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Woodworking Math

Wood species

Grand fir wood

Grand fir is a softwood (Abies grandis). At 12% moisture content it has a Janka hardness of 490 lbf (2,180 N) and it weighs about 26 lb/ft³ (414 kg/m³), 2.2 lb (0.98 kg) per board foot.

Also called: Abies grandis.

Key numbers

Janka hardness, 12% MC
490 lbf (2,180 N)
Green: 360 lbf (1,601 N)
Weight at 12% MC
26 lb/ft³ (414 kg/m³)
2.2 lb per board foot
Specific gravity (oven-dry weight)
0.37 at 12% MC volume
0.35 on green volume
Shrinkage, green to oven-dry
7.5% tangential
Radial 3.4%, volumetric 11.0%

One source: USDA Forest Products Laboratory, the authority for species properties it measured

Why: Measured by the USDA Forest Products Laboratory; grand fir's density is worked from its specific gravity with the Handbook's own equation.

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How much grand fir moves

A 12 in wide flatsawn board of grand fir that goes from 6% to 12% moisture content swells about 0.19 in (about 3/16 in, 4.8 mm). Quartersawn, the same board moves about 0.08 in (about 3/32 in, 2.1 mm). Flatsawn faces move 2.2 times as much as quartersawn ones, because the wood shrinks 7.5% around the growth rings but only 3.4% across them.

Worked with the Wood Handbook's dimensional change coefficients for grand fir (Table 13-5: 0.00263 tangential, 0.00116 radial per 1% change in moisture content), which hold between 6% and 14%. Individual boards vary: the Handbook gives shrinkage a coefficient of variation of about 15% (p. 4-11).

Work out how much your board will move

Color, grain and working

Color
Creamy white to pale brown, like the other true firs.
Working and character
A western true fir: light in weight, somewhat stronger than balsam fir, with low to moderately high shrinkage.
Uses
Western true firs are sold as white fir for framing, subflooring, sheathing, boxes, sashes, doors and millwork.

The Handbook says the true firs cannot be told apart by their wood alone.

Adapted in our own words from the Wood Handbook, Chapter 2, p. 2-12.

Strength

Bending strength is the modulus of rupture (MOR); stiffness is the modulus of elasticity (MOE). Clear, straight-grained samples of grand fir tested by the Forest Products Laboratory (Wood Handbook Table 5-3b). Knots and cross grain make lumber weaker than these clear samples (Handbook Chapter 5).

PropertyGreen12% MC
Bending strength (MOR)5,800 psi (40 MPa)8,900 psi (61 MPa)
Stiffness (MOE)1,250,000 psi (8.6 GPa)1,570,000 psi (10.8 GPa)
Crushing strength (compression parallel to grain)2,940 psi (20 MPa)5,290 psi (36 MPa)
Compression perpendicular to grain270 psi (2 MPa)500 psi (3 MPa)
Shear parallel to grain740 psi (5 MPa)900 psi (6 MPa)
Tension perpendicular to grain240 psi (2 MPa)240 psi (2 MPa)

A dash means the Handbook prints no value; none is filled in.

Dust and health

This is what the named authorities publish, not medical advice.

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Buying and finishing grand fir

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Why these numbers

Why these numbers?
  1. The situation

    The USDA Forest Products Laboratory measured grand fir at 490 lbf of side hardness at 12% moisture content, on clear, straight-grained samples (Wood Handbook Table 5-3b).

    One source: USDA Forest Products Laboratory, the authority for species properties it measured , sources [1]

  2. What that means

    Side hardness (Janka) is the load needed to press a 0.444 in (11.28 mm) steel ball halfway into the wood across the grain; a higher number dents less (Handbook p. 5-5).

    One source: USDA Forest Products Laboratory, the authority for species properties it measured , sources [1]

  3. So

    Density at 12% is water's density × specific gravity × (1 + 0.12) (Handbook Eq. 4-14): 62.43 × 0.37 × 1.12.

    Arithmetic: exact by definition , sources [1]

  4. The number

    About 26 lb/ft³, or 2.2 lb per board foot (1/12 ft³), at 12% moisture content.

    Arithmetic: exact by definition

How we source these numbers