Introduction
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In the video, we investigate timber posts and their carrying capacity. The video starts with an explanation of the general failure modes of columns. Further emphasis is cast on buckling and the Euler critical buckling formula. The buckling formula is investigated and explained with simple and intuitive examples. The video concludes with the calculation of the carrying capacity as per the design codes and compares that with the analytical capacity obtained for a perfect column.
References:
[1] J. M. Gere and B. J. Goodno, Mechanics of Materials, Cengage Learning, 2013.
[2] J. Dinwoodie, Timber: Its nature and behaviour, London: BRE, 2000.
[3] Canadian Wood Council, Wood Design Manual, Canadian Wood Council, 2017.
[4] J. Porteous and A. Kermani, Structural Timber Design to Eurocode 5, Blackwell Publishing, 2007.
Content
As you can imagine, the capacity of a wooden post is not a single number that you can write down and memorize, but it’s rather design-specific and changes based on the loading conditions.
In this video, we will see what these limits are and what has the biggest influence on them.
We will investigate a 4 by 4 timber post, whose dimensions are 89 by 89 mm., But to understand the limits of the carrying capacity of a column.
First, we need to know how columns actually fail.
In general, a column can fail in two main modes: buckling or material yielding and crushing.
Material.
Crushing can be seen only on short and stocky columns.
This failure consists of the wood grains being compressed to the point where they start to wrinkle.
Locally.
Buckling, on the other hand, is a sudden lateral failure caused by a loss of stability.
Buckling may sound like a complicated phenomenon, but in fact it is very intuitive.
We all have intuitive knowledge as to what would make an object susceptible to buckling.
This can be illustrated by compressing a ruler.
If the ruler is short, it can carry a significantly higher pressure before it breaks.
Consequently, a long ruler is much easier to bend or buckle under even a small compressive load.
That is the longer the column the weaker it becomes.
This same intuition also applies to the design of columns that carry dozens of floors and thousands of tons in the real world.
This intuitive idea was turned into sound mathematics by the Swiss mathematician Leonhard Euler and has ever since been used in the design of columns.
[ 1 ] Here in this video, we will reach this same equation by simply using our intuition.
As we already figured out, the length of the column is inversely proportional to the column’s capacity.
To reiterate the longer, the column is the less load it can carry.
Furthermore, we know that the stiffness of the material has to also play a role, because stiffer materials are harder to bend.
The same goes for the shape of the column, whose effects are captured by the moment of inertia of the column.
If you want to learn more about the effects of the shape check out our previous video on “the secret of the I-beam”., Going back to the equation, we can see an additional pi squared term that arises from the solution of the differential equation and is related to The shape of the buckled curved, which follows a sinusoidal function., The last remaining factor is related to the end conditions of the column, which we will assume to be pin-connected.
This means that the column is held in place, but is allowed to rotate about its ends, which makes the column more susceptible to bending.
Fully fixing the ends would increase the carrying capacity of the post, however, providing a full moment fixity is difficult to achieve when it Comes to wood, connections.
Semi-rigid connections are much more common, but for simplicity.
We will assume no rotational stiffness in the connection, which would also produce a conservative estimation of the load-carrying capacity.
Based on Euler’s Formula.
The only parameter that is not fixed and can affect the load-carrying capacity is the length L.
Theoretically, speaking as the length gets smaller, the load capacity will increase indefinitely.
But of course, this is not the case because at some point the compressive capacity of the material itself starts to govern the strength of the column rather than the buckling being the governing factor.
For that reason, the Euler’s curve is capped at the limit strength of the material.
Failure in the material takes the form of local budging, crushing or wrinkling of the wood grains.
The right side of the curve corresponds to the global buckling of the entire member.
In essence, a loss of stability.: If we lived in a perfect world, our analysis would have stopped here.
However, wood is far from a perfect material and neither is our construction practice.
Unless the compressive load is applied perfectly at the centroid of our column.
The Euler formula is not exactly correct.
Applying the load, even with a slight eccentricity, creates an undesired bending of the column that lowers its capacity., For example, applying the load only 10mm off-centre lowers the capacity by nearly 50 % when it comes to timber posts., But that’s only imperfections due to construction.
The wood itself has many irregularities, such as knots, warping, irregular grains and so on.
Furthermore, wood suffers from creep and rotting, which are significantly worsened if the member is exposed to a humid environment.
Codes and standards around the world.
Try to simplify these conditions with factors that engineers could select from a design manual.
These factors and equations are mainly based on the Euler Formula.
However, they are modified to fit empirical data.
As an example, we used the Canadian Wood Design Manual for comparison to the theoretical equation of a perfect wood., The Eurocode 5 [ 4 ] and American Wood Design Standard conclude similar results.
We assumed a 4 by 4 spruce-pine-fir timber post of a standard grade.
