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HW 16 Prob 5_36

# HW 16 Prob 5_36 - PROBLEM 5.36 Determine by direct...

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Unformatted text preview: PROBLEM 5.36 Determine by direct integration the centroid of the area shown. Express your answer in terms of a. and h. SOLUTION ‘1 For the element (EL) shown d XE \t‘ At 35:61: y=h2 h=ka3 or k=£3 L.- a T— a 1/3 ‘1 Then x=——y . .L... hm . {ﬁx . s NOW dA=xay=~fﬁ U3 dy _ ‘1 1 a 1,3 XEL=—2-X=-2-Zl/—3 37m"); h _ - him -3L 4/3 -3 Then A“ I‘M—IO h1/3 dy~4hy3(y )0—401’1 ‘ H a a 1 a 3 h 3 — _ ____1/3__1/3 _________5/3 =__2 and JxELdA‘Iozhw [kl/3 dy) 2h [5y )0 10" h h — -h 3.1/3 __a_§m :2 IyELdA_I Jib”); layj—hAﬂ )0 7ah Hence 35A: EELcZA: 35 iahj=ia2h 35:32—a 4 10 5 _ _ _ _ 3 _3 2 ~_£ yA—IyELdA y[—4— hj—7ah y—7h4 ~__________________——————————————»——-———-—~—‘———’_‘—"“ ...
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