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assignment 13 solutions

assignment 13 solutions - ” PROBLEM 5.2 Locate the...

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Unformatted text preview: ” PROBLEM 5.2 Locate the centroid of the plane area shown. SOLUTION or X=8.22in.{ _Z‘LA_1102 ' 2A 134 or 17:4.00i114 PROBLEM 5.12 240 mm —*l—T . Locate the centroxd of the plane area shown. 150 mm SOLUTION m =12000 4()3240 =1801—3—(=150) 45 —2160000 —540000 __ mom moo PROBLEM 5.29 Determine the distance h so that the centroid of the shaded area is as close to line 88’ as possible when (a) k = 0.2, (b) k = 0.6. SOLUTION — _ % Then y - 2A a (a + h) _ _ 2(ab) [ 2 ][kb(a — h)] or y _ ba — kb(a — h) _ la2(l—k)+kh2 ‘ 2 a(1— k) + kh h Let c = 1— k and C = — (1 Then _ _ 3c + k§2 (1) y _ 2 c + k; — Now find a value of C (or h) for which i is minimum: 2 ,5 a2k§(c+k§)—k(c+k§) 2 — _=_——_=0 or 2 c+k —c+k§ =0 (2) a dc 2 (“My c( C) ( ) Expanding(2) 2c§+2§2—c—k§2 = 0 or k§2+2c§—c = o 2 Then g = —2c :1; "(20) — 4(k)(c) 2k Taking the positive root, since h > 0 (hence C > 0) h _ a—2(1 — k) + J40 — k)2 + 4k(1— k) ' 2k —21—0.2 +44 1—0.22 +4 0.21—0.2 (a) k = 0.2: h = (1% or h = 0.472a 4 2(0.2) —21—0.6 +J41—0.62+4 0.61—0.6 (b) k = 0.6: h = aw or h = 0.387a 4 2(0.6) ...
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