Lecture Notes
Introduction to Timber Structures
7PPX0 Dimensioning of structures
ir. W.H. de Groot
2018-2019
Eindhoven University of Technology
Faculty Architecture, Building and Planning
Unit Structural Engineering and Design
Den Dolech 2
5612 AZ Eindhoven
Content
Content .................................................................................................................................................... 1
Part 1: GENERAL ................................................................................................................................... 2
1
Introduction ...................................................................................................................................... 2
2
Use of wood ..................................................................................................................................... 4
3
Coniferous and deciduous wood [3] ................................................................................................ 6
4
Dendrochronology ......................................................................................................................... 10
5
Wood properties ............................................................................................................................ 12
5.1
Density ................................................................................................................................... 12
5.2
Wood Moisture Content ......................................................................................................... 13
5.3
Shrinkage and Swelling ......................................................................................................... 15
5.4
Fungal degradation ................................................................................................................ 16
5.5
Strength and stiffness ............................................................................................................ 16
5.6
Load duration ......................................................................................................................... 16
5.7
Load duration classes ............................................................................................................ 17
5.8
Volume effects ....................................................................................................................... 17
5.9
Heat-properties ...................................................................................................................... 19
5.10 Electrical conduction .............................................................................................................. 19
5.11 Durability ................................................................................................................................ 20
5.12 Preservation........................................................................................................................... 21
5.13 Modification............................................................................................................................ 22
5.14 Summary ............................................................................................................................... 22
6
Structural design calculations ........................................................................................................ 23
6.1
Strength analysis (Safety) ..................................................................................................... 23
6.2
Stiffness analysis (Serviceability) .......................................................................................... 27
7
Grading: wood quality and strength .............................................................................................. 29
7.1
Quality classes and strength classes .................................................................................... 29
7.2
Quality marking ...................................................................................................................... 33
8
Wood products .............................................................................................................................. 36
9
Literature........................................................................................................................................ 37
Part 2: DESIGN OF WOODEN LOAD-BEARING STRUCTURES ...................................................... 38
10
Introduction ................................................................................................................................ 38
11
Rules of thumb for girders and columns .................................................................................... 40
11.1 Rules of thumb for girders ..................................................................................................... 40
11.2 Rules of thumb for columns ................................................................................................... 45
12
Rules of thumb for three-hinge-frames ...................................................................................... 46
13
Structural detailing ..................................................................................................................... 48
14
Stability ...................................................................................................................................... 54
15
Literature.................................................................................................................................... 58
Annex 1:
Calculation example: Unity Checks of the stresses in a single span beam ...................... 59
Annex 2:
Tables Eurocode 5 ............................................................................................................ 62
Annex 3:
Floor beams: ratio span versus beam height (rules of thumb) .......................................... 66
Annex 4:
Rules of thumb for Timber Constructions .......................................................................... 69
Annex 5:
Standard timber sizes ........................................................................................................ 74
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Introduction to Timber Structures
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Part 1: GENERAL
1 Introduction
This is the introduction to the course “Timber structures” developed by the Faculty Architecture,
Building and Planning, Unit Structural Engineering and Design (SD), at Eindhoven University of
Technology.
For centuries wood has been an important construction material. After the development of "modern"
materials like concrete and steel, a steady decline in the amount of wood as construction material
occurred. This is illustrated in Figure 1.1 [1].
Figure 1.1 Development of wood in the construction as a percentage of the total
material usage.
Since a number of years the application of wood in constructions is increasing. The material is
"rediscovered". Especially the visual qualities and the "cuddle factor" of the material, whatever that
may be, contributes to this increase. Also other positive qualities such as the high strength and
stiffness parallel to the grain in relation to the mass, the high fire resistance, “free form” production
possibilities, chemical resistance, the natural durability, the very low energy use in production and very
low emissions of so-called greenhouse gases (e.g. CO2) contribute.
The low natural durability of different wood species is often seen as a negative property. However, the
natural durability is no indicator for sustainability of structures realized with certain wood species.
Wood constructions realized with low durable wood species still function after hundreds of years
because the conditions for damaging mechanisms (fungi – insects – bacteria) are absent or very low
in many circumstances.
The variation in wood appearance is very large. Even within one tree significant differences occur.
This results in possible fascinating designs. Also with regard to the structural properties big variation
can be expected. Also in this case: every piece of wood is different. Result is that considerable efforts
need to be made to get a well-defined impression of the properties. Hundreds, if not thousands, of
wood species exist. Only a limited number, ca. 45, are classified in so-called strength classes, so that
these species can be used structurally in a sound, well defined way. However, for most of these
species all the wood is classified in only one strength class limiting the efficient use.
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Wood is a natural material. It can be applied directly as raw material (round wood); e.g. as foundation
pile, which outnumbers all other raw material usage. A rough estimate indicates, that in the
Netherlands, especially in the western part (Holland) about 25 million tree trunks used as foundation
piles support all kind of structures. Recent data provided by suppliers of wooden foundation piles,
indicate that there is still a (small) market for wooden piles in Netherlands and Flanders.
Wood can be cut (sawn) into all kind of elements (girders, columns, boards, laths, etc). Sawn elements
can be combined into so-called composite elements, with glue (glulam) and/or mechanically (wire
nails, bolts, etc.). Veneer, usually obtained by peeling the tree, is glued on less attractive wood
species to obtain plate material for furniture manufacturing or finishing panels. Veneer layers can be
glued together to obtain, plywood, a sheet material, or LVL (laminated veneer lumber). Thicker boards
glued together crosswise result in so-called CLT (cross laminated timber).
From waste, from sawdust to chips other sheet materials like particle board, composed plate OSB
(oriented strand board), MDF (medium density fibre board) and HDF (high density fibre board) are
manufactured. Generally the structural properties reduce with increasing amount of glue needed (e.g.
MDF needs relatively much glue and plywood relatively little). All these products are used in the
construction, often as finishing (embellishing, fire resistance, etc.). In a number of cases structurally for
which plywood, CLT, LVL, fibre board, OSB and particle board are most suited.
In Netherlands in the construction practice a number of organizations, so-called industrial
associations, are active. Of these organizations are the Wood Centre (Centrum Hout - www.centrumhout.nl), located in Almere, the Dutch Branch Association of Timber products manufacturers (NBvT),
located in Bussum (www.nbvt.nl), the Association of timber frame builders (VHSB), since July 1, 2013,
part of the NBvT (www.vhsb.nl), the VVNH (Association of Dutch timber traders), located in Almere
and the VHC, the association of structural timber designers (www.houtconstructeur.eu) the most wellknown. In the Dutch language area a number of journals on building with wood with some regularity
are issued. “Het Houtblad”, see www.houtblad.nl, is issued 8 times per year; via the website
https://www.houtblad.nl/Abonneren/Abonneren_student students find how to get “Het Houtblad” for
free. Additionally, Het Houtblad issues an on-line weekly news magazine for free. “De
Houtconstructeur”, magazine of the VHC focuses on structural design (www.houtconstructeur.eu); it is
issued rather irregularly. “Houtwereld” (www.houtwereld.nl) is issued every other week and “De
Houtkrant” (www.houtkrant.nl) is issued every other week as well.
More specific information, can be obtained via www.nehosoc.nl (the website of the Dutch Association
of wood collectors), a Web site that divulges the information only after membership of the Association
and www.probos.net, where extensive information on, among others, the (Dutch) forest and forest
management can be found.
For Belgium additional information can be found on www.srfb.be, www.pmg.be, www.fedustria.be
(federation for textile, wood and furniture industries), www.wood.be (research and technical support for
the wood and furniture industry), www.hsob.be (timber frame association), www.houtinfobois.be
(support of the use of Belgian grown timber), www.woodforum.be (the national Belgian wood
information center).
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2 Use of wood
Timber and timber products are obtained by cutting trees and processing the raw material in some
way. Figure 2.1 shows the use of this wood, averaged over the entire world.
Figure 2.1 Wood use (worldwide) [2].
Figure 2.1 shows, that more than half of the felled trees is used as firewood. In Western Europe, North
America and Japan the ratio is completely different. There is the portion firewood relatively small (can
be ignored). For the Netherlands the use of wood is shown in Figure 2.2.
Figure 2.2 Wood use (The Netherlands) [2].
The use of the forests, the suppliers of wood, differs. These different purposes do not always
strengthen each other (these purposes compete). Different purposes are:
•
Human shelter (especially in certain areas in Africa, Asia and South America) and animal
habitat.
•
Recreation (especially in the so-called Western world).
•
Supplier of food, medicine, etc.
•
Supplier of wood for all kinds of applications.
•
A positive contribution to the so-called CO2 (carbon dioxide) balance.
Worldwide about 0,5 m3 of wood is used per person per year. In Netherlands this is approx. 1 m3, in
Japan and the United States even slightly higher. Despite we hardly use wood for cooking in
Netherlands we use more than twice as much as the average world inhabitant. Figure 2.3 shows
values in tabular form.
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Wood availability
land surface
[· 103 ha]
Netherlands
(2012)
EU
World
forest surface
[· 103 ha]
%
annual growth
3
[m / ha]
Annual usage
3
total [m ]
[m3]
3390
360 (+)
10.6
8.0
(4.4 cut)
2.9·106 (+)
12,2·106 (+)
311,900
113,600 (+)
36.4
5.3
602.1·106 (+)
≈ 300·106 (+)
12,980,000
3,454,400 (-)
26.6
4.0
13,800·106 (-)
≈ 3300·106 (+)
Figure 2.3 Worldwide wood usage in relation to available surface area and the annual
wood growth (global data from the year 2000 [2]).
Figure 2.3 shows, that the wood use worldwide, despite the occasionally ominous messages in the
media about huge deforestation of especially tropical deciduous forests, is smaller than the growth.
