Geodynamics

[moertle]

A granite plate freely supported at its ends spans a gorge 20m wide. How this does the plate have to be if granite fails in tension at 20 MPa? Assume density is 2700 kg m^3.

This is a question in the textbook "Geodynamics" by Turcotte and Schubert. It is a question in chapter 3 (Elasticity and Flexure) question 3-14.

I've been working on this for two days and cannot figure out how to solve the question. I know the answer is 0.405m from the back of the book. I cannot figure out the equation to use for the problem. I have tried multiple equations from the book and I haven't figured out which equation to use.

 

Thanks!

[studiot]

 

How this does the plate have to be if granite fails in tension at 20 MPa? Assume density is 2700 kg m^3.

 

 

 

I am going to guess (I don't know the book) that your question should read

 

How thick this does the plate have to be if granite fails in tension at 20 MPa? Assume density is 2700 kg m^3.

 

Since no further information is provided (about the plate dimensions or tother loadings) I am further going to guess that you are meant to analyse the plate as a series of 1metre wide strips.

 

That will give you a volume and therefore a uniformly distributed load on each strip.

 

You can thus calculate the maximum bending stress in the middle.

This stress can be related to the horizontal tension and compression (shearing stress) distribution at that section by the usual 'bending equation' which will give you a value for the half-depth.

 

This is homework help so show us how you get on with this information and see if more help is required.

Don't just pick equations at random from the book, have a good reason for choosing.

 

Edit:

I thought someone had asked this before and I see that was about this time last year, but the OP never came back.

 

http://www.scienceforums.net/topic/86844-problem-314-turcotte-and-schubert-geodynamics/

 

We can certainly help you understand the problem so that you can arrive at the correct answer, what was the difficulty with the answer given in that thread?

 

Edited September 30, 2015 by studiot

[moertle]

I wrote this post before I saw the other one. I have actually figured it out. Thank you for taking your time to respond.