# What thickness do I need for a 30x30 (cm) aluminium plate to hold 350Kg on three points?

I want to make a strong connected weight-scale Arduino project, for which I already own 3×350Kg sensors (red). I plan to make the plate (green) around 30cm×30cm in 99.5 Brut aluminum, with my three sensors placed in T (two on rear of left and right sides and the third one in the middle of the front side), and the local pressure on the plate should not exceed 5 Mega Pascal (Yellowish). However, I know nothing about strength of materials computation. What minimal thickness would I need in order for my plate to bear such a load ?

I have read somewhere that I should avoid the deformation to be more that 0.1%×dimensions (i.e : 0.3mm), and, according with Wikipedia,

• Young's modulus = 70 GPa
• Shear modulus = 26 GPa
• Bulk modulus = 76 GPa
• Poisson ratio = 0.35

However, I have no idea what to do with those numbers. All explanations I found on the net were much too complicated in regard with the problem and to know what to do with it.

• The modulus numbers (and poisson's ratio) describe the elastic behavior -- stiffness. I'm guessing you just want to support a load and can accept some deflection. If so, you would want a measure of "strength" of the material, describing its plastic deformation and/or failure. Specified as a stress (units of force/area, like pressure). Yield strength would be a good one to use, with some safety factor. For the three point support you'd need to look up a formula that converts the geometry and load to a measure of max stress (a side discussion in itself), and compare that to the yield stress. Jan 23, 2021 at 4:11
• A I told in the post, I know nothing about that, and I don't understand much about what you just said. X-D Jan 23, 2021 at 4:15
• So is your load 3 * 350 kg point loads or 5 MPa evenly distributed? Jan 23, 2021 at 6:39
• Tip: 'kg' for kilogram, 'Kg' would mean kelvin-gram (nonsense). Similarly 'Pa' or 'pascal'. SI units named after a person have their symbols capitalised and are lowercase when spelled out. Capitals matter! Jan 23, 2021 at 11:04
• Ooops, sorry about that. When I was a kid in the seventies, I was taught that multiple were to be written uppercase et submultiples lowercase (in order to differentiate deci and Deca), and I didn't know that this was changed with the international system. Jan 23, 2021 at 15:09

My reputation is too low to comment so I'll give some pointers in an answer :)

Looking at your design your structures weak points are the areas where the plate and the sensors interface, especially the ones in the corners. This is because you have a very long lever from your load to the feet of your sensors and a very small contact area between the sensor and plate. If you could move the sensors feet closer together this would dramatically reduce the stress on the middle plate, as close as you can without making the scale too unstable.

Regarding stress and deformation they actually don't matter for your application as long as the sensors remain level and nothing but the sensors feet touch the ground/table. This assuming you are not planing on loading this scale millions of times and failure due to fatigue start to matter.

As it is right now the question can not be answered because the dimensions of the sensors, and the details about how the plate will/can interface with the sensors, are unknown.

If you could provide some more details about your sensors, preferably a model name and datasheet, perhaps you could get a more elaborate answer.

EDIT: Based on your feedback I did some simple simulations to illustrate how your plate will behave and give you some numbers to work with. I'm not sure what material you are planing on using because 99.5 Brut seems to be related to purity and does not specify any specific alloy.

In my examples i use Alloys 1060 and 6061-T6. The deflections in the simulation are highly exaggerated for illustrative purposes, in reality you can barely see that it bends.

Deflection 8mm, 6061-T6, 3500N evenly distributed.

Stress (Von Mises). 8mm, 6061-T6, 3500N evenly distributed.

As you can see, the plate is barely loaded and the maximum deflection is 1.3 mm which is fine for your case unless your feet are a fraction of a millimeter.

Since both materials have the same Modulus of Elasticity, about 70 GPa, the stress and deflections are valid for both. However, 1060 has a yield stress of 27,6 MPa meaning it's no longer elastic deformation, it's plastic (permanent) deformation.

Simulating plastic deformation is a lot more complicated and nothing I will go elaborate further on here, it means however that the result is not valid for 1060 and a 8mm 1060 plate would not satisfy your requirement.

A 10mm 1060 plate would however work but be on the limit.

For 6061-T6 you can go a lot thinner since it can handle much higher stress. Here are som plate thicknesses and their corresponding deflections. 6mm => ~3mm 5mm => ~5mm 4mm => ~10mm 3mm => ~22mm

At 3mm thickness we are really at the limit of what 6061-T6 can handle. Even though 3mm 6061 can handle the load, at 22mm deflection your sensors are no longer upright and their output will no longer be valid for your application.

I hope this gives you some more insight into how the plate thickness (and choice of aluminum) would affect your scale :)

• Hello @Jollerprutt, Thank-you for your reply. I designed it that way, in order to avoid having to put an additional spacer between the captors and the plate. My problem is more about knowing the resistance of aluminum than to improve the design (I could always do it, but first I need to evaluate how it behaves in regard of the thickness). I have no Idea how to use those numbers i got from Wikipedia. Here is the sensors I bought : fr.aliexpress.com/item/32618535872.html (the pictures are correct, but the drawing does not match it - The dimensions are approximately 15×4×4 (cm) ) Jan 24, 2021 at 18:41
• Thank you for your reply and simulations. The deformation is more than I expected. It's good that I asked the question ;-). I can also have an alloy, but I have no idea about it's characteristics (all I know is "Quenched Almgsi 1", so I will compare the prices (and the weight) for the 10mm "pure" and the 8mm alloy. Thank you again. - Oh, And by the way, what software did you use to make those simulations ? Jan 25, 2021 at 8:20
• @Camion Al-Mg-Si sounds like 6000 series Wikipedia, like I used in the example :) I used the built in simulator in Solid Edge 2020, which I think is NX Nastran under the hood. Jan 25, 2021 at 11:57