Wood Engineering Basics
- 1 Introduction
- 2 Wood Structure
- 3 Shrinkage
- 4 Moisture Content
- 5 Shrinkage Calculations
- 6 Wood Design Manual
- 7 References
Wood has been used as a building material for many years. It is a beautiful, natural and sustainable material with a high strength to weight ratio, making it ideal for building purposes. There are existing wood structures that date back to the 7th century, attesting to its durability. There are some disadvantages to using wood in construction however, including the anisotropy of the material as well as its susceptibility to fire, termites and water. Understanding the basics of wood is essential to successful building design.
When talking about the properties of wood, it is important to be able to categorize the different types of wood. Tree species can be classified as hardwood or softwood. The difference boils down to the cell structure but in appearance, hardwood trees have leaves that fall off in the winter and softwood trees have pine needles.  Some examples of hardwood trees include maples, oaks, birches, elms, and walnut trees. Some examples of softwood trees are spruces, pines, firs, cedars, hemlocks and larches. Hardwoods are usually used for furniture, decks and flooring whereas softwoods are typically made into lumber. Hardwoods tend to take longer to grow, have a higher density, and cost more than softwoods.
Regardless of the species of tree, wood grows in circumferential layers around the tree trunk . Each layer represents a year of growth and consists of early wood (spring wood) and late wood (summer wood). The age of a tree can be found by counting the rings on the cross section. When looking at the cross section of a tree trunk, three main sections can be found . The innermost layers of rings are called the heartwood . The heartwood is the inactive part of the tree, meaning that sap no longer flows through these layers. The layers in the heartwood are the darkest in colour in the cross-section and are being used as the main form of support. These layers have a lower moisture content due to their inactivity. The middle section is called the sapwood. These rings are lighter in colour than the heartwood, and more moist. The main tree activity occurs in these layers, so this is where sap can be found. The high moisture content in these layers result in greater shrinkage during drying. The outermost section is called the bark . The bark consists of the cambium as well as the inner and outer bark. The cambium is the layer between the bark and the sapwood and this is where the new layers of sapwood are produced. The inner bark and outer bark are there for protection purposes.
The behavior of wood can be more clearly understood when looking at the microscopic wood cell. In each tree, there are millions of wood cells that are aligned longitudinally along the trunk of the tree . These cells vary in length and width and are different in hardwoods and softwoods. This is where the main difference occurs. Both have a cell width of 0.02-0.04mm but softwood cells tend to be much longer, ranging from 3-5mm compared to 1mm in hardwood. A wood cell is tubular in appearance and consists of secondary walls and a primary wall. All of the cells are held together by a lignen binder. The cell axis is in line with the direction of the tree (longitudinal) and all of the walls are configured to this axis. Each cell wall is composed of microfibrils. The innermost layer of the secondary wall, is aligned parallel to the cell axis. The middle layer of the secondary wall is the thickest and is essential to the strength of wood. The microfibrils in the middle wall are aligned at an angle of 15 degrees from the longitudinal axis. This allows for tensile stress resistance. The outer layer of the secondary wall is aligned perpendicular to the cell axis 
As mentioned, wood cells are much longer in one direction than the other. The texture along the longitudinal axis is referred to as the grain. The difference in lengths attribute to varying strengths in different directions. Wood strength is often talked about both parallel and perpendicular to grain for this reason.
There are many ways to divide a tree into usable wood. The tree can be split into dimensional lumber, made into specialty lumber, or made into an engineered wood product. The manufacturing process for each of these types of wood members are different, but depend on the size of the tree being cut.
Lumber is the term used to describe pieces of wood with a square or rectangular cross-section that have been cut out of the tree longitudinally. The pieces are then surfaced, meaning the edges are smoothed and straightened . The naming of the lumber is based on the dimensions of the cross-section prior to surfacing and as a result the actual dimensions of sold lumber are slightly smaller than the name of the piece. There are three standard categories of lumber that are used to distinguish between cut pieces, and the categories are determined by the nominal thickness of the piece (thickness before surfacing). The three categories are boards (thickness less than 2 in), dimension (thickness between 2-5 in) and timber (thickness greater than 5 in). The number and type of pieces produced from one tree depend on the age of the tree and the way that it is divided.
