How to Calculate Change in Wall Thickness Under Axial Compressive Load

[Biru]

Homework Statement

A steel pipe..has a diameter of 116mm...length of 1.8m...and wall thickness of 8mm...gets pounded down by an axial compressive load of 180kN... Let's say that E (the elasticity) = 200GPa...and V(the poisson's ratio) is 0.3... i need to work out the CHANGE IN WALL THICKNESS ...how?? anyone??

Homework Equations

change in diameter = -0.3 x (change in length / initial length) x initial diameter
change in length = (bob x initial length) x E
bob = Force / Area (CSA)
CSA = Pi x radius squared

The Attempt at a Solution

I don't know where to go from here..HELP!

 

[Mapes]

Hi Biru, welcome to PF. What is the physical interpretation of the Poisson's ratio?

 

[Biru]

physical interpretation of poisson's ratio? how do you mean?

 

[Mapes]

What is Poisson's ratio?

 

[Biru]

0.3 haha sorry!

 

[Mapes]

Yes, for this problem. But what does Poisson's ratio mean?

 

[Biru]

its basically lateral strain / direct strain...the ratio between the two strains in other words...its mostly always 0.28 - 0.38... helps??

 

[Mapes]

- lateral strain / axial strain to be precise. So can you apply this information to the change in wall thickness?

 

[Biru]

rite..will i have to do it for both..the outside diameter and the inside diameter?

 

[Biru]

so change in diameter = -0.3 x -(change in length/initial length) x initial diameter?

 

[Mapes]

Looks like you've got the right idea. What's your final answer?

 

[Biru]

umm...the wall thickness changes by 204 nano meters??

 

[Mapes]

I'm getting a slightly different answer; how did you calculate yours?

 

[Biru]

well first I worked out bob = Force / Area (CSA)..soo -180kn / pi x (116mm/2)squared! got sumthing like -17.032 mega pascals...

then i worked out the change in length..using..

(bob x initial length) / Elasticity so (-17.032..MPa x 1.8) / 200GPa ..got me -153.289 nano meters...so bascially when the pipe got pounded by that 180kn the length shook by -153.29 nano meters..rite??

then I used that to work out the change in diameter (of the outer circle)...so delta d got me..2.964 nano meters..so the outside diameter increased by 2.96 nano meters...

then using the SAME change in length value (-153.29 nano meters)... I did the change in diameter again but this time using the inner circle so diameter of 100mm rather than 116mm... that got me 2.55 nano meters...

so the inner circle increased from 100mm to 100.00000255 mm...and the outer circle increased from 116mm to 116.00000296mm ..the difference between them two numbers was 204 nano meter higher than 8mm..

SO the wall thickness changed by 204 nano meters...NO??

 

[Mapes]

Check that cross-sectional area again; it's a hollow pipe!

 

[Biru]

umm...the only formula i kno is that.. pi x radius squared...

so wat wud it be for hollow pipe??
Pi x (bigger radius - smaller raidus) squared??

 

[Mapes]

Not quite. Keep thinking about it.

 

[Biru]

is it Pi/4 x ((d1^2) - (d2^2))??

 

[Biru]

Or is it...Pi x r1 squared - Pi x r2 squared??

 

[Biru]

i got -61.316 KPa for bob...is that rite??
bob = force / area..

 

[Mapes]

Is there a difference? Anyway, that looks good to me.

EDIT: That was addressed to your posts #18 and #19.

 

[Biru]

So the length decreased by 596.831 nano meters?
hence the outer circle diameter increased by 11.539 nano meters..so made it...116.0000115 mm...
and the inner circle diameter increased by 9.947 nano meters..so made it 100.0000099 mm..

So..the wall thickness changed by 776.4085 pico meters?? NO?

 

[Biru]

have i got it wrong again??

 

[Mapes]

I can't tell when you only show bits of your work at a time. Try showing your calculations systematically: for example,

Area = $\pi(r_o^2-r_i^2)$ = ... (value and units)
Load = force / area = ... (value and units)
Axial strain = (equation, value, and units)
Lateral strain = (equation, value, and units)
Change in wall thickness = (equation, value, and units)

This approach will be clearer to you, me, and future readers.

 

[Biru]

Sorry abt that..i shall do it rite away..2 mins..

 

[Biru]

im very new to this forum..so i dunt quite know how to have all those fractions and powers and stuff.. so it will take me years to write the stuff i have got scribbled on a piece of paper infront of me