Calculating Minimum Plate Thickness

In summary, the conversation centers around a project involving a 5052 Aluminum plate that will be subjected to 2200 lbs of force for load testing purposes. The dimensions of the plate are 27"x6.25"x?, and there are 14 bolts around the edges that affix it to a structure. The support conditions of the plate are discussed, with the suggestion to consider the long edges as fixed and the short edges as free. The conversation then shifts to finding an equation to relate plate thickness to max load without permanent deformation, and a formula for calculating stress on the beam is suggested. The concept of maximum failure or yield stresses for a given material is also discussed, with the recommendation to use the tensile yield strength for the specific
  • #1
7
0
I'm working on a project where I know that force will be applied by a bolt pulled through a hole in the center of an aluminum plate for load testing purposes (2200 lbs, actual worst case max force around 1500 with a 1.5 times safety factor), the dimensions (27"x6.25"x?), and the material (5052 Aluminum -- I thought about 6061 but I'm afraid it is probably too brittle).

We will be pulling on the plate with a static 2200 lbs for 1 minute for real world load testing. I was hoping to get an equation that related plate thickness to max load without permanent deformation. I would prefer to do the work myself(might come back for confirmation), but if needed I can provide more details! Thanks a lot for any help!
 
Last edited:
Engineering news on Phys.org
  • #2
You first need to specify the support conditions of the plate...is it supported on all 4 sides along the edges...fixed or simple, ,,,or just at the ends, fixed or simple.
 
  • #3
There are 14 bolts around the edges of the plate which affix it to a structure of very heavy aluminum. 7 (equidistance -- 4" apart) along each 27" side. I'm not sure what you mean by fixed vs simple. Thanks for your help.
 
Last edited:
  • #4
A fixed edge support means that there is no plate rotation at that edge. A simply supported edge means that there is plate rotation at the edge. Plate bending stresses and deformations depend on the support conditions. With so many bolts along the long edges, you can probably consider the long edges fixed, and the short edges free, although in reality, the 'fixed' edge is not quite fully fixed . You would need a plate handbook or computer program to solve for these stresses and deformations. I don't have one handy.

EDIT: In the absence of plate tables or a computer software program, you can conservatively assume that the plate is a simply supported beam 4 inches wide by 6 inches long with a concentrated load at the center, calculate the max moment, and then the section modulus required, and find the plate thickness required. You can try this yourself if you are familar with stress/deflection beam equations. I know what thickness I would use, but if I tell you that, I'd have to put a disclaimer on it, for obvious reasons.

__________________
 
Last edited:
  • #5
Isnt this a homework question?
 
  • #6
Nope, this is a problem for an actual project I'm doing on the side.
 
  • #7
PhanthomJay said:
EDIT: In the absence of plate tables or a computer software program, you can conservatively assume that the plate is a simply supported beam 4 inches wide by 6 inches long with a concentrated load at the center, calculate the max moment, and then the section modulus required, and find the plate thickness required. You can try this yourself if you are familar with stress/deflection beam equations. I know what thickness I would use, but if I tell you that, I'd have to put a disclaimer on it, for obvious reasons.

__________________

You have piqued my curiosity. Why are you using 4"x6" for the beam dimensions?

The equation I was looking at was

Deflection[meters]= ((Force[Newtons]*(Length[meters]/2))/(48 * Elastic Modulus[Newtons/Meter^2] * Moment of Inertia[meters^4])) * (2 Length[meters]^2)

Is this the correct equation for a single point load on a beam? I'm getting insanely small deflection (10^-8 m). I'm really not familiar with deflection of materials, so maybe this is correct? Thanks.
 
  • #8
cntchds: Your formula in post 7 is correct for deflection. However, post 1 indicates you need stress, not deflection. The formula for stress on the beam in post 4 is, sigma = 1.5*P*L/(b*t^2), where b = beam width.

In post 4, PhanthomJay is giving you dimensions of an equivalent beam that will give you a stress close to the maximum stress on your given plate.

