Moment of inertia in shear stress formula

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Discussion Overview

The discussion revolves around the moment of inertia in the context of shear stress formulas, particularly focusing on its calculation about different axes in relation to a beam's neutral axis. Participants explore the implications of these calculations in a homework context.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions whether the moment of inertia calculated in a provided example is correct, noting the distinction between the neutral axis and the axes used in the calculations.
  • Another participant clarifies that the moment of inertia is indeed calculated correctly about the horizontal neutral axis, defining the axes in relation to the beam's orientation.
  • A participant expresses a misunderstanding but later clarifies their understanding of the moment of inertia as being about the neutral axis, specifically Ixx, and questions the necessity of considering Iyy.
  • It is noted that bending moments are about the horizontal neutral axis, and shears are along the y-axis, indicating that Iyy is not relevant for the current problem unless the loading direction changes.
  • One participant defines the y-axis differently than the textbook, suggesting a potential source of confusion.

Areas of Agreement / Disagreement

Participants generally agree on the calculation of the moment of inertia about the neutral axis, but there are differing interpretations regarding the definitions of the axes and the relevance of Iyy in this context. The discussion remains somewhat unresolved regarding the definitions and their implications.

Contextual Notes

There are limitations in the definitions of axes as understood by participants, which may affect their interpretations of the moment of inertia calculations. The discussion does not resolve these definitional discrepancies.

foo9008
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Homework Statement


In the first photo , i was told that the I represent the moment of inertia about the neutral axis ... But , in the 2nd photo , i found that the author calculate the moment of inertia about the x-axis (parallel to neutral axis ) and y -axis ( perpendicular to neutral axis) ...

Homework Equations

The Attempt at a Solution


So , is the example in the second photo wrong ?
 

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Not sure what you mean. The moment of inertia is correctly calculated about the horizontal neutral axis of the beam's cross sectional area. If you call the x-axis as the axis along the beam's 8 m length, and the y-axis as the vertical axis, then the horizontal neutral axis in question lies along the z axis into the plane of your screen.
 
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PhanthomJay said:
Not sure what you mean. The moment of inertia is correctly calculated about the horizontal neutral axis of the beam's cross sectional area. If you call the x-axis as the axis along the beam's 8 m length, and the y-axis as the vertical axis, then the horizontal neutral axis in question lies along the z axis into the plane of your screen.

sorry , i misunderstood something . Clear now .

For second question , i let the horizontal axis as x-axis ( which is also the neutral axis) ...So , the moment of inertia is about the neutral axis , which is only Ixx only , right ? We don't have to consider Iyy ( moment about vertical axis , right ) ?
 
foo9008 said:
sorry , i misunderstood something . Clear now .

For second question , i let the horizontal axis as x-axis ( which is also the neutral axis) ...So , the moment of inertia is about the neutral axis , which is only Ixx only , right ? We don't have to consider Iyy ( moment about vertical axis , right ) ?
That is correct, because the bending moments are about the horizontal neutral axis and shears are along the y axis. If the moments were about the vertical neutral axis (loading into the plane of the screen) then you would have to consider Iyy. This is not the case here.
 
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PhanthomJay said:
That is correct, because the bending moments are about the horizontal neutral axis and shears are along the y axis. If the moments were about the vertical neutral axis (loading into the plane of the screen) then you would have to consider Iyy. This is not the case here.
I defined y-axis as the axis that is up , which is not into the book ...
 
You don't have to worry about the y axis. Not for this problem. If applied loading was into the book, only then would you need to consider weak axis bending about the vertical y axis.
 
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