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)
400
mild steel
300
200
100
wood (parallel to grain)
-20
-10
10
concrete
-100
-200
-300
-400
20
Strain, %
30
Fire resistance
• One of the biggest challenges in light timber construction
• Also an important benefit of heavy timber construction
Probability of occurrence
Reliability and Safety
Strength distributions
Load
distributions
Probability of failure
(overlap area)
Load, Resistance
Probability of occurrence
Safety Factors
Load
distribution
Strength distribution
Global safety factor = Ravg/Lavg
Lavg
Probability of failure
(overlap area)
Ravg
Load, Resistance
Probability of occurrence
Safety factors
Load
distribution
Resistance
distribution
Nominal safety factor = R95/L05
95th percentile
L95
5th percentile
R05
Measure of safety
Load, Resistance
Probability of occurrence
Probability of occurrence
Safety
Index
Load
distribution
Strength distribution
Probability of failure
(overlap area)
(Resistance – Load)
distribution
Probability of
failure
β = Safety Index
β (SDEV)
Resistance - Load
Probability of occurrence
Normal Distribution
1.645 SDEV
Resistance
distribution
R05
Ravg
Load, Resistance
Design equation
Factored Action ≤ Factored Resistance
From National Building Code
(same for all materials)
Load factor
From material specific
design code, e.g. O86.1
L ≤  R
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)
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
1
Compression perpendicular to grain ( fcp )
8
8
30
10
1
1
Strength property
Bending ( fb )
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 ….. ?
Effect of density
Density values:
Douglas fir 0.49
Pine
0.37-0.44
Hemlock
0.43
Spruce
0.37-0.43
Strength (MPa)
200
150
Modulus of elasticity
Modulus of rupture
Compression parallel
100
Compression perpendicular
50
0
0
0.2
0.4
0.6
Relative density
0.8
1.0
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
– 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
Full size members are tested
(a) To failure (full
distribution is obtained)
(b) Up to a proof load (only
lower tail end of
distribution is obtained)
Probability of
occurrence
Bending test
Proof load
Strength
distribution
5th percentile value
Strength
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:
Select Structural
No.1 or No.2
fb
0.88
0.77
E or E05
1.00
0.90
Variability of material properties
Bridging
(load sharing)
Selection of members
for specific applications
(grading)
Closely spaced members
(load sharing)
Defects are
distributed
among many
laminations
Large glulam
beams in
buildings
and bridges
Design values for
Douglas fir glulam
(MPa)
Probability of occurrence
Design concepts
Engineered wood product
Load
distribution
Probability of failure
(overlap area)
Sawn lumber
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
Wall
construction
These elements
for shearwalls
only
Loads on
walls
Gravity loads
(dead load, snow,
occupancy)
Shear loads
(wind, earthquake)
Lateral loads
(wind)
Shrinkage of wood
shrinkage (%)
10
5
lengthwise shrinkage
0
0
5
10
15
20
moisture content of wood (%)
25
30
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
constructi
on
Post and
beam
construction
C.K. Choi
building, UBC
campus
Design values for posts and timbers (MPa)
Mechanical grading of lumber
P
• elastic modulus is measured
over entire length and
averaged
• E-values are correlated with
strength values
Probability of
occurrence
Machine stress rating
• non-destructive
• continuous feed
MSR
Visual
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
??