Principal stress at surface of thin walled pipe

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Discussion Overview

The discussion revolves around calculating the principal stress at the surface of a thin-walled pipe, specifically focusing on determining the axial stress and the necessary parameters for using Mohr's circle for stress transformation. The context is a homework problem that involves stress analysis in engineering mechanics.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant seeks guidance on how to find the axial stress (σx) and the transverse stress (σy) for a thin-walled pipe under an axial load, noting that internal pressure should be ignored.
  • Another participant asks if a free-body diagram has been drawn and if the axial stress has been determined, also inquiring about the stress due to internal pressure.
  • A participant provides a calculation for the area (A) of the pipe's cross-section and computes the axial stress (σax) based on an axial force of 200 lb.
  • Subsequent replies challenge the accuracy of the area calculation, with corrections suggested regarding the method of calculating the area of a circle.
  • Participants express frustration over calculation errors, with one participant acknowledging confusion over diameter and radius in their calculations.
  • Finally, a participant claims to have resolved their calculations and submitted the assignment, although the accuracy of their final values remains unverified by others.

Areas of Agreement / Disagreement

There is no consensus on the correct calculation of the area or the resulting axial stress, as multiple participants challenge each other's calculations without reaching an agreement on the final values.

Contextual Notes

Participants express uncertainty regarding the correct method for calculating the area of the pipe's cross-section, and there are unresolved issues related to the assumptions made about internal pressure.

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Homework Statement


See attached jpg for problem statement and diagram.

I know we didn't discuss this type of problem in class. The rest of this homework set has been solving stress transformations with Mohr's circles for a given state of stress. I know how to find τxy (that was supposed to be "tau"). So, once I find σx and σy, I know what to do with Mohr's circle to find the principal stress.

If someone could point me in the right direction for how to find σx and σy, that would be great.

Thank you!
Any hints would be greatly appreciated.

P.S.
This is due in about 12 hours.***Just remembered that my professor told us to ignore the internal pressure. So, to find sigma x and sigma y, I only use the 200 lb axial force?
 

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Have you set up an axis system and drawn a free-body diagram of the problem yet?
Do you know how to determine the axial stress?
Do you know how to determine the stress in the pipe wall due to internal pressure?
 
1. Yes, I have.
2. I believe so:
A = ∏(0.5)2-∏(0.5-0.025)^2 = 0.0766 in2
σax=P/A = 200 lb/ (0.0766 in2)
= 2611.77 psi
3. just remembered that we were told to ignore the internal pressure

Is my axial stress correct? And how do I get σ1,2 from here?
 
Your calculation of A is incorrect. Re-read the description of the pipe carefully.
 
Oops. I read it as the outer diameter. Now I get A = 0.0805 in^2 and σ = 2484.37 psi.
 
Sorry, A is still incorrect. You should review how to calculate the area of a circle.
 
Wow. Maybe I should try doing homework when I am actually awake. diameter...radius
So, A = 0.0131 in^2, and σ= 15238.1 psi.
 
Sorry, you are just not calculating the correct A. you have forgotten to multiply by pi.
 
Well, I think I've got it now, and in any event, I've now turned in the assignment.
 

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