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

In summary, the formula for calculating shear stress is τ= (V)(Q)/ (I)(t). In this problem, the author chooses to use Ixx instead of Iyy because the shear force is applied in the vertical direction, making Ixx the appropriate value to use. The reason for choosing the greater value of I is not because it can withstand greater stress, 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 can be calculated using the formula τ = (V)(Qx)/ (Ixx)(t), where V is the shear force, Qx is the first moment of the area between
  • #1
chetzread
801
1

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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  • #2
Yes, but the reason is to see which one is greater.
 
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  • #3
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...
 
  • #4
David Lewis said:
Yes, but the reason is to see which one is greater.
why we need to choose the greater ?
 
  • #5
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" ?
 
  • #6
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 ?
 
  • #7
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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  • #8
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...
 
  • #9
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.
 

1. What is shear stress and why is it important to calculate?

Shear stress is the force per unit area that acts parallel to a surface. It is important to calculate because it helps determine the strength and stability of a structure or material.

2. What is the difference between Ixx and Iyy when calculating shear stress?

Ixx and Iyy refer to the two principal moments of inertia, which are used to calculate shear stress. Ixx refers to the moment of inertia about the x-axis, while Iyy refers to the moment of inertia about the y-axis.

3. How do I know which moment of inertia to use for point P when calculating shear stress?

The moment of inertia to use for point P depends on the orientation of the shear force acting on the structure. If the shear force is acting parallel to the x-axis, then Ixx should be used. If the shear force is acting parallel to the y-axis, then Iyy should be used.

4. Can I use both Ixx and Iyy in my calculation for point P?

No, only one moment of inertia should be used for each calculation. Using both Ixx and Iyy may result in an inaccurate calculation of shear stress.

5. Are there any other factors that should be considered when calculating shear stress using Ixx or Iyy?

Yes, the material properties and cross-sectional shape of the structure should also be taken into account. Additionally, the location of point P and the magnitude of the shear force should be considered when determining the appropriate moment of inertia to use.

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