# Elastic moduli question

1. Jan 21, 2014

### KiNGGeexD

Question;

The shank of the bold has a diameter of 1.2cm and a head height of 0.8cm. What is the maximum tensile load that the bolt can withstand if it's ultimate shear strength is 3.5*10^8 N/m^2

I have attached a photo of the diagram given in the question.

My attempt

I noticed that this is a question about shear modulus and could easily compute the force but the only thing I don't have in order to do so is the change in x?

Any help would be fantastic I should say this is merely a practice text book question and not an assignment or anything:) cheers again!

Oh and the answer given was 1.06*10^4 N :):)

2. Jan 21, 2014

### nschaefe

I think i'm doing this right as I was able to get the answer you provided but no promises...

First off, I am assuming you know the difference between shear stress and normal stress. From the diagram, where on the bolt will it be experiencing a shear stress? Specifically, you want to identify the area under consideration. Remember for shear, the direction of force should be parrallel with the area you are considering

Secondly, look at the units of stress, and figure out how you can form those units from what your given in the problem statement

3. Jan 21, 2014

### KiNGGeexD

Yea I know that shear stress is caused by a tangential force applied!:) also I image that the stress is on the bolt head?

4. Jan 21, 2014

### KiNGGeexD

I know stress is N/m^2

So F/A

5. Jan 21, 2014

### KiNGGeexD

So is the max shear strength not the shear modulus?

6. Jan 21, 2014

### KiNGGeexD

But even though the units match up the change in x/initial x is unit less so wouldn't affect the dimensional analysis

7. Jan 21, 2014

### nschaefe

You are on the right track, now you need to identify the correct area to use

No, ultimate shear strength is the breaking point of the material, i.e. the maximum shear stress it can withstand before catastrophic failure, whereas the shear modulus is more like a spring constant which relates change in length to applied shear stress as you noted.

I don't believe you will need the shear modulus at all for this problem.

8. Jan 21, 2014

### KiNGGeexD

Ahh ok I was confusing myself :) thanks for your help. Much appreciated

9. Jan 21, 2014

### nschaefe

On second though I may be incorrect... My answer was 10.55 E4 which is a whole magnitude off of yours. Sorry if I'm approaching this incorrectly. Can you confirm that the answer is 1.06 E4 not 10.6E4?

10. Jan 21, 2014

### KiNGGeexD

Yea 1.06, I also got 10.6 though:( haha