It has become more popular to use modified lumber as a building material. One example of this is structural-glued dimensional lumber. These products can be glued by the edges, faces, or by finger joints. Structural-glued lumber is typically made out of wood with a low moisture content. Finger jointed lumber is made by cutting holes into the end of a piece of lumber. The end product resembles the shape of fingers. The pieces are connected by gluing the fingers to the holes of another piece .
Engineered Wood Products
Engineered wood products are products that have undergone a process to provide better or more predictable properties. Types of engineered wood products include:
- oriented strandboard
- Parallel strand lumber (PSL)
- Laminated Veneer lumber (LVL)
- Laminated strand lumber (LSL)
- Cross laminated timber (CLT)
In wood engineering there are three kinds of shrinkage that are considered. When green wood dries out it shrinks in these three directions however the shrinkage is larger in particular directions. The three directions in which shrinkage occurs in wood are the tangential, radial and longitudinal. The image below of a cross section of wood shows the radial and tangential directions of shrinkage. As for longitudinal shrinkage, it is along the length of the member if it is cut as shown below. Shrinkage also depends on the cut of the wood in question. Many types of warp can be caused by shrinkage such as bows, twists, crooks and cups. Generally speaking, warp in members can be prevented by controlled drying, proper piling and moderately controlled moisture content in an environment. Depending on how wooden members are attached, shrinkage in wood may cause cracking, failure as well as gaps in the wood. For these reasons it is important that shrinkage be considered in wood design where appropriate.
This is the largest shrinkage that occurs in wood. It is represented as a percentage in the moisture content equation below.
Radial Shrinkage is a critical shrinkage in wood engineering although it is not at the magnitude of tangential shrinkage. Radial shrinkage occurs in a way that makes the circle of the wood want to decrease in size. This radial or hoop stress will cause tangential cracking if the drying process is too fast.
Longitudinal shrinkage is the shrinkage that occurs along the length of a member. This type of shrinkage is by far the least critical when it comes to wood design. When consulting a moisture content versus shrinkage graph, longitudinal shrinkage is approximately a quarter of the value of tangential shrinkage. In some cases, primarily simplification purposes, longitudinal shrinkage is assumed to be zero.
For shrinkage it is always important to remember: $ Tangential > Radial >> Longitudinal $
Calculation of Moisture Content
Moisture content is another concept that is linked to shrinkage. Moisture is calculated as followed:
where $ W water = W wet wood - W oven dry wood $
and $ W - weight $
Fiber Saturation Point
The fiber saturation point of wood occurs when the wood fibers or cells contain as much water as they can hold before the inner cavity of the cells fill with water. This point is at approximately 28% water content. When wood is above fiber saturation point excess water fills up the inner cavity of the cell, this is the case when the tree is still living. At any point above fiber saturation point there is no change in the size of the wood cells or of a total member of wood. When wood falls below this fiber saturation point shrinkage begins to occur. Oven dry condition is a condition below fiber saturation point where no water is present in the wood. One a graph of water content, oven dry would be found at the 0% region. Green dimensions are those dimension measured at fiber saturation point (FSP) or above fiber saturation point. Dry dimensions are those dimensions taken at oven dry conditions. Naturally due to shrinkage the dry dimensions and green dimensions will be different, where the green dimensions are larger than the dry dimensions.
Equilibrium Moisture Content
Equilibrium Moisture Content or EMC is a moisture content which depends on the temperature and humidity of the surroundings where a specimen of wood is present. Wood will typically cycle with this equilibrium state depending on the variation of moisture contents.
