<Tr> <Td> A filled ellipse whose radius along the x-axis is a and whose radius along the y - axis is b </Td> <Td> </Td> <Td> I x = π 4 a b 3 (\ displaystyle I_ (x) = (\ frac (\ pi) (4)) ab ^ (3)) I y = π 4 a 3 b (\ displaystyle I_ (y) = (\ frac (\ pi) (4)) a ^ (3) b) </Td> <Td> </Td> </Tr> <Tr> <Td> A filled rectangular area with a base width of b and height h </Td> <Td> </Td> <Td> I x = b h 3 12 (\ displaystyle I_ (x) = (\ frac (bh ^ (3)) (12))) I y = b 3 h 12 (\ displaystyle I_ (y) = (\ frac (b ^ (3) h) (12))) </Td> <Td> </Td> </Tr> <Tr> <Td> A filled rectangular area as above but with respect to an axis collinear with the base </Td> <Td> </Td> <Td> I x = b h 3 3 (\ displaystyle I_ (x) = (\ frac (bh ^ (3)) (3))) I y = b 3 h 3 (\ displaystyle I_ (y) = (\ frac (b ^ (3) h) (3))) </Td> <Td> This is a result from the parallel axis theorem </Td> </Tr> <Tr> <Td> A filled triangular area with a base width of b and height h with respect to an axis through the centroid </Td> <Td> </Td> <Td> I x = b h 3 36 (\ displaystyle I_ (x) = (\ frac (bh ^ (3)) (36))) I y = b 3 h 36 (\ displaystyle I_ (y) = (\ frac (b ^ (3) h) (36))) </Td> <Td> </Td> </Tr>

Moment of inertia of the l cross section of beam