Wood shrinkage and moisture

How much wood framing shrinks as it dries in service, piece by piece and level by level up a multi-story wood frame, by the method of the USDA Forest Products Laboratory Wood Handbook (FPL-GTR-282). The shrinkage of each story and the cumulative shrinkage at the top are checked against the movements you allow. US and metric units.

The Wood Handbook is not in our reference library yet. Its coefficients are built in from knowledge and marked "to confirm against the code text" wherever they appear.

Inputs of the shrinkage calculation #

• Species: the FPL species (Douglas-fir, larch, hemlock, the true firs, the southern pines, lodgepole and ponderosa pine, the spruces, redwood, western redcedar), or Other with your own values. The commercial groups map to them: Douglas Fir-Larch is Douglas-fir and western larch, Hem-Fir is western hemlock and the true firs, SPF is the spruces, lodgepole pine and subalpine fir, and Southern Pine is loblolly, longleaf, shortleaf and slash.
• Coefficients from:
  • the dimensional change coefficients CR (radial) and CT (tangential) per percent of moisture content (Handbook Table 13-5), or
  • the total shrinkage green to oven-dry, SR and ST (Table 4-3), spread evenly below the fiber saturation point: C = S / (100 fs).
• Across the grain: framing lumber comes with any ring orientation.
  • The average of radial and tangential is common practice.
  • Tangential is the upper bound (flat-sawn).
  • Radial is the lower bound (edge-grain).
• Longitudinal shrinkage SL: green to oven-dry along the grain. The Handbook gives 0.1 to 0.2 % for normal wood; juvenile and compression wood shrink more. It sets the coefficient of studs and posts, CL = SL / (100 fs).
• Fiber saturation point fs: about 30 %. Wood does not shrink above it, so the moisture contents are capped at fs.
• Moisture content at installation Mi: the lumber as delivered.
  • S-DRY: at most 19 %.
  • KD-15 or MC15: at most 15 %.
  • S-GRN: above 19 %; take fs.
  • Rain during framing raises it.
• Equilibrium moisture content in service Mf: the Handbook's values for the interior of heated buildings (Table 13-1) are about 8 % in most of the United States, 6 % in the dry southwest and 11 % in damp, warm coastal areas. Framing commonly ends between 8 and 12 %.
• Framing stack: every piece in the vertical load path, from the foundation up, one row per piece. Each row gives:
  • the level (1 is the lowest);
  • the piece: sill, bottom or top plate, rim or band joist, floor joist bearing on the wall, beam or header, blocking, studs, a post, or engineered wood;
  • the number of pieces (two top plates: 2);
  • its vertical dimension (a plate's thickness, a rim's depth, a stud's length);
  • optionally its own coefficient C, required for engineered wood (from the manufacturer; LVL, LSL and I-joist rims installed near their equilibrium moisture content are often taken near zero), and its own initial moisture content.

  A floor's rim or joists belong to the level below them.

• Movement limits: both are your criteria and are checked by default.
  • Allowed shrinkage of one story: what the connections at each floor take (slip joints in risers and ducts, cladding joints).
  • Allowed cumulative shrinkage: the differential movement allowed where the frame meets something that does not shrink: a concrete or masonry core, a steel column or frame, an elevator, a podium stair, or a take-up device's travel.

There is no auto-design: the calculation reports movements. The pieces and the moisture contents are the design, and you change them.

Checks performed #

The drawing is a schematic section of the framing stack. It shows each level's true height, its shrinkage and the cumulative shrinkage at its top. It is not to scale: the levels are drawn equal and the pieces across the grain are drawn thicker.

Limitations #

• Coefficients from knowledge: the Handbook values (Tables 4-3, 13-1 and 13-5) and the form of the method are built in from knowledge, to be confirmed against FPL-GTR-282. So is the IBC 2304.3.3 wording.
• Coefficient range: the Table 13-5 coefficients are stated for 6 to 14 % moisture content. Used from 19 % down, as is common practice, they are an approximation. The total shrinkage form spreads the green to oven-dry shrinkage evenly below fs.
• Not included:
  • elastic shortening and creep under load;
  • crushing and seating at plates and bearings;
  • construction gaps;
  • thermal movement;
  • the drying time.
• Shrinkage only: the movement of the non-shrinking element is not computed. The cumulative value is the wood's movement relative to the foundation.
• Uniform moisture: one species and one equilibrium moisture content for the whole stack. A piece of another species can be entered with its own coefficient.

Verification examples #

Verification status: 10 values compared in 8 examples (0 published, 8 hand calculations from the cited equations): 10 within tolerance, 0 recorded deviations. No published example: every value is a hand calculation. That checks the program against this reading of the code, not the reading itself. Code basis: not yet recorded for this module.

No published worked example is on disk: the Wood Handbook itself is listed as needed. Every value is a hand calculation of ΔD = n D C ΔM with the coefficients the module carries:

• one block, radial and tangential;
• the total-shrinkage form;
• green lumber capped at fs;
• the default three-story stack, level by level and cumulative;
• an engineered rim with its own coefficient and moisture content;
• a Southern Pine rim;
• swelling.