Central "through" crack with a concentrated load

[kajalschopra]

Hi, Please consider the problem below of a central through crack with a concentrated load as shown below.

Can someone please help where does one come across such a problem in a practical world?

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

Regards
Kajal

 

[jrmichler]

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.

 

[kajalschopra]

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.

 

[jrmichler]

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.

 

[Tom.G]

This is a known problem with airplanes where stress cracks develop around the rivet holes holding the skin on. (and other locations)
https://www.nytimes.com/2011/04/06/business/06air.html
https://theconversation.com/the-airbus-a380-wing-cracks-an-engineers-perspective-5318

This Google search returns over 8 000 000 hits.
https://www.google.com/search?&q=stress+cracks+in+airplanes

Cheers,
Tom