Bending Strength of Edge Loaded Plywood

Barry
I apologize for the crude drawing. I didn't want to take the time to draw a bird's mouth type of construction where the edges get rounded off and there is adequate glue lines to hold everything together. I was more interested in showing the difference between what I would think would be panel loaded verses edge loaded. Maybe a hypothetical mast was not a good choice. I was just thinking of something nautical instead of beams in a building.

SamSam
I have a fair amount of woodworking experience. Everything from making furniture to general construction to finish carpentry to making my own dinghy's and helping a friend build out the interior from a bare fiberglass hull and deck. I don't know which would be stronger in my crude mast drawing. I do know that edge loaded plywood has a significantly higher bending strength than panel loaded plywood.

 

Barry

Axial shear flow is only related to:-

1) Torsional resistance of the member, ie will it twist/warp
and
2) Horizontal shear stress which only occurs of there is a varying bending moment on the member; or on very short members.
(Not considered for isotropic materials as it does not dictate the vertical shear, whereas for composite build up beams, it does).

In the simple point load diagram posted #3, this does not exist, thus no horizontal shear stress to consider.

 

Some interlaminate shearing can be expected in loaded plywood structures, particularly the cyclic nature of a freestanding mast. This rolling shear is yet another reason to avoid a plywood mast, in all but very small craft. Weight is another concern, comparatively with modulus and strength over solid lumber, built the same way (birdsmouth).

Attached are a birdsmouth section and a more traditional solid lumber arrangement. Now picture the end grain arrangement on the birdsmouth build, with plywood. On the symmetrical stave notch layout (upper left), 2/3's of the glue line will be on end grain and the asymmetrical stave layout will 100% end grain in the joint, neither of which is desirable, regardless of building material physical properties. If the more traditional "built up" method was employed, there'd still be a fair bit of glued end grain, but the internal corners could be solid lumber helping to tie things together.

If absolutely bent on building a plywood mast, use a mandrel and cold mold 1/8" over it in very slow, long, opposing (naturally) spirals. A damn difficult way to do it, but I have seen solid veneers used this way, with very good success.

 

Shear flow exists in any beam that is subject to bending
If you take two 1 inch by 2 inch pieces of wood and position them one on top of each other, flat to flat, between two supports and load them simply in the middle, they will resist the load by twice what each one can carry.

There will be movement, slippage, between the corresponding positions at the interface between the two pieces of wood

If you glue or screw them, the pieces will act as then a 2 inch by 2 inch piece of wood. But at the interface between
the two pieces will be a horizontal shear force that the glue or screws are resisting. The maximum shear flow value occurs at the neutral axis. At the outside position, top or bottom of the beam, this shear is zero.

If you were to do a stress analysis of a beam element above the neutral axis but below the outside fibre, you would need to include, shear flow, vertical shear, and compressive or tensile stresses ( caused by the bending moment) to find out the maximum stresses on that element

 

This thread is starting to stray off my original topic which was looking for studies testing the strength of edge loaded plywood. Can anybody point me to a study of this. I really appreciate everybody's posts.
Par
The west system books show making either masts or windmill blades by cold molding over internal framework and one Eric Sponberg's designs has a mast of carbon fiber over an internal framework. I really like the concept of free standing masts. Too bad they never caught on.

 

Chuck,

You can't understand the answer to your question without understanding how the wood is loaded.
That is where this moved from your simple question.

You were the one who introduced the freestanding mast issue.

The simple fact is that an "edge loaded" piece of ply is significantly "thicker" than a "panel loaded" piece of ply. This is comparing the thickness in the direction of the load.

That alone will make the largest difference.

If you don't have the math/ engineering, you could do a test your self.
If you try a test, you will have to pay attention to sideways bending (buckling) of the edge loaded panel. Something will have to be done to keep it stable without adding to the bending strength.

But I don't know of any place where an edge loaded piece of ply won't be supported on the edges, which changes the whole question.
Normally you have to treat the whole system at once if you want to know the strength.

 

I don't think it would be if they are the same thickness, as it is in your drawing. Every other ply would be short pieces of end grain which seems would be very easy to bend and very easy to split.

