I know the moment of inertia about X and Y axes. The area has been rotated through an angle theta. How to calculate the moment of inertia about x1 and y1 axes?
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$\begingroup$ If the answer here is what you looking for (i think the answer is correct) then you can mark it as answer, your action avoid the question pops up someday day later in Home page. $\endgroup$– user14407Commented Dec 4, 2018 at 9:21
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Say your Iy is the max and Ix is minimum I before rotation of the axis.
We build the Mohr circle plotting Ix and Iy on its x axis. And we draw a vertical along Y axis and call it xy axis, somewhere on the left outside of the circle.
So the center of circle is at $ (Ix+ Iy)/2 \ $ and its radius is $ R = (I_y - I_x)/2 \ $
now say you want to calculate the Ix' at 30 degrees anticlockwise rotation wrt x axis. So you cut an angle 60 degrees, twice the 30, and mark the coordinates of where it intersects the circle.
The Y is the Ixy max of the new rotated axis and if you draw a line from this point passing through the center of the Mohr circle it intersect the circle on the other side at Ixy min. If you want you could also wright these as equations.