However, the situation is still worrying, not least for those population groups that traditionally depend
for their entire existence on the forests (for example, Pygmies in Cameroon and the Dayak in
Kalimantan-Malaysia). The situation for different animals is also critical. On the other hand, in certain
areas more wood grows than is harvested. In these areas the (economic) value of wood is recognized
and ensured in a sustainable way. In these areas, forests are maintained like farms. See also the table
in figure 2.4.
Annual change [km2]
remark
1990 to 2000
2000 to 2010
10 countries with largest annual net loss of forest
area (a)
-79.260
-60.400
slowing down
10 countries with the largest annual net gain in
forest area (b)
+33.990
+44.140
increasing
Figure 2.4 Annual change in forested area.
(a) Brazil, Indonesia, Sudan, Myanmar (Birma), Nigeria, Tanzania, Mexico,
Zimbabwe, Congo (Kinshasa), Argentina.
(b) China, USA, Spain, Vietnam, India, France, Italy, Chile, Finland,
Philippines.
Socially, ecologically and economically, it is becoming less accepted, that the used wood contributes
to the negative effects of deforestation of the Earth. It is more and more expected that the wood used
is coming out of sustainably managed forests, aimed at forest conservation and at positive socioeconomic development for all involved. Organizations like FSC (Forest Stewardship Council) or PEFC
(Programme for the Endorsement of Forest Certification) define global standards for forest
management. Basis for these standards, which need to be developed in more detail for each country
or region, are the 10 FSC principles, which can be found on www.fsc.org, describing good forest
management. If forest owners meet the FSC standards their forest can be certified. Independent
inspectors ensure compliance with the rules.
The table in Figure 2.3 shows the situation of all wood, deciduous and coniferous wood, together. In
the Netherlands mainly softwood (mostly coniferous) wood species are used, which is almost
completely originating in the European Community. The wood species used most are Norway Spruce,
Pine, Larch and Douglas Fir. See the table in Figure 2.5 for a bit more detailed information [2].
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Wood usage in the Netherlands
Origin
Percentage
Mainly
EU
75
coniferous
Russia
10
coniferous
Northern America
10
coniferous
Tropical forests
5
deciduous
Figure 2.5 Wood use in Netherlands with pictures of the species most used (Dutch
names between brackets)
Deciduous wood species are mostly used in furniture, facade carpentry (window frames, doors, etc.)
and civil engineering structures (bollards, scaffolding, alignments, etc.). This wood is predominantly
originated from tropical forests. Historically, in the Netherlands the used tropical deciduous wood is
originated from Indonesia (Merbau, Meranti in construction), Suriname (Basralocus, Demerara
Greenheart, etc. in hydraulic engineering constructions) and West Africa (Azobé in hydraulic
engineering constructions). It is clear, that the origin of these wood species is linked to the Dutch
colonial past. The last decade’s wood from FSC certified tropical forests in Brazil (Massaranduba,
Angelim Vermelho, Cumaru, Itauba, Piquia, etc.) are increasingly used.
3 Coniferous and deciduous wood [3]
There is a clear difference in structure, properties and growth area between coniferous and deciduous
wood species. In general coniferous wood is softer, lighter and less strong than deciduous wood. Also,
generally, the natural durability of coniferous wood is less compared to deciduous wood.
Most coniferous wood species grow between 70 and 50 latitude as a belt bordering the Arctic across
North America, Europe and Asia. Also in the southern hemisphere forests with coniferous wood
species can be found (e.g. in in New Zealand, South Africa and Argentina-Chile, where large areas
are forested with so-called Radiata Pine trees).
Tropical forests (in which deciduous trees are found) are present in the rest of the world: globally in the
temperate, subtropical and tropical zones between the 50 latitude north latitude and 50 South latitude.
Figure 3.1 shows the global growth areas.
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Figure 3.1 Growth areas (something more than 25% of the land surface is forested
worldwide) [3].
Deciduous trees respond strongly to the changing of the seasons. The food intake in the root structure
occur especially in spring time resulting in a relative high growth rate (creating so-called early wood)
and leave creating, through which moisture evaporates. Summer growth conditions for the tree are
more hazardous resulting in slowing down of the growth rate and leave creating, which almost fully
stops in autumn and winter periods. The wood created in summer, autumn and winter periods, the socalled “late wood”, is denser than the wood created in springtime. The “late wood” is visualized by the
so-called annual rings. Consequently, no annual rings develop in regions where the differences
between the seasons are negligible. Deciduous wood trees lose their leaves in winter time; coniferous
wood species, except Larch, do not loose leaves (needles).
The wood structure of deciduous wood species is different from that of coniferous wood species.
There are also similarities. Both are shortly discussed with the help of figures 3.2, 3.3 and 3.4.
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Figure 3.2 Tree trunk cross section and three dimensional trunk views.
Fibre structure
A tree grows in two directions, longitudinally and radially (height and in thickness directions). In
longitudinal direction, the cells split at the top of the branches, the stem and the roots. Actually, these
cells stretch themselves. The thickness growth in the stem, the roots and the branches takes place in
the cambium, a single cell layer between the bark and the sapwood. Growth rings are formed.
The cambium cells remain active throughout the
life of the tree. By cell division to the outside the
inner bark (also called soft bark) is formed. By
cell division to the inside, wood cells (sapwood)
are formed. Usually, the number of cells formed
for the inner bark is much smaller than the
number of wood cells (a tree contains more
wood than bark). Because the tree thickens, the
cambium layer increased in the tangential
direction also (the circumference increases).
Creation of these cells in the circumference is
called dilation. As described earlier in this
chapter, annual rings are formed by the
changing of the seasons
Figure 3.3 Coniferous wood (Pine)
Nutrition from the roots to the tree crown takes place through the outer parts (inner bark to sapwood)
of the trunk: in the sapwood the rising flow takes place, the inner bark the descend flow. Horizontal
moisture transport is possible via the rays.
After some years, the middle section no longer contributes to the nutrition transport. This part, the
heartwood, "dies" after the cells present herein may be filled with natural chemicals to enlarge natural
durability, after which in most species these cells are closed (for durability reasons too).
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In deciduous wood species the organisation of the fibres and fibre groups (tissues) looks much less
uniform than in coniferous wood species. In deciduous tubes, called vessels, develop if cells grow
together in length direction. For deciduous wood, these vessels are an important feature. Softwood
lacks these vessels. In coniferous wood the moisture transport (nutrition transport) from one cell to the
other takes place through (small) lockable openings, called bordered pits (pits that connect cells), see
Figure 3.4.
Figure 3.4 Difference in structure between coniferous and deciduous wood [3].
All important wood properties such as strength, stiffness and shrinkage / swell behaviour are explained
on the basis of the chemical structure and the anatomy, or the structure of the cells and the properties
of the cell wall material. If the cell wall material degenerates due to e.g. wood degradation or fire, the
material and thus the mass and strength properties reduce.
Because wood is a natural product, growth “failures” and imperfections like knots and growth
disturbances (due to geometrical imperfections) can be expected. The wood grain is not completely
straight resulting in strength and stiffness reductions.
Wood is characterized by its fibre direction (longitudinal direction). Due to this typical structure, the
wood anatomy, physical and mechanical properties vary widely in different directions (e.g. the material
strength is higher parallel to the fibre direction than perpendicular to the fibre direction).
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When observing wood with help of an electron microscope, the cells can be seen as an integrated
bundle of fibres. These can be compared to vertical tubes. Under the microscope also the annual rings
can be seen. The fibres (tubes) can be loaded in different directions. The strength and stiffness
properties vary in different directions. This is meant when talking about the anisotropic nature of wood.
In axial direction, or parallel to the fibre direction, wood very strong, both in tension as in compression.
Perpendicular to the wood fibre, on the other hand, wood is less strong and stiff. Compression
perpendicular to the fibre direction may lead to fibre crushing, which does not lead to failure (and is
therefore a safe “failure mechanism). However, tension perpendicular to the fibre direction, wood is
weak. Tension perpendicular can lead to brittle failure which must be avoided (unsafe failure
mechanism). See also Figure 3.5.
The cell walls thickness and the size of the void
cavities varies per wood species. The density of the
cell wall material itself is independent of the type of
wood and is approximately 1550 kg/m³; a high
density of wood means that the cell walls are thick
and robust.
The density of wood is the mass of 1 m³ of wood at
specific moisture content, usually 12% or 15%
(relative to the dry mass, see chapter 5). Generally
Figure 3.5 Directional sensitivity of wood.
heavier wood species show higher values for the
mechanical properties than lighter wood species. That is also logical. A high density means a relatively
high amount of wood fibre material per mm² cross-section and consequently the strength properties
(tensile, pressure and bending) parallel to the fibre directions show relatively high values.
The strength properties generally exhibit a slightly larger variation in softwood than in deciduous wood,
due to the difference in the presence of knots. Generally deciduous wood is also heavier than
softwood, which is reflected in the strength properties. The differences in wood structure and the
dependence of the strength and stiffness on the fibre direction is clearly shown in the strength classes
of wood (tables 6.1 and 7.1).
4 Dendrochronology
Dendrochronology, or tree ring research, is the scientific discipline that deals with dating of wooden
objects or archaeological findings on the basis of recognizable annual rings in the objects (growth
rings). Large parts of the world exhibit seasons. The largest growth occurs in the spring, the smallest
in the winter. As a result, the spring wood (early wood) with large wide cells distinguishes itself, see
Figure 3.4, from the late wood (formed in summer, autumn and winter). This results in a "circular" lines
pattern, also known as annual rings. This enables the age determination of a tree, by counting the
number of rings between the edge and the center (pith). This can easily be done after the tree is cut
down. For still standing trees this can also be done after retaining a wood cylinder form the tree using
a special wood drill, designed for this purpose (increment drill, which is a hollow drill).
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Because trees of the same species from the same area are exposed to the same climatic conditions
exhibit the same pattern in the same growth years; broad annual ring pattern (generally a sign of good
growth conditions), narrow annual ring pattern or abnormalities on the growth ring pattern.
By comparing ring patterns of trees from the same growth area with an overlap in time (two time
periods with an overlap), these time periods can be linked to one period. By linking several periods
together, the age of wooden objects found can be determined which is important for the identification
of remains of old construction and/or archaeological findings.
The annual ring patterns can be captured by studying a slice of wood under a microscope and by
measuring accurately the width (and disturbance) of each annual ring. Based on these measurements,
for several regions of provenance dating calendars are developed.
Thus, dendrochronology is not limited to living, or recently felled, trees. With a piece of
(archaeological) wood containing older unknown annual ring information in addition to known annual
ring information the dating calendar can be expanded. Figure 4.1 shows this principle based on a tree
cut in 1973 whose ring pattern perfectly suits the growth ring patterns in older wood.
Figure 4.1 Use of dendrochronology.
It is essential to realise that the dating calendars are attached to a combination of growth area and
wood species. Consequently, the correct dating calendars must be used. If this is done correctly,
information on the growth areas of the wood used can be obtained. Based on these studies it is
shown that the oak for the Dutch ships during the Dutch Golden Age was obtained from the Baltic
Area (North Estonia, Latvia, Lithuania, Poland, Germany).
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5 Wood properties
The following items are briefly discussed in this chapter
• density
•
wood moisture content
o shrinkage and swelling
o durability; biological resistance
o strength and stiffness
•
load duration
o strength and stiffness
•
volume effects
o strength and stiffness
•
heat properties
o conduction coefficient
o heat capacity
o expansion coefficient
•
electric properties
o conduction
•
chemical characteristics
o chemical degradation
o chemical resistance
5.1 Density
The density of wood varies from ca. 150 kg/m3 (balsa) until ca. 1230 kg/m3 (lignum vitae). The density
is calculated with formula (5.1).
 =
m
[kg/m3]
V
With
(5.1)

