Rotated Section - Moment of Inertia

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SUMMARY

The discussion centers on calculating the moment of inertia for a rotated 2D area, specifically seeking a formula to derive new moments of inertia (Ix, Iy, Pxy) after rotating the area around the origin by a specified angle (theta). The user, Eduardo, seeks clarification on whether there exists a formula for this scenario, distinct from the existing formulas for inertia moments about a rotated axis. A participant suggests that rotating the area is equivalent to rotating the axes in the opposite direction, implying that the same formulas can be applied with a negative rotation angle.

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  • Understanding of moment of inertia concepts, specifically Ix, Iy, and Pxy.
  • Familiarity with 2D geometric transformations and rotation.
  • Knowledge of the second moment of area and its applications in engineering.
  • Basic proficiency in using mathematical formulas for area calculations.
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Engineers, students in mechanical and civil engineering, and professionals involved in structural analysis and design who need to understand the effects of area rotation on moment of inertia calculations.

eriveraa80
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Hi everybody:

I can see that there are formulas to calculate the moment of inertia of a 2D Area (Second moment of area) here: http://en.wikipedia.org/wiki/Second_moment_of_area"

In the same link, there is a formula to calculate the Inertia moments about a ROTATED AXIS (Axis Rotation). But, is there a formula to calculate the Inertia moments of a ROTATED SECTION (rotated area) ??

Thanks in advance.
Eduardo
 
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Not sure what you mean. Can you provide additional explanation by means of a diagram or other hand waving?
 
Ok, i will explain a little bit:

1. You have a 2D Area in a XY axis. You can calculate the Moments of Inertia Ix, Iy, Pxy.
2. You rotate the 2D Area around the origin, with a tetha angle.
3. So, known Ix, Iy, Pxy and tetha: Is there a formula so i can calculate the new Ix, Iy, Pxy around the same axis?

In wikipedia, you can see that there is a way of calculating the Ix', Iy' and Pxy' around the rotated axis, but that is not what i want, because i am not rotating Axis. I am rotating only the 2D Area and i want calculate Ix, Iy, Pxy in the same axis based on the previously Ix, Iy, Pxy calculated.

Any ideas?
 
Hello Eduardo, you should not create duplicate posts in different sections.

Can you see that rotating the area in one direction is the same thing as rotating the axes in the other direction?

So you should use the same formulae, but the rotation angle is negative.
 

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