nails, bolts, or metal straps - is the responsibility of the engineer and is not checked by this calculator.

Rafter bending check

The rafter moment diagram is computed from the tributary gravity loads and the reaction from the tie. The critical moment occurs in the lower rafter segment (bearing plate to tie) for typical rafter tie positions, and across the full rafter span for collar ties placed in the upper third. The adjusted allowable bending stress is:

F'b = Fb × CD × CM × Ct × CF × Cfu × Ci × Cr × CL

The rafter top face is assumed to be continuously braced by roof sheathing, which suppresses lateral-torsional buckling on the compression face. For standard framing with adequate sheathing, this permits CL = 1.0. The repetitive member factor Cr = 1.15 may apply when three or more rafters at 24 in. spacing or less share a load-distributing element.

The bending check is:

M / M' ≤ 1.0, where M' = F'b × S

S is the section modulus about the major X-X axis. The rafter is assumed oriented with depth vertical.

Rafter shear check

The adjusted allowable shear stress is:

F'v = Fv × CD × CM × Ct × Ci

Shear demand is conservatively evaluated at the absolute highest location along the rafter span - not at distance d from the support face, which NDS 2024 would otherwise permit. The check is:

V / V' ≤ 1.0, where V' = F'v × (2/3) × A

Rafter bearing check

At the wall plate, the rafter bears perpendicular to grain. The adjusted allowable compression perpendicular to grain is:

F'c⊥ = Fc⊥ × CM × Ct × Ci × Cb

where Cb is the bearing area factor from NDS 2024 §3.10.4. Bearing at the ridge is not checked - the engineer should verify that connection separately where no structural ridge beam is present.

The bearing check is:

R / R' ≤ 1.0, where R' = F'c⊥ × bearing area

Rafter deflection checks

Two deflection limit states are checked for the rafter:

• Short-term (ST): instantaneous elastic deflection under the specified live or snow load combination.
• Long-term (LT): total deflection including creep, computed as the ST deflection amplified by the applicable creep factor for the in-service moisture condition.

Deflection limits are user-specified as span-ratio thresholds (L/n) and may be supplemented by an absolute inch limit. Deflections are computed from the elastic stiffness EI of the rafter section. When shear deflections are explicitly enabled, an approximation method is applied per the Calcs.com support article referenced in the calculator assumptions.

NDS 2024 vs. NDS 2018

This calculator applies reference design values and adjustment factor procedures 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 timberRoofTieASD calculator instead. The calculation methodology is otherwise identical between the two versions.