24_ch 03 Mechanical Design budynas_SM_ch03

# 24_ch 03 Mechanical Design budynas_SM_ch03 - ¯ y = 16(2...

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Chapter 3 37 A = 1 . 732 0 . 557 = 1 . 175 in 2 ¯ y = 1 . 732(0 . 577) 0 . 557(0 . 577) 1 . 175 = 0 . 577 in Ans. I a = bh 3 36 = 2(1 . 732) 3 36 = 0 . 289 in 4 I b = 1 . 134(0 . 982) 3 36 = 0 . 0298 in 4 I 1 = I a I b = 0 . 289 0 . 0298 = 0 . 259 in 4 Ans. because the centroids are coincident. σ A = 10 000(0 . 577) 0 . 259 = 22 . 3(10) 3 psi Ans. σ B = 10 000(0 . 327) 0 . 259 = 12 . 6(10) 3 psi Ans. σ C =− 10 000(0 . 982 0 . 327) 0 . 259 =− 25 . 3(10) 3 psi Ans. σ D =− 10 000(1 . 155) 0 . 259 =− 44 . 6(10) 3 psi Ans. (c) Use two negative areas. A a = 1in 2 , A b = 9in 2 , A c = 16 in 2 , A = 16 9 1 = 6in 2 ; ¯ y a = 0 . 25 in, ¯ y b = 2 . 0in, ¯ y c = 2in
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Unformatted text preview: ¯ y = 16(2) − 9(2) − 1(0 . 25) 6 = 2 . 292 in Ans. c 1 = 4 − 2 . 292 = 1 . 708 in I a = 2(0 . 5) 3 12 = . 020 83 in 4 I b = 3(3) 3 12 = 6 . 75 in 4 I c = 4(4) 3 12 = 21 . 333 in 4 D C c a B b A G a G b G c c 1 ± 1.708" c 2 ± 2.292" 2" 1.5" 0.25" 1 1...
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