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5-35, 5-43, 5-44

# 5-35, 5-43, 5-44 - |5*351 Locate the centroid of the shaded...

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Unformatted text preview: |5*351 Locate the centroid of the shaded area shown SOLUTION The shaded area can be divided into a rectangle with two circles removed. The centroid for the composite area is determined by listing the area. the centroid looatiOn, and the first moment for the individual parts in a table and applying Eqs. 5-13. Thus, M Ye. M v 1 x in? in. (in?) 1440 10 2400 —37.?1 4 —50.28 -113.13 16 -201.12 1289.16 2148.60 M _ _1 _ 1289.16 _ . - A — -§TET§§ u 6.00 in. 10.00 in. 15-43 Locate the centroid of the shaded area shown in Fig. P5—43. SOLUTION The shaded area can be divided into a square, a half circle. and a quarter circle with a circle removed. The A centroid for the composite area is determined by listing the area, the centroid location. and the first moment for the individual parts in a table and applying Eqs. 5—13. Thus, A2 = éﬂr2= %ﬁ{6)2= 55.55 in? _ £5 _ 4{6) _ . yea — 6 + 3n — 6 + 3n — 8.546 1n. 51 = inr2= %ﬂ{6}2= 23.2? in? _ £3 _ 4(6) _ . xc3 — 6 + 3“ — 6 + 3n — 8.546 1n. _ 4; _ _ 4(6) _ . A4 = Hr2= n(312= 28.27 in? Part Ai xci My yCi Mx (in?! {in.} (in?) (in.} gin?) 1 36 3 108 3 108 I 2 56.55 6 339.3 8.546 483.3 3 28.27 8.546 241.6 3.454 9?.6 4 -28.27 6 -169.6 6 -169.6 E 92.55 519.3 519.3 M Axe — EAixCi — My xc — A - 92.55 - 5.61 1n. Ans. M _ _ _ _5 _ 519.3 _ . Aye - EAini — Mx yc — A - 55:35 - 5.61 in. Ans. '2'??? ‘5-44 lLocate the centroid of the shaded area shown SOLUTION The shaded area can be divided into a square with a circle and a quarter circle removed. The centroid for the composite area is determined by listing the area, the centroid location, and the first moment for the individual parts in a table and applying Eqs. 5—13. Thus, A2 = Hr2= ntsoiz = 11.310 mmz A3 = %ﬂr2= %ﬂ{120}2 = 11,310 mmz _ _ 3; _ _ 411201 _ xc3 - 240 3” - 240 3” - 189.07 mm _ 3; _ _ 411201 _ yes — 240 — 3n — 240 3“ — 189.07 mm Part Ai XCi My yCi Mx {mm2) (mm) {mus} {mm} {mmgi 1 57,600 120 6,912,000 120 6,912,000 2 -11,310 100 -1,131,000 80 -904,800 3 -11:310 189.0? -2,138.382 189.07 -2,138,332 2 34.930 3,642,618 3,868,813 M 3 642 618 Axc = EAixCi = My xc = 31 = -i§Z-\$§ﬁ— = 104.1 mm Ans. ! M Aye = 2:11in‘ = M3 yc - E: = §4%%§\$§%§ = 110.6 mm Ans. , nae-a ...
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5-35, 5-43, 5-44 - |5*351 Locate the centroid of the shaded...

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