Area moment of inertia of a finned hollow cylinder

[rww88]

Can someone comment on the validity of the following theorem I have suspicioned:

A cross-section that is symmetrical and identical about both the XX and YY axes maintains a constant area moment of inertial irrespective of the section's rotation about its geometric axis.

Is there a standard area moment of inertia formula for this figure?

 

[Deleted member 4993]

Can someone comment on the validity of the following theorem I have suspicioned:

A cross-section that is symmetrical and identical about both the XX and YY axes maintains a constant area moment of inertial irrespective of the section's rotation about its geometric axis.

Is there a standard area moment of inertia formula for this figure?View attachment 27825

instead of "suspicion" - why don't you prove/disprove by integration?

 

[rww88]

I would be delighted to prove/disprove the statement by integration if I knew how to do so. Would you consider giving me a hint as to how to get started?

 

[rww88]

Wow! 96 views for this topic and still no informative responses.

 

[Deleted member 4993]

Wow! 96 views for this topic and still no informative responses.

That is because you did not show any "informative" effort to give us a starting point.

Do you know parallel-axis theorem for "moment of area" of a composite figure (like a rectangle touching a circle)?

 

[Eugenio]

Can someone comment on the validity of the following theorem I have suspicioned:

A cross-section that is symmetrical and identical about both the XX and YY axes maintains a constant area moment of inertial irrespective of the section's rotation about its geometric axis.

Is there a standard area moment of inertia formula for this figure?View attachment 27825

What data are given? Diameters? width of the fin? height? If you have that data you can use formulas directly, without the need for integration solving. Put the all the data you have and I will help you