Bending Strength of Edge Loaded Plywood

In home building in many areas the sheer loading on a wall is developed by plywood.

Might be a place to look but beware as ply has vastly different grades and manufacturing differences.

A sheet that is thick in the center with a thin skin on either side will be vastly different in every direction from the same thickness in 5 , 7 or 9 thin plys.

House, boat and aircraft all will be different wood and specification.

 

Plywood with "in plane" compression loads on the ends can fail by local failure of the plywood, or by buckling of the panel. For larger panels buckling is likely to occur before local failure. Buckling depends on the loads, material characteristics, panel shape, panel size and panel thickness.

 

Chuck- If you edge load a plywood, you will get only half the strength. If you look at the fiber alignment half would be vertical and half would be in the horizontal position (assuming equal plies). This is because the top portion will be in compression and the bottom portion will be in tension. The middle portion will be in shear.

In shear, it would be best to cut the plywood in bias cut, at 45 degree angle. This way, the fibers are criscrossing each other like trusses on a bridge.

To achieve ultimate loading, the top and bottom end must be capped by a solid wood. This in effect becomes an I beam with the caps taking up the compression and tensile load. The middle portion (or web) absorbs the shear.

This method is called "engineered wood/lumber" and can be analyzed in the traditional way of beam analysis.

 

Typical example.

 

''If you edge load a plywood, you will get only half the strength. If you look at the fiber alignment half would be vertical and half would be in the horizontal position (assuming equal plies). This is because the top portion will be in compression and the bottom portion will be in tension. The middle portion will be in shear.''

This is not correct as the vertical plys are glued to the plys that are horizontal and contribute to the strength of the beam.


''"The middle section will be in shear.""
This is misleading as there will be a constant shear load across the length of the beam within the end supports. If you are meaning shear flow, the middle section will have the highest amount of shear flow, diminishing to the edges


""In shear, it would be best to cut the plywood in bias cut, at 45 degree angle. This way, the fibers are criscrossing each other like trusses on a bridge.""
You cannot equate putting the plys at 45 degrees as acting like a trussed bridge. In a truss system, the truss components are either in tension and compression,( mainly) but your 45 degree plys that are glued to the other plys, will be under mainly compressive/tension and shear flow due to the beam load (excluding vertical shear for now) AND IN THE DIRECTION OF THE BEAM.
To suggest that orienting the strands at 45 degrees will make the plywood act like and be under the same loading/stresses as a truss is not correct

 

""you will get only half the strength""

If this were true then all the Parralam beams and other plywood beams used in construction would have the plys flat to the load. Which they are not

 

In this discussion it's necessary to distinguish between stress and strain, because wood is very strongly anisotropic. The top of a +/-45 angled web has the same strain as the top cap, since they are glued together. But because the extensional and shear moduli are very different, the web will have a larger shear stress while the cap will have a larger axial stress. And shear stress is exactly equivalent to compressive/tensile stress on the diagonals. So when discussing stresses (not strains), a +/-45 web does indeed function like the diagonal members of a truss.

Plywood set at +/-45 has the best shear strength and stiffness for that type of wood, and hence in theory makes a better shear web than plain wood or plywood set at 0/90. But this assumes that web's glue joint to the spar cap is stronger than the plywood, which is not easy to do. For more practical and economical construction, a 0/90 web or just plain lengthwise-grain wood may be a better solution in some applications.

 

The link that Barry provided about Canadian Plywood design has the following formula.

