# Mechanical engineering - Stress concentration

• Mechstudent
In summary, the conversation revolves around determining the maximum force that can cause failure in a block with two drilled holes. The approach involves calculating D/W ratios and corresponding K factors, using the stress concentration chart and dividing the result by the factor K. There is some uncertainty about how to handle multiple stress concentration areas and the dimensions of the block. The conversation also suggests seeking help from an engineering forum for further assistance.
Mechstudent
1. In my materials science's exam, I had the following question: What would be the maximum force F to cause failure in a block that has been drilled at two place?
See following drawing:

(Lame paint skills, I know..)
2. Homework Equations

1) D/W
2) σ = F/S

## The Attempt at a Solution

1)First, I calculated both D/W ratios. In this case, D/B and d/B
2)Once I had this ratio, I found the corresponding K factors by using the Stress Concentration Chart for hole in a plate.
3) This is where I get blocked. I am unsure what to do with the factors. What I did was pick the hole with the highest corresponding K factor, and ignore the other. I do not know if I have to interpolate between or add them somehow.
4) Using σ = F/S, I know that σ*S = F and that:
S = C * (B-d-D) which is the area of the top rectangle
Since the material is brittle, The ultimate strength is the maximum
So:
x * C * (B-d-D) = F
Because there is stress concentration, The result has to be divided by the factor K.
So my answer was
(x * C * (B-d-D))/K = F max
I wasn't able to find an example where there is more than a single stress concentration area(in this case, two holes instead of one), So I do not know how it adds up, and whether all the necessary information is in the image or not.

#### Attachments

• drawing.png
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• chart.png
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This is not an area I know anything about, and all I could find on the net that might handle this level of complexity is behind pay walls.
That said, a possible approach is notionally to split the block with a vertical partition between the holes. The idea is that the split should be where the "flow line" is straight. The external load would be apportioned in proportion to the width of the block piece.
If you have a formula/chart, whatever, that handles a single hole placed asymmetrically in a block then you could define this split such that each hole would fail at the same external load.

Edit2:
Do you have the actual dimensions? If the gap between the holes is no greater than the distance from each hole horizontally to the edge of the block then you can probably treat the plate as infinite and just concentrate on failure of the section between the holes. So each side of the partition is a semi-infinite plate. I do at least see links to such analysis, but, again, behind pay walls.

Edit: this is probably the wrong forum for such a question. Have you tried posting it on an engineering forum here? https://www.physicsforums.com/forums/engineering-and-computer-science-homework.158/

Last edited:

## 1. What is stress concentration in mechanical engineering?

Stress concentration refers to the phenomenon where stress in a material is significantly increased at a specific point due to a geometric or material discontinuity. This can lead to failure of the material at lower stress levels than expected.

## 2. What causes stress concentration in mechanical engineering?

Stress concentration can be caused by a variety of factors, including sharp corners, changes in cross-sectional area, holes, and notches in a material. These discontinuities can cause stress to become localized, leading to higher stress levels.

## 3. How is stress concentration calculated?

The stress concentration factor (Kt) is used to quantify the increase in stress at a specific point compared to the average stress in the material. It can be calculated using theoretical equations or determined experimentally through testing.

## 4. How can stress concentration be reduced in mechanical engineering?

There are several ways to reduce stress concentration, including using gradual transitions in geometry, smoothing sharp corners, and adding fillets or grooves to distribute stress more evenly. Material selection and proper design considerations can also help reduce stress concentration.

## 5. What are the implications of stress concentration in mechanical engineering?

Stress concentration can have serious implications for the structural integrity and longevity of mechanical components. It can lead to premature failure, which can be costly and dangerous. Therefore, it is important for engineers to consider stress concentration when designing and analyzing mechanical systems.

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