Here is an arbitrary example of the above stress formula. sigma = 1.5*P*L/(b*t^2) = 1.5(10 000 N)(152.4 mm)/[(101.6 mm)(7.20 mm)^2] = 434 MPa.

Here is an arbitrary example of your deflection formula. y = P*(L^3)/(48*E*I) = (10 000 N)[(152.4 mm)^3]/{48(69 000 MPa)[(1/12)(101.6 mm)(7.20 mm)^3]} = 3.38 mm.
 
  • Like
Likes 1 person
  • #9
In the case of the stress formula that you have provided is there a way to know the max stress possible with a given material? I can see that for any value of t as it goes up stress decreases exponentially, and the opposite as it decreases. There must be a point at which the material fails from being too thin.
 
  • #10
For a given material, maximum failure or yield stresses are a property of the molecular structure of the material. Steel for example will yield at somewhere between 30,000 to 100,000 psi depending on its chemical content and grade etc. Wood pine or fir species might fail at 8000 psi or so. These are axial or bending stress maximums. Shear failures occur at lower stresses. Concrete unreinforced might rupture at 4000 psi compression or just say less than 1000 psi in tension, depending on the mix (primarily water/cement ratio). These values are found in tables and often determined by testing. One would hesitate to come up with a plate thickness in your example without looking at all possible failure parameters. In nvn's example, you are looking at about 5/16 inch thick plate for the assumed max stress noted. But as I mentioned, check other factors...like punching shear or bearing stresses.
 
Last edited:
  • Like
Likes 1 person
  • #11
cntchds said:
In the case of the stress formula you provided, is there a way to know the max stress possible with a given material?
Yes, I currently would say, probably use the tensile yield strength (Sty) for your material, instead of tensile ultimate strength (Stu). You will need to know the alloy name and number, including heat-treatment condition (or temper) number. What is the alloy name, number, and heat-treatment condition number, for your material? Do you have Stu and Sty for your specific material? E.g., for Al 5052-O (i.e., annealed), Stu and Sty might be Stu = 182 MPa, and Sty = 78 MPa (?). Is your plate at room temperature?
 
Last edited:

1. What is the purpose of calculating minimum plate thickness?

The purpose of calculating minimum plate thickness is to ensure that a plate or structural element is strong enough to withstand the anticipated loads and stresses it will experience in its intended use. It is an important aspect of structural design to ensure safety and structural integrity.

2. What factors are considered when calculating minimum plate thickness?

The factors that are typically considered when calculating minimum plate thickness include the type and magnitude of expected loads, the material properties of the plate, and the desired safety factor. Other factors such as corrosion, temperature, and environment may also be taken into account.

3. How is minimum plate thickness calculated?

Minimum plate thickness is typically calculated using engineering principles and equations, taking into account the factors mentioned above. This may involve considering the maximum stress in the plate, the material's yield strength, and the desired safety factor. Finite element analysis may also be used to accurately determine the minimum required thickness.

4. What are the consequences of not calculating minimum plate thickness?

Not calculating minimum plate thickness can have serious consequences, including structural failure, which could lead to injuries, property damage, or even loss of life. It could also result in the need for costly repairs or replacements, as well as potential legal consequences.

5. Are there any codes or standards for calculating minimum plate thickness?

Yes, there are various codes and standards that provide guidelines for calculating minimum plate thickness, such as ASME Boiler and Pressure Vessel Code, American Institute of Steel Construction (AISC) Manual, and American Society of Civil Engineers (ASCE) Minimum Design Loads for Buildings and Other Structures. It is important to consult these codes and standards when performing calculations for structural design.

Similar threads

  • General Engineering
Replies
2
Views
1K
Replies
1
Views
6K
Replies
10
Views
141K
  • Other Physics Topics
Replies
1
Views
1K
Replies
11
Views
1K
Replies
1
Views
799
  • Mechanical Engineering
Replies
7
Views
4K
  • General Engineering
Replies
11
Views
6K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
  • General Engineering
Replies
12
Views
3K
Back
Top