Plate with hole, mechanics problem

In summary, the conversation is about finding the maximum stress in a mechanics problem. The plate is fully constrained at one edge and the stress is expected to be at the top and bottom of the hole. The speaker calculates the average tensile stress in section A and notes that the distribution is not even. They then ask for a hint and are advised to correct the thickness for the area calculation and use a stress concentration factor to get the peak stress.
  • #1
Dafe
145
0
Hey, I'm trying to solve a little mechanics problem and I'm stuck.

PlateWithHole.jpg


I want to find the maximum stress in the system. I know that it should be at the top and bottom of the hole. The plate is fully constrained at the left edge.

I find the average tensile stress in section A:

sigma = F/A = 2000N/(100-40)*2 = 1,67N/mm^2

I also know that the stress distribution in section A is not even.

Could someone give me a little hint?
Thanks
 
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  • #2
You're missing a 0 on the thickness for the area calculation. Once that is taken care of, you need the stress concentration factor that will be a function of the width of the plate and the hole diameter. That will multiply the average stress to get your peak stress.
 

1. What is a plate with a hole in mechanics?

A plate with a hole in mechanics refers to a common problem in solid mechanics where a plate with a hole is subjected to external loads, such as tension or compression. This problem is used to analyze the stress and strain distribution in the plate and is often used as a benchmark in engineering design.

2. What are the assumptions made in the plate with hole mechanics problem?

The assumptions made in the plate with hole mechanics problem include the plate being thin, isotropic, and homogeneous. The material is assumed to be elastic, and the deformation is assumed to be small. The hole is also assumed to be small compared to the dimensions of the plate.

3. How is the stress concentration factor calculated in the plate with hole mechanics problem?

The stress concentration factor is calculated by dividing the maximum stress at the hole by the nominal stress in the plate without the hole. This factor is used to determine the stress intensity factor and the critical stress for failure in the plate.

4. What is the purpose of studying the plate with hole mechanics problem?

Studying the plate with hole mechanics problem helps engineers and scientists understand how different materials and geometries behave under external loads. It also allows for the optimization of designs to reduce stress concentrations and prevent failure.

5. What are some applications of the plate with hole mechanics problem?

The plate with hole mechanics problem has many practical applications, including in the design of structures such as bridges, airplanes, and pressure vessels. It is also used in the analysis of cracks and notches in materials to determine their strength and durability.

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