For the viewers outside of North America, that is an 89 by 89 mm square post, with a compression strength parallel to grain of 10.8 MPa.
After performing the calculation as per the provisions in the Design manual, it turned out that the code is conservative for longer columns.
However, it allows higher loads for shorter columns that could not buckle.
This is because, when buckling is not an issue, the material can be loaded past its yielding point, but still away from its ultimate capacity, which is associated with a complete loss of strength.
Any accidental eccentricity is not directly accounted for in the code, however, its effects are captured by sufficient safety factors built into the codified equations.
As a result, the maximum compressive load for a timber post of a length of 1m is around 8.7 tonnes around 5 tonnes.
For a 2m long post and only 2.25 tonnes for a 3m long column., These numbers clearly illustrate the effects of buckling for longer members subjected to compressive loads.
As always, this video is a short and simplified version of an actual column, design practice with its sole focus on the compressive load.
The design of end connections is ignored in this video.
Further factors such as duration of the load, treatment of the wood, combined loading conditions and so on, add additional complexity and considerations that need to be accounted for.
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FAQs
How many pounds can a 6x6 post support? ›
If you assume a conservative 1400psi allowable bending stress, a single 6x6 with 12' span can support about 2000 lbs. So your double 6x6 can support at least 4000 lbs (possibly more if you do a good job bonding the two members together so that there's no slip between the faces).
What is the bearing capacity of timber? ›The bearing capacity is calculated by multiplying the loaded area times the standard compressive strength times a factor kc. Both standards refer only to one specific design situation given in Fig. 5 in which two beams overlap. One is the continuously supported bearing beam locally loaded by the top beam.
How much load can a 6x6 post take? ›They need to bear the weight of the structure (wooden floors, walls, roof), a small wood stove, bed, table/chairs, sundries, and up to maybe 10 occupants (for small gatherings). So, perhaps 6000-7000 pounds total.
How much weight can a 2x12 hold horizontally? ›One 2x12 can support about 180 lbs. per foot or about 2,100 lbs. total for a 12' span.
How much weight can a 4x4 wood post support vertically? ›KEY TAKEAWAYS: Horizontally, a 4×4 can bear up to 500 lbs of centralized weight and up to 1,000 lbs of evenly distributed weight. As a vertical support, a 4×4 can bear upwards of 4,300 lbs.
How deep should a hole be for a 6x6 post? ›Dig, align, and finish the job
Dig an 8"-diameter hole at least 6" deeper than your area's frost line for each 4x4 post, using a power auger, hand auger, or post-hole digger. A 6x6 post requires a 10"-diameter hole. Shovel a 6" layer of gravel into the hole to provide drainage.
The tensile strength of soft- woods parallel to grain at 12% moisture content generally ranges between 70 to 140MPa. The compression strength is lower and is usually in the range 30 to 60 MPa. For hard- woods, these values are generally higher. These values are for clear, straight-grained wood samples.
What is the tensile capacity of timber? ›Tensile strength: When timber is enough strong to the tensile force. If perpendicular force is made then timber is weaker. 500-2000 kg/cm2 is the range of tensile strength load.
How do you calculate load on a post? ›There is little weight on the end walls, so to calculate the load on the footing, the only data points needed are the building width and post spacing. The FootingPad calculator pre-fills the dead weight load of a common steel-roofed at 5 lbs. per square foot. Total load = (½ building width x Post spacing) x (5 lbs.
Can you join two 6x6 posts? ›Yes, they can be connected and they should have an adequate connection. The Code does not stipulate how they're connected, but says it needs to be adequate. If the two ends are not cut perfectly “square” and there is jumping on the post, it could “slide” past the other post, especially if it's a little wet.
How far can a 6x12 beam span without support? ›
75 m is the maximum possible span.
How far can a 2x12 beam span without support? ›A 2×12 with an E of 800,000 psi and Fb of 790 psi also works, since it can span 15 feet and 10 inches. Given a design span of 15 feet 1 inch and a 16 inch joist spacing, first determine which size lumber will work.
How do you span 30 feet with wood? ›As a rule of thumb - divide the span by 18–22 to get a safe and suitable depth (depending on rib spacing and the expected load). 30 Feet is a long span (that's almost 10 meters) — assuming it is for a regular residential building, you will need a set of 4″X16″ logs spaced at 20″ minimum.
How much weight can a 2x10 post support vertically? ›In fact, each 2x10 will support 1,200 lbs. To be clear, spans are measured as "clear spans". That is to say, from face of support to face of support. Also, if your BBQ is located in the middle of the span so that people can stand around the BBQ, then there will be an additional "Live Load" acting on the joists.
How deep should a wood post go? ›Dig post hole so diameter of the hole is 3 times the width of the post (i.e., the hole for a 4” wood post should be about 12 inches wide). The depth of the hole should be 1/3-1/2 the post height above ground (i.e., a 6-foot tall fence would require a hole depth of at least 2 feet).