density at the wood moisture content 
m
mass at the wood moisture content 
V
volume when the wood moisture content 
It is usual to determine the density at a wood moisture content (  ) of  = 12 %.
The mass of the solid material in the cell wall is, at  = 12 %, approximately 1550 kg/m3 for every
wood species. The proportion of air, the hollow spaces (void cavities), is the reason for the large
differences in density between the different wood species. The amount of void space relative to the
material without void cavities is expressed in the pores share [%] that is calculated using formula (5.2).
 

p = 1001 − 12  [%]
 1550 
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(5.2)
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For three wood species the pore share is calculated in table 5.1.
Table 5.1. Pore share for three wood species.
wood species
density [kg/m3]
Pore share [%]
Lignum vitae (pokhout)
1230
100 −
1230
100 = 21
1550
Spruce
440
100 −
440
100 = 72
1550
Balsa
150
100 −
150
100 = 90
1550
5.2 Wood Moisture Content
The wood moisture content is calculated according to formula 5.3.
=
m − m = 0%
100 [%]
m = 0%
(5.3)
Formula (5.3) shows the definition of the wood moisture content: the mass of the water in the wood,
expressed as a percentage of the mass of the dry wood. Note that wood moisture content values
higher than 100% is realistic. For example: the void cavities in spruce occupy, see table 5.1, 72% of
the total (wood) volume. If these void cavities are filled with water the wood weighs ca. 400 + 720 =
1120 kg/m3 and the wood moisture content  
1120 − 400
100 = 180 % (+12%) .
400
Moisture in wood is partly bound and partly free. Bound water is chemically bound to the cell walls.
Free water is located in the hollow spaces (void). If all positions where moisture can be bound to the
cell walls are occupied, the wood has reached the so-called saturation point (FSP: Fibre Saturation
Point); see also Figure 5.3.
The wood moisture content is governed by climatic conditions, described with the relative humidity
(RH) and temperature, see Figure 5.1.
Figure 5.1 Relationship between the wood moisture content (equilibrium moisture
content) and climatic conditions (Temperature and Relative air humidity).
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The wood moisture content that sets itself in certain climatic conditions, mainly determined by the
relative air humidity, is called equilibrium moisture content. With regard to this equilibrium moisture
content three climate classes are defined as can be seen in figure 5.1.
•
Climate class 1: the equilibrium moisture content is expected not to exceed  = 18 %.
•
Climate class 2: the equilibrium moisture content is expected not to exceed  = 20 %.
•
Climate class 3: the equilibrium moisture content is dominantly higher than 20% (   20 %).
These climate classes are defined in table 5.2 in a bit more detail.
Table 5.2. Climate classes.
Climate class
average
Description
[%]
1
2
3
12
20
>20
Standard indoor conditions
Outdoor, covered structures
- poorly ventilated spaces (indoor)
- fully exposed to outdoor conditions (not covered)
- structures in and underneath water
If the climatic conditions change, the wood moisture content will also change. The change rate of the
wood moisture content depends on the wood species, the surface area of end grain cut (moisture
exchange with the environment through end cut surfaces(parallel to the grain) is much faster than
perpendicular to the grain) and dimensions of the wood. In any case there is a delay between the
changes in climatic conditions and setting the associated wood moisture content (preferably the
equilibrium moisture content). This is illustrated in Figure 5.2; the graph shown in figure 5.2 is called
hysteresis.
Most wood species show a fresh wood moisture
content of 50-60% (moisture content
immediately after felling). There are, of course,
exceptions such as the Poplar, with a fresh
wood moisture content above 100% (a result is
that the water from the wood flows out of the
wood after felling).
Wood under water is completely saturated and
most hollow spaces are completely filled with
water.
Figure 5.2 Hysteresis [4].
adsorption: increasing wood moisture content
desorption: decreasing wood moisture content
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The bound water influences the wood properties
up to a high extend. The properties are hardly
affected by moisture content changes above
Fibre Saturation Point; see figure 5.3.
Introduction to Timber Structures
14
Figure 5.3 Effects of the wood moisture content on wood properties.
5.3 Shrinkage and Swelling
The dimensions of wood react to changing wood moisture content:
•
Wood shrinks when the wood moisture content reduces.
• Wood swells when the wood moisture content increases.
This applies, however, only if the wood moisture content is less than the FSP (Fibre Saturation Point).
Wood shrinks and swells negligible
parallel to the wood fibre direction.
Shrinking and swelling in perpendicular
to the grain directions cannot be
neglected. From the perpendicular to
the grain directions the dimensional
changes are most expressed in
tangential direction being about twice as
big as in radial direction, see Figure 5.4.
Figure 5.4 Shrinkage and swelling in perpendicular
to the grain directions (radial and tangential) [4].
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5.4 Fungal degradation
Wood is a natural (living) material, which serves as nutrition for many mechanisms resulting in
degradation of the wood (structural) properties. One of the best-known effects of this degradation due
to fungi attack resulting in wood rotting. The wood rotting fungi can for sure not live below a certain
wood moisture content. A safe upper limit value is wood moisture content of about 21%: fungi do not
develop in wood when the wood moisture content does not exceed 21% (fungi develops for sure for
wood moisture contents exceeding the Fibre Saturation Point.
5.5 Strength and stiffness
Dry wood is stronger and stiffer than wet wood. In general, this applies, however, only at wood
moisture content below the Fibre Saturation Point (see figure 5.3).
From the above it can be concluded, that wood moisture content values exceeding the Fibre
Saturation Point, result in filling up the void spaces (free water), and almost exclusively causing the
density to increase.
5.6 Load duration
The mechanical wood properties (strength-and stiffness) respond to load duration: long term loading
result in increased deformations. This phenomenon is called creep (increasing deformation under
constant load), shown in figure 5.5.
Figure 5.5 Effect of the load duration (and wood moisture content) on the deformation
of a permanently loaded beam.
On the other hand, the stresses reduce in time when an element is deformed with a constant value;
this phenomenon is called relaxation (decreasing internal stresses under constant deformation).
The strength of wood is reduced for long term loaded elements compared to the strength of short term
loaded elements. This is illustrated in Figure 5.6.
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Figure 5.6 Effect of load duration on strength.
The load duration effects on strength are described on experimentally-based models. One of these
models, the so-called Madison Curve [5], is indicated in Figure 5.6. This is a so-called regression
equation based on many experiments (with which only the average values are accessed). The
Madison curve is important, because the modification factors kmod , involved in construction
calculations, described in formula (6.1), are based on this model.
5.7 Load duration classes
The load duration of loads differ (e.g. the load duration of permanent loading is much longer than of
short term variable loading). Therefore, the loads usually applied are classified in so-called load
duration classes. Table 5.3 shows the load duration classes defined in Eurocode 5 [9].
Table 5.3. Load duration classes.
Load duration class
Cumulative duration of the
characteristic load
Examples
Permanent
Longer than 10 years
Dead load
Long
6 months - 10 years
Storage
Medium-Long
1 week - 6 months
Life loads on floors
Short
Less than 1 week
Snow, wind (The Netherlands)
Instantaneous
Accidental load, wind (Belgium)
5.8 Volume effects
Volume effects are perhaps best to understand on the basis of a loaded chain. If one link in the chain
breaks, the load carrying capacity of the complete chain (the whole system) has disappeared. Actually
this illustrates so-called brittle failure.
Consider the chains in Figure 5.7. The individual links have certain strength. Due to variation in
individual link properties, the "links" are of wood, the individual links vary in strength. This strength
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variation is also shown in Figure 5.7. The chance that besides strong links also (very) weak links are
present increases with increasing chain length: in figure 5.7 chain (a) is most probably less strong than
the shorter chain (b).
In analogy the probability on a weak spot in a large timber element is greater than in a small timber
element. The chain represents so-called brittle failure modes (no redistribution possible: if one link
breaks, the full system fails). For practical calculations, this volume effect is translated into a volume /
height factor. This factor is therefore only applicable to those material properties showing brittle failure
modes. Wood in tension and/or bending show brittle failures and consequently the factor applies to
these material properties. On the other hand, wood under compression shows tough failure behaviour
and consequently the volume Factor (or height factor) is not applicable to compression.
Figure 5.7 Brittle Fracture (virtually linear behaviour until failure).
The values for the volume / height factors are derived from the so-called Weibull distribution (a
probability distribution), displayed with formula (5.4).
Probability [  1 = f for a given Volume V1 and given probability [  0 = f for a given Volume V0 ]
In which
1
= tensile stress level in volume V1 [N/mm ]
0
= tensile stress level in volume V0 (reference volume)
f
= tensile strength [N/mm2]
(5.4)
2
The tensile strength corresponds to a volume V0 = 0.01 m3 which is subjected to a uniform tension
stress. The volume V0 is so-called reference volume. Elaboration of formula (5.4) results in, see [10],
formula (5.5).
d 
 V0 
 
