0

enter image description here

In the image is a design for a chemical etched piece of metal. Shown in white are holes formed in a sheet of metal, which is shown in grey. Highlighted in the red circle is one of four sections that connect the circular shape in the centre to the rest of the sheet, which is larger than shown in the image. In order to prevent these connecting sections breaking under the weight of the circular shape, how can the required thickness vs length of these connecting sections be calculated? 

The thickness of the metal sheet is known. The weight of the circular shape is known. The flexural strength, tensile strength and shear strength of the material is known. Can a safe working minimum thickness, and maximum length for the four connecting sections be calculated, or estimated based on this information?

EddieP
  • 121
  • 2
  • If you know the shear strength, the area of the connection and the mass of the centre piece you should be good to go. – Solar Mike Jan 17 '23 at 14:34
  • Pay attention to any dynamic or external loads, though. It'll avoid nasty surprises when you build the physical article and use it for a while. – TimWescott Jan 17 '23 at 16:18

2 Answers2

1

If we assume both the Disk and the sheet are rigid compared to the tabs. Then we can figure stresses in the tab by considering it as a beam with length $l$ under a load $P$ a quarter of the weight of the disk, as per the figure.

This is a fix-fix joint beam that will deflect as shown, so by symmetry, we can calculate only the shear and bending moment on half of it as a cantilever beam.

  • Length = L/2
  • width = b
  • depth = h $$M=\frac{PL}{2}$$ $$\sigma= \frac{MC}{I}=MS=Mbh^2/6$$ $$V=P$$ $$v = 1.5V/A= 1.5 \frac{P}{bh}$$

.

cant beam

kamran
  • 21,714
  • 2
  • 18
  • 38
  • Thank you for your answer. That is exactly what I was looking for. Can I just confirm something? It is my understanding that I can use the formula M=PL/2 to find the Bending Moment M, and I can then use the Bending Moment M, in the formula =ℎ2/6 to find the Bending Stress - is this correct? Can I just also confirm the units for each value? P - kilograms. L, b, h - millimeters. M - newton meters? - newtons per square millimeter? I was not clear on this point. Thank you so much again. I really appreciate your answer! – EddieP Jan 18 '23 at 13:59
  • @EddieP, yes exactly. you can youse any system of units, except you have to be consistent. If you use lbs. inch you get the stress lbs/in^2 if you use kg .centimeter you get the stress kg/cm^2. – kamran Jan 18 '23 at 20:14
0

Short answer is, yes, it can. You need to calculate the total force acting normal the sheet (shear). You also need to know the material strength to calculate the resistance to applied force through 2nd moment of area (moment of Inertia).

Consider the force required to bend a flat plastic ruler. Now consider the forces required to bend that same ruler edgeways. That's the difference implied in what you need to know.

The longer the connecting pieces the greater the torsional twisting effect there will be under applied load.

If the connector pieces are rectangular with greater depth than breadth then higher force tolerance may be expected. As the length of them increases, so will torsional bending occur.

Depending on the material used, you may want to consider more connections to the disc

Rhodie
  • 942
  • 4
  • 15