Calculating Shear Stress: Choosing Between Ixx and Iyy for Point P

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Discussion Overview

The discussion revolves around the calculation of shear stress at a specific point (P) in a structural member, focusing on the choice between using the moment of inertia about the x-axis (Ixx) versus the y-axis (Iyy). Participants explore the implications of this choice in the context of shear stress calculations, referencing the formula τ = (V)(Q)/(I)(t). The conversation includes elements of homework-related inquiry and technical reasoning.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants assert that both Ixx and Iyy should be considered to determine which yields a greater shear stress at point P.
  • Others clarify that the problem specifically asks for the shear stress at P, not the maximum shear stress, raising questions about the relevance of comparing Ixx and Iyy.
  • One participant seeks clarification on the problem statement, noting that part of the image is unclear, which may affect the understanding of the shear force applied.
  • Another participant explains that the choice of Ixx is due to the orientation of the shear force and the neutral axis, indicating that if the shear were applied horizontally, Iyy would be used instead.
  • It is mentioned that the proper value of I is chosen based on how the shear is applied, rather than simply which is greater.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of comparing Ixx and Iyy, with some advocating for this comparison while others emphasize the specific context of the shear stress calculation at point P. The discussion remains unresolved regarding the best approach to take.

Contextual Notes

There are indications of missing assumptions regarding the clarity of the problem statement, as well as the implications of the shear force's direction on the choice of moment of inertia.

chetzread
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Homework Statement


i know that to calculate the shear stress, formula is τ= (V)(Q)/ (I)(t)
So, why the author choose to use Ixx, but not Iyy for shear stress at P?

Homework Equations

The Attempt at a Solution


IMO, we should done the question in 2 ways, which are by using Ixx and Iyy respectively...Am i right?
 

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Yes, but the reason is to see which one is greater.
 
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David Lewis said:
Yes, but the reason is to see which one is greater.
but, the problem ask detremine shear stress at P , not maximum shear stress at P...
 
David Lewis said:
Yes, but the reason is to see which one is greater.
why we need to choose the greater ?
 
chetzread said:

Homework Statement


i know that to calculate the shear stress, formula is τ= (V)(Q)/ (I)(t)
So, why the author choose to use Ixx, but not Iyy for shear stress at P?

Homework Equations

The Attempt at a Solution


IMO, we should done the question in 2 ways, which are by using Ixx and Iyy respectively...Am i right?
The last part of the first line of the attachment is unclear. Does it say "... vertical shear force V = 3 kN" ?
 
SteamKing said:
The last part of the first line of the attachment is unclear. Does it say "... vertical shear force V = 3 kN" ?
Ya , so , what are you trying to say ?
 
chetzread said:
Ya , so , what are you trying to say ?
I'm asking for clarification of the problem statement is all. Part of image is too blurry for me to read.
 
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SteamKing said:
I'm asking for clarification of the problem statement is all. Part of image is too blurry for me to read.
Yes, it is...
 
chetzread said:
Yes, it is...
Do u know why Ixx is used here? Why not Iyy ?
 
  • #10
chetzread said:
Do u know why Ixx is used here? Why not Iyy ?
If you would answer my questions in Posts 5 and 7, I could probably tell you.

Why are you being so evasive in your replies?
 
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  • #11
SteamKing said:
If you would answer my questions in Posts 5 and 7, I could probably tell you.

Why are you being so evasive in your replies?
Yes, it's vertical shear force of 3kN...
 
  • #12
Because if a structural member can withstand the greater stress, it can also withstand lesser ones.
 
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  • #13
chetzread said:
Yes, it's vertical shear force of 3kN...
Thanks.

Since the shear force is applied in the vertical direction, the shear stress depends on Ixx rather than Iyy. From the diagram of the cross section, the neutral axis runs parallel with the x-axis.

Therefore, ##I_{xx} = \int y^2 \, dA##

which just happens to be greater than Iyy due to the orientation of the cross section.

The proper value of I is chosen not because it is greater, but because of how the shear is applied. If the shear were applied horizontally, then the shear stress at P would depend on Iyy instead of Ixx.

The shear stress at P is ##\tau = \frac {V ⋅ Q_x}{I_{xx} ⋅ t}##, where V is the shear force, Qx is the first moment of the area between P and the top of the cross section, calculated w.r.t. the neutral axis, Ixx is as discussed above, and the thickness of the section t is equal to the width of 100 mm.
 

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