Vh 
 1

 Vh
0,2
  max; d

Vh  ( ( x, y, z) ) dV 
0,2
 f d [N/mm2]
(5.5)
In practice, formula (5.4) is for tension and bending parallel to the fibre direction simplified to a height
factor kh and length factor k l . The length factor is exclusively used for laminated veneer lumber
(LVL); see Chapter 7.
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The fact, that, at least for bending, the volume factor can be reduced to a one-dimensional height
factor is probably best to understand if one realizes that the span (length), the beam height and beam
width are linked to each other. The beam height for beams can approximately be set to:
span
20 to 25
for roof beams
span
15 to 20
for floor beams
5.9 Heat-properties
Heat conduction, heat capacity and expansion due to temperature increase are defined.
The heat conduction is expressed with the conduction coefficient
 W 

. Wood is a material with
 m  K 
different properties in different directions. In radial and tangential direction both perpendicular to the
grain directions, the values for  globally equal. The value parallel to the wood fibre is 2 to 3 times as
large. Wood has, relative to many other materials, a low thermal conductivity. This makes wood a
suitable material in heat-insulating constructions. See table 5.5 in which some values for  are given.
 Joule 
The heat capacity is expressed in  3
 =
m  K 
Dry wood has a specific heat of ca. 1880
 energie 
 m3  Kelvin  .
 Joule 
3
 kg  . With a mass of 500 kg/m , this leads to a heat


 Joule 
capacity of 500 1880 = 940 103  3
 . Stone has a specific heat of ca. 840
m  K 
 Joule 
 m3  K  . At a mass of


 Joule 
1800 kg/m3, this leads to a heat capacity of 1800  840  1500 103  3
 . From this it can be
m  K 
concluded that a wooden wall heats up considerably faster than a stone wall. The wooden wall cools
down, however, also significantly faster. From this it can be concluded, that for energy reduction
spaces which are not constantly heated can better be realised in wood than in stone.
Wood tends to expand when temperature increases. At the same time the wood moisture content
reduces resulting in shrinkage. The effect of shrinkage due to moisture decrease is much larger than
the temperature expansion and consequently thermal expansion is seldom regarded.
For European coniferous wood the following values for the coefficient of thermal expansion can be
used: 0  4 10−6 ; 90;radial  20 10−6 ; 90;tangential  20 10−6
5.10
Electrical conduction
Dry wood conducts electricity poorly. Wet wood on the other hand, conducts electricity well. The extent
to which electricity conducts depends, below Fibre Saturation Point, on the wood moisture content.
Based to this property electrical moisture content measurement devices have been developed; figure
5.8 shows one.
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So-called calibration graphs are determined for different wood species, which must be set before the
measurements can start.
Voltage difference between pegs
initiating an electric current of which
the value depends on the wood
moisture content.
The pegs are driven into the wood,
perpendicular to the fibre direction,
for about 5 to 30 mm.
Figure 5.8 Electrical moisture measurement device.
5.11
Durability
The wood moisture content has a big impact on the durability of timber structures. This is illustrated in
Figure 5.3: provided that the wood moisture content is ca. 21%, no fungi (causes of wood rotting)
develop. Durable detailing and construction is based on reducing the wood moisture content to below
21%.
There are big differences in the so-called
natural durability between different wood
species. General statements in the practice of
"common deciduous wood is more durable
than softwood" and "tropical (hard) wood
species (these are deciduous species) are
much more durable than the most commonly
used uses coniferous wood species" are to a
certain extent true. These statements need,
however, nuances which can be understood
by studying the tree cross section from Figure
5.9.
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Figure 5.9 Tree (trunk) cross section
Roughly spoken, a tree consists out of dead
area, the heartwood, and a living area, the
sapwood, cambium and inner bark (the outer
bark protects the tree, e.g. against forest fires, an consists out of dead material as well).
Before on the border of heartwood and sapwood wood cells are added to the heartwood, many wood
species add components to these cells (e.g. natural toxins), which increase the resistance against
fungal degradation. In addition, the cells are closed (in coniferous wood species the border pits, see
Figure 3.4, are closed). After the addition of the cells to the (dead) heartwood, these cells are no
longer active and the tree itself is no longer capable to protect these cells. Some wood species, e.g.
beech, do not protect the cells before adding to the dead heartwood which explains that the heartwood
of these wood species can be destroyed by fungi completely.
The living part (mainly sapwood) is protected by the tree itself. At the moment the tree is cut, this part
is hardly affected by fungi, insects, etc. On the other hand, the tree did not take precautions to protect
this part. In other words, the sapwood is not protected like the heartwood. Consequently, the sapwood
of each type of wood has a rather low natural durability. The variation in natural durability between
different wood species is therefore only true for the heartwood. Consequently, the durability classes
given in table 5.4 only reflect the heartwood.
The heartwood of different wood species is classified in a so-called durability class based on
experimental research, the so-called "graveyard” test.
.
Five durability classes are distinguished, see table 5.4.
Table 5.4. Durability classes (natural durability).
class
I
Time [years] in ground
contact without fungi attack
≥ 25
II
≥ 15
III
≥ 10
IV
V
≥5
<5
Wood Species
HEARTWOOD
Azobé, Afzelia, Bilinga, Cumaru, Iroko, Piquia,
Masseranduba, Teak
European oak, Basralocus, sweet chestnut, mahogany,
Merbau, Robinia, Wengé, Western Red Cedar
Larch, Douglas Fir, white American oak, Meranti, Pitch
Pine
Pine, American oak, Hemlock, spruce,
Beech, Poplar, Birch, Radiata Pine
Notes: (1) durability is always guaranteed when the wood moisture content does not exceed 21%. In
that case all wood species, regardless the natural durability, can be applied.
(2) under certain conditions wood from durability class III can be applied in an unprotected
outside environment (climate class 3), see table 5.2. From table 5.4 it follows that for this
application the heartwood of deciduous wood species (tropical) is most suitable. For (almost)
vertical elements however, the heartwood of Larch and Douglas Fir (durability class III) are
suitable as well in these conditions.
5.12
Preservation
To prevent the wood from fungi attack it can be treated with toxic substances. This is called wood
preservation. Two of the most well known processes are the so-called "waterborne preservatives",
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very suitable for pine, and “coal tar creosote”. During the waterborne preservatives process copperchromium-arsenic compounds, solved in water, are pressed into the wood. During the “coal tar
creosote” process liquids based on hydrocarbons are pressed into the wood. Both processes are
realized with vacuum-pressure cycles.
For environmental reasons and due to social acceptance, the legal and social opportunities for wood
preservation with toxic compounds are increasingly restricted in recent years.
5.13
Modification
Due to the fact that preservation with toxic compounds is increasingly restricted in recent years, new
environmental friendly alternatives have been developed. The so-called modification techniques, both
thermal as chemical, are well upgraded to industrial scale and used more and more frequently.
5.14
Summary
Table 5.5 shows a number of wood properties discussed in this chapter. A much more extensive table
can be found in the “Houtvademecum” [6] (in Dutch).
durability class (heartwood)
remark
deciduous
0.27
0.11
IV
coniferous
IV
coniferous
III
coniferous
II
deciduous
III
coniferous
IV
coniferous
0.36
European oak
720
15
0.16
0.26
0.12
Silver Fir
Scotch pine
460
12
0.15
0.30
0.13
Oregon Pine (Douglas)
530
14
0.18
0.31
0.13
Edible Chestnut
540
12
Larch
590
12
Norway Spruce
440
12
Steel
tang.
35·10-6
0.17
rad.
20·10-6
12
1880
720
specific heat [J / kg · K]
II
European beech
tang.
λ [W / m·K]*
0.18
moisture content ω [%]
deciduous
density [kg/m3]
V
rad.
species
thermal expansion [mm / K]
shrinkage (at 6 ≤ ω ≤ 20)
Table 5.5. Some wood properties at a glance [6].
0.13
0.14
7850
0.26
0.11
50
12·10
6
*according to ISO 10077-2 for window frames
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6 Structural design calculations
6.1 Strength analysis (Safety)
For structural design calculations strength and stiffness properties of materials used are essential.
Analyses related to safety are carried out to predict the ultimate load carrying capacity (failure level);
for these calculations so-called ultimate limit states (ULS) are recognized. For this purpose so-called
design values have to be defined for which formula (6.1) is used.
fd =
fk
m
With:
 kmod  kh  kl
(6.1)
fd
design value of the strength-property [N/mm2]
fk
characteristic value of the strength-property [N/mm2]
kmod
modification factor, mainly determined by load duration. To a lesser extent determined
by climatic conditions in which the structure is located (to which the wood moisture
content is related).
kh , k l factors, taking structural element dimensions into account (see volume effects in
Chapter 5).
Characteristic value of a strength property
The characteristic strength value depends on the type of wood and the wood quality. Based on these
two identifications the wood is classified into so-called strength classes. The strength classes are, with
characteristic strength values, given in EN 338 [7] for sawn timber and in EN 1194 [8] for glued
laminated timber. Table 6.1 is a short version of the given tables in EN 338.
Table 6.1. Strength classes [7].
Strength class
Ultimate
Limit
States
(ULS)
Seviceability
Limit
States
(SLS)
C18
C24
D30
D40
D50
D70
GL24h
f m,k
2
N/mm
18
24
30
40
50
70
24
f t ,0, k
N/mm2
10
14.5
18
24
30
42
19.2
f t ,90, k
N/mm2
0.4
0.4
0.6
0.6
0.6
0.6
0.5
f c ,0, k
N/mm2
18
21
24
27
30
36
24
f c ,90, k
N/mm2
2.2
2.5
5.3
5.5
6.2
12.0
2.5
fv,k
N/mm2
3.4
4.0
3.9
4.2
4.5
5.0
3.5
k
kg/m3
320
350
530
550
620
800
385
Em ,0, k
N/mm2
6,000
7,400
9,200
10,900
11,800
16,800
9,600
Em,0, mean
N/mm2
9,000
11,000
11,000
13,000
14,000
20,000
11,500
Em,90, mean
N/mm2
300
370
730
870
930
1,330
300
Gmean
N/mm2
560
690
690
810
880
1,250
650
Note: more detailed information follows in Chapter 7.
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Material factor  m
The material factor  m , see formula (6.1), depends on the accuracy with which the characteristic
values of the material properties can be determined. For sawn wood this is depending on the accuracy
with which the wood can be classified into strength classes.
Industrial manufactured products such as glued laminated wood, plywood and Laminated Veneer
Lumber (LVL) exhibit less variation in strength and stiffness properties than sawn wood.
Consequently, the characteristic values of industrial manufactured products can be determined more
accurate. For this reason, the material factors for industrial manufactures products are smaller. Table
6.2 shows the in EN 1995-1-1 (Eurocode 5) [9] given material factors.
Table 6.2. Material factors  m .
material
sawn timber
glued laminated wood
LVL, plywood, OSB
connections
metal plate connectors
Material factor  m
1.30
1.25
1.20
1.30
1.25
For structural calculations using the accidental load combinations, e.g. in seismic design, the material
factors all reduce to  m = 1.0 . Also for calculations in Serviceability Limit States  m = 1.0 .
Modification factor kmod
The characteristic strength and stiffness properties, given in table 6.1, are based on the short-term
strength values, obtained by testing in which failure is obtained in roughly 300 +/- 200 seconds, at a
wood moisture content of 12% (climate class 1 according to table 5.2).
If the load duration differs from the ca. 300 +/- 200 seconds, which is mostly the case, and / or the
wood moisture content differ considerably from 12%, the strength values must be modified.
In this paragraph, the influence of the load duration on the modification factor kmod is analyzed. For
this reason Figure 5.5 is extended to figure 6.1.
Figure 6.1 Effect of the load duration.
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The failure load curve shown in Figure 6.1 indicates, that a constant load   Fu  F1  Fu result in
failure at time t1. If the constant load F1    Fu no failure is expected (at any time). Consequently the
permanent load must be lower than   Fu . However, the total load value, which is the result of
'
permanent load and a (number of) variable load, can exceed the   Fu for a period of time ( t1  t1 )
without failure of the structure.
'
At t = t1 the load value increases from permanent load level to F1 due to an increased variable load.
The strength is not considerably reduced compared to the short duration strength (perhaps this
strength is slightly reduced due to load history and ageing). Consequently the load duration should
be slightly less than t1 and the failure load curve is shifted in time.
Occasional increased load levels F1    Fu are therefore no problem and allowed provided that the
cumulative value of the time that F1    Fu does not exceed t1 (  ti  t1 ). The time spans referred to in
table 5.3 equal these cumulative values.
The time span ti for load level F1 is determined by the load duration of the variable load. The variable
load is the shortest load in the load combination (permanent + variable load). Consequently, for the
analysis of the structure loaded with permanent + variable loading the load duration effects due to the
load duration of the variable loading has to be considered. Since the load duration effects are taken
into account by a modification factor kmod , the kmod values have to be taken from the variable load.
In general: the modification factor value depends on the shortest load in the considered load
combination.
Generally, load combinations consist out of permanent loads and variable loads (long, medium or
short duration) and often the modification factor associated to the medium or short hour loading has to
be taken into the calculations. Additionally for construction with a high level of dead load a
combination considering only the permanent load has to be taken into account
On an average level the value   0.56 (see figures 5.5 and 6.1) On the characteristic value level this
value is higher. Table 6.3 shows a number of values for the modification factor kmod according to EN
1995-1-1 [9].
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Table 6.3. Values of kmod .
Material
Standard
Climateclass
(table 5.2)
Load duration class (table 5.3)
permanent
long mediumlong
short
very short
Sawn timber
EN 14081-1
1
2
3
0.60
0.60
0.50
0.70
0.70
0.55
0.80
0.80
0.65
0.90
0.90
0.70
1.10
1.10
0.90
Glued
laminated
wood
EN 14080
1
2
3
0.60
0.60
0.50
0.70
0.70
0.55
0.80
0.80
0.65
0.90
0.90
0.70
1.10
1.10
0.90
LVL
EN 14374 ,
EN 14279
1
2
3
0.60
0.60
0.60
0.70
0.70
0.55
0.80
0.80
0.65
0.90
0.90
0.70
1.10
1.10
0.90
Plywood
EN 636
Parts 1, 2 and 3
Parts 2 and 3
Part 3
1
2
3
0.60
0.60
0.50
0.70
0.70
0.55
0.80
0.80
0.65
0.90
0.90
0.70
1.10
1.10
0.90
EN 300
OSB/2
OSB/3, OSB/4
OSB/3, OSB/4
1
1
2
0.30
0.40
0.30
0.45
0.50
0.40
0.65
0.70
0.55
0.85
0.90
0.70
1.10
1.10
0.90
OSB
Factors kh and k l
The factors kh (height factor) and k l (length factor) are both "volume factors”, described in Chapter 5.
The volume effect is only considered for those material properties showing brittle failure.
Consequently, the volume effect derived from formula (5.5), repeated as formula (6.2), is exclusively
for tension both parallel and perpendicular to the grain and for bending. For bending and tension
parallel to the grain equation (6.2) is reduced to the factors kh (height factor) and k l (length factor).
d 
 V0 
 
