How to Calculate Change in Wall Thickness Under Axial Compressive Load

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Homework Help Overview

The discussion revolves around calculating the change in wall thickness of a steel pipe subjected to an axial compressive load. The original poster provides specific dimensions and material properties, including diameter, length, wall thickness, elasticity, and Poisson's ratio, while seeking assistance on how to determine the change in wall thickness due to the applied load.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the implications of Poisson's ratio and its physical interpretation. There are attempts to apply the ratio to the problem, with questions about whether to consider both the outer and inner diameters in calculations. Some participants share their calculations and results, while others question the accuracy of the cross-sectional area used in the calculations.

Discussion Status

The discussion is ongoing with various interpretations and calculations being shared. Some participants have provided guidance on the correct approach to calculating the cross-sectional area of a hollow pipe. There is a mix of agreement and differing results, indicating a collaborative effort to clarify the problem without reaching a definitive conclusion.

Contextual Notes

Participants express uncertainty about the formulas and calculations involved, particularly regarding the treatment of a hollow pipe's cross-sectional area. There are indications of missing information and varying levels of familiarity with the forum's posting conventions, which may affect the clarity of the discussion.

Biru
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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 :confused: ...how?? anyone??:smile:

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! :bugeye:
 
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Hi Biru, welcome to PF. What is the physical interpretation of the Poisson's ratio?
 
physical interpretation of poisson's ratio? how do you mean?
 
What is Poisson's ratio?
 
0.3 haha sorry!
 
Yes, for this problem. But what does Poisson's ratio mean?
 
its basically lateral strain / direct strain...the ratio between the two strains in other words...its mostly always 0.28 - 0.38... helps??
 
- lateral strain / axial strain to be precise. So can you apply this information to the change in wall thickness?
 
rite..will i have to do it for both..the outside diameter and the inside diameter?
 
  • #10
so change in diameter = -0.3 x -(change in length/initial length) x initial diameter?
 
  • #11
Looks like you've got the right idea. What's your final answer?
 
  • #12
umm...the wall thickness changes by 204 nano meters??
 
  • #13
I'm getting a slightly different answer; how did you calculate yours?
 
  • #14
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??
 
  • #15
Check that cross-sectional area again; it's a hollow pipe!
 
  • #16
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??
 
  • #17
Not quite. Keep thinking about it.
 
  • #18
is it Pi/4 x ((d1^2) - (d2^2))??
 
  • #19
Or is it...Pi x r1 squared - Pi x r2 squared??
 
  • #20
i got -61.316 KPa for bob...is that rite??
bob = force / area..
 
  • #21
Is there a difference? Anyway, that looks good to me.

EDIT: That was addressed to your posts #18 and #19.
 
  • #22
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?
 
  • #23
have i got it wrong again??
 
  • #24
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.
 
  • #25
Sorry abt that..i shall do it rite away..2 mins..
 
  • #26
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
 

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