L13. Wood Strength and Mechanical Properties
Wood is frequently used as the framing material for homes, farm buildings, and office buildings. But have you ever seen it used to build a skyscraper? Why not?
In this lesson, we are going to talk about some of the properties of wood that need to be considered in ensuring safe building structures. Those of you who are interested in building or engineering may use some of these principles yourself. Even if you don't, after this lesson, you should be able to appreciate what kinds of properties engineers, architects, city building code inspectors, etc, need to consider when building our homes, our decks, and other wooden structures.
We already learned about moisture and rot - a key factor to consider in building materials. Other factors include resistance to heat transfer, fire resistance, and aesthetics. But before we can consider any of that, our first concern is a material's strength properties. Strength is how well a material can carry applied loads or forces without failing (breaking or permanently deforming). The properties of material that determine its strength are also referred to as its mechanical properties.
In this lecture, we focus on the mechanical properties of dimensional lumber. The mechanical properties discussed here are applicable to any material used in building structures such as concrete and steel (the other two main building materials).
By the end of this lesson you should:
- Be familiar with various measures of strength
- Understand how strength and stiffness properties are determined
- Use strength and stiffness formula to estimate mechanical behaviors of wood
- Tell us why the "Prom Photo Deck" failed
Measures of Strength: In What Ways Does Wood Need to be Strong?
Which mechanical property is most critical in any given product depends on the type of loading to which that product will be subjected. In other words, the relative importance of the different strength properties depends on the application.
Wood is considered an orthotropic material, meaning that the strength of wood differs in the longitudinal, tangential, and radial directions, though the radial and tangential directions don’t differ much. (If you don’t remember these directions, you can refresh your memory with figures from the previous lecture). Strength properties parallel to the grain are 20-30 times higher than those same properties measured perpendicular to the grain. You’ll notice that when a beam needs to carry a heavy load, the orientation of the grain is parallel to the direction of force produced by the load.
A number of different strength tests are applicable to lumber and structural composite products. Some common tests for structural materials are presented below. The green and red arrows show the forces being applied.
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Compression perpendicular to the grain - application of a load to the surfaces of a beam or column at a right angle to the grain direction. In railroad ties, crushing (compression) strength perpendicular to the grain is of primary importance because of the weight of the trains.
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Compression parallel to the grain - application of a load to the ends of a column. Compression parallel to the grain is important for poles or columns that carry a heavy weight. The wood in these deck columns is in compression. |
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Static bending - the gradual application of a load to a beam which causes deflection of that beam. The columns of a deck must be strong in compression parallel to the grain. On the other hand, the wooden beams running horizontally beneath a deck must be strong in bending. |
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Shear strength parallel to the grain - the measure of the ability of wood to resist internal slipping of one part upon another along the grain. Think of shear as pulling apart or separating. Force is applied parallel to the grain. Beams need to be strong in terms of static bending, but also in shear. |
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Shear strength perpendicular to the grain - The compressive force is perpendicular to the grain and causes the wood to split along the grain |
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Impact bending or resistance - a measure of the impact load required to cause failure of a beam. This test is accomplished by dropping a given weight over known distances to a beam until failure of the beam occurs. It is useful in determining how well the wood absorbs shock. |
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Hardness - a measure of the resistance of wood to wear. It is determined by the measurement of the load required to embed a 0.444-inch ball to one-half its diameter in the wood. This is also known as the Janka hardness test. A common use of Janka hardness ratings is to determine whether a species is suitable for use as flooring. |
Concepts of Stress and Strain
Wood can undergo a certain load, or stress, before breaking. Stress is a distributed force per unit area, and occurs when a force or load acts on a solid member, such as a load on a column. Stress is often expressed in units of pounds per square inch (psi) or pascals (Pa or N m-2). When stress is applied to a rigid body like a block of wood, distortion of the wood occurs. A large stress will cause the wood to fail and break.
Low stresses will cause the wood to distort (bend or shrink) without actually breaking. The change in length divided by the original length is is called strain. Strain is a unit-less measure. These concepts are illustrated in the figure below. On the left, we have a column without stress, while on the right, the column has been subjected to an 8000 lb force that is compressing the wood. This compression results in a slightly shorter beam.
