Moment of inertia in shear stress

[chetzread]

Homework Statement

In the question , the author calculated the Ixx and Iyy , but he used the greater value (Ixx) in the calculation to calculate the shear stress , why did he do so ? why the greater value is used ?

Homework Equations

The Attempt at a Solution

 

[chetzread]

btw , Ixx means he author applied the force at the top of the T beam ??

 

[SteamKing]

Homework Statement

In the question , the author calculated the Ixx and Iyy , but he used the greater value (Ixx) in the calculation to calculate the shear stress , why did he do so ? why the greater value is used ?

Homework Equations

The Attempt at a Solution

It's not clear why the author chose to calculate the moment of inertia (MOI) about both axes, since there is a loading applied to this beam in only one direction. My guess - the author wanted to illustrate how the calculation changes when different axes are used.

The MOI used by the author to calculate bending stress is greater about the x-x axis because the T-section is deeper than the top flange is wide. Therefore, orienting the T so that its deeper dimension is parallel to the plane of the applied load will produce a beam having the maximum strength, and consequently, the lowest bending stresses.

This article explains how the MOI is calculated and how it is related to finding the bending stress in a beam:

http://adaptivemap.ma.psu.edu/websites/moment_intergrals/rectangular_area_moment_of_interia/rectangularareamomentofinteria.html

btw , Ixx means he author applied the force at the top of the T beam ??

Not necessarily.

The cross section of the beam is a plane, and typically the axes of this plane are assumed to be x-axis parallel with the neutral axis, and the y-axis is vertical, or otherwise noted in the problem statement.

 

[chetzread]

It's not clear why the author chose to calculate the moment of inertia (MOI) about both axes, since there is a loading applied to this beam in only one direction. My guess - the author wanted to illustrate how the calculation changes when different axes are used.

The MOI used by the author to calculate bending stress is greater about the x-x axis because the T-section is deeper than the top flange is wide. Therefore, orienting the T so that its deeper dimension is parallel to the plane of the applied load will produce a beam having the maximum strength, and consequently, the lowest bending stresses.

This article explains how the MOI is calculated and how it is related to finding the bending stress in a beam:

http://adaptivemap.ma.psu.edu/websites/moment_intergrals/rectangular_area_moment_of_interia/rectangularareamomentofinteria.htmlNot necessarily.

The cross section of the beam is a plane, and typically the axes of this plane are assumed to be x-axis parallel with the neutral axis, and the y-axis is vertical, or otherwise noted in the problem statement.

well， I read the link... But, still didn't understand what does Ixx means, I know it's moment of inertia about x axis..
Does it mean the author apply the force at the top of beam ?

 

[SteamKing]

well， I read the link... But, still didn't understand what does Ixx means, I know it's moment of inertia about x axis..
Does it mean the author apply the force at the top of beam ?

Not necessarily. Ixx and Iyy are two geometric properties of the cross section of the beam. Their calculation is not dependent on how the load is applied to the beam.

Which moment of inertia, Ixx or Iyy, is used to calculate bending stress does depend on how the load is applied.

 

[chetzread]

Which moment of inertia, Ixx or Iyy, is used to calculate bending stress does depend on how the load is applied.

can you explain further ?

 

[SteamKing]

can you explain further ?

I don't know how to explain further.

The calculation of Ixx and Iyy is laid out in tabular form by the author.

How you use these values to calculate bending stress is covered by elementary beam theory.