Vh 
 1

 Vh
0,2
  max; d

Vh  ( ( x, y, z) ) dV 
0,2
 f d [N/mm2]
(6.2)
In the denominator of formula (6.2) the volume-integral is elaborated resulting in one single value for
different cases. The values listed in NEN-EN 1995-1-1, 6.4.3 [9], Eurocode 5, are repeated in table
6.4.
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Table 6.4. Height factors k h and length actor k l .
Material
tension parallel to the grain direction and bending
0.2
Sawn timber with k  700 kg/m
 150 
1.0  kh = 

 h 
Glued laminated timber
 600 
1.0  kh = 

 h 
LVL (laminated veneer lumber)
Depending on variations to be determined according to EN 14374
Wood-based panels
1.0
3
 1.3
0.1
 1.1
Note: the reference length for the length factor k l is L = 3000 mm (element length).
6.2 Stiffness analysis (Serviceability)
The serviceability of a realised building must also be guaranteed. Movements / vibrations (for
example: floor vibration) must be limited and large deformations must be avoided. These aspects are
related to the so-called Serviceability Limit States (SLS) for which material properties are given in
e.g. table 6.1.
Generally for calculations in the Serviceability Limit States the average values of the modulus of
elasticity ( Em,0, mean ) and shear modulus ( Gmean ) are used. Depending on load duration, possibly
resulting in creep, and the climate class the expected deformations are calculated. Figure 6.2 shows
the basis for these calculations.
Figure 6.2 Deformations.
From figure 6.2 it follows that
With
u fin = uinst + ucreep − uc
u fin
final deformation [mm]
uinst
the immediate deformation [mm]
ucreep
the creep deformation [mm]
uc
the pre camber [mm]
u net , fin
final deformation minus pre camber [mm]
(6.3)
The creep deformation is dependent on the load duration. The load duration differs for different loads
(e.g. the load duration for permanent loading is much larger than for variable loading). From the
variable load only small part is permanently present. This part is taken into account wit a factor  2
(0 ≤  2 ≤ 1,0), with which the quasi-permanent value of a variable load is calculated, defined in EN
1990 (Eurocode 0) [11]. In principle, the load calculated by multiplying the characteristic variable load
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by the factor  2 results in the variable load which is on average permanently present over the
complete life time of the structure. For the permanent tax follows:  2 = 1,0. For variable loads the
values given in table 6.5 [11] apply.
The quasi-permanent value of a variable load indicates the variable load part resulting in creep
deformation. In chapter 5 - Wood properties, part “Wood moisture content” – it is described, that the
wood moisture content (in response to the climatic conditions) also has an impact on the stiffness and
therefore on the deformations. In practical calculations according to the Eurocodes ([9], [11]) this
dependency is only regarded for the time dependent deformations (creep) by introducing a climate
class dependent creep factor k def . The deformations u fin can be calculated according to formulas
(6.4) to (6.6).
u fin,G = uinst ,G  (1 +  2,G  kdef
(
 (
)
= uinst ,G  (1 + kdef
)
for permanent loads G
) for a variable load Q
 k ) for simultaneous variable loads Q
u fin,Q1 = uinst ,Q1  1 +  2,Q1  kdef
u fin,Qi = uinst ,Qi
0, i
+ 2,Qi
(6.4)
(6.5)
1
def
(6.6)
i
With  0,i = combination value of simultaneous variable loads.  0 and  2 are zero for loading by
wind, rainwater, temperature and snow so no for these situations no simultaneous variable loads are
present. For variable loads on floors usually only one single variable load is prescribed. Overall this
results normally in only one single simultaneously variable load in the combination. However for every
occurring load the final deformation needs to be checked. For determining the final deformation ( u fin )
formula 6.4 to 6.6 can then be simplified in formula 6.7:
(
)
u fin = uinst + ucreep − uc = uinst ,G  (1 + kdef ) + uinst ,Q1  1 +  2,Q1  kdef − uc
(
u fin = uinst ,G  (1 + kdef ) + uinst ,Q1  1 +  2,Q1  kdef
)
(keep this in mind!)
(6.7)
Example calculations are made during the exercises. Values for  0 and  2 (and  1 ) are given in
table 6.5 (based on EN 1990 [11]).
Table 6.5.
 -factors for variable loads.
Load type
a
Description
0
1
2
0.5
0.3
0.5
0.3
Category A
dwellings
0.4
Category B
offices
0.5
a
Category C
congresses, meeting places, theatres, conferences
0.6 / 0.4
0.7
0.6
Category D
shopping
0.4
0.7
0.6
Category E
storage
1.0
0.9
0.8
Category H
roofs
0.0
0.0
0.0
snow
0.0
0.2
0.0
wind
0.0
0.2
0.0
for escape routes like stairs: 0.6, other situations: 0.4
Note: the factor  1 is used to determine the so-called frequent value of the variable loads in case
of fire design calculations. The factor  1 is also used to determine the immediate deformations
due to the frequent value of the variable loads. These deformations are with the load combination
7PPX0
Introduction to Timber Structures
28
according to formula (6.15 b) in EN 1990 [11]. Traditionally there are no requirements for these
deformations in the Netherlands.
Values for k def for a number of wood products are given in table 6.6, based on EN 1995-1-1 [9].
Table 6.6. k def factors for wood and wood-based materials.
Climate class
1
2
3
Sawn timber
EN 14081-1
0.6
0.8
2.0
Glued laminated wood
EN 14080
0.6
0.8
2.0
LVL
EN 14374, EN 14279
0.6
0.8
2.0
Plywood
EN 636
Part 1
Part 2
Part 3
0.8
0.8
0.8
1.0
1.0
2.5
EN
OSB/2
OSB/3, OSB/4
2.25
1.50
2.25
-
OSB
Note: if it is to be expected, that the wood dries under permanent loading after erection, k def shall
be increased with 1,0.
7 Grading: wood quality and strength
7.1 Quality classes and strength classes
Wood is classified into quality classes. For each quality class requirements are set per wood species
related to visual aspects as slope of grain, knots, pith, cracks, deformations, reaction wood, wane, ....
etc. Traditionally, before the wood is traded, the wood is marked showing the origin (possibly, not
always) and from which the wood quality can be read. Figure 7.1 shows some of these marks.
Figure 7.1 Example of marked wood (on the end grain cut of the element).
For wood applications, a distinction must be made between quality classes and strength classes. For
the classification in quality classes, as described above, visual aspects apply. These visual
requirements may also be linked to strength classes. However, for the classification in quality classes
other requirements for the visual aspects apply than for the classification in strength classes.
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29
Quality Classes (not for structural applications: non load-bearing)
The Dutch quality class format is governed by the standards of the KVH 2010 series (quality
requirements for wood), NEN 5461, NEN 5466, .... etc. A distinction is made in four classes: A t/m D.
Class A:
Class B:
Class C:
Class D:
for application with very high demands on the appearance, for example furniture.
for applications with high demands on the appearance, for example constructions with
extra demand on the visual aspects.
common quality, for example timber for regular constructions
for applications with no requirements on the appearance; for example,
non-load-bearing studs and battens or products like pallets.
Strength Classes (for structural applications: load bearing)
For calculations according to EN 1995 (EUROCODE – Wood constructions: Eurocode 5) the so-called
characteristic values of the material properties are necessary. Calculations related to strength and
stability (safety) are carried out in the Ultimate Limit States (ULS) for which the characteristic values
are 5% lower values. Calculations related to deformations are carried out in the Serviceability Limit
States (SLS) for which the characteristic values are the mean values of the modulus of elasticity and
shear modulus.
The characteristic values are taken from a table with strength classes like table 7.1 (extension of table
6.1 – based on EN 338 [7]); the strength class itself is chosen by the structural designer. The choice is
mainly based on availability.
The Dutch strength class format is related to the European and is enshrined in EN 338 [7] for sawn
timber and EN 1194 [8] for glued laminated timber.
Table 7.1 shows the strength classes for sawn timber (C-classes with “C” from Coniferous and
D-classes with “D” from Deciduous). Moreover, the D-classes indicated in table 7.1 are based on the
(relatively strong and stiff) tropical deciduous species, also called hardwoods. Result is, that most
deciduous species from the temperate regions (Poplar - beech - Birch - oak -.... etc.) do not meet the
strength valued listed in table 7.1 and are therefore in classified to C-classes.
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Table 7.1. Strength classes for wood.
Strength class
Ultimate
Limit
States
(ULS)
Seviceability
Limit
States
(SLS)
C18
C24
D30
D40
D50
D70
GL24h
f m,k
2
N/mm
18
24
30
40
50
70
24
f t ,0, k
N/mm2
10
14.5
18
24
30
42
19.2
f t ,90, k
N/mm2
0.4
0.4
0.6
0.6
0.6
0.6
0.5
f c ,0, k
N/mm2
18
21
24
27
30
36
24
f c ,90, k
N/mm2
2.2
2.5
5.3
5.5
6.2
12.0
2.5
fv,k
N/mm2
3.4
4.0
3.9
4.2
4.5
5.0
3.5
k
kg/m3
320
350
530
550
620
800
385
Em ,0, k
N/mm2
6,000
7,400
9,200
10,900
11,800
16,800
9,600
Em,0, mean
N/mm2
9,000
11,000
11,000
13,000
14,000
20,000
11,500
Em,90, mean
N/mm2
300
370
730
870
930
1,330
300
Gmean
N/mm2
560
690
690
810
880
1,250
650
•
A distinction is made between C-classes ("softwood") and D-classes ("hardwood").
•
Any constructive element must be classified in class a strength (no batch approval allowed
based on the approval of random pieces).
•
Wood for structural applications can mechanically or visually be graded. If the wood is
visually graded, in the Netherlands this has, for “softwoods” to be carried out according to
NEN 5499 [13]. The class T1 defined in NEN 5499 equals class C defined in the
“KVH”. The class T2 defined in NEN 5499 equals class B defined in the “KVH”.
•
Visually graded Pine, spruce, larch, Douglas (European) and classified in class T1
according to NEN 5499 [13] meets the requirements for strength class C18.
•
Visually graded Pine, spruce, larch, Douglas (European) and classified in class T2
according to NEN 5499 meets the requirements for strength class C24.
•
Visually graded Douglas (European) and classified in classes T2 according to NEN 5499:
C22
•
Oak (Central European), classified in class B accordance to “KVH”: C20
•
Meranti (red): strength class D24
•
Oak (Polish): D18 / D24 / D30
•
Iroko: D24 (unsorted)
•
Vitex, Robinia, Sucupira vermelho: D30
•
Bilinga: D24 / D50
•
Merbau: D30 / D50
•
Teak, Iroko (sorted) Sucupira, Itauba, amarelo, Piquia: D40
•
Bangkirai, Sapucaia, Angelim vermelho, Denya: D50
•
Masseranduba, Cumaru: D60
• Azobé: D70
Note: the strength classes for the different wood species are based on "Wood hand Strength data
[12], a publication of “Centrum Hout” in Almere, the Netherlands.
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Wood can be assigned to strength classes on the basis of:
1. Visual strength grading
2. Machine strength grading
Both procedures are non-destructive.
Visual strength grading (structural applications)
Traditionally the strength properties are based on visual aspects. Before assigning the strength and
stiffness values to a piece of wood , the visual characteristics must be linked to these values. This
relationship is established on the basis of experimental research (by testing in the laboratory). For the
most common wood species used in structural applications, this relationship is established.
The following steps are performed:
•
The type of wood is determined
•
The Visual characteristics are quantified. In the Netherlands this is for coniferous wood
species carried out according to NEN 5499 (quality requirements for visually graded
coniferous wood species for structural applications) [13]. This standard provides a
classification and associated requirements on aforementioned visual aspects for strength
graded sawn timber (and wood intended for lamellas to be used in glued laminated wood) with
a rectangular cross-section of the wood species European spruce, European larch and
European pine for load-bearing structures
•
On the basis of this classification for solid wood, four strength classes are distinguished: T0,
T1, T2 and T3.
•
These four classes are linked to the European strength class system listed in EN 338 [7] via
the European document (European standard) EN 1912 (wood for structural applicationsstrength classes-allocation of visual collation classes and wood species) [14]. Table 7.2 shows
this link.
Table 7.2. Link between the strength classes determined according to NEN 5499 with the European
strength classes in EN 338.
NEN 5499
EN 338
T0
C14
T1
C18
T3
C24
T4
C30
Machine strength grading (structural applications)
A parameter which can be measured non-destructively, e.g. mass, modulus of elasticity, etc. is used
for strength prediction. This parameter is called “indicating parameter” (IP). Figure 7.2 shows a
relationship between the modulus of elasticity (IP) and the bending strength.
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Introduction to Timber Structures
32
Figure 7.2 Relationship between the modulus of elasticity (IP) and the bending strength
of spruce.
Figure 7.2 is based on bending tests. Figure 7.2 clearly shows that the relationship between the
modulus of elasticity and the bending strength is ambiguous. Given the measurement of
E = 8000 N/mm2, the bending strength can (on the 5% lower and 95% upper levels) vary between
f m = 33 N/mm2 and f m = 78 N/mm2 (more than a factor of 2!). However, the majority of the test results
is close to average making it very unlikely that on the basis of the measured modulus an extremely low
or extremely high bending strength is obtained. Figure 7.2 shows abundantly clear that on the basis of
the indicator (modulus of elasticity) mistakes are made. The extent to which errors are created can be
minimised by considering, besides the modulus, other indicators: for example: density, visible
discolorations, knots, slope of grain, etc. For capturing these indicators devices are developed which
are useful in the grading process (for example, X-ray measurements of the density, knot recognition,
reaction wood, ... etc.; Laser Scan to capture dimensions, slope of grain ... wane, etc.).
7.2 Quality marking
Many different indications are stamped on the wood (one example is given in figure 7.1, which is used
by the timber traders). Marks indicating the non-structural quality, e.g. classes A to D according to the
“KVH”, as described in part 7.1, are generally not stamped on the wood.
From safety considerations it is necessary that the correct strength (and stiffness) values are applied
for structurally applied wood. In one way or another the strength class of any constructive element
should therefore be known and consequently every piece of wood intended for structural use must be
marked properly.
There are two marks available in the Netherlands:
•
KOMO
•
CE
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Introduction to Timber Structures
33
KOMO
KOMO is the quality mark for the construction market in the Netherlands, originally founded by the
industry to distinguish themselves from other players on the market. The KOMO certificate is therefore
an important tool to improve the quality of supplied construction elements. The use of construction
products/elements/materials supplied by companies that do not possess the KOMO certificate is
therefore greatly reduced.
From Law, in this case the building Act “Bouwbesluit” - part of the “Woningwet”), a KOMO certificate
with certificate is not mandatory. The fact that most construction products equipped with a KOMO
certificate is required is the consequence of the legal appointments between parties serving as
contracts between market parties (principal – contractor/supplier).
The law, public law, establishes minimum requirements for the realisation of construction works while
a KOMO certificate is a guarantee that these requirements are generally exceeded.
The requirements to which the product/element/material must meet before the KOMO certificate is
issued are listed in a so-called assessment directive (BRL). All public safety and health requirements
