Calculating the Thickness of a Load Distribution Plate

Hi all

I have a distributed stress (a few tons) and centered on a solid wood board (high resistance) working in bending. As I am approaching the limit of elastic resistance (in the direction perpendicular to the fibers, this resistance is very low), I decided to insert an aluminum plate (screwed in its four corners to my board) to distribute the load over a larger area. OK so far only classic. However, I wonder about the minimum thickness to choose for my aluminum plate? Indeed, if I take a very thin thickness (0.1 mm), the plate has little chance of playing its role. If I take 10mm thick, I think my plate is going to work well to distribute the load. But how do you calculate the minimum thickness? This is a general problem that can apply to many situations as I have seen on this forum. So if someone has the solution, I'm interested.

Kind regards

Ralph

You have to determine the quadratic moment supplement to keep your flexion within the allowable limit.

I assume you are reasoning about bending?
Rather than a plate that allows a distribution for matting, I would rather take 2 profiles in angle or U. Given the difference in strength between the profile and the board, I would directly calculate the profile for the load, even if it meant slightly reducing the safety coef.

Hello stefbeno,

First of all, thank you for your answer,

However, the profiles are to be excluded because I want the solution to remain discreet. I'm more into carpentry work than construction. I have mastered the RDM calculations for the beam but what about a plate? This is a recurring problem that comes up in a multitude of situations. I have seen a few articles dealing with ground support (construction subject) and the solution was a finite element simulation to see the lifting of the plate on the periphery, which is what we don't want to aim for. But I'm really looking for a simple solution (distributed but centered load, known resistances as well as moduli of elasticity). There may be charts that can be used for this case, I'm interested. If there are courses dealing with this subject with analytical formulas, it becomes the best. But if it requires 2D finite element modeling or whatever, it seems difficult to me.

Kind regards

Ralph

Hello Ralph

I share the point of view of stefbeno ;-)  however can you give us an indication of the size of the wooden surface and its thickness.

In addition, when you indicate ""solid wood plank (high resistance)", it leads us to think that the width of this plank is not very important (apart from a redwood or baobab or oak plank). Solid indicates that it would not be glued laminated.

In addition, the four screws at the corners will make them work in shear, but do not allow for a good load distribution. You say " distributed stress (a few tons) ". How many tons is that????

Can you tell us what latitudes you have under the board and possibly above. In other words, what are the surfaces you have to put reinforcements if I follow Steffeno's proposal :-)
A few dimensions or a drawing, even freehand, would be welcome.

I have used several times a type of profile made of fairly thin sheet metal which gives a very good reinforcement, it is a V with two wings. The Vé can have triangle-shaped holes by the way. if you don't have problems with weight or inertia.
The screws are on the flat of the wings, it's super strong, light and doesn't take up any space at the top.  The Vé system with wings  = v=      has  other advantages to reinforce the wooden structure. Bolt mounting is easy and allows the shape of the reinforcements to be modulated according to deformation or support stresses.

Kind regards

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Hi all

I don't want the particular solution of my problem but rather the general methodology:

* a centered distributed load: known force and application surface

* a load distribution plate: known dimensions and material (aluminum, steel, stainless steel, ...)

* basic surface (floor, concrete, ...) in my case it will be a 45 mm thick oak plank, but it doesn't matter much, if you take moabi, the thickness needed for my case will be lower.

I don't want to use a profile, just a plate. I know that it is practically impossible to solve this particular case because when taking wood (anisotropic material) it would be necessary to take into account the resistance following the parallel and perpendicular directions to the fibers. Regardless, I will calculate an average value. If anyone knows the method for calculating the necessary thickness, I am interested. Naturally, this thickness depends on the load and the characteristics of the different materials. 

Kind regards

Ralph

This solution poses 2 problems:
- a plate has virtually no flexural stiffness;
- and above all the connection between the sheet metal and its support determines enormously or even exclusively the result...

Therefore, it is necessary to determine the missing inertia to respect the elastic limit/deformation. This inertia allows you to determine the thickness (I=b*e^3), b being the width of the plate.

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thank you Stefbeno,

But how do you determine this missing inertia?

Once again this is a very general case so the solution to this problem will allow me to approach the solution but should also help many Internet users who have to solve this problem (heavy load on concrete or floor, ...). The formula takes up the calculation of the quadratic moment for a rectangular beam (b*e^3/12), here we have a plate resting on a support (wood) whose resistance limits are known. I know it's a difficult problem but I really need to find a solution  without going through a rather heavy and not always accessible numerical modeling. We can forget about the 4 locking screws to identify a basic solution (perfectly centered load at first with perfect load distribution so no shear). It is first necessary to find a solution corresponding to an idealized situation and then we adjust as usual.

Kind regards

Ralph