# Why are two pieces of wood stronger when bound together?

## Summary:

The ultimate compressive strength of two 2*4s bound together (say screwed together securely) is greater than one 4*4. Why is this the case?
The answer learned in class is that the two 2*4s are able to distribute the load over both of them, but I don't think this is an actual answer because that's balanced by the fact that each block is half the area. Does anyone know of the reason for this observation? Thanks!

Alex Ford

## Answers and Replies

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jrmichler
Mentor
Two possible reasons:

1) Real world 2 X 4's have knots in them. With doubled 2 X 4's, the knots do not line up, so the assembly is stronger.

2) If it's used as a long column, the maximum load is limited by buckling in the thin direction. The thin direction is twice as thick in doubled 2 X 4's, so has eight times the resistance to buckling.

Caveat: The above is simplified. The reality is much more complex, but does not change the overall conclusions.

Alex Ford and person123
Two possible reasons:

1) Real world 2 X 4's have knots in them. With doubled 2 X 4's, the knots do not line up, so the assembly is stronger.

2) If it's used as a long column, the maximum load is limited by buckling in the thin direction. The thin direction is twice as thick in doubled 2 X 4's, so has eight times the resistance to buckling.

Caveat: The above is simplified. The reality is much more complex, but does not change the overall conclusions.
I think the first point makes good sense to me. I think on a similar point, the grains between the two blocks wouldn't be aligned so would failure along grains potentially be blocked along the boundary?

I don't really understand the second point though (assuming that the two 2X4s would buckle as a single beam) because the 4X4 and the two 2X4s would both have the 4in by 4in dimensions.

Another reason given is that there would be variation between the mechanical properties of the two pieces of wood; one 2X4 would have a greater compressive strength for example. However, it seems to me that the ideal scenario, in which it would fail at the highest possible load, the total load would be distributed in proportion to their compressive strengths; if one 2X4 was three times as strong for example, it would take three times the load. This would be just as good as far as I can tell to a compressive strength equal to the average of the two, so the two 2X4s at best would be equally strong on average for this reason, but it could be less strong. I'm not sure if I fully understand the given reason though, so if someone could explain it to me I would greatly appreciate it.

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jrmichler
jrmichler
Mentor
OOPS, I misread the OP. Two 2 X 4's bound tightly will have the same buckling strength as one 4 X 4. And it's good that you are thinking about these things.

person123
256bits
Gold Member
I don't really understand the second point though (assuming that the two 2X4s would buckle as a single beam) because the 4X4 and the two 2X4s would both have the 4in by 4in dimensions.
Actually not.
A 2 x 4 is milled 1-1/2 x 3-1/2, so two together on the wide side would produce and area of 3 x 3-1/2
A 4 x 4 milled is 3-1/2 x 3-1/2, a greater area than two 2 x 4's.
Milled lumber is what one gets in a hardware store.

Rough lumber - perhaps you can find that at the sawmill before they trim the lumber.

phinds
256bits
Gold Member
I think the first point makes good sense to me. I think on a similar point, the grains between the two blocks wouldn't be aligned so would failure along grains potentially be blocked along the boundary?
I would think so.
The boundary between the two 2 x 4's is a barrier to crack propagation.

Plus, the less large an object is, the less large the biggest defect can be.
A knot, for example, of a certain size for a 4 x 4 , and the lumber will probably hold together from the surrounding material.
A knot of the same size for a 2 x 4, and the lumber may be rejected as unit for sale.

Actually not.
A 2 x 4 is milled 1-1/2 x 3-1/2, so two together on the wide side would produce and area of 3 x 3-1/2
A 4 x 4 milled is 3-1/2 x 3-1/2, a greater area than two 2 x 4's.
Milled lumber is what one gets in a hardware store.

Rough lumber - perhaps you can find that at the sawmill before they trim the lumber.
Yes, I forgot the 4X4 actually has dimensions of 3.5 in by 3.5 in. For the sake of simplifying the situation, I wanted to assume that the cross sectional area of one is twice as great as the other and adds up to make the equivalent shape, so 2in by 4in vs 4in by 4in for example.

Plus, the less large an object is, the less large the biggest defect can be.
A knot, for example, of a certain size for a 4 x 4 , and the lumber will probably hold together from the surrounding material.
A knot of the same size for a 2 x 4, and the lumber may be rejected as unit for sale.
I didn't think of that! So that difference is due to the quality control of the lumber as well?

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jim mcnamara
Mentor
Lumber is graded based on defects (wane, knots, warp, drying defects like case hardening) and moisture content. In the US construction 2x4's are kiln dried to S-DRY (15%-18% MC).

So,yes, bigtime, grading reflects physical quality like strength. Lumber grading is a big predictor of strength - You would want to use Select grade red oak for example to make the rockers for a rocking chair. #3 common grade oak would not take the load.

@phinds knows a lot more about this. And I think has some good links to lumber grading.

The only one I know is a book: Bruce Hoadley 'Understanding Wood' - Amazon or a college library.

phinds
Science Advisor
Gold Member
2019 Award
The boundary between the two 2 x 4's is a barrier to crack propagation.
Plus, the less large an object is, the less large the biggest defect can be.
I didn't think of that! So that difference is due to the quality control of the lumber as well?
So,yes, bigtime, grading reflects physical quality like strength. Lumber grading is a big predictor of strength
All good points and all true. I think the barrier to crack propagation is the biggest factor. Four 1" thick planks glued together make a stronger glulam than two 2" thick planks and that in turn is stronger than a single 4" thick plank.