Figure 1: Illustration of stress and strain in a wood column.
The stress the column is subjected to is equal to the force per unit area, which in this case is an 8000 lb force on a beam that is 2 inches by 2 inches is calculated as:
In this example, the units of stress are pounds (measured of force) per square inch (measure of area), which is shortened to “psi”.
The strain is the ratio of the change in length between the stressed and unstressed column:
Proportional Limit: Elasticity
This stress and deformation is called elastic if when the stress is removed the wood goes back to it's original shape. This “recoverable distortion” is a unique and very useful property of wood.
However, with enough stress (force applied) the wood fibers will break. When this happens, the wood is said to have reached its proportional limit. Having an understanding of the relationship of stress and strain below this limit is important in characterizing how a piece of wood will respond to loads.
At stresses below the proportional limit the relationship between stress and strain can be plotted on a graph. For each stress (Y-axis) there is a corresponding deformation (strain). A line can be drawn through all the points and the the slope of the called the Modulus of Elasticity (MOE) or Young's Modulus. MOE is a value that represents how stiff or rigid the wood is.
For bending, the concepts of elasticity and stress and strain are slightly more complicated than for simple compression. Think of a deck board that is supported on either end (Figure 2). A force applied to the middle of the board will cause compression on the upper face of the board, while the bottom face undergoes tension (stretching). The deflection (Δ) is the distance the board “bows” in response to the applied force. The math is more complex but there is still the relationship between stress and strain used when assessing building materials.
Figure 2: Bending force applied to a beam. When a force is applied to the center of the beam, the upper surface undergoes compression, while the bottom of the board undergoes tension, resulting in a bowing of the board.
The maximum bending strength of wood is expressed in terms of the Modulus of Rupture (MOR). The MOR is calculated from the maximum load — the load that causes the wood to fail AKA break.
Why Do We Care About Stress and Strain?
Understanding the concepts of stress, strain, MOE, and MOR are important because they are used in determining allowable design stresses, or the maximum stress the wood can be exposed to with reasonable assurance that the wood will not fail. This information, in combination with strength properties, gives us the ability to use wood with confidence that it will be able to meet the design stresses.
Now about that prom deck
When we think about the force on a deck (or any floor) we have to design the system to withstand certain forces. The forces in homes are either static loads (sometimes called dead loads) and live loads. The "dead load" is the weight of the structure itself. The live load is the the added load in the form of people or furniture. A dead load for a deck might be 20 psf (lbs per square ft) and the live load is 50 psf. The size of the beams and deck boards used to build the structure must then be able to hold the total of 70 psf of force averaged over the area of the deck. The cause of the prom deck failure was either:
- The concentration of people created a force on the deck that exceeded the maximum load of the deck structure - causing a rupture. Decks are not designed for 13 people to be standing all together in one spot.
- There was some rotting of the deck that weakened the structure.
Summary of Key Strength Properties
To help you keep track of the strength properties discussed, the key strength properties that are tested for in wood are summarized in the table below:
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Strength Properties |
Definition |
How this is important |
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MOE (Modulus of Elasticity) |
Stresses which bend the wood, but where the deformation (bending) is recoverable—take the load away, the wood will bounce back to original shape. Measures wood's relative stiffness. |
Measure of the resistance to bending (when force applied perpendicular to the grain) or compression (when force applied parallel) |
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Compression strength parallel to grain |
Maximum stress sustained by compression parallel to grain (before wood is crushed; stress at the proportional limit) |
Determines maximum load a short post or column will carry |
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Compression strength perpendicular to grain |
Maximum stress sustained by compression perpendicular to the grain (Stress at the proportional limit) |
Important in design of the connections between wood members in a building and the supports for a beam |
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Shear strength parallel to the grain |
Ability to resist internal slipping of one part on another along the grain |
Often determines the load-carrying capacity of short beams |
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Impact bending |
A hammer of a given weight dropped on a beam until rupture occurs or the beam deflects 6+ in. |
Ability of wood to absorb shocks that cause stresses beyond the proportional limit |
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Hardness |
Resistance to indentation (load required to embed a ball into the wood) |
Relates to the resistance to denting (such as in flooring) |
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MOR (Modulus of Rupture) |
Maximum carrying capacity in bending which result in wood failure or permanent deformation |
Determines the load a beam will carry |
The video below is optional, but it demonstrates some of the strength principles we've discussed. At the end of the video you see the stress strain curve.
