Wood as a structural material

Kestrel Bay Engineering has a third phase of work at the municipal operations centre in Thunder Bay. The city wants a timber training pavilion beside the main entrance, a two-storey wood-frame office annex for the parks crews, new glulam posts in the salt storage shed, a masonry pump house above the lift station designed in CIV-341, and a concrete block wash bay on the end of the garage. Priya Raman leads the design again, Owen Lachance runs the calculations, and Sofia Martel checks them in Python. None of the members are steel or concrete, so the team needs two more design standards: CSA O86 for wood and CSA S304 for masonry. This course follows those members from material properties to a finished design.

This first lesson is about wood itself. Wood is a natural, cellular material grown by a tree to carry its own weight and resist wind, and its structure explains almost every rule in a timber design standard: why strength depends on the direction of load, why moisture matters, why a beam can carry more load for a few minutes than for fifty years, and why two pieces of the same species and grade can differ in strength by a factor of two.

The structure of wood

A tree trunk is made mostly of long, hollow cells called tracheids in softwoods, aligned with the axis of the trunk. Each cell wall is a composite of cellulose fibres wound in a matrix of lignin and hemicellulose. Bundled together, the cells act like a handful of drinking straws glued side by side: stiff and strong along their length, much weaker across it. Structural lumber in North America is almost all softwood, from species such as spruce, pine, fir, larch and hemlock.

Three directions matter. The longitudinal direction runs along the grain. The radial direction runs from the pith out to the bark, across the growth rings, and the tangential direction runs along the rings. Tension and compression parallel to grain are strong. Compression perpendicular to grain, the bearing of a joist on a plate, is perhaps a tenth as strong, and tension perpendicular to grain is so weak and variable that designers avoid relying on it at all.

Each growth ring has light earlywood, laid down quickly in spring with large thin-walled cells, and denser latewood laid down in summer. Density, measured as relative density or specific gravity, is a good predictor of strength and of the holding power of nails and bolts. That is why species are grouped by density and strength for design purposes, and why connection design uses the relative density of the species directly.

Grading and species groups

Sawn lumber is graded piece by piece. Visual grading rules, published in Canada by the National Lumber Grades Authority (NLGA), limit the size and location of knots, the slope of grain, wane, splits and other characteristics that reduce strength. A No.1 or No.2 piece may contain a knot a third of its width; a Select Structural piece has much smaller defects. Machine stress-rated (MSR) lumber is bent through a machine that measures its stiffness and is then assigned a grade such as 2100Fb-1.8E. Glued-laminated timber (glulam) has its own stress grades, such as 24f-EX, built up from graded laminations.

Species with similar properties are grouped for design. O86 lists four main groups for sawn lumber: Douglas fir-larch (D.Fir-L), Hem-Fir, Spruce-Pine-Fir (S-P-F) and Northern species. Most of the dimension lumber sold in Ontario is S-P-F, and that is what the office annex will use. The standard tabulates specified strengths for each group and grade: bending \(f_b\), longitudinal shear \(f_v\), compression parallel \(f_c\) and perpendicular \(f_{cp}\) to grain, tension parallel to grain \(f_t\), and the modulus of elasticity \(E\) with its lower fifth percentile \(E_{05}\) for buckling.

Because these values come from tests of real lumber, they are lower percentiles of a wide distribution, typically the fifth percentile for strength. A grade is a sorting rule, not a guarantee that every piece is as strong as every other; the system works because members rarely act alone, and because the design values sit well below typical strength.

Moisture content

Green wood in a living tree may hold more water than wood substance by weight. Water sits both inside the cell cavities, as free water, and inside the cell walls, as bound water. As wood dries, the free water leaves first. When only bound water remains, at about 25 to 30 per cent moisture content, the wood has reached its fibre saturation point. Below that point, further drying shrinks the cell walls, and the wood becomes stronger and stiffer as it does.

In service, wood comes to equilibrium with the humidity around it. In a heated building it settles at roughly 8 to 12 per cent moisture content, while outdoors under cover it may sit at 12 to 18 per cent. Dry lumber is surfaced at 19 per cent or less, so lumber installed in a heated building keeps drying for months after it is built in.