(building Act) are automatically of the BRL. The industry also imposes additional requirements in order
to be able to differentiate (from your colleague – concurrent). The system for developing and obtaining
a KOMO certificate is in principle shown in Figure 7.3.
Figure 7.3 KOMO.
The system shown in figure 7.3 “guarantees” that an element/product/material carrying a KOMO
certificate automatically meets all requirements from public law (“Bouwbesluit” requirements).
Consequently, an element/product/material carrying a KOMO certificate can be applied without any
additional testing.
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Introduction to Timber Structures
34
CE
CE marking is in the (near) future mandatory for all products traded within the European Union. CE is
in contradiction to KOMO mandatory. However, the underlying documents to CE do not set “limit
values” regarding the performance requirements. The products are developed for a well-defined
purpose, e.g. a fire wall, and the documents describe the properties to be determined and with what
accuracy. The limit values are to be set by the individual Member States of the European Union.
Consequently it is possible that a product matches the performance requirements in one Member
State and not in another. Construction products carrying CE mark does therefore not automatically
meet the national requirements.
CE marking is based on the so-called construction products regulation in which the essential
requirements (for example, safety, health, and environment) are described. Taking into account these
basic requirements on The European standardisation Institute (CEN) produces so-called product
standards which take these basic requirements into account. These standards serve as basic
documents for CE marking. For products for which standards are missing (not developed) the
organization EOTA (European Organisation for Technical Approvals) produces so-called ETAG's
(European Technical Approval Guidelines, which serve as a basic document for an ETA (European
Technical Approval). Products for which an ETA has been derived can be CE marked. The national
certification bodies (for example, SKH = Foundation Inspection Wood - “Stichting Keuringsbureau
Hout”) are members of EOTA.
In CEN standards and ETA’s assessment methods and accuracy requirements for the relevant
properties (e.g. fire resistance). The values obtained are part of the CE marking and must therefore be
enclosed with each delivery. If not, it cannot be determined whether the properties meet the national
requirements and the product cannot be applied. This is different for the strength and stiffness values
of a timber element intended for structural use since the strength class is printed (stamped) on these
elements as shown in figure 7.4. These stamps can, after thorough research, even be found on the
timber sold in the DIY market. CE marking on elements for structural use is carried out on the basis of
EN 14081 [15].
Figure 7.4 CE marking on an element intended for structural use.
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Introduction to Timber Structures
35
Figure 7.5 CE.
8 Wood products
Sawn timber and round timber
See powerpoint slides lectures on:
https://canvas.tue.nl/courses/7506
7PPX0 (2018-2) Dimensioning of structures
Glued laminated timber (GlueLam)
See powerpoint slides lectures on:
https://canvas.tue.nl/courses/7506
7PPX0 (2018-2) Dimensioning of structures
Cross laminated timber (CLT)
See powerpoint slides lectures on:
https://canvas.tue.nl/courses/7506
7PPX0 (2018-2) Dimensioning of structures
Laminated Veneer Lumber (LVL or Kerto)
See powerpoint slides lectures on:
https://canvas.tue.nl/courses/7506
7PPX0 (2018-2) Dimensioning of structures
Sheet material
See powerpoint slides lectures on:
https://canvas.tue.nl/courses/7506
7PPX0
7PPX0 (2018-2) Dimensioning of structures
Introduction to Timber Structures
36
9 Literature
[1] Josef Kolb. Systems in Timber Engineering. Birkhäuser, Lignum, DGfH, Switzerland, 2008, ISBN
978-3-7643-8600-4.
[2] Leen Kuiper and Rino Jans (eds). ‘Dutch wood use in image’ ProBos Foundation, Zeist, 2001.
[3] J. Kuipers. ‘Wood and Wood constructions’ Technische Hogeschool Delft, 1979 (in Dutch).
[4] Jan f. rijsdijk and Peter b. Laming. ‘Physical and related properties of 145 timbers, Infomation for
practice’ Kluwer Academic Publishers, Dordrecht/Boston/London, 1994, ISBN 0-7923-2875-2.
[5] Paragraph Foschiand Z.C. Yao. ‘Another look at three duration of load models’ Proceedings of CIBW18/paper 19-9-1, 1986, Florence, Italy.
[6] Klaassen René. ‘Wood vademecum’ Centrum Hout, Almere, 2018.
[7] EN 338. Wood for structural applications – strength classes. Dutch, Delft Standards Institute, 2016.
[8] EN 14080. Timber structures – Glued laminated timber — Strength classes and determination of
characteristic values. European Committee for Standardisation (CEN), Brussels, 2013.
[9] EN 1995-1-1. Eurocode 5: design and calculation of wood constructions – Part1-1: general –
common rules and rules for buildings. Dutch Standardization Institute, 2005.
[10] W. Weibull. ‘A statistical theory of the strength of materials’ 1939.
[11] EN 1990. EUROCODE – basis of the constructive design. Dutch Standardization Institute, 2002.
[12] Wood wiser ' Strength ', a publication of the Data Centre Wood to Almere, located under
http://www.houtinfo.nl/pdf/Houtwijzer%20Sterktegegevens%20van%20hout.pdf
[13] NEN 5499. Requirements for visually graded softwood for constructive applications (in Dutch).
Dutch Standardisation Institute, Delft, The Netherlands, 2007.
[14] EN 1912. Structural timber – Strength classes – Assignment of visual grades and species.
European Committee for Standardisation (CEN), Brussels, 2012.
[15] EN 14081. Timber structures - Strength graded structural timber with rectangular cross section.
European Committee for Standardisation (CEN), Brussels, 2016.
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Part 2: DESIGN OF WOODEN LOAD-BEARING STRUCTURES
10 Introduction
When designing you start with a course draft, which has to be refined. Designing is a multidisciplinary
process. Input from every relevant discipline is necessary. Within the building industry all kind of
construction works within the built environment, usually buildings, and civil engineering objects.
This part of “Introduction to Timber Structures” focuses on buildings in which architecture, urban
planning, building physics, accommodation of installations and structural design are involved in the
multidisciplinary designing process.
The design process needs a systematic approach. The first design at the start of the building process
is extremely important. In this phase, the preliminary design phase, the design effort pays off. Further
on in the design process the effect of efforts reduces. This is illustrated in figure 10.1.
Figure 10.1 Influence on the design in the various phases of the construction process.
During the design phase a (large) number of possibilities should quickly and efficiently be assessed.
Experienced designers use their experience where rules of thumb and/or simplifications (for example,
the reduction of complex structures into easy to understand static structures) play an important role.
The rules of thumb are based on earlier experience. In this part of the course rules of thumb are
presented for dimensions based on [1]. Only profiles with a rectangular cross-section are considered.
Generally it can be stated that:
•
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Bending moments require relatively more material (larger cross section dimensions) than axial
forces. In an economical design the bending, moments are reduces as much as possible. This
means, that the geometry, the position of the neutral axis, follows as close as possible the socalled “line of thrust”. An example of this is the (parabolic) arch structure shown in figure 10.2,
where the bending moments due to an evenly distributed load are zero (no bending
moments).
Introduction to Timber Structures
38
Figure 10.2 Parabolic truss (follows almost the pressure line for evenly distributed
layer.
On the basis of figure 10.2 three hinge arches can be optimised. Since hardly ever an element
loaded in bending is subject to constant moment loading, material is saved by introducing nonprismatic elements. In these cases an option can be to vary the cross section dimensions in
relation to the variation in bending moment. Figure 10.3 shows an example.
Figure 10.3 At the custom profile height gradient moments.
Non prismatic elements must be designed with great care since stresses perpendicular to the
grain are introduced and wood is significantly weaker perpendicular to the grain than parallel
to the grain. Especially cases where tension stresses perpendicular to the grain are introduced
should be avoided (to avoid brittle failure).
•
High narrow cross sections are usually more economical than low wide cross sections. It
should be noted, that this is especially true for glued laminated bending elements, for which
cross sections with
h
 8 are common. Sawn timber profiles are generally stocky (from
b
b x h = 59 x 146 to 69 x 269). For rafters in prefabricated roof elements sawn timber cross
sections are more slender: approximately 30 ≤ b ≤ 40 mm with height ≤ 286 mm).
•
Since higher strength and stiffness properties result in smaller cross section dimensions, it can
be efficient to find an optimal match between these properties and the application conditions.
•
For elements in bending, the most outside fibres are stressed most. Therefore, for glued
laminated timber so-called combined cross sections are produced (so-called GLc – in which
“GL” denotes Glued Laminated and “c” denotes combined) for which the outer lamellas are
chosen from a higher strength class.
7PPX0
Introduction to Timber Structures
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•
From a durability point of view (for prevention degradation due to fungi) projects should be
carried out, so that exposure to wind and weather is minimised. For example, for housing
projects with a number of homes in a row, this means vertical realisation (covered by the roof
structure as soon as possible) instead of the usual horizontal construction, which is the usual
way in the realisation of brick houses.
•
To design a building, we are dealing with a main load carrying structure, a secondary load
carrying structure, foundation, etc. Structures to ensure stability are also needed. The cost of
the load carrying structure is a sum of the costs of these elements. Usually the in between
distance of the main load carrying elements is about 5 meters. For larger distances the
secondary elements should be glued laminated, which is considerably more expensive than a
secondary support structure of sawn timber. However, the cost of the main support system
reduces if the distance is increased. For this reason, it is advisable to choose in between
distances in the range outside 5 meters to 7 meters.
11 Rules of thumb for girders and columns
11.1
Rules of thumb for girders
The main characteristic of structural components in sawn timber (also called solid timber) is the limited
dimensions in terms of both cross section dimensions and length. Usual trade dimensions of sawn
timber elements show a length range from 1.80 meters in ascending steps of 30 cm up to a maximum
of 6,0 meters. However, as mentioned in Chapter 1, it is not expedient to design lengths greater than
5.0 meters because of limited availability resulting in higher costs. In any case it is advisable to inform
on the availability in the market if application of elements with length values > 5 meter is intended.
Extension of the length above 5.0 meters can be achieved by full cross section finger jointing, which is
regularly applied for multi supported beam elements (and purlins) and rafters in roof structures.
The application of sawn timber is limited to relatively small spans in roofs and floors, storey high
columns and facade poles.
Glued Laminated timber on the other hand, is much wider applicable. The dimensions are not limited
by the tree dimensions.
For standard timber floors and roofs a first estimation of the cross section dimensions can be obtained
using rules of thumb as indicated in figure 11.1.
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Introduction to Timber Structures
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Figure 11.1 Rules of thumb for girders (beams in bending).
Note:
The cross section width for the sawn timber beam types given in figure 11.1can be calculated
according to b =
c.t.c.
c.t.c.
for floor beams and b =
for roof beams. (with c.t.c.. = beam
10
15
spacing). The cross section width for glued laminated elements varies from b =
h
h
to .
8
5
In many cases deformation limits are governing the design and consequently the cross sectional
dimensions can be corrected by keeping b  h3 constant. In those cases that strength is governing,
b  h2 must be kept constant.
Example: flat roof with beam span
L = 4.8 m and beam spacing c.t.c.. = 0.6 m
Design bar dimensions
h=
4800
= 250 mm
19
b=
600
= 40 mm
15
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Introduction to Timber Structures
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Cross section dimensions (standard available): h 
3
40  2503
= 208 mm : 69 x 219 mm
69
Of course, after some simplification, the cross section dimensions can be determined by a global
calculation. Girders (or beams) are loaded in bending. A design on strength is carried out in the socalled Ultimate Limit State (ULS) and the cross section height can be determined according to formula
(2.1).
6 Md
mm
b  f m ,0, d
h
With
(11.1)
b
width [mm]
h
height [mm]
Md
design value of the bending moment [Nmm]
f m ,0, d
design bending strength according to equation (6.1). In the Netherlands the strength
and stiffness properties for glued laminated timber are usually taken from the GL24h
strength class: f m,0, d =
24
 0,9 = 17.3 N/mm2. For sawn timber the strength values are
1.25
taken from the C18 or C24 strength classes: f m ,0, d =
18
 0,9 = 12.5 N/mm2 or
1.3
24
 0,9 = 16, 6 N/mm2 respectively.
1,3
Fore uniformly loaded beams on two or three supports the governing design bending moments M d
are given in figure 11.2.
Figure 11.2 Values for M d (design of girders on the basis of strength; ULS).
In many cases, certainly for most beams on more than two supports, deformations are governing the
design. Deformations are assessed in the so-called Serviceability Limit States (SLS). The required
cross section dimensions can be calculated according to formula 11.2.
I
C  qd
1
 b  h3 =
mm4
12
E
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and
h3
12  C  qd
bE
[mm]
Introduction to Timber Structures
(11.2)
42
With
C
coefficient [mm3]. For girders on two and three support points loaded uniformly
distributed with qd , C is given in figure 11.3.
E
modulus of elasticity (average value E0,mean ) [N/mm2]. For glued laminated timber the
stiffness values are taken from strength class GL24h: E0, mean = 11,500 N/mm2. For
sawn timber the strength and stiffness values are taken from strength class C18 or
C24: E0, mean = 9, 000 N/mm2 respectively. E0, mean = 11, 000 N/mm2.
Figure 11.3 Girder (beam) designs based on stiffness (SLS).
For a preliminary design phase the loads can be taken from figure 11.4.
qd =  G  Gk +  Q  Qk
ULS:
 G = 1.08 ,  G = 1.35 (consequence class CC1)
qkr = q fin = Gk  (1 + kdef ) + Qk  (1 +  2  kdef
SLS:
)
k def = 0.6 (climate class 1)
floors
dwellings
 2 = 0.3
Roofs
office buildings
 2 = 0.3
sloped
flat
 2 = 0.0
 2 = 0.0
Gk = 0.50 kN/m
Gk = 0.50 kN/m
Gk = 0.75 kN/m (tiles)
Gk = 0.50 kN/m2
Qk = 1.75 kN/m2
Qk = 2.50 kN/m2
Qk = 0.80 kN/m2
Qk = 1.00 kN/m2
2
2
2
Figure 11.4 Loads.
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43
Example: flat roof with beam span
L = 4.8 m and beam spacing c.t.c.. = 0,6 m
 2 = 0.0 , k def = 0.6 , strength class C24
qd = c.t.c.  (  G  Gk +  Q  Qk ) = 0.6  (1.08  0.50 + 1.35 1.0 ) =1.13 kN/m
ULS
1
1
M d =  qd  L2 = 1,13  4,82 = 3.3 kNm
8
8
b = 44 mm : h 
6  Md
6  3.3 106
=
= 165 mm
b  f m,0, d
44 16.6
(
qkr = c.t.c.  Gk  (1 + kdef ) + Qk  (1 + 2  kdef
 max =
SLS
I
)) = 0.6  ( 0.50  (1 + 0.6) + 1.00  (1 + 0.0  0.6)) = 1.08
kN/m
4,800
= 0, 004  4,800 = 19.2 mm
250
5
L4 qkr
5 4,8004 1.08