To calculate shrinkage due to a change in moisture content the following equation can be used:
$ S=DMC $
where $ S $is the shrinkage in mm,$ D $ is the initial dimension subjected to shrinkage in mm,$ M $is the change in moisture content in % and $ C $is the shrinkage coefficient in 1/% (in shrinkage per percent change in moisture content--each species has a different c value and each direction has a different c value)
For design purposes we can assume C in the radial and tangential directions be 0.002/% which avoids having to know the grain orientation. As mentioned above for longitudinal, C may be assumed to be 0. However, for design in order to have a conservative design C for longitudinal can be assumed to be 0.00005/%.
Wood Design Manual
Wood is one of the most environmentally friendly building materials. Its manufacture is green (it grows naturally), it is renewable, and quite abundant in Canada. The updated Ontario Building Code, which took effect as of January 1st, 2015, now allows residential and office buildings up to six storeys to be built with wood frame construction.  This section will describe how to use the 2010 Wood Design Manual published by the Canadian Wood Council, which is adapted from the Canadian Standards Association standard CSA-O86-09 and the National Building Code of Canada. 
The handbook covers design requirements for lumber and glued-laminated (Glulam) members, working in tension or compression. It gives the predicted strengths of different species and sizes of elements, and factors for the strength reductions or increases for treated wood, different service conditions and load durations, systems of members working together and built-up member specifications. The first 11 sections in the book provide tables for the simple initial selection of members based on strength and size requirements, whether they are compression or tension members, shear or bearing walls, and even fasteners. There you will find many examples and diagrams on the calculations required to determine the strength of these members. There are also sections on applications of wood in engineering, fire safety procedures, and information about the grading and specifications on wood members and fastenings.
After these sections, you will find commentary on CSA O86. This commentary discusses many of the clauses found in the standard in further detail, to clarify any misunderstandings or to give further information on the design provisions. Following the commentary is a reprint of the CSA standard, which sets out the design process and requirements for all wood structures, member by member.
Limit States Design
The handbook takes a limit states design approach when deriving their design methods. This approach designs all members within an acceptable range of their limit states, which include ultimate limits such as the absolute failure of the member, and serviceability limits such as exceptional deflections and cracking. The approach ensures that the resistance of any member exceeds the load which is expected to be applied to it. This load is calculated through a series of factored load cases, where the most critical case is selected for design. The load cases can be seen in the tables below, taken from page 7 in the manual:
Where D is the expected dead load, L is the live load, W is the wind load, S is the snow load and E is the earthquake load.
Types of Wood Members
There are about 140 species of trees in Canada , which can provide a broad range of strengths and degrees of stiffness. The Wood Design Manual deals with many different species and grades of lumber and Glulam members, and lumps them into categories as will be laid out below.
In terms of Canadian Lumber, there are four categories of species combinations designated in the manual. The strongest group of species includes the Douglass fir and the western larch, and is designated by the identification code of D Fir-L. The next category is Hem-Fir, and includes Pacific coast hemlock and amabilis fir trees. The third, and possibly largest, category is made up of all species of spruce trees (except Sitka spruce), Jack and lodgepole pines, and the balsam and alpine firs. These trees have the second lowest strength of the categories but are more economical, and are designated by the stamp S-P-F. The final species combination is the weakest, and is made up of any other Canadian species, designated by the stamp "North Species". An example of the S-P-F identification stamp from the manual can be seen in the image to the right.
These species are then graded for their applicable uses and strengths. Dimension lumber (for joists and planks) and timber is graded into Select Structural (SS), No.1, No.2, or No.3, SS being the strongest. Then there are also stud, construction and standard grades for dimension lumber meant for light framing and stud applications.
The Glulam timber stress grades are very similar to the sawn lumber, but are split into three categories: Douglas Fir-Larch, Spruce-Lodgepole Pine-Jack Pine and Hem-Fir and Douglas Fir-Larch. Each of these categories have members designed for specific applications. An example grade annotation is 20f-E. The f denotes a member meant to be strong in flexure, while a c would denote a compression member, and t a tension member.