Factors Influencing Wood Strength
As we know, the strength of wood is different in each direction (i.e. tangential vs radial). Other factors that can influence the strength of a given piece of wood include: specific gravity, moisture content, knots, and slope of grain.
Wood specific gravity: The specific gravity of wood is a measure of how much “solid” cell material there is relative to void volume (or “empty” space). It is equal to the wood’s oven-dried density (AKA how much weigh-able stuff there is from the wood cells relative to the volume of the piece of wood), divided by the density of water at 4°C. The density of water at 4°C is equal to 1 g cm-1. Specific gravity units are mass per unit volume of the wood divided by mass per unit volume of water; an example of units would be g cm-1/g cm-1. Different species of tree have wood of different specific gravity (table 2). The higher the specific gravity, the greater the strength, since there is more “solid” substance to carry the load. Furniture makers are more apt to use certain woods for chair legs. The "stronger" woods they use (such as maple, birch, or hickory) are stronger because they have a higher specific gravity.
Table 1: Specific gravity and strength properties important for consideration in building furniture for different tree species in the US. Note that higher values of specific gravity correspond to higher MOE and compression strengths, meaning stronger furniture.
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Tree Species |
Avg. Specific Gravity (oven-dry sample) |
MOE (106 psi) |
Compression Parallel to the Grain |
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White Ash |
0.60 |
1.74 |
7,410 |
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Yellow Birch |
0.62 |
2.01 |
8,540 |
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Cottonwood |
0.34 |
1.1 |
4,020 |
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Red Maple |
0.54 |
1.64 |
6,540 |
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Black Spruce |
0.42 |
1.61 |
5,960 |
Moisture Content: As wood dries below the fiber saturation point, most strength properties increase. Living trees are very strong, needing to sustain compression forces from the weight of the tree, as well as needing to have extreme bending ability in order to deal with wind. When wood is wet, the cell wall fibers are more pliable. When they dry out, they become more rigid and harder, which is the quality we want when we use wood as a building material. You can think of this like an orange peel. When it's on the wet orange, it is soft and pliable, but once you take the peel off, it becomes hard and rigid.
Knots: If you remember from our lesson on plant growth, knots form when a branch dies or is removed and the base of the branch becomes enclosed by subsequent layers of trunk wood. The direction of the grain in a knot can be completely different than that in the rest of the wood. This change in direction in the grain represents a decrease in wood strength. In fact, the effect of a knot is often considered to be equivalent to that of a hole.
Slope of grain: Wood is strongest along the alignment parallel to its grain. Processed boards don’t always have a straight grain, however. This can occur when the tree itself has a spiral grain, or due to improper processing of the lumber. The slope of the grain refers to how straight the grain is, relative to the outside of the board. Ideally, we want the grain to be in a straight line from each end. If it is more slanted, the wood has a higher slope of grain, and will not be as strong. In professional baseball, there are restrictions on the slope of grain of bats, requiring the grain to be almost perfectly straight from the handle to the end. This rule was enacted because bats with non-straight grains can fail dangerously Links to an external site..
Summary
Wood is a strong material used often in construction. Additionally, its ability to bend or flex without breaking makes it unique compared to other building materials, such as concrete. However, wood as described here (think a single 2x4 piece of lumber), isn’t as strong as other building materials, like concrete or steel—which is why we don’t see it used as the framing material in projects that experience really high loads, like those found in skyscrapers. New technologies and methods of gluing these individual boards together as cross-laminated timber are changing this though. We'll talk more about new technology in our next lecture.