=


= 0.0353  109 · mm4
384  max E 384 19.2 11, 000
b = 44 mm : h  3
12  C  qkr 3 12  0.0353 109
=
= 213 mm
bE
44
The calculation in the Serviceability Limit States results in a higher height value. Consequently SLS is
governing. Cross section dimensions (standard available): 44 x 219 mm.
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11.2
Rules of thumb for columns
Columns are loaded in compression. In many application a horizontal load result in additional bending
(e.g. facade post). The rules of thumb for elements loaded in compression and bending are given in
figure 11.5.
Buckling
h=
L
20
bh =
F 
e
 1 + 3  
5 
h
glued laminated timber b  h =
F 
e
 1 + 3  
7 
h
sawn timber
with b  h2 = constant
Figure 11.5 Rules of thumb for elements loaded in compression (and bending) [1].
Example: flat roof with beam span
L = 4.8 m and beam spacing c.t.c.. = 0.6 m,
strength class C24
qd = c.t.c.  (  G  Gk +  Q  Qk ) = 0.6  (1.08  0.50 + 1.35 1.0 ) =1.13 kN/m
1
1
M d =  qd  L2 = 1,13  4,82 = 3.3 kNm
8
8
Additional the element is subjected to a design compression load of Fd = 100 kN. The calculation is
carried out in the Ultimate Limit State (ULS) only.
h=
4,800
= 240 mm
20
e=
M 3.3 106
=
= 33 mm
F 100 103
b=
F 
e  100 103 
33 
 1 + 3   =
 1 + 3 
 = 118 mm
h5 
h  240  5 
240 
The profile 118 x 240 mm is not a commercial size. With b = 121 mm it follows that
h
118  2402
= 237 mm. Commercial size: 121 x 245 mm.
121
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12 Rules of thumb for three-hinge-frames
The in between distance, truss shape (curved/fragmented), the span, the gutter height, and the ridge
height and slope, determine the dimensions of the frame. This is graphically shown in figure 12.1, in
which figure 10.2 (“line of thrust”) plays a key role.
Figure 12.1 Three-hinge kinked frame (left half) and curved frame (right half).
The dimensions of the cross section of three hinge frames are mainly determined by bending
moments. The axial forces are of minor importance.
Figure 12.1 also shows the so-called “line of thrust” for uniform distributed loading. If the system line of
the frame coincides with this “line of thrust” no bending moments develop; the load is transferred by
the frame by axial forces only indicated with "N" in Figure 12.1. This is the roughly case for a parabolic
arch truss.
If the truss system line does not coincide with the “line of thrust” bending moments develop which can
be calculated by multiplying the axial load by the distance between the system line and the “line of
thrust”; e.g. the bending moment in the cranked corner (figure 3.1 – left) equals M = ek  N . The
deviations are indicated in figure 12.1 with " ek " for the cranked truss (left half) and " eb " for the curved
truss (right half). Since " ek  eb " the bending moments developed in the frame with the cranked corner
(left) are larger than in the frame with the curved corner (right). Consequently, frames with cranked
corner require more material than frames with a curved corner. This is reflected in the application of
the rules of thumb given in figure 12.2.
The cross section dimensions obtained by the rules of thumb in figure 3.2 can be transformed into
available dimensions by keeping b  h2 = constant.
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Figure 12.2 Rules of thumb for three-hinge frames.
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13 Structural detailing
Structural detailing is the analysis of all forces on the joint to facilitate these forces to pass the joint.
The most efficient way to achieve this is by contact pressure. In those cases connectors are only
necessary to position the elements and not for load transfer. However, that is not always possible; for
example, the load transfer in truss joints have to be taken care for by mechanical fasteners (or glued
connections) for which mostly dowel type fasteners are used. Figure 13.1 shows a wide variety of
dowel type fasteners available in the market nowadays.
Figure 13.1 Dowel type fasteners.
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In the preliminary design phase the strength of a connection with dowel type fasteners can be
estimated by the equations shown in figures 13.2. and 13.3.
Figure 13.2 Load carrying capacity of a connection with a single dowel type fastener,
depending on the timber thickness (t1 and t2)
Figure 13.3 Rules of thumb for determining the design load carrying capacity of
connections with dowel type fasteners.
Note: n = number of fasteners (parallel or perpendicular to the grain)
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Figure 13.3 (continued) Rules of thumb for determining the design load carrying
capacity of connections with dowel type fasteners.
Note: n = number of fasteners (parallel or perpendicular to the grain)
Example: calculation of the maximum normal force N for the connection below
Step 1: Minimum dimensions:
h  2  3d + (m − 1)  4d = 2  3 12 + (4 − 1)  4 12 = 216 mm
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For table A the following condition should apply: t1  5d = 5 12 = 60 mm → t1 = 60 mm
OK
For table A the following condition should apply: t2  4.5d = 4.5 12 = 54 mm→ t2 = 80 mm
OK
L  2  ( 2  7d + (n −1)  7d ) = (n + 1) 14d = (n + 1) 14d = (3 + 1) 14 12 = 672 mm
Step 2: Determine design force Fv , Rd
Graph A in figure 13.3 Fd = nef  40d 2
n  2: nef = 0,75
Fv, Rd = nef  40d 2 = 0.75  40 122 = 4,320 N per shear plane
Fv, Rd ,tot = nshear plane  nbolts  Fd = 2 12  4,320 = 103.68 103 N
= 103.7 kN
Step 3: Unity Check of the forces in the connection
UC=
N Ed
100 103
=
= 0.96  1.00
Fv , Rd ,tot 103.7 103
OK
Note: check the normal stresses in the timber elements, reduced by the holes for the bolts, as an
additional assignment
Connections in tension are, in the past, also realised with so-called carpentry joints (traditional timber
connections). An example is shown in figure 13.4 (Angera castle, Lago Majore, Italy).
Figure 13.4 Tensile connection using a so called carpentry connection.
The effectiveness of the connection shown in figure 13.4 is low because only a small portion of the
timber element is activated for load transfer (only the compressed area). The effectiveness of the
connection shown in the example on page 50 is much bigger. This is the main reason the so-called
carpentry connections are not applied often nowadays. However, aesthetic reasons and because of
the fact that due to automatic production processes the prefabrication is much faster and accurate
than they used to be, carpentry connections revived up to a certain extend.
Examples where the forces are mainly transferred by contact pressure, the most efficient way of
detailing, are developed for prefabricated roof structures. One possible detail is shown in figure 13.5.
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Figure 13.5 One of the details developed for prefabricated roof structures.
The axial and shear loads, indicated in Figure 13.5, are transferred into vertical and horizontal loads H
and V introducing compression and tension perpendicular to the fibre and rolling shear in the wall
plate. Additionally, bending stresses are introduced into the F-shaped steel element. The screw only
serves to position all elements and for transferring an upward shear load due to wind suction (loading
the screw in withdrawal).
Figure 13.6 shows an example of a post and beam structure where the mechanical fasteners (in this
case: dowel type fasteners) play a key role in the load transfer.
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Figure 13.6 Post-and-beam connection (church in Daarle, Overijssel, The Netherlands).
In principle the beam shear force results in a compression force in the column. The connection has to
transfer this force. The shear force is transferred to the T-shaped steel element by fasteners “A” from
which the force has to be transferred to the column central axis. Obviously an eccentricity, resulting in
a bending moment “M”, develops. The bending moment due to the eccentricity in the connection (in
the case shown in figure 13.6 M = 140 · shear force) is transferred by fasteners “B”, through which de
beam is loaded parallel to the grain.
Since the fasteners “B” transfer load parallel to the fibre direction, the holes for these bolts in the Tshaped steel plate can be oval shaped (with the large oval axis vertically) allowing the timber to shrink
and swell without developing tension stresses perpendicular to the grain. This becomes important
when the distance between the bolts “B” in glued laminated timber exceeds 500 to 600 mm and in
sawn timber 180 to 200 mm (the reason for this difference between glued laminated timber and sawn
timber is that during erection generally the wood moisture content of sawn timber is much higher).
Obviously the bending moment on the column resulting in bending stresses is shown in figure 13.6 as
M = eccentricity · shear force.
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14 Stability
In general, timber construction elements like beams and columns are designed to transfer load in one
plane. To ensure that the load can actually be transferred, the stability of these elements must be
assured. Stability elements are often combined with structures for horizontal wind load transfer.
Walls, roofs and floors are loaded perpendicular to the plane. Forces due to stability load these
elements in plane for which they can be designed properly (by activating the sheet material with which
these elements are usually finished). For walls and roofs, however, often special bracing elements are
added.
For roofs of houses the sheet material is, however, mostly activated. This is illustrated in figure 14.1.
Figure 14.1 Stability provided by the roof sheet material.
Note: the sheet material is loaded due to the wind load on the gable wall.
Legend to figure 14.1: N1
A
Normal force due to the wind load perpendicular to the Gables [kN].
qw = wind load in kN/m2.
force parallel to the Gables needed for moment equilibrium [kN]
The connection between the gable and roof sheet material must be designed on a force which is a
combination of the forces “N1” and “A”. The connection between the individual elements in the roof
must be able to transfer the shear force A and a portion of the load N1.
Bracing systems can be carried out using inclined steel bars, exclusively on loaded in tension (e.g.
the cross bracing system shown in figure 14.4). They can also be realised with inclined timber
elements (also cross bracing) of which half of the elements is loaded in tension and the other half in
compression; see figure 14.3.
No eccentricities should be introduced. This is illustrated in Figure 14.2: it is useful to situate the steel
rods underneath the beams. However, than an eccentricity is introduced resulting in an eccentricity
moment causing the main girder to rotate: figure 14.2 (a). Figure 14.2 (b) shows an example where
this eccentricity, and its negative effects, is overcome.
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Figure 14.2 Connection of the (steel) cross bracing system.
Wooden bracing, whether or not in cross bracing, have the advantage that the elements are able to
transfer both tension or compression resulting in half of the force in the elements (compared to the
situation above, where, due to the steel cross bracing, the elements can be loaded in tension only).
Consequently, the connections can be designed on half of the force as well. Figure 14.3 shows a
cross bracing with timber elements.
Figure 14.3 Cross bracing with timber elements (detail).
Because of the element cross sectional dimensions they need to be notched at the intersection (in the
middle). This notch is a disadvantage regarding the buckling behaviour of the element in compression
(which is, however, supported by the element in tension through the bolt indicated in figure 14.3).
The notches cause an eccentricity, resulting in a bending moment, resulting in deformation of both the
element in tension and compression. Consequently, the deformation of the element in compression
reduces the buckling resistance. The annoying thing is that both the elements in tension and in
compression tend to deform in the same direction.
When assessing the stability in plane of the cross bracing system, half of the element length (see
figure 14.3) can safely be taken as buckling length. In the other direction, perpendicular to the cross
bracing plane, this somewhat more nuanced; in this direction 0.75 times the element length can safely
be taken as buckling length. Due to this larger buckling length, the orientation of the elements with the
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55
largest cross sectional dimension (height) perpendicular to the cross bracing plan is the most effective
orientation.
For halls (many main elements parallel to each other, the best location for the cross bracing is
immediately after the gables. In that case the wind load on the gables is directly transferred into the
roof bracing system. However, gable frames are often not applied. In that case the cross bracing is
shifted away from the gable.
In order to transfer the gable wind load directly into the roof bracing system it is advisable to match the
purlins in the roof structure with the façade poles.
The "width" of the bracing, in figure 14.4 indicated with "L", must be large enough to prevent
overloading of the frames / trusses.
Figure 14.4 Cross bracing (wind loading).
In the bracing section of the building, as shown in figure 14.4, vertical loads develop for slopes > zero.
These loads, in figure 14.4 indicated with V, increase with increasing slope; for a flat roof the effect is
not existing. The effect reduces with increasing “L” (see figure 14.4).
Table 14.1 gives a number of recommendations (rules of thumb) to keep this effect acceptable.
Table 14.1. Minimum “L” (figure 14.4).
 = slope
L
  25o
L  10 m
25    35o
L  15 m
  35o
L  20 m
Note:  L total “width” of the cross bracing; e.g.  L in figure 5.5 is the total “width” of the three
bracing systems. The cross bracings are spread over the roof structure. Choose a maximum
spacing between the cross bracings of about 20 to 25 meters.
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Figure 14.5 Location of the cross bracings.
Cross bracing systems transfer wind loads and support elements which are loaded in compression
and/or in bending. For elements in bending cross bracings are most effective when supporting the
cross section zone subjected to compression. However, timber is a very light weight material also
applied in large span flat roof structures where wind suction is higher than the dead weight of the
structure. Consequently the compression zone is not located near the roof, where it is rather easy to
support, but at the opposite side causing this zone to buckle (this phenomenon is called torsion
buckling). To avoid torsion buckling the cross section has to be supported against rotation. Figure
14.6 shows some possibilities.
Figure 14.6 Support of the cross section against rotation (avoiding torsion buckling).
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15 Literature
[1] W.J. Raven. ‘Rules of thumb for determining of floors, beams and columns in wood, steel and
concrete' Faculty of civil engineering of the Technical University in Delft, 2003.
[2] EN 1995-1-1. Eurocode 5: design and calculation of wood constructions – part 1-1: general –
common rules and rules for buildings. Dutch Standardization Institute, Delft, 2007.
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Annex 1:
Calculation example: Unity Checks of the stresses in a single span
beam
As a calculation example a floor beam on two supports and a span of 10 m will be checked. No normal
forces are taken into account. The loads and safety factors (Consequence Class 1) are:
-
Gk = 4.0 kN/m1 (including dead load of the beam),  g = 1.2
-
Qk = 8.0 kN/m1 (including dead load of the beam),  q = 1.35
For the assessment of the wooden beam material and modification factors are needed to determine
the design value for strength:
-
Partial factor (  M ) for the material properties for glulam:  M = 1, 25
-
Modification factor ( kmod ) for climate class and the duration of the load: kmod = 0,9 (climate
class 1, short term action)
-
Modification factor ( k def ) for creep: k def = 0.6 (climate class 1, glued laminated timber)
-
Factor for variable load:  2 = 0.3 (Category A: dwellings)
Glulam beam with dimensions: width x height = 130 x 680 mm (h: L/16, w: h/5) Strength class GL28h
For indoor conditions the thickness of the lamellas is 40 mm, for outdoor conditions the thickness is 27
mm. A total of 17 lamellas gives a height of 680 mm.
Bending strength (  m , d  f m , d )
The design value of the load is:
qd =  g  Gk +  q  Qk = 1.2  4.0 + 1.35  8.0 = 15.6 kN/m1
The design value of the bending moment is:
1
1
M d =  qd  L2 = 15.6 102 = 195 kNm = 195 106 Nmm
8
8
The moment of resistance:
1
1
W =  w  h 2 = 130  6802 = 10, 019 103 mm3
6
6
The design value of the bending stress is calculated as:
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 m, d =
Md
195 106
=
= 19.5 N/mm2
W 10, 019 103
The design value of the strength is:
f m,d =
f m, k
M
 kmod  kh =
28.0
 0.90 1.0 = 20.2 N/mm2
1.25
Check of the stresses in the Ultimate Limit State (ULS):
Unity Check:
 m, d
f m, d
=
19.5
= 0.97
20.2
≤
OK
1.00
The beam satisfies the conditions with a marge of 3%.
Shear stress (  v , d  f v , d )
The theory of the calculation of the shear force and the associated shear stresses is also based on a
completely elastic behavior of the cross-section. Thus, the shear stress curve is assumed to be
parabolic about the height. For the maximum shear stress
 v ,d
in the heart of the beam, therefore,
applies:
f
3 Vd
 fv ,d = v,k  kmod
2 bh
M
 v ,d = 
For the calculation example the design shear force is:
1
1
Vd =  ( g  Gk +  q  Qk )  L =  (1.2  4.0 + 1.35  8.0 ) 10 = 78.0 kN
2
2
For the shear stresses it follows:
3 V
3 78 103
 v,d =  d = 
= 1.32 N/mm2
2 b  h 2 130  680
The design value of the allowable shear stress is:
f v ,d =
f v ,k
M
 kmod =
Unity Check:
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3.5
 0.9 = 2.52 N/mm2
1.25
 v,d
fv,d
=
1.32
= 0.52
2.52
≤
1.00
OK
Introduction to Timber Structures
60
Deflection ( u fin  wlimit )
(
u fin = uinst ,G  (1 + kdef ) + uinst ,Q1  1 +  2,Q1  kdef
)
→
q fin = Gk  (1 + kdef ) + Qk  (1 +  2  kdef
)
q fin = Gk  (1 + kdef ) + Qk  (1 +  2  kdef ) = 4.0  (1 + 0.6 ) + 8.0  (1 + 0.3  0.6 ) = 15.84 kN/m1. This is the load
including all the creep factors! No adjustments are now needed anymore for the stiffness (elastic
modulus E0,mean ).
The moment of inertia of the gluelam beam is:
I=
1
1
 b  h3 = 130  6803 = 340, 634 104 · mm4
12
12
The final deflection, including creep, now becomes:
u fin =
4
5 q fin  L
5
15.84 10, 0004