How do you stabilize a wooden post? ›Stabilize Your Fence Post
You'll first want to dig a few inches of soil out from around the post's perimeter. From there, you can fill the hole with gravel and top the gravel with a rapid-set cement mix. Finally, pound the fence post back into place using a mallet.
How Much Weight Can Plywood Support? The thickness of plywood plays a big role in its strength. A 12 inch by 36 inch sheet of plywood that is 1/4 inches thick will only support 5 pounds per square meter. Whereas a 12 inch by 36 inch sheet of plywood that is 3/4 inches thick will support 50 pounds per square meter.
Can you put dry concrete in a post hole? ›Dry concrete is a fast-setting concrete mix that does not require mixing. It comes in a bag and can be poured directly into the post hole. Dry concrete is ideal for setting posts because it eliminates the need for mixing and sets quickly.
Is it normal for 6x6 posts to crack? ›The crack in your photo in the center of a 6x6 pressure treated post is common, it's called "checking", and it has no structural significance at all.
Is a 6 inch hole good for a 4x4 post? ›The diameter of your post hole should be three times the diameter of your post. So, if you're planning on using a four-inch round or 4x4-inch square post, your post hole will need to be 12 inches in diameter. For a six-foot-high fence post, we would need a hole that's 36 inches deep and 12 inches in diameter.
Is timber as strong as steel? ›
While it takes longer to work with, steel is stronger and lighter than timber. Its strength means it can cover greater spans than timber and its lightness means it is better suited to sites with difficult access. However, timber can undertake various treatments to improve its strength.
What are the weakness in timber? ›Most timbers are prone to pest, rot, mold and fungi attacks, some are far better than others but they both require a minimum of LOSP or ACQ treatments for outdoor structures. Timbers tend to silver or look old if left natural and unpainted. Timber maintenance can seem to be higher than other building materials.
What is the toughest timber? ›1. Australian Buloke – 5,060 IBF. An ironwood tree that is native to Australia, this wood comes from a species of tree occurring across most of Eastern and Southern Australia. Known as the hardest wood in the world, this particular type has a Janka hardness of 5,060 lbf.
What is maximum bearing load? ›The Bearing Static Capacity, Co, is the maximum load that can safely be applied to a non-rotating bearing that will not cause subsequent bearing operation to be impaired. It is based on calculated contact stress at the center of the most heavily loaded rolling element where it contacts the Inner Race.
What is maximum load bearing capacity? ›Bearing capacity - Bearing capacity of a foundation is the maximum load that can be applied on a foundation, before failure or uncontrolled deformations occur.
What is allowable bearing capacity? ›The allowable bearing capacity of soil is the amount of load the soil can take without experiencing shear failure or exceeding the allowable amount of settlement. This is the figure that is used in the design of foundations.
Can timber be stronger than steel? ›Super wood is stronger and tougher than steel - ASME.
How do you calculate the strength of timber? ›Compression or shear strength of a wood beam or truss used extensively for construction can be calculated based on the following equation: Sigma (σ) = P/A, where σ is stress, P is load and A is surface area.
How do you test the strength of timber? ›The strength of wood can also be measured using a three-point bend test. The width (w) and height (h) of wood samples are measured, and the specimens are placed in the three-point bend testing apparatus with the height of the wood orientated vertically in the apparatus.
What is the maximum point load? ›For a point load at the center, the maximum moment is (P*l)/4. If the load is not centered, the maximum moment is (P*a*b)/l and it occurs at the location of the point load. For a triangle load the maximum moment is located at (√3 *l)/3 and it is (√3 *w*l2)/27.
What are the load calculation methods? ›
Commercial Load Calculation Methods
ASHRAE has TETD (Total Equivalent Temperature Difference), CLTD (Cooling Load Temperature Difference), TFM (Transfer Function Method), HB (Heat Balance) and RTS (Radiant Time Series).
Load Calculation For Columns:
Self weight of Steel is around 8000 kg per cubic meter. Even if we assume a large column size of 230 mm x 600 mm with 1% steel and 3 meters standard height, the self weight of column is around 1000 kg per floor, which is equivalent to 10 kN.
RE: 6"x6" post strength
Allowing for buckling, allowable compressive stress is roughly 475 psi, Area is 30 sq in, so the allowable force in the post is 14,300 lb. However, if the post is a stronger grade, the strength goes up quite dramatically. The first thing you should do is check the grade stamp.
A PT post will last a long time in concrete, maybe 5 to 10 years in soil alone. I suggest you embed the post in concrete, trowel a peak around the post so water runs off, and don't let the PT post come in contact with the ground.