Another factor is that the glue is always stronger than the wood so even though it is a thin layer it has a big effect, adding to the deterrence of crack propagation.

Large glulams are used for bridges, for example, in ways that equally thick beams from a single tree bole would NEVER be used. Glulams are also used for structural beams in other ways. The statement that glulams are Doug fir (in the image below) is not correct. They MAY be Doug fir or they may be Southern yellow pine, or even a few other woods.

256bits and person123
phinds
Science Advisor
Gold Member
2019 Award
@phinds knows a lot more about this. And I think has some good links to lumber grading.
I do have a link somewhere to a university site that has a great article on grading, and a data table as well, but I don't pay much attention to that stuff since I'm interested in wood identification much more than wood use and I can't remember where I put the link (or even which university it is).

I also have a big, fat, expensive, tome "Wood Engineering and Construction" that goes into it all in enormous detail. I bought it back before I realized that I'm just not into that aspect of wood.

DaveC426913
Gold Member
@phinds has introduced something that was not in the OP: glue. The OP states "screwed together securely".

Yeah. 2 2x4s glued together should be stronger than 1 4x4 because of the glue, but not necessarily stronger in the case of the OP's planks screwed together.

phinds
Science Advisor
Gold Member
2019 Award
@phinds has introduced something that was not in the OP: glue. The OP states "screwed together securely".

Yeah. 2 2x4s glued together should be stronger than 1 4x4 because of the glue, but not necessarily stronger in the case of the OP's planks screwed together.
Not quite. The screws are not as effective as the glue for strength but the fact that particular grain flaws are only in half of a piece does make a two 1-unit planks screwed together stronger than a piece of single 2-unit wood.

Still, glue IS what is normally used, thus the term glulam (for glued up lamination)

Summary:: The ultimate compressive strength of two 2*4s bound together (say screwed together securely) is greater than one 4*4. Why is this the case?

The answer learned in class is that the two 2*4s are able to distribute the load over both of them, but I don't think this is an actual answer because that's balanced by the fact that each block is half the area. Does anyone know of the reason for this observation? Thanks!
With regard to the wood, I suspect it is a molecular answer as well as a philosophical answer: First, a third element is added, the bonding agent (screws, glue, etc.) which is a variable to be measured. Secondly, molecules have structures and no two grains in 2X4's are alike. There resistant (bending, breaking) strengths are different from one another. Just as chain is as strong as weakest link, the 2X4 is strengthened to a degree as presented by the stronger of the two 2x4's that are mated. AF

Just as chain is as strong as weakest link, the 2X4 is strengthened to a degree as presented by the stronger of the two 2x4's that are mated.
I don't quite understand this point (if anything the chain analogy would indicate two beams of different strengths would be weaker because it would fail at the weaker beam). This was my response to a similar point:

Another reason given is that there would be variation between the mechanical properties of the two pieces of wood; one 2X4 would have a greater compressive strength for example. However, it seems to me that the ideal scenario, in which it would fail at the highest possible load, the total load would be distributed in proportion to their compressive strengths; if one 2X4 was three times as strong for example, it would take three times the load. This would be just as good as far as I can tell to a compressive strength equal to the average of the two, so the two 2X4s at best would be equally strong on average for this reason, but it could be less strong. I'm not sure if I fully understand the given reason though, so if someone could explain it to me I would greatly appreciate it.

Two possible reasons:

1) Real world 2 X 4's have knots in them. With doubled 2 X 4's, the knots do not line up, so the assembly is stronger.

2) If it's used as a long column, the maximum load is limited by buckling in the thin direction. The thin direction is twice as thick in doubled 2 X 4's, so has eight times the resistance to buckling.

Caveat: The above is simplified. The reality is much more complex, but does not change the overall conclusions.
Adding the mention of knots adds to the discussion. This is essentially the same thing as discussing the grain. As you say, some wood types have larger knots, some smaller and some wood (much more expensive have cuts without the knots. Lumberyard employees and owner are well-aware of the strength characteristics of wood and they are priced accordingly. The initial question was for two pieces of wood. No two are exactly alike in strength. The piecing together has been mentioned with the word glulum which is later defined in a comment. Different forms of laminates, including the use of wood in lamination, as well as the use of plywood of different grades, all attempt to answer the needs that are raised by the question. I brought out the bonding aspect of glue in my initial answer and a couple of people then brought that out without reference. One person thoughtfully brought up kiln drying which is one way of speeding up the curing process. Sufficiently dried lumber does not exhibit the characteristic of, "bleeding." When new support posts were installed under my lanai, I observed for several months, bleeding of sap or pitch from various openings or pores. It Kind of bothered me since I both asked for the more expensive support 4X4's in which had already been, "bled." "Wet," lumber will have the tendency to, "bend," under load as it does its job. Variables include the types of bonding agents and the methods of application of those agents. Some of these questions are theoretical, in which the variables are sort of eliminated in use of computer aided analysis of strengths with a sort of constant built in. Those figures are predetermined by prior testing limits for the certain kinds of woods selected. The physics of the answer must include a lot of variables to be valid in its answer, and also in its practical application. Some bonding agents mixed with sawdust, to make various by-product wood products can actually be quite weak.