Question

Find the moment of inertia for the cross-sectional shape about the x and y axes, given: L1 = 6 in, L2 = 4 in, L3 = 4 in, LA = 2 in (ans: lx = 1.41 x10° in, ly = 5.9 x10 in) Select problem completion status from drop-down list: Click for List

Answer 1

Helo my dear student i hope you will understand the discriptions i mentioned below, if you have any doubts feel free to ask me.please give me thumbs up if you are satisfied.

Here we are using the method of parallel axis theorem for determining the moment of inertia about any given axis for mixed geometries.

The used equations and worked details are given below

in 152 in4 MIT in 4 Ay ² 14 MI (IX); Area Segment Own x Ag from is O 3 1024 1365.3 cGfrom a xanis y Lin 8/3 4 8*8 3x8x6 - 17x22 12 348% 1024 1365.3 X 6x88 170.6 255,93 - TTX 29 -192-201.06 -213.626 : moment of inertion about x axis Ix = [x); : 1365.3 + 255.93 – 213.626 1.41X103 in4

162 in 154 in4 Segment Area CG from Taxis (9) own - MITH A y² 0 Same 12. 0 * 8 88 x 8x 6 -Tx22 10 4 10 8683 6400 6741.3 X 8x8 384 432 -1X 24 4007 40411 Cyz = Litha = 10 in y = 6+4 = loin steps for Y axis Moment of inertion about Yay asis Iy = {(Iy) = 6741.3+432_40455 = 5.9x103 in 4 = Gyer ? ant
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