Design of Timber Structures

Timber as a structural material The oldest construction material and still one of the most versatile A natural material with inherent flaws and variability We need to recognize its strengths and weaknesses Timber design therefore as much an art as a science

One of nature’s most efficient structures: an Arbutus tree facing the onslaught of West Coast storms

Decay of wood Requirements: nutrition (wood) modest temperature (~ 20 C) moisture (the only one that can be readily controlled)

Preservative treatment of wood in marine environment

Decay in a poorly constructed building envelope

Wet column bases

Comparative material properties Stress (MPa) -20 -100 -200 -400 300 30 20 10 -10 400 -300 200 100 mild steel wood (parallel to grain) concrete Strain, %

Fire resistance One of the biggest challenges in light timber construction Also an important benefit of heavy timber construction

Reliability and Safety Load distributions Strength distributions Probability of occurrence Probability of failure (overlap area) Load, Resistance

Safety Factors Load distribution Strength distribution Probability of occurrence Global safety factor = Ravg/Lavg Lavg Ravg Probability of failure (overlap area) Load, Resistance

Safety factors Load distribution Probability of occurrence Resistance Nominal safety factor = R95/L05 95th percentile 5th percentile L95 R05 Load, Resistance Measure of safety

Safety Index β = Safety Index Load distribution Strength distribution Probability of occurrence Probability of occurrence Probability of failure (overlap area) (Resistance – Load) distribution β = Safety Index Probability of failure β (SDEV) Resistance - Load

Normal Distribution Probability of occurrence Resistance distribution 1.645 SDEV Probability of occurrence Resistance distribution R05 Ravg Load, Resistance

Design equation L ≤  R Factored Action ≤ Factored Resistance From National Building Code (same for all materials) From material specific design code, e.g. O86.1 L ≤  R Load factor Resistance (R05) Load (L95) Calibration factor

Material properties of wood … imagine a bundle of straws held together with elastic bands lignin cellulose fibres tension parallel to grain compression parallel to grain tension perpendicular to grain compression perpendicular to grain shear

Design properties (approximate values, D-fir No.1/2) Strength property Clear wood (MPa) Structural timber (MPa) Tension parallel to grain ( ft ) 20 6 Compression parallel to grain ( fc ) 18 14 Tension perpendicular to grain ( ftp ) 1 Compression perpendicular to grain ( fcp ) 8 Bending ( fb ) 30 10 Shear parallel to grain ( fv )

Consequences of different design values Avoid tension perpendicular and shear stresses at all cost Make use of compression strength of wood as much as possible Simplify connections and use compression load transfer when possible Avoid stress concentrations and complex stress patterns

Brittle failure of wood Tension perpendicular to grain Tension parallel to grain Shear

Factors that affect the strength of clear wood Decay Direction of load w.r.t. grain orientation Others ….. ?

Compression perpendicular Effect of density Density values: Douglas fir 0.49 Pine 0.37-0.44 Hemlock 0.43 Spruce 0.37-0.43 Modulus of elasticity 200 Modulus of rupture 150 Compression parallel Strength (MPa) 100 Compression perpendicular 50 0.2 0.4 0.6 0.8 1.0 Relative density

Defects that affect the strength of timber Grading of timber Defects that affect the strength of timber

Visual Grading of Lumber Lumber is sorted for a specific application, e.g. For tension members all knots and defects have a significant effect For beams and stringers, the grader focuses on edge knots For posts and timbers sloped grain is more important The larger the members, the higher the probability of missing some important defects

The sorting process Sorting by species Visual grading Species of similar strength characteristics are lumped together Visual grading A certified grader sorts wood by hand according to visual appearance Lumber gets sorted according to end use Grading criteria: Knots (type, location, size, frequency), wane, checks, slope of grain, pitch pockets Mechanical grading

Testing of lumber Tension test Bending test Strength distribution Probability of occurrence Strength 5th percentile value Proof load Full size members are tested To failure (full distribution is obtained) Up to a proof load (only lower tail end of distribution is obtained)

Use of dimension lumber in residential construction

Platform construction

Platform construction

Residential construction

Design values for structural joists and planks (MPa) General purpose members

Design values for beams and stringers (MPa)

Beams and stringers on the flat Adjustment factors when using beams or stringers on the flat: fb E or E05 Select Structural 0.88 1.00 No.1 or No.2 0.77 0.90

for specific applications Variability of material properties Bridging (load sharing) Selection of members for specific applications (grading) Engineered wood products (less variability) Closely spaced members (load sharing)

Large glulam beams in buildings and bridges Defects are distributed among many laminations Large glulam beams in buildings and bridges

Design values for Douglas fir glulam (MPa)

Design concepts Engineered wood product Probability of occurrence Load distribution Engineered wood product Sawn lumber Probability of occurrence Probability of failure (overlap area) Load, Resistance

Engineered wood products - pick the best member for each application laminated veneer lumber I-joists laminated strand lumber oriented strandboard finger-jointed studs plywood

Structural design To minimize the probability of a very high stress (extreme load case) occurring at a location of very low strength (extreme weakness) low strength area high stress area

These elements for shearwalls only Wall construction These elements for shearwalls only

Loads on walls Gravity loads (dead load, snow, occupancy) Shear loads (wind, earthquake) Lateral loads (wind)

moisture content of wood (%) Shrinkage of wood 10 shrinkage (%) 5 tangential shrinkage radial shrinkage lengthwise shrinkage 5 10 15 20 25 30 moisture content of wood (%)

Wood shrinkage in platform construction 2x12 (38x235) joists 2x4 (38x89) top plates When using green wood (25% MC) Shrinkage @ 5% results in (0.05)(235+38+38) = 15.6mm

Post and beam construction

Post and beam construction C.K. Choi building, UBC campus

Design values for posts and timbers (MPa)

Mechanical grading of lumber P MSR Machine stress rating non-destructive continuous feed elastic modulus is measured over entire length and averaged E-values are correlated with strength values Visual Probability of occurrence 5th percentile values Strength

Design values for MSR lumber (MPa) Note: no species separation

Use of MSR lumber in trusses

Engineered wood products A way to reduce the variability of the material Use low quality material to produce a high-grade product Use high quality material in high stress zones No size limitations (almost) Can be made for special applications

Shrinkage in woodframe construction

Shrinkage in connections

Wood properties and connection design Avoid connections as much as possible Work with the strong properties of wood (compression) Avoid weak properties (tension perpendicular and shear) Consider shrinkage Design for durability Strive for simplicity

Efficient use of timber for a long span roof (minimal connections)

Bearing connections

Bearing connections

Bearing connections

Bearing connections

Complex connections ??

The connection palace

Wood in bending and compression

The ultimate tree ??