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NDS · HankinsonAngle to grainFree

Wood Bearing
at an Angle

Apply the Hankinson equation to two adjusted values supplied by you. The result is an interpolation only; it does not select design values or approve a wood connection.

Who it's for: timber designers who have already established the applicable adjusted parallel and perpendicular values at construction documents and need transparent angle interpolation.

F_θ = (F∥ · F⊥) / (F∥·sin²θ + F⊥·cos²θ)
F∥ = bearing parallel to grain (use F_c for end bearing); F⊥ = bearing perpendicular to grain (F_c⊥); θ = angle between the load and the grain direction. At θ = 0° you get F∥; at 90° you get F⊥. Use NDS-adjusted (allowable) design values. Multiply by bearing area for capacity.
Angled Bearing
F_θ

How to use this calculator

1
Enter F∥ — the parallel-to-grain bearing value
Use the NDS-adjusted F'c (compression parallel to grain) for end-grain bearing. This value must already include all applicable factors — CD, CM, Ct — before you enter it here.
2
Enter F⊥ — the perpendicular bearing value
Use the NDS-adjusted F'c⊥. For Douglas Fir-Larch No. 2, the unadjusted reference value is 625 psi — multiply by all applicable factors before entering.
3
Set the load angle θ
Enter the angle between the applied load and the grain direction. For a bird's-mouth rafter bearing, θ equals the roof pitch angle. At 0° the load acts along the grain; at 90° it acts perpendicular.
4
Enter the bearing area (optional)
Provide the contact area in square inches to see total bearing capacity (Fθ × A) in pounds. Leave blank to see only the allowable bearing stress.
5
Read the interpolated value F_θ
The result is the equation output at angle θ. The tool does not decide whether the supplied values are applicable or whether a connection is adequate.

The formula

The Hankinson equation interpolates between two orthogonal values supplied by the user. It returns the parallel value at 0°, the perpendicular value at 90°, and a smooth intermediate value.

Fθ = (F∥ · F⊥) / (F∥·sin²θ + F⊥·cos²θ)

Fθ = interpolated value at angle θ
F∥ = user-supplied adjusted parallel value
F⊥ = user-supplied adjusted perpendicular value
θ = angle between the load and grain (0° = parallel; 90° = perpendicular)
The optional area output is multiplication only and is not a connection-capacity determination.

Worked example

Example
A Douglas Fir-Larch No. 2 rafter bears on a sill plate at a 30° bird's-mouth. Adjusted values: F∥ = 1,350 psi, F⊥ = 625 psi. Bearing area: 11.25 in² (a 1.5″ × 7.5″ seat).
Denominator = 1,350 × sin²30° + 625 × cos²30° = 337.5 + 468.75 = 806.25. Numerator = 1,350 × 625 = 843,750. Fθ = 843,750 ÷ 806.25 = 1,047 psi. Total bearing capacity = 1,047 × 11.25 = 11,773 lb.

When this estimate will be off

  • Input values must already include all NDS adjustment factors (C_D, C_M, C_t, C_b, etc.) — entering unadjusted tabulated reference values produces an unconservative result for wet service or short-duration loads.
  • Covers bearing and compression at an angle to grain only; fastener lateral capacity (bolts, nails, lag screws) uses the NDS yield-limit equations, not the Hankinson formula.
  • Assumes uniform bearing contact over the full stated area; partial or eccentric contact — common at a rough bird's-mouth cut — overstates capacity.
  • Does not check shear stress at a notch; a bird's-mouth also requires a notch-shear check per NDS, which this calculator does not perform.

Frequently asked questions

A common mistake: Input values must already include all NDS adjustment factors (C_D, C_M, C_t, C_b, etc.) — entering unadjusted tabulated reference values produces an unconservative result for wet service or short-duration loads.

Enter adjusted design values F'c and F'c⊥ — already multiplied by CD (load duration), CM (moisture), Ct (temperature), and Cb (bearing-area factor for perpendicular values). The Hankinson formula does not apply those factors itself. Entering unadjusted tabulated reference values produces an unconservative result for wet service or short-duration loads.

The Hankinson formula is a smooth interpolation between two boundary states. At θ = 0° the denominator reduces to F∥ and Fθ = F∥; at θ = 90° it reduces to F⊥ and Fθ = F⊥. At any angle between, the result lies between the two — perpendicular-to-grain bearing is always the weaker limit in wood.

No. It only evaluates the Hankinson equation using values you supply. A design still needs applicable adjusted values plus checks for contact geometry, notch shear, member forces, fasteners, eccentricity, and every other governing limit state.

Bolts and lag screws transfer load through dowel bending and wood embedment, governed by the NDS yield-limit equations in §11.3 (dowel connections). The Hankinson formula covers bearing and compression-at-an-angle in the wood fiber only — it is not applicable to fastener lateral design values. Use the Z-value equations for fastener sizing.

Sources

  • NDS-2024 §3.10 — Hankinson formula for bearing at an angle to grain

This free Wood Connection Designer is built and maintained by DataDrivenAEC, using the relevant codes and standards. It does not substitute for professional judgment.