calculating the second moment of area

huangyhg

calculating the second moment of area
hi,
basically i am trying to calculate the load required to deflect the finger of a collet. its a pipe with slots milled along its length and these fingers will deflect when the collet is inserted into another pipe. so the finger is sort of circular in cross-section. i'm finding it hard to calculate the second moment of area for it and would appreciate any help. i seem to have forgotten a lot of the beam theory that i once knew. i have found the centroid of the shape, do the neutral axes run through the centroid? cheers
jonny
yes, the neutral axis runs through the centroid.  the moment of inertia is then the integral of y2 da.  the solution is shown as "sector of hollow circle" in the table "properties of sections" in roarke's formulas for stress and strain.  judging by the solution, i wouldn't even try to derive it.