 

Sam Sam,

What do you mean by thickness? Did you mean the same sized panel tested in two directions?

Like a 2' long by 6" wide by 1/4" panel - 3ply with the outer plys in the direction of the 2'? Lets make it Marine Okoume just to be specific. Of course it should be metric thickness so 6mm.

Then the test would be to take one of the identical panels and position it vertically and the other an position it horizontal.

If you agree that represents what was being discussed - you need to do the test your self - the vertical panel will be much stronger.

 

No, I mean like in this illustration he used...



along with this statement...

which would mean both " 2' long by 6" wide by 1/4" panel(s)" would be tested in the 'panel loading' orientation, with neither in the 'edge loading' orientation.



I'm thinking that with every other ply being only end grain (in your example only 1/4" inch long) on his glued up plywood strip 'board', no matter how you tested it, the 'regular' ply board would be much stronger as far as stiffness was concerned. In the panel load test mode, the end grain ( 1/2 of the board ) would offer very little stiffness before it would split/break (the same as end grain balsa without any skins). If edge loaded, the 1/4" end grain would offer very little shear strength and would be easily ripped apart, thus destroying any integrity, thus stiffness, of the 'board'.
.

 

I understand chuck's sketch like SamSam.
A simple method to compare bending strenght of edge loaded and panel loaded plywood, would be the following:

Cut (e. g. with a table saw) from a Panel of plywood two small stripes parallel to one edge of the panel. Breadth eaqual to the panel thickness (quadratic cross section). So you have two specimen of a "beam" for a bending test. The height and the width of the "beams" are interchangeble. Place one of them with endgrain up/down (edge loaded position) and the other one with endgrain to the sides (panel loaded position).

 

SamSam,

Thanks, I didn't look close enough at the mast illustration.
If each of those strips in the upper panel were plywood, it certainly wouldn't be worth much, since 1/3 of the wood would not have the grain going the length of the mast.

This theoretical study has suddenly turned into nothing of value.
I'm going to drop out.

 

Yes, even short strips would work, like 1 or 2 foot long. In fact I'll go try that, as now I'm not so sure I am right.

 

If you look at my post #23 I did the math and a 12mm x 12mm piece of plywood should have 22.8 times more bending strength when edge loaded verses panel loaded. This increase in bending strength increases dramatically as the depth of the panel increases. This is what I based my assumption in my drawing that the edge loaded section would be stronger that the panel loaded section.

 

http://www.google.ca/url?sa=t&rct=j...d=3817&usg=AFQjCNFH3Im6i4bNOe9n8pDaim6MF13srA

not sure about the length of this link but it has an easy explanation of plywood beam information

 

You’re confusing different types of analysis and theory with different types of structural members.

For example the statement here:

This is bending stress, not shear stress.

If the orientation of the joint is perpendicular to the applied load, it behaves differently to one that is parallel to the applied load. It is a composite that is orthotropic.

If the 2 pieces of wood are different thickness's (but same width), but same overall dimension of the member and if the glue line is perpendicular to the applied load, the glue line is no longer coincident with the NA. Thus the strength of the member is the weakest link..the glue, not the wood’s properties. That is very basic composite analysis.

So let’s look at the analysis.

So at the joint between the flanges of a beam and the web, the horizontal shear stress is…zero. So if it is zero, what’s all the fuss about?

The issue is with the type of member and the analysis of each member and how it is applied.

So let’s take an I-beam of say a typical RSJ used in many applications worldwide from ships, to houses, to bridges etc. It is 350x200mm, with a web of say 12.5mm and a flange of 25mm….or 1/2inch and 1inch in crazy imperial units.

If we wanted to weld the web to the flanges, rather than have a uniform extruded section, from shear theory what is the maximum horizontal shear stress?

From theory the horizontal shear stress = (F.a.y)/I.B

The max Horz. Shear stress = F[(200x25x162.5)+(150x12.5x75)]/(Ix12.5)

Where 'I' (2nd moment of area) can be calculated as 293x10-6m^4 or 29,300cm^4

Therefore the HSS = 260F (in rounding up numbers thus using m rather than mm’s and using F as the force)

So the maximum vertical shear stress = F/A = F/(300x12.5) =266F

Therefore, we can see that the vertical shear stress has a value of 266F and the horizontal has a value of 260F.

