Moment of Inertia Calculation for a Horizontal Element

[kieranl]

can somebody please tell what i am doing wrong with this moment of area question?

question and working in the attached doc

thanks alot

 

[ideasrule]

To calculate the second moment about the x-axis, you have to choose a horizontal element dA, because only a horizontal element has a constant y. I don't know why you chose vertical strips and used their centers as the y value, but your method is not right.

To calculate Ix, express dA in terms of y and you'll get dA=(sqrt(ay)-y)dy. Integrate y^2 dA from 0 to a and you'll get the correct answer, a^4/28. I have no idea how your lecturer got to his equation for Ix, but it's probably unnecessarily complicated because the method I just described leads to the right answer very quickly.

To calculate Iy, choose vertical elements and express dA in terms of x. Then integrate x^2 dA from 0 to a.