Problem 3.14 Turcotte and Schubert, geodynamics

[artoriusdidier]

Problem 3.14

A granite plate freely supported at its ends spans a

gorge 20 m wide. How thick does the plate have to

be if granite fails in tension at 20 MPa? Assume ρ =

2700 kg m−3.

Hello,

I must resolve this problem ("Geodynamics"), but I don't understand the methodology to obtain the answer (0.405 meter). If someone may explain me how begin this problem, I'm very interested.

Regards

Artorius

[studiot]

Good morning Artorius.

 

I do not know your background so I don't know what you should know about this question.

 

I can confim that if I take the acceleration due to gravity as 10 m/sc² then I get the figure of 0.405m, using the simplest beam theory.

 

That is dividing the plate into 1mete wide strips and considering each strip as a separate beam.

 

So lets start at the beginning

 

What do you understand freely supported to mean?

If you can state in words what you think might be happening, perhaps together we can convert that to math.

Edited December 13, 2014 by studiot

[studiot]

Looking in the opus citatus I see you are studying section 3.10, where the necessary theory is developed.

 

Are you attempting all the questions 3.12 through 3.15 or just 3.14?

 

The actual formula you need is not stated in section3.10, although similar situations are discussed, but the formula you need is the subject of question 3.13.

 

Are you bothering to come back to SF?

There is a lively Earth Science section, with several knowledgable members.

Edited December 14, 2014 by studiot

[moertle]

Studiot,

 

I have a question regarding this post. I am currently working on the problem and cannot figure out the equation to use for this problem. You mention the simple beam theory but I cannot seem to find the correct equation from that theory to use for this question. Can you please elaborate?

 

Moertle