Moment of inertia in shear stress formula

[foo9008]

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 ?

 

[PhanthomJay]

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.

 

[foo9008]

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 ) ?

 

[PhanthomJay]

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.

 

[foo9008]

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 ...

 

[PhanthomJay]

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.