# Central "through" crack with a concentrated load

• kajalschopra
In summary, the conversation discusses a problem with a central through crack and a concentrated load. The speaker shares their knowledge of elliptical cracks and their use in calculating stress concentration factors. They also mention that this type of problem is commonly found in textbooks of Fracture Mechanics and provide examples of where it may occur, such as in cracks around rivet holes in airplanes. The conversation ends with the speaker providing additional resources for further reading on the topic.
kajalschopra
Hi, Please consider the problem below of a central through crack with a concentrated load as shown below.

How will I have a concentrated load opening the crack? In the physical world, what is that "concentrated load"?

Regards
Kajal

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I have never heard of an elliptical crack with a concentrated load. The usual case of an elliptical crack is as shown below:

The figure is from Advanced Strength of Materials, by J.P. Den Hartog. Elliptical cracks have a simple analytical solution that is valid for any ratio of b/a. They are used to calculate theoretical stress concentration factors for holes ranging from round all the way to sharp cracks. The general topic is Theory of Elasticity.

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The problem is in every textbook of Fracture Mechanics. Can someone please help - in what practical scenarios does one come across such a problem, it is mentioned ina text that the scenario occurs in cracks in rivet holes, however, I cannot understand how.

I cannot think of a practical scenario involving a concentrated load in a crack. It certainly does not apply to riveted joints because rivets are ductile, as is the material being riveted. Standard analysis methods for riveted connections assume ductility, so are not based on calculated stress concentration factors.

## 1. What is a "Central" through crack with a concentrated load?

A "Central" through crack with a concentrated load is a type of structural crack that occurs when a concentrated force is applied to the center of a material, causing it to fracture along its entire width.

## 2. What causes a "Central" through crack with a concentrated load?

A "Central" through crack with a concentrated load is typically caused by a sudden impact or overload on a material, such as a heavy object being dropped on a surface or excessive pressure being applied to a single point on a structure.

## 3. How is a "Central" through crack with a concentrated load different from other types of cracks?

Unlike other types of cracks that may occur due to fatigue or corrosion, a "Central" through crack with a concentrated load is a result of a single, concentrated force being applied to a material. This type of crack is also more likely to occur in brittle materials such as ceramics and glass.

## 4. What are the potential consequences of a "Central" through crack with a concentrated load?

A "Central" through crack with a concentrated load can significantly weaken a material and compromise its structural integrity. This can lead to catastrophic failures, especially in critical structures such as bridges and buildings.

## 5. How can "Central" through cracks with a concentrated load be prevented?

To prevent a "Central" through crack with a concentrated load, it is important to use materials with appropriate strength and durability for the intended application. Regular inspections and maintenance can also help identify and address potential cracks before they become a safety hazard.

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