Variation of shear stress at the rectangle cross section

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Discussion Overview

The discussion revolves around the variation of shear stress in a rectangular cross-section of a beam, focusing on the maximum shear stress locations and the applicability of shear stress formulas. Participants explore different diagrams and concepts related to shear stress distribution, particularly in the context of engineering mechanics.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants express confusion about why shear stress is considered maximum at the edge of the beam, suggesting that it varies parabolically across the vertical length.
  • Others clarify that vertical shear stress distribution is parabolic along the height, while horizontal shear stress is linear across the flange, and that it can be assumed constant across the thickness of the web or flange.
  • One participant notes that the shear formula may not yield accurate results at the flange-web section due to stress concentrations, questioning the suitability of the shear formula in these cases.
  • Another participant mentions that the shear stress formula is an approximation adequate for most applications, but acknowledges that more complex topics like stress concentrations require advanced knowledge.
  • There is a discussion about the complexity of deriving exact solutions for shear stress, with some participants suggesting that it is a graduate-level topic and may not be necessary for current understanding.
  • Clarifications are made regarding the interpretation of figures related to shear stress, with participants confirming the views represented in the diagrams.

Areas of Agreement / Disagreement

Participants generally express confusion and seek clarification on the concepts, indicating that multiple competing views remain regarding the interpretation of shear stress distribution and the applicability of the shear stress formula. The discussion does not reach a consensus on these points.

Contextual Notes

Participants highlight limitations in the shear stress formula's accuracy at points of stress concentration and the complexity of advanced topics such as elasticity theory, which may not be fully understood at the current level of discussion.

fonseh
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Homework Statement



In the notes , I don't understand why the shear stress is maximum at the edge ( circle part) .

Homework Equations

The Attempt at a Solution


I think it's wrong . Refer to another diagram attached , i found that the shear stress varies parabolically across the vertical length of the beam ... Or they are different case ? Can you explain the case in photo 1 ? [/B]
 

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fonseh said:

Homework Statement



In the notes , I don't understand why the shear stress is maximum at the edge ( circle part) .

Homework Equations

The Attempt at a Solution


I think it's wrong . Refer to another diagram attached , i found that the shear stress varies parabolically across the vertical length of the beam ... Or they are different case ? Can you explain the case in photo 1 ? [/B]
fonseh you are getting way too deep on this this is grad school level stuff. Stick to the basics. Vert shear stress distribution is parabolic along the height and horiz shear stress is linear across the flange. You may assume that it is constant across the thickness of the web or flange or rectangle,
 
PhanthomJay said:
fonseh you are getting way too deep on this this is grad school level stuff. Stick to the basics. Vert shear stress distribution is parabolic along the height and horiz shear stress is linear across the flange. You may assume that it is constant across the thickness of the web or flange or rectangle,
ok , that's the explanation for figure 2 in post # 1 , and I understand it . Can you explain based on figure 1? what is it about ? I don't really understand it
 
It's also stated at the bottom of the notes, the shear formula will not give accurate results when used to determine the shear stress at flange -web section, stress concentration here ... why the shear formula is not suitable to caluculate the stress at stress sudden change part ?
 
fonseh said:
It's also stated at the bottom of the notes, the shear formula will not give accurate results when used to determine the shear stress at flange -web section, stress concentration here ... why the shear formula is not suitable to caluculate the stress at stress sudden change part ?
The shear stress formula is an approximation which is good enough for most applications. If you want to learn grad school topics at this stage, , like stress concentrations at discontinuities or non constant shear stress across a width, then first learn about partial differential equations and then google on Theory of Elasticity and then I wish you luck.
 
PhanthomJay said:
The shear stress formula is an approximation which is good enough for most applications. If you want to learn grad school topics at this stage, , like stress concentrations at discontinuities or non constant shear stress across a width, then first learn about partial differential equations and then google on Theory of Elasticity and then I wish you luck.
do you mean the notes in photo 1 is another way we can find the shear stress which is at grad school stage ?
 
fonseh said:
do you mean the notes in photo 1 is another way we can find the shear stress which is at grad school stage ?
Yes, but it is quite complex to get an exact solution and you should not dwell on it. I was ready to quit engineering when I took elasticity theory in grad school land I've long forgotten it except to know that sttess concentrations occur at corners and edges and holes . Forget about it!
 
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PhanthomJay said:
Yes, but it is quite complex to get an exact solution and you should not dwell on it. I was ready to quit engineering when I took elasticity theory in grad school land I've long forgotten it except to know that sttess concentrations occur at corners and edges and holes . Forget about it!
just to be sure , the figure in 7-6 a and 7-6 b is the view of the blue plane, am i right ?
 

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fonseh said:
just to be sure , the figure in 7-6 a and 7-6 b is the view of the blue plane, am i right ?
Yes, that is the plane, but the plane is within the beam at a cut cross section. The vertical (and longitudinal) shear stress is maximum at the neutral axis and can be assumed constant across the width of the section, although in actuality is higher at the edges of the neutral axis.
 
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PhanthomJay said:
Yes, that is the plane, but the plane is within the beam at a cut cross section. The vertical (and longitudinal) shear stress is maximum at the neutral axis and can be assumed constant across the width of the section, although in actuality is higher at the edges of the neutral axis.
thanks , i am much clearer on this concept now !
 
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