What Does a 0 Degree Show in Elongation for Strain Gages?

[berdan]

Question from one of my exams,I am lgoing crazy becaue this is against everything I understand.
Please please please help me :
http://imageshack.us/f/189/examh.jpg/

Basicaly,I need to found what the "0" degree shows me on elongation.
As I look at the hole in the figure,I see the pressure everywhere is perpendicular to its surfice.
That means,the stress is perpendicular to the surfice,and there is no stress in direction of "a".
All the stress goes in direction of "b".

In my logic,that meansthis is case of simple Hook Law with use of Poisson ratio.Because the stress in the direction of b,then elongation there must be bigger.

But it is not the case.Why why why oh god why!??

Thanks in advance.

 

[NascentOxygen]

If the pressure causes the hole to enlarge, then (picturing it in 2D for simplicity) the circumference of the hole must increase, meaning 'a' is going to register strain.

A balloon stretches as contained air pressure increases, though pressure acts perpendicularly to the surface. Yes, it's not rigid, but the same idea would apply.

 

[berdan]

If the pressure causes the hole to enlarge, then (picturing it in 2D for simplicity) the circumference of the hole must increase, meaning 'a' is going to register strain.

A balloon stretches as contained air pressure increases, though pressure acts perpendicularly to the surface. Yes, it's not rigid, but the same idea would apply.

Offcourse,and according to Hook law,there will be strain even in the directions there is no stress.That is,perpendicular directions to stress will also change dimentions,according to Poison ratio.

What I don't understand is:
According to the exam,there is pressure "P" acting inside the hole,meaning it is perpendicular at every point to the hole circumference.

So-the bigger strain will be in the direction of the pressure.So,the strain gage "b",which is in the direction of the pressure (as it is perpendicular to the hole) should move more,than "a".
But infact,the answer is exactly the opposite:

"a" measure strain of 10^(-3)
"b" measures 2.5*10^(-4),which is exactly a*v (v-poison ratio).How can that be?Its supposedto be a=b*v,not the other way around!"b" should bebigger than "a"!

I hate this,nothing makes sense...

 

[NascentOxygen]

Imagine the pressure causes the "rigid" body to yield such that the "spherical" hole increases by 1mm in radius all around. (Simplifying to 2 dimensions) This will cause the circumference to increase by 2Pi mm. Hence you see the strain will be 6 times greater circumferentially (gage a) than radially (gage b). This is for 2 dimensions, so is only a rough guide to reality where we are involved with 3 dimensions.

Now, is that a sound basis on which to get you to revise your thinking?

 

[DeeNos]

Dear student,

I understand that you are struggling with a strain gage problem on your exam and it is causing you a lot of stress. I want to assure you that it is normal to feel overwhelmed when facing a challenging problem, especially in the field of science where there are often multiple factors and variables to consider.

Firstly, take a deep breath and try to calm your mind. It is important to approach this problem with a clear and focused mind in order to find the solution. Let's break down the problem step by step.

From the figure provided, it seems like you are dealing with a situation where there is a hole and a pressure acting on the surface of the material. You have correctly identified that the stress is perpendicular to the surface and that there is no stress in the direction of "a". This means that the stress is only acting in the direction of "b".

Now, you mentioned that you are using the simple Hook Law with the Poisson ratio. This is a good starting point, but it is important to consider the specific conditions of this problem. In this case, the stress is not evenly distributed throughout the material, as it is only acting in the direction of "b". Therefore, the Poisson ratio may not be applicable in this situation.

I would suggest looking into other equations or theories that may be more suitable for this type of problem. It could also be helpful to review any relevant class notes or textbook chapters to refresh your memory on different concepts and equations.

Remember, it is okay to ask for help when you need it. I would recommend reaching out to your professor or a teaching assistant for clarification or guidance on this problem. They are there to support you and help you understand the material better.

I hope this helps and I wish you all the best in solving this problem. Keep a positive attitude and don't give up, you can do it!