Bending on Edge
The factored bending resistance of plywood loaded on edge
in the plane of a panel that is adequately braced to prevent
lateral buckling shall be taken as:
Mr = FTpdp2/6
where:
F = 0.95
Tp = tp (KD KS KT)
tp = Specified strength capacity in tension (N/mm)
dp = Depth plywood panel in plane of bending (mm).

dp2 in the above is actually dp squared. KD, KS and KT are adjustments for different types of plywood.
For the sake of simplicity assume tp = 1 and ignore the adjustments. The formula can then be simplified to Mr = .95dp2/6. For a 12mm (1/2inch) panel depth the bending strength on edge would be 22.8=.95*12*12/6. If I did this correctly it would seem that a square section of 12 mm plywood is 22.8 times stronger in the edge loaded direction then when panel loaded. This would increase dramatically for small increases in panel depth. A 24mm panel depth would be 91.2 and a 48mm panel depth would be 364.8. This doesn't seem correct to me. Where is my mistake?

 

You have it right Chuck, though unsupported panels will tend to move (dramatically) with a lot of "edge set". This gets complicated once you introduce some twist (conical or cylindrical section) into the edge set. It's the very reason taped seam construction works so well.

In a practical sense, when designing a small(ish) boat, for panel construction, say some stringers set on edge in the bilge or how hefty the side panels need to be, the usual limitation isn't the strength or stiffness, but what's reasonable. An example might be a light as practical, performance oriented kayak. Well the "numbers" tell you, the hull shell only needs to be 1/8", but practicality suggests you might consider 1/4" on the bottom at least, so a big footed skipper can step in, without his paw punching through and getting wet.

 

""But because the extensional and shear moduli are very different, the web will have a larger shear stress while the cap will have a larger axial stress. """

Not exactly as the stress, pounds per square inch, can be easily changed/reduced by merely changing the size of the top cap. Double the cap width, ie if the top cap is 1 1/2 by 3 inches to say 1 1/2 by 6 inches and the STRESS will drop by close to half.


""So when discussing stresses (not strains), a +/-45 web does indeed function like the diagonal members of a truss. ""

A 45 degree truss system will have forces in each diagonal member that along the length of the beam will be at 90 degrees to each other and at alternating directions 45 degrees to horizontal.
There are not any compressive or tension forces acting at 45 degrees to the horizontal in a plywood beam.

Tension and compression and shear flow act axial to the beam length and shear from the load acts vertically

I would like you to send a force diagram that shows that there are compressive, shear or tension forces acting at 45 degrees to the horizontal.

 

Here is a hypothetical application. Let's assume you are making a 20' catboat and the design calls for a wooden mast. No wood is available but you have plywood. Everything I have read says that plywood is not good for a mast because plywood only has about 2/3 the strength of wood due to the cross ply's providing little or no strength. But what if you cut the plywood into strips and edge glue the plywood together to form the staves for the mast. Now the plywood is edge loaded which should be stronger then the original wooden mast called for in the design. See my crude sketch showing a top view.

 

I don't think so. The 'panel' orientation would be much stronger. Have you much experience with wood working?

 

What is a normal stress (tension and compression), and what is a shear stress is in the eye of the observer. More specifically, it depends on what axes along which you choose to pick to define the stress tensor components.

The PDF page is for an short article I wrote on shear stresses in wing spars for the RC Soaring Digest. The middle diagram in the PDF shows the two different views of the web stress. The square-oriented web element sees pure shear stresses. The square-oriented element sees +/- normal stresses.

The quantitative transformation between the stresses in any two sets of axes can be performed using standard formulas, or graphically using the "Mohr's Circle".

 

This is a different from the original post
If the original mast called for say a 6 inch diameter solid mast of fir but instead you built a 6 inch diameter, not exactly round due to the ply constraint as per your drawing, the six inch solid mast would be stronger.
Additionally, it would be difficult to get the strength in the joints to carry the loads with glued joints as shown

 

"""What is a normal stress (tension and compression), and what is a shear stress is in the eye of the observer."""
In a normal beam in bending, as per the original post and the drawings supplied, what are normal stresses are not in the eyes of the observer. The compression and tension stresses act axial to the length of the beam. Shear Flow acts along the axis of the length of the beam.
Vertical shear, due to the loading of the beam acts vertical to the axis of the length of the beam.