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Woodworking Math

Wood species

Beech wood

Beech is a hardwood (Fagus grandifolia). At 12% moisture content it has a Janka hardness of 1,300 lbf (5,783 N) and it weighs about 45 lb/ft³ (717 kg/m³), 3.7 lb (1.69 kg) per board foot.

Also called: American beech.

Key numbers

Janka hardness, 12% MC
1,300 lbf (5,783 N)
Green: 850 lbf (3,781 N)
Weight at 12% MC
45 lb/ft³ (717 kg/m³)
3.7 lb per board foot
Specific gravity (oven-dry weight)
0.64 at 12% MC volume
0.56 on green volume
Shrinkage, green to oven-dry
11.9% tangential
Radial 5.5%, volumetric 17.2%

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

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

Work out what your boards weigh

How much beech moves

A 12 in wide flatsawn board of American beech that goes from 6% to 12% moisture content swells about 0.31 in (about 5/16 in, 7.9 mm). Quartersawn, the same board moves about 0.14 in (about 1/8 in, 3.5 mm). Flatsawn faces move 2.2 times as much as quartersawn ones, because the wood shrinks 11.9% around the growth rings but only 5.5% across them.

Worked with the Wood Handbook's dimensional change coefficients for American beech (Table 13-5: 0.00431 tangential, 0.0019 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
Nearly white sapwood and reddish-brown heartwood, sometimes with no clear boundary between them.
Grain and texture
Close, uniform texture with little figure.
Working and character
Heavy, hard, strong and tough, and very good for steam bending. It shrinks a lot, so it needs careful drying, then machines smoothly and turns well.
Uses
Flooring, furniture, brush blocks, handles, veneer, wooden ware and containers.

Adapted in our own words from the Wood Handbook, Chapter 2, p. 2-5.

Strength

Bending strength is the modulus of rupture (MOR); stiffness is the modulus of elasticity (MOE). Clear, straight-grained samples of American beech 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)8,600 psi (59 MPa)14,900 psi (103 MPa)
Stiffness (MOE)1,380,000 psi (9.5 GPa)1,720,000 psi (11.9 GPa)
Crushing strength (compression parallel to grain)3,550 psi (24 MPa)7,300 psi (50 MPa)
Compression perpendicular to grain540 psi (4 MPa)1,010 psi (7 MPa)
Shear parallel to grain1,290 psi (9 MPa)2,010 psi (14 MPa)
Tension perpendicular to grain720 psi (5 MPa)1,010 psi (7 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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Why these numbers

Why these numbers?
  1. The situation

    The USDA Forest Products Laboratory measured American beech at 1,300 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 × 0.64 × 1.12.

    Arithmetic: exact by definition , sources [1]

  4. The number

    About 45 lb/ft³, or 3.7 lb per board foot (1/12 ft³), at 12% moisture content.

    Arithmetic: exact by definition

How we source these numbers