For close shaped section, polar moment of inertia can be calculated from perpendicular axis theorem (adding both the 2nd moment of area in cross sectional axis). But how to calculate polar moment of inertia (2nd moment of area in perpendicular direction of the cross section) of I beam?
Don't fully understood the question... Just to clarify: polar moment is moment with respect to a pole (i.e. a point in the cross section). Axis moment is moment with respect to an axis belonging to the planar cross section (if two axis are perpendicular and crossing at the pole, then the polar moment is the sum of the two axis moments). Then, in your question, what is the _polar_ moment with respect to the _perpendicular direction_ to the cross section?
I think torsional constant might be relevant to your question. Please check: https://www.projectengineer.net/what-is-the-torsion-constant/ .
Hope it is helpful.
I am looking for 2nd moment of area in y direction of this shape.
The statement "I am looking for 2nd moment of area in y direction of this shape." is not correct. Maybe you are looking at the polar moment of the section with respect to y axis:
Iyy =Izz+Ixx
(I assume, although not shown in your drawing, that (xyz) has origin at the barycenter of the section)
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