Wood Roof Tie (LRFD)

How it calculates

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.