But, and this is the important part, the horizontal shear stress is zero, yes, zero (or almost zero in an I-beam) at the ends of the web, where the web joins the flange. It is only a maximum at the centre (or NA) of the section. What is then causing the ‘slipping’..?

Since the two sections are not joined each member acts independently and adopts a different radius of curvature under an applied bending moment. The top FB has tension on the lower surface that is touching the lower FB’s upper surface that is in compression of thus is slipping as the two forces are in opposite directions and different radius of curvature.

Well, this can then be seen as a typical leaf spring. Layers and layers of flat bar simply placed on top of each other. They are neither welded, nor glued or riveted together, they simply lay on top. Yet they can slip and slide away from each other. Thus the stiffness, and hence, the resistance to bending is related to the bulk of the material – its stiffness or 'EI'. The more flat bars the stiffer the section thus the lower the bending stress.

The shear force of the vertical load on the springs is then transmitted by vertical shear web area alone, of the bulk of the material in cross section. the fact each leaf is not joined makes no difference.

So, back to the I-beam.
If the I-beam is not an extruded section thus the web is welded to the flange the horizontal shear forces is almost zero at this joint just above the web, i.e. in the flange, yet just below the joint it is increasing from the near zero. The shear stress distribution from the horizontal shear stress is parabolic with the maximum at the centre and zero at the ends.

The value of the shear is directly related to the XSA of the section and hence the vertical shear. Since the value of 260F of the horizontal shear is less than that for vertical shear of 266F. It only increases the shear at the centre of the section using superposition.

Additionally the horizontal shear, with a max stress at the centre can clearly be seen to be wholly dependent upon the length of the member. Since if the I-beam is a typical long slender member, the amount of shear stress available at the centre is huge, compared to the very small amount of just the vertical depth of the web. If the web depth is d the thickness is t thus ‘dt’ is the limiting factor. Whereas the length L and thickness t of the web longitudinally the area is thus ‘Lt’. When L is large so is the available shear area ergo it is considerably more than that of ‘dt’. Thus the vertical XSA is the limiting factor of sectional slender shapes, otherwise the material yields.

In other words, horizontal shear stress is not usually considered for standard sections and loading. It is only applicable when the structural members is very short (its primary stress is shear not bending per se)along with a constant rectangular shape like a solid block and/or has varying bending moments i.e several loads being applied on the member thus cause horizontal shear in various locations. When using composite type of structural arrangements, ie welded or riveted/glued, the amount of shear area of the joint must satisfy the shear stress requirement of the joint. That is the first basic check.

And can be seen the weld length required for the joint of the web to the flange of the I-beam is wholly dictated by the vertical shear force. Since whatever the horizontal shear force is, the amount of sear area required is less than that required by the shear area for the force vertically.

Now back to the 2 blocks of wood glued v the leaf spring. The leaf spring is designed so that each leaf is the same dimension and material. As such it shall adopt the same radius of curvature for bending. Therefore the bending stress is directly related to the bulk of the material, be it 1 leaf or 2 or 10 leaves being strapped together; to increase the stiffness of the section.

Whereas if two blocks of wood are glued and one of the blocks is of a different size, (thus a glue line not coincident with the NA) the radius of curvature of the thinner section shall be different from that of the thicker one because the I (stiffness) is different between the two members, ergo, the bending moment is different ergo, the stress is different and becomes more dependent upon the strength of the glue as the weak point.

Thus, in summary, horizontal shear stress is really only applicable to members that are dictated/driven by the shear stress alone, rather than bending/stiffness. In other words short and stubby as their length to depth ratio is closer to or is unity unlike normal structural members where the length to depth ratio is considerable, and thus bending stresses dominate related to its stiffness. Since most structural members in ship design are long/slender, like the RSJ example above, thus it is not applicable and additionally the web area is more than sufficient to accommodate the horizontal shear force alone.