The selection tables, as introduced above, are a useful tool in the initial design phase of any member. There are tables for each type of member, but this section will describe how to use the selection tables for the two main types of members: compression and tension. Once you have used the limit states design approach to predict the factored load on your member, you may use these tables to select a member to begin design calculations with.
The tension tables are the most straight forward, so we will begin with those (Section 4 - Tension Members). The tables for sawn lumber and timber can be found from pages 163 to 167 and for Glulam on pages 168 to 169. The Tension Member Selection Tables are arranged by Species and by grade for sawn lumber, and by stress grade for Glulam. An example of one of these tables can be seen in the figure to the right. This table displays the unfactored tensile resistance of different grades and species for members with a smaller dimension of 89 mm. For example, if the member is required to resist a tensile force of 180 kN, one might choose to use a S-P-F element of dimensions 89 mm x 286 mm, or a D.Fir-L. element of dimensions 89 mm x 184 mm. The choice between these members is left up to the designer, and whether the design constraints are concerned with cost efficiency, or size efficiency. The Glulam tables work in much the same way. One very important thing to remember while using the selection tables, however, is that they are just a starting point. The resistances calculated are unfactored, so the designer must use the CSA O86 standards to calculate the actual resistance of the member on a case-by-case basis.
The Compression Member Selection Tables are also commonly used as a preliminary design tool, and can be found on pages 121 to 132 for sawn timber and pages 133 to 139 for Glulam members. These tables work in much the same way as the tension tables, with just a few more parameters. Firstly, it is important to understand that the governing failure mode of a compression member is not crushing, but buckling. Because of this buckling effect, the strength of the member does not depend on its size, but on its slenderness. The slenderness ratio of any column can be calculated as follows (Wood Design Manual 2010, page 34 in the gray pages):
If you have two members with the same cross-sectional area, the longer member will be more slender than the shorter one, which will cause it to buckle more easily. For this reason, one of the parameters in the Compression Member Selection Tables is the length of the member. An example of a Glulam Column Selection Table for 365 mm members is shown in the figure to the right. The table is split down the middle for two different stress grades, a Spruce-Pine 12c-E, and a D.Fir-L 16c-E. Another noteworthy difference from the tension tables is the fact that each member size and length has two given compressive resistances, instead of one. This is because, as can be seen in the formula for the slenderness ratio, the slenderness of a column depends not only on its length, but also on its corresponding depth. Since most members are not square they will have two different slenderness ratios, depending on which axis you're looking at. When selecting a compression member for a column, both axes must be able to withstand the predicted loading, represented by Prx and Pry.
- Hardwood vs. Softwood. Web. http://www.diffen.com/difference/Hardwood_vs_Softwood.
- The Nature of Wood: Wood Grain. Web. http://workshopcompanion.com/KnowHow/Design/Nature_of_Wood/1_Wood_Grain/1_Wood_Grain.htm.
- The Structure of Wood. Web. http://www.doitpoms.ac.uk/tlplib/wood/structure_wood_pt2.php
- Heartwood or Sapwood?. Web. http://woodworking.about.com/od/typesofwood/p/Heartwood.htm.
- Inner and Outer Bark. Web. http://www.botgard.ucla.edu/html/botanytextbooks/generalbotany/barkfeatures/innerandouterbark.html.
- Straube, J.Wood. University of Waterloo. Web. http://www.civil.uwaterloo.ca/beg/CE265/Wood.pdf.
- How Lumber is Made. Web. http://www.madehow.com/Volume-3/Lumber.html.
- Structural Glued (Finger Jointed) Lumber. Web. http://www2.wwpa.org/TECHGUIDE/FingerJointed/tabid/861/Default.aspx
- Wood Design Manual 2010. Ottawa, ON: Canadian Wood Council (2010).
- CodeNews Issue 232 - Amendments to Ontario’s Building Code Allowing Mid-Rise Wood Frame Buildings. Ontario Ministry of Municipal Affairs and Housing, (2014).
- Rowe, J. S. Trees. The Canadian Encyclopedia, (2013).