=

= 48.1 mm
384 E  I
384 12, 600  340, 634 104
wlimit = 0.004  L = 0.004 10,000 = 40.0 mm
Unity Check:
u fin
wlimit
=
48.1
= 1.20
40.1
≥
1.00
not OK
Adjustments are needed to increase the stiffness to satisfy the conditions for the deflection.
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Annex 2:
Tables Eurocode 5
Table 2.1. Material factors  m .
material
sawn timber
glued laminated timber
LVL, plywood, OSB
connections
metal plate connectors
Material factor  m
1.30
1.25
1.20
1.30
1.25
Table 2.2. Height factors k h and length actor k l .
Material
tension parallel to the grain direction and bending
0.2
Sawn timber with k  700 kg/m
 150 
1.0  kh = 

 h 
Glued laminated timber
 600 
1.0  kh = 

 h 
LVL (laminated veneer lumber)
Depending on variations to be determined according to EN 14374
Wood-based panels
1.0
3
 1.3
0.1
 1.1
Note: the reference length for the length factor k l is L = 3000 mm (element length).
Table 2.3. Climate classes.
Climate class
average
Description
[%]
1
2
3
12
20
>20
Standard indoor conditions
Outdoor, covered structures
- poorly ventilated spaces (indoor)
- fully exposed to outdoor conditions (not covered)
- structures in and underneath water
Table 2.4. Load duration classes.
Load duration class
Cumulative duration of the
characteristic load
Examples
Permanent
Longer than 10 years
Dead load
Long
6 months - 10 years
Storage
Medium-Long
1 week - 6 months
Life loads on floors
Short
Less than 1 week
Snow, wind (The Netherlands)
Instantaneous
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Table 2.5. Values of kmod .
Material
Standard
Load duration class
permanent
long mediumlong
short
very short
Sawn timber
EN 14081-1
1
2
3
0.60
0.60
0.50
0.70
0.70
0.55
0.80
0.80
0.65
0.90
0.90
0.70
1.10
1.10
0.90
Glued
laminated
wood
EN 14080
1
2
3
0.60
0.60
0.50
0.70
0.70
0.55
0.80
0.80
0.65
0.90
0.90
0.70
1.10
1.10
0.90
LVL
EN 14374 ,
EN 14279
1
2
3
0.60
0.60
0.60
0.70
0.70
0.55
0.80
0.80
0.65
0.90
0.90
0.70
1.10
1.10
0.90
Plywood
EN 636
Parts 1, 2 and 3
Parts 2 and 3
Part 3
1
2
3
0.60
0.60
0.50
0.70
0.70
0.55
0.80
0.80
0.65
0.90
0.90
0.70
1.10
1.10
0.90
EN 300
OSB/2
OSB/3, OSB/4
OSB/3, OSB/4
1
1
2
0.30
0.40
0.30
0.45
0.50
0.40
0.65
0.70
0.55
0.85
0.90
0.70
1.10
1.10
0.90
OSB
Table 2.6.
 -factors for variable loads.
Load type
a
Climateclass
(table 5.2)
Description
Category A
dwellings
Category B
offices
Category C
congresses, meeting places, theatres, conferences
Category D
0
1
2
0.4
0.5
0.3
0.5
0.5
0.3
0.6 / 0.4a
0.7
0.6
shopping
0.4
0.7
0.6
Category E
storage
1.0
0.9
0.8
Category H
roofs
0.0
0.0
0.0
snow
0.0
0.2
0.0
wind
0.0
0.2
0.0
for escape routes like stairs: 0.6, other situations: 0.4
Note: the factor  1 is used to determine the so-called frequent value of the variable loads in case
of fire design calculations. The factor  1 is also used to determine the immediate deformations
due to the frequent value of the variable loads. These deformations are with the load combination
according to formula (6.15 b) in EN 1990 [11]. Traditionally there are no requirements for these
deformations in the Netherlands.
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Table 2.7. k def factors for wood and wood-based materials.
Climate class
1
2
3
Sawn timber
EN 14081-1
0.6
0.8
2.0
Glued laminated timber
EN 14080
0.6
0.8
2.0
LVL
EN 14374, EN 14279
0.6
0.8
2.0
Plywood
EN 636
Part 1
Part 2
Part 3
0.8
0.8
0.8
1.0
1.0
2.5
EN
OSB/2
OSB/3, OSB/4
2.25
1.50
2.25
-
OSB
Note: if it is to be expected, that the wood dries under permanent loading after erection, k def shall
be increased with 1,0.
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Table 2.8. Strength classes for wood.
Strength class
Ultimate
Limit
States
(ULS)
Seviceability
Limit
States
(SLS)
C18
C24
D30
D40
D50
D70
GL24h
f m,k
2
N/mm
18
24
30
40
50
70
24
f t ,0, k
N/mm2
10
14.5
18
24
30
42
19.2
f t ,90, k
N/mm2
0.4
0.4
0.6
0.6
0.6
0.6
0.5
f c ,0, k
N/mm2
18
21
24
27
30
36
24
f c ,90, k
N/mm2
2.2
2.5
5.3
5.5
6.2
12.0
2.5
fv,k
N/mm2
3.4
4.0
3.9
4.2
4.5
5.0
3.5
k
kg/m3
320
350
530
550
620
800
385
Em ,0, k
N/mm2
6,000
7,400
9,200
10,900
11,800
16,800
9,600
Em,0, mean
N/mm2
9,000
11,000
11,000
13,000
14,000
20,000
11,500
Em,90, mean
N/mm2
300
370
730
870
930
1,330
300
Gmean
N/mm2
560
690
690
810
880
1,250
650
•
A distinction is made between C-classes ("softwood") and D-classes ("hardwood").
•
Any constructive element must be classified in class a strength (no batch approval allowed
based on the approval of random pieces).
•
Wood for structural applications can mechanically or visually be graded. If the wood is
visually graded, in the Netherlands this has, for “softwoods” to be carried out according to
NEN 5499 [13]. The class T1 defined in NEN 5499 equals class C defined in the
“KVH”. The class T2 defined in NEN 5499 equals class B defined in the “KVH”.
•
Visually graded Pine, spruce, larch, Douglas (European) and classified in class T1
according to NEN 5499 [13] meets the requirements for strength class C18.
•
Visually graded Pine, spruce, larch, Douglas (European) and classified in class T2
according to NEN 5499 meets the requirements for strength class C24.
•
Visually graded Douglas (European) and classified in classes T2 according to NEN 5499:
C22
•
Oak (Central European), classified in class B accordance to “KVH”: C20
•
Meranti (red): strength class D24
•
Oak (Polish): D18 / D24 / D30
•
Iroko: D24 (unsorted)
•
Vitex, Robinia, Sucupira vermelho: D30
•
Bilinga: D24 / D50
•
Merbau: D30 / D50
•
Teak, Iroko (sorted) Sucupira, Itauba, amarelo, Piquia: D40
•
Bangkirai, Sapucaia, Angelim vermelho, Denya: D50
•
Masseranduba, Cumaru: D60
• Azobé: D70
Note: the strength classes for the different wood species are based on "Wood hand Strength data
[12], a publication of “Centrum Hout” in Almere, the Netherlands.
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Annex 3:
Floor beams: ratio span versus beam height (rules of thumb)
Gk = 0, 46 kN/m2
Qk = 1.75 + 0.50 = 2.25 kN/m2
Center to center: 600 mm
u fin = 0, 004  L =
L
250
q fin = Gk  (1 + kdef ) + Qk  (1 + kdef  2 ) = ( 0.46  (1 + 0.6 ) + 2, 25  (1 + 0.6  0.3) )  0.6 = 2.03 kN/m1
q fin = 2, 04 kN/m1
4
L
5 q fin  L
=

250 384 E  I
E = 11, 000 N/mm2
I=
1
 b  h3
12
b = 32 - 59 mm
b = 32 mm
b = 59
wlimit = u fin
wlimit = u fin
mm
L
5 q fin  L
=

250 384 E  I
4
L
5 q fin  L
=

250 384 E  I
384  E  I
L4
=
250  5  q fin
L
384  E  I
L4
=
250  5  q fin
L
4
1
 32  h3
L4
12
=
250  5  2.03
L
384 11, 000 
4439  h3 =
(16, 4  h )
3
L4
L
= L3
L
= 16, 4
h
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 59  h3
L4
12
=
250  5  2.03
L
384 11, 000 
8184  h3 =
( 20, 2  h )
3
L4
L
= L3
L
= 20, 2
h
66
h=
Rule of thumb:
L L
á
15 20
Example
h=
Estimate the beam height:
L
3000
=
= 162 mm
18,5 18,5
→
46 x 171 mm
Check the final deflection in Serviceability Limit State (SLS):
I=
1
1
 b  h3 =  46 1713 = 1917 104 · mm4
12
12
u fin =
5 q fin  L

384 E  I
u fin =
5
2.03  30004

= 10.2 mm
384 11, 000 1917 104
4
L
3000
=
= 12.0
250 250
wlimit = 0, 004  L =
Unity Check:
u fin
wlimit
=
10.2
= 0,85
12.0
≤
1, 00
OK
Check of the stresses in Ultimate Limit State (ULS):
qd = Gk   g + Qk   q = ( 0.46 1.08 + 2.25 1.35)  0.60 = 2.12 kN/m1 (Consequence Class 1)
1
1
M d =  qd  L2 =  2.12  3.02 = 2.39 kNm
8
8
1
1
W =  b  h 2 =  46 1712 = 224 103 · mm3
6
6
d =
M d 2.39 106
=
= 10.7 N/mm2
W
224 103
f m,d =
7PPX0
f m, k
m
 kmod =
24
 0.8 = 14.8 N/mm2
1.3
Introduction to Timber Structures
67
Unity Check:
 d 10.7
=
= 0, 72
f m , d 14.8
≤
1, 00
OK
Wherein is:
=
moment of inertia, in mm4
b
h
=
=
=
modulus of elasticity, in N/mm2
width of the beam, in mm
height of the beam, in mm
L
=
span in mm
Md
=
design value of the bending moment, in kNm
Gk
=
permanent load, in kN/m2
Qk
=
variabel load, in kN/m2 (floor load = 1.75 kN/m2 variabel lightframe walls = 0.50 kN/m2)
q fin
=
representative load for determining the deflection including creep
qd
=
design load, including the safety factors
u fin
=
final deflection (including creep)
wlimit
=
maximum deflection
d
=
design value of the bending stresses, in N/mm2
f m,d
=
design value of the strength, in N/mm2
I
E
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Annex 4:
Rules of thumb for Timber Constructions
COLUMNS AND WALLS
Element
Horizontal en vertical section
Usual height
L
d
between the
Critical factors for
dimensioning
remarks
- compression (
Columns with extensive
loads (several floors)
supports
≤ 4.0 m1
Glulam wooden
column
15 to 20
L
 15 )
d
needs a lower ratio
- compression and
buckling (
≤ 4.0 m1
Posts in light
frame walls
20 - 35
L
d
L
 15 )
d
- compression and
buckling
- thickness for minimal
With nailed plywood for
stability
isolation ( Rc = 4,5
m2·K / W)
center to center usually 400 to 600 mm
(standard plywood dimensions)
Sawn wooden
columns
≤ 4.0 m1
15 - 30
Columns with extensive
loads (several floors)
needs a lower ratio
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L
d
69
FLOORS AND FLOOR BEAMS
Element
section and plan
Usual thickness
[mm] /
height [mm]
Usual span L
[m]
L
L
or
d
h
Critical factors for dimensioning / remarks
Plywood floors
12 - 30
0,3 - 0,9
30 - 40
- deflection
- concentrated loads
- bending strength
Sawn wood floors
16 - 25
0,6 - 0,8
25 - 35
- deflection
- bending strength
With tongh and….
Sawn wood floor
beams
140 - 286
2-5
15 - 20
- deflection
Maximum length: 5,5 m1
Center to center: 305 - 407 - 488 – 610 mm
width: b 
h
3
Strength class C18 / C24
Spruce and pine
Glulam floor beams
300 - 1000
6 - 15
14 - 18
- deflection
width: b 
h
for instability
8
center to center distance approx. 4 to 5 m1
Spruce, larch and iroko
CLT floors
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60 - 400
4 - 12
28 - 32
Introduction to Timber Structures
70
ROOFS AND PURLINS 1
Element
Purlins flat roofs
Sawn wood
section and plan
Usual height [mm]
Usual span
L [m]
140 - 286
2 - 5,5
L
d
Critical factors for dimensioning / remarks
18 - 22
- deflection
Maximum length: 5,5 m1
Center to center: 305 - 407 - 488 – 610 mm
width: b 
h
3
Strength class C18 / C24
Spruce and pine
Purlins flat roofs
Gluelam
300 - 1400
6 - 30
16- 18
- deflection
width: b 
h
for instability
8
center to center distance approx. S 
L L
−
3 5
Spruce, larch and iroko
pre-arched:  
Purlins sloped roofs
140 - 286
2-5
18 - 22
L
150
- deflection
Maximum length: 5,5 m1
Center to center: 305 - 407 - 488 – 610 mm
width: b 
h
3
Strength class C18 / C24
Spruce and pine
Stressed skin panels
100 - 250
3-7
30 - 35
- deflection
- supported by purlins
a  300 - 500 mm
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ROOFS AND PURLINS 2
Element
section and plan
Usual height [mm]
Usual span
L [m]
Trusses without
girders
1200 - 2000
6 - 10
4-6
- Strength of the connections
- Bending in the edge beams
Center to center  600 mm
Trusses with girders
1000 - 3000
6 - 20
5-7
- Strength of the connections
L
d
Critical factors for dimensioning / remarks
Center to center  2 - 5 m1
Truss parallel
1500 - 3000
12 - 25
8 - 10
- Strength of the connections
Center to center  4 - 6 m1
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PORTALS
Element
front view
c.t.c [m1]
h
Usual span L
[m]
Critical factors for dimensioning / remarks
Glulam beam on columns
Portal frame
Three hinged portal frame
Angled corners
Three hinged portal frame
Arched corners
Arched frame
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Annex 5:
Standard timber sizes
Sawn Timber
Scandinavian
Lumber Standard
(SLS)
Other
38 x 89 mm
32 x 100
40 x 146 mm
59 x 146 mm
71 x 146 mm
38 x 120 mm
32 x 125
40 x 171 mm
59 x 156 mm
71 x 171 mm
38 x 140 mm
32 x 150
46 x 146 mm
59 x 171 mm
69 x 194 mm
38 x 184 mm
32 x 200
46 x 171 mm
57 x 194 mm
69 x 219 mm
38 x 194 mm
44 x 194 mm
69 x 244 mm
38 x 235 mm
44 x 219 mm
69 x 269 mm
38 x 286 mm
Glued Laminated Timber (Mayr-Melnhof)
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Cross Laminated Timber
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