Shrinkage across the grain is roughly 0.25 per cent of the dimension for each 1 per cent change in moisture content below the fibre saturation point, with tangential shrinkage about twice radial shrinkage. Along the grain, shrinkage is negligible. The difference explains why a joist gets shallower but not shorter, why wood-frame buildings settle at each floor, and why checks open on the faces of large timbers as their outer layers dry first.

Strength depends on moisture as well. O86 gives specified strengths for dry service conditions, where the average equilibrium moisture content will not exceed 15 per cent and does not exceed 19 per cent at any time. For wet service, such as an unheated salt shed open to blowing snow, service condition factors \(K_S\) reduce the strengths and the modulus.

Duration of load

Wood carries a high load for a short time much better than a sustained load for years. A specimen that fails in a few minutes in a test will fail at about 60 per cent of that load if the load stays on for decades. The cause is slow damage in the cell walls under stress, which is why wood also creeps: a beam under permanent load keeps deflecting slowly for years.

O86 accounts for this with the load duration factor \(K_D\). Specified strengths correspond to standard-term loading, such as snow and occupancy loads, with \(K_D = 1.0\). For short-term loads such as wind and earthquake, \(K_D = 1.15\). For permanent loads, \(K_D = 0.65\). When the specified dead load \(P_D\) exceeds the specified standard-term live or snow load \(P_S\), the standard reduces the factor:

The rule matters for heavy roofs, archive storage and other members where most of the load is dead load; for the pavilion and the office annex, the snow and occupancy loads exceed the dead load, so \(K_D = 1.0\).

The design format

O86 is a limit states standard with the same structure as CSA S16 and CSA A23.3. Factored load effects from the National Building Code load combinations must not exceed factored resistances. The resistance is a resistance factor \(\phi\) times a modified specified strength times a section property. For bending of sawn lumber:

Here \(K_H\) is the system factor, which rewards repetitive members that share load through sheathing; \(K_{Sb}\) the service condition factor; \(K_T\) the treatment factor; \(K_{Zb}\) the size factor, because larger pieces are more likely to contain a strength-reducing defect; and \(K_L\) the lateral stability factor, which is 1.0 when the compression edge is held in place. Resistance factors are 0.9 for bending, shear and tension and 0.8 for compression.

Defects, checks and natural variability

Knots are the remains of branches. A knot interrupts the grain, and the grain deviates around it, so a knot on the tension edge of a beam weakens it far more than the same knot near the neutral axis. Slope of grain, where the fibres run at an angle to the edges of a piece, weakens it in tension and bending. Checks and splits, the separations along the grain caused by drying, reduce shear capacity near the ends of a beam. Grading rules limit all of these.

The result is that the coefficient of variation of the bending strength of a visually graded lumber population is often 25 to 35 per cent, far higher than for steel. Engineers live with this in three ways: by using low percentile values, by taking advantage of load sharing in repetitive systems, and by using engineered products, such as glulam, laminated veneer lumber and cross-laminated timber, that spread defects through many thin layers and so behave much more uniformly.

Engineered wood products

Glued-laminated timber is made of 38 mm (1-1/2 in.) laminations finger-jointed end to end and glued face to face into members of almost any length and depth. The best laminations are placed in the outer tension and compression zones, where stresses are highest. Laminated veneer lumber (LVL) and parallel strand lumber (PSL) are made from thin veneers or strands glued under pressure, giving uniform, high-strength beams and columns. Wood I-joists combine LVL or lumber flanges with an OSB web. Cross-laminated timber (CLT) is made of layers of lumber glued with alternate layers at right angles, forming large panels for floors, roofs and walls; lesson 4 designs the pavilion roof with it.

Proprietary products such as LVL and I-joists are not covered by tabulated values in O86. Their design values come from evaluations by the Canadian Construction Materials Centre (CCMC) and from the manufacturer, and the designer uses the manufacturer's literature with the same load combinations.

Durability

Wood decays when its moisture content stays above about 20 per cent for long periods, because decay fungi need moisture, oxygen and a moderate temperature. Keep wood dry and it lasts for centuries. Good details, such as sloped tops, drained connections, clearance from soil and concrete, ventilated cavities and roof overhangs, matter more than any chemical. Where wood must be exposed to wetting, preservative-treated lumber is used, with treatment factors that may reduce strength and with corrosion-resistant fasteners, because some preservatives corrode plain steel.

