Rafters and ceiling ties

A sloped sawn lumber rafter with the tie that resists its thrust: a pair of rafters on two walls, a ridge board with ceiling joists or rafter ties at the plate or raised above it, or a structural ridge beam or wall with no thrust. The rafter, the tie and the nails at their joint are designed to NDS 2024 with ASCE 7-22 load combinations in ASD or LRFD, and the nailing is compared with IRC Table R802.5.2.

With a ridge board the two rafters and the tie form a three-hinged frame. The walls give vertical reactions only, the ridge carries a horizontal thrust H and the tie pulls the rafters together. Moments about the heel give H = M0 / (Hr − Hc), with M0 the moment of the loads on one rafter about the heel, Hr the height of the ridge and Hc the height of the tie above the plate. A uniform load w on the plan, with no overhang, gives H = w L² / (2 Hr) at the plate; raising the tie multiplies it by 1 / (1 − Hc/Hr) and bends the rafter at the tie.

Inputs of the rafters and ties #

• Rafter: species and grade, size (dimension lumber 2" to 4" thick, NDS Supplement values), or Other with the reference values you enter (including the size factor) and the specific gravity G for the nails; spacing; the repetitive member factor (three or more rafters at 24 in. or less joined by the sheathing, NDS 4.3.9: your call); the self-weight and the wood density.
• Roof geometry: the slope as a rise in 12, the horizontal span L of one rafter (wall to ridge, half the building span for a gable), the overhang beyond the wall on the plan, and the seat length lb: the horizontal length of the birdsmouth seat cut on the plate. The notch depth at right angles to the rafter is lb sin θ.
• Ridge: ridge board (the tie takes the thrust) or structural ridge beam or bearing wall (a sloped simple beam; the reaction at the ridge is reported for you to design that support, for example with the wood beam or glulam beam type).
• Tie: at the top plate or raised, with its height Hc above the plate. IRC R802.5.2 keeps ceiling joists in the bottom third of the rafter height unless the ridge is designed as a beam: a higher tie here is your engineered design.
• Ridge connected for tension: under net uplift the rafters pull apart at the ridge. On: a strap, gusset or collar tie carries the force, which is reported for you to design it (IRC R802.4.2). Off, with a raised tie: the ridge opens, the tie balances the moment about the heel (T = M0 / Hc) and the wall takes the horizontal balance, which is reported. Off, with the tie at the heel: nothing else can hold the rafter, so an advisory tells you the force the ridge must carry.
• Roof loads: dead load along the slope or on the plan (your choice of how it is measured), roof live load Lr and snow S on the plan, wind toward and away from the roof, normal to it, as strength-level components and cladding pressures, and vertical point loads at a distance from the wall (negative on the overhang). Both rafters are loaded alike: for drifts or unbalanced snow enter the heavier side.
• Ceiling joist / rafter tie: species, grade and size, one at every rafter; the ceiling dead load and attic live load it carries in bending (0 for a rafter tie with no ceiling), its span between supports and the unbraced length of its top edge; the nail and the number of nails at the rafter-to-tie joint (face nailed through the rafter, single shear); an optional lap splice and its nails.
• Lateral bracing: the unbraced top edge (0 = sheathed, CL = 1.0), and how the bottom edge is braced: at the supports and the tie, continuously, or at a spacing. The bottom edge is in compression under uplift and over the wall with an overhang.
• Service conditions: wet service, temperature, incising.
• Deflection limits: span / n for live load and wind and for total load (IBC Table 1604.3; 0 skips the check), and how they are measured: perpendicular to the rafter over the span along the slope, or the horizontal projection used by the AWC span tables and the IRC (the same stiffness; the deflection is multiplied by cos²θ and the span is the plan span). The wind factor for deflection (IBC Table 1604.3 note f), creep on the dead load (NDS 3.5.2) and unseasoned lumber.
• IRC comparison: the table of the edition your jurisdiction adopted (2021 or 2018) and the ground snow load for its column. The table does not govern the design; it is compared with your nail count.
• Load duration (code options): CD per load type (ASD) and the live load type for λ (LRFD).

Auto-design (editor toolbar) varies the rafter size and the tie size and derives the number of nails for each candidate from the tie force of the input as given (5 % more, for a heavier rafter's self-weight). Species and grades are kept unless unlocked; slope, span, overhang, loads, seat, nail size and code options are never changed. Objectives: least wood; lowest cost index. See Auto-design.

Checks performed #

Limitations #

• Both rafters are loaded alike. A drift, unbalanced snow or wind on one side is entered as the heavier side's load; the asymmetric frame (shear at the ridge) is not analysed.
• The ridge beam or wall, the ridge board's own design, collar ties (other than as the ridge connection you say exists), purlins and struts, hips and valleys are not designed.
• The rafter-to-plate connector, the ridge strap or gusset and the wall under the horizontal force are not designed; their forces are reported. Nail spacing is yours (nails under 1/4 in. take no geometry factor; NDS 12.1.6, 12.5.1.1).
• The tie's shear, bearing and deflection under the ceiling loads are not checked (use the wood beam type); its bending is a simple span.
• The strong-axis column length is the whole rafter along the slope. A raised tie or an overhang does not shorten it (conservative); the sheathing is taken to brace the weak axis.
• Rafter shortening and nail slip are left out of the ridge drop. The deflection check is relative to the chord: the rigid rotation of the rafter is the ridge drop, reported separately.
• A rafter with no overhang notched at the seat is treated as an end notch; the code limit that applies with an overhang is the interior notch limit.
• Wind on the soffit of the overhang is not added.
• Reference values come from the NDS 2024 Supplement Tables 4A and 4B, read on 2026-11-08 (as the wood beam). The model IRC is sold: its tables were read in the 2021 and 2018 Seattle Residential Codes. The 2024 IRC has not been read.

Verification examples #

Verification status: 79 values compared in 35 examples (33 published, 2 hand calculations from the cited equations): 78 within tolerance, 1 recorded deviations. Code basis: partial. Only some provisions were read in the target edition; the rest rests on older editions, examples or summaries.

The deviation. The HUD example resolves the bearing reaction through the rafter axis as a pinned truss joint. That treats the rafter as carrying its load only at its ends; the moment balance of the rafter gives half that force. The AWC span tables have no thrust, but the ClearCalcs printouts and the module agree on this statics, and the IRC table's own counts match it. The HUD guide itself says that its 12 nails exceed conventional practice.

No free worked example of the full set of NDS checks on a rafter pair was found: the checks of bending with axial force, Hankinson at the seat and the birdsmouth are hand calculations from the cited equations (research/DOCUMENTS_NEEDED.md).