Strain gages problem

1. Sep 11, 2011

berdan

Question from one of my exams,I am lgoing crazy becaue this is against everything I understand.
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!!??

2. Sep 12, 2011

Staff: Mentor

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.

3. Sep 12, 2011

berdan

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...

4. Sep 12, 2011

Staff: Mentor

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?