The salt shed is a good example of where wood shines. Road salt rapidly corrodes steel and attacks the reinforcing in concrete, but wood is chemically resistant to salt. The existing shed, framed with glulam three-hinged arches in CIV-224, has stood for decades. Its new wall posts will be glulam too, with stainless or hot-dip galvanized fasteners and a concrete curb that keeps the post bases above the salt and meltwater.

Shrinkage in the office annex

The office annex is a two-storey platform frame: each floor of joists sits on the walls below, and each wall stands on the floor below. In platform framing, the wood that lies across the grain in the load path, the plates and the floor joists, determines the vertical shrinkage. If the annex is clad in brick, the brick does not shrink with the frame, and the details at windows, at the roof and at every tie must allow for the difference. Sofia's script estimates it.

# Office annex floor joists: S-P-F No.1/No.2, 38 x 235 mm, CSA O86 limit states design
import math
fb, fv, E = 11.8, 1.5, 9500.0        # specified strengths and modulus (MPa)
b, d = 38.0, 235.0                   # mm

# Modification factors
KD = 1.0       # standard-term load (office live load)
KH = 1.10      # system factor, case 1: three or more members at 610 mm or less
KSb = 1.0      # dry service
KT = 1.0       # untreated
KZb = 1.1      # size factor for bending at this depth (from the standard's table)
Fb = fb * KD * KH * KSb * KT
print(f"Fb = {fb} x {KD} x {KH} x {KSb} x {KT} = {Fb:.2f} MPa")
S = b * d**2 / 6
Mr = 0.9 * Fb * S * KZb / 1e6
print(f"S = {S/1e3:.0f} x 10^3 mm3, Mr = 0.9 x Fb x S x KZb = {Mr:.2f} kN.m per joist")

# Duration of load: the same joist under permanent load only
for name, PD, PL in [("office (D < L)", 1.0, 2.4), ("archive storage (D > L)", 3.0, 1.5)]:
    if PD <= PL:
        kd = 1.0
    else:
        kd = max(0.65, 1.0 - 0.50 * math.log10(PD / PL))
    print(f"{name:26s}: PD/PL = {PD/PL:.2f}, KD = {kd:.2f}")

# Shrinkage across the grain as the joist dries in service
MC0, MC1 = 19.0, 10.0                # per cent, at installation and in service
coef = 0.0025                        # dimensional change per 1 % change in MC, across the grain (approx.)
shrink = d * coef * (MC0 - MC1)
print(f"Depth shrinkage {MC0:.0f}% -> {MC1:.0f}%: {shrink:.1f} mm per joist")
print(f"Two floors of joists plus three plates of 38 mm: {2*shrink + 3*38*coef*(MC0-MC1):.1f} mm")

Fb = 11.8 x 1.0 x 1.1 x 1.0 x 1.0 = 12.98 MPa
S = 350 x 10^3 mm3, Mr = 0.9 x Fb x S x KZb = 4.49 kN.m per joist
office (D < L)            : PD/PL = 0.42, KD = 1.00
archive storage (D > L)   : PD/PL = 2.00, KD = 0.85
Depth shrinkage 19% -> 10%: 5.3 mm per joist
Two floors of joists plus three plates of 38 mm: 13.1 mm

About 13 mm of shrinkage accumulates over the two floors. That is small for the frame, which simply settles, but lesson 11 will show that it controls the gap under every window sill in the brick veneer. Using kiln-dried lumber, letting the frame dry before the finishes go on, and detailing for movement keep it from causing damage.

Wood and the environment

Wood stores carbon absorbed by the tree as it grew, and producing sawn lumber and glulam takes far less energy than producing steel or cement. Whole-building life cycle assessments therefore often show lower embodied carbon for timber structures, although the result depends on forest management, transport distance, the end-of-life assumption and the rest of the building. The city has asked for a timber pavilion partly for this reason and partly because exposed wood makes a warm, welcoming space for public training sessions.