Understanding a stress equation

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Discussion Overview

The discussion revolves around understanding a specific stress equation presented in a book, focusing on the derivation and interpretation of the equation as well as the associated diagram. The scope includes conceptual clarification and technical explanation related to mechanics and material stress.

Discussion Character

  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • One participant expresses confusion about how the equation was derived, indicating a need for clarification on the steps involved.
  • Another participant explains that the confusion may stem from the division by dz and the cancellation of terms, providing a breakdown of the forces acting on the top and bottom surfaces.
  • A participant acknowledges their misunderstanding of the diagram, which contributed to their confusion about the equation.
  • There is a question about how to type formulas into the forum, indicating a desire for better communication of mathematical expressions.

Areas of Agreement / Disagreement

Participants generally express confusion about the equation and seek clarification, but there is no consensus on the understanding of the derivation or the interpretation of the diagram. Multiple viewpoints regarding the source of confusion and the steps in the derivation remain.

Contextual Notes

Limitations include potential misunderstandings of the diagram and the steps involved in the derivation of the equation, which have not been fully resolved in the discussion.

EGill
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I really need help understanding how the book created the equation from the book. I would really appreciate help understanding it. The attachment shows an image and the equation.
 

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They've divided by dz and canceled out some terms; that might be why it's a little confusing. The force (pressure times area) on the top surface is

[tex]\left[\sigma_y+\left(\frac{\partial \sigma_y}{\partial y}\right)dy\right]dx\,dz[/tex]

and the distance (lever arm length) is [itex]dx/2[/itex]. But the force on the bottom surface is

[tex]\sigma_y\,dx\,dz[/tex]

which creates a moment in the opposite direction that cancels out part of the moment from the force on the top surface. Starting to make sense now?
 
Wow, thanks so much. The cancelling of dz was part of what was confusing me. Also, I was just looking at the diagram incorrectly for no particular reason, but since I saw it wrong initially I could not get it out of my head.

Also, how do you type formulas into this forum?
 
Just click on the formula to see the markup language.
 
EGill said:
I really need help understanding how the book created the equation from the book. I would really appreciate help understanding it. The attachment shows an image and the equation.

tanks
 

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