What is the max space between posts? ›For most residential fences 8′ between posts is the maximum. Commercial fences (industrial chain link, for example) typically can handle up to 10′ spacing because of their stronger frames. All things being equal, the closer the posts are together the better it is for the fence.
Can a 2x10 span 16 feet? ›The most common lumber sizes for floor joists are 2x6, 2x8, 2x10, and 2x12. Larger joists can span across wider areas. For example, a 2x6 joist would have a 12-foot, 6-inch maximum span, and a 2x10 joist would have a 21-foot maximum span.
Can a 6X6 span 10 feet? ›To answer you question, no a 6X6 will not carry that span, even if you have only a roof to support. The strength is in the height of the beam, not so much for the width.
What size I beam do I need to span 60 feet? ›You're looking in the range of a W8x18 or a W10x12. For NO snow load or roof load or any other load. Just the beam going from one wall across 60 ft of air and then onto the other wall. Each beam would weigh 720 pounds for that length in a W10x12.
Can you span 20 feet with a 2X12? ›There's not quite enough information here to give a definitive answer, but for decks, a rule of thumb is when supporting joists that span 12 feet, a double ply beam can span in feet a value equal to its depth in inches. Thus, a double 2x12 beam could span 12 feet - with 20' beams, posts at 10' might look the best.
How far can you span a triple 2X12 beam? ›| Joist Spans | ||
|---|---|---|
| Southern Pine | 3-2X10 | 9'-9" |
| 3-2X12 | 11'-7" | |
| Douglas Fir-Larch, Hem-Fir, Spruce-Pine-Fir, Redwood, Cedars, Ponderosa Pine, Red Pine | 3X6 OR 2-2X6 | 3'-11" |
| 3X8 OR 2-2X8 | 5'-1" | |
What is the longest span for a 2X12? ›
| Maximum Span (ft - in) | ||
|---|---|---|
| Nominal Size (inches) | Joist Spacing Center to Center (inches) | Lumber Grade |
| 2 x 12 | 24 | 15' - 10" |
| 2 x 14 | 12 | 23' - 11" |
| 16 | 21' - 8" | |
LVL beams cost on average $3 to $12 per linear foot for the material or $50 to $200 per foot installed.
Can I-joist span 40 feet? ›Use of I-Joist: These are engineered wood joists that are made of an I-shaped cross-section and are stronger than traditional solid sawn lumber. They are well suited for long-span applications and can be used to span up to 40 feet.
Does double joists increase span? ›Double joists are added to increase the span of a floor, as they provide more support to bear the additional weight. They also come in handy to build a second floor without the need for adding extra columns from the roof to the foundation.
How far can 2x10 span without sagging? ›A 2x10's maximum span depends on where it's used. According to IRC 2021, a 2x10 with 16-inch spacing can span up to 18'-9" as floor joists, more than 26' as rafters and ceiling joists,4'-3" as beams, and 7' as headers without providing additional support.
How far can a double 2x10 span without support? ›A double 2x10 can thus span 10 feet. It's for typical deck construction.
Can a 6x6 span 10 feet? ›To answer you question, no a 6X6 will not carry that span, even if you have only a roof to support. The strength is in the height of the beam, not so much for the width.
How deep should a 6x6 post be in the ground for a deck? ›The general rule of thumb when setting a post is that the depth of the post's hole needs to be one-third to one-half of the actual above-ground height of the post. So, a six-foot-high finished post ideally needs to be buried three feet into the ground.
How big of a beam to span 12 feet? ›I use thumb rule “ 1 inch for one foot” which means you can use 12 “ deep beam. width depends on your architectural requirements like width of wall. try not to provide less then 6” wide beam. if loads are extra ordinary then better perform structural analysis.
Why are my 6x6 posts splitting? ›Splits and cracks (known as wood checks in the industry) occur when wood shrinks as it dries.
How deep to bury a 6-foot post? ›
The depth of the hole should be 1/3-1/2 the post height above ground (i.e., a 6-foot tall fence would require a hole depth of at least 2 feet).
Is it OK to bury pressure treated lumber? ›Exploring Pressure-Treated Lumber
All treated wood is now “ground contact”. “Ground contact” has a high chemical retention level and can be placed directly on or in the ground. This provides better protection against rot and decay.
Postsaver® is the number one choice for preventing fence post rot because it will literally block rot. It is a heat-shrinkable outer sleeve that fits over the base of the fence post.
How big should a footing be for a 6x6 post? ›FOOTINGS: - Poured concrete footings should be a minimum of 8” wider than the posts (4x4 post – 12” min. width, 6x6 post – 14” min. width), a two level deck or deck with roof – 24”x24”.
How far apart can 6x6 posts be? ›The two most common sizes used for deck posts are 4×4 and 6×6. When using 4×4 posts, place them no more than 6 feet apart, and when using 6×6 posts, no more than 8 feet apart.