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26_ch 03 Mechanical Design budynas_SM_ch03

# 26_ch 03 Mechanical Design budynas_SM_ch03 - 4 ρ = ± ±...

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Chapter 3 39 (e) A a = 6(1 . 25) = 7 . 5in 2 A b = 3(1 . 5) = 4 . 5in 2 A = A c + A b = 12 in 2 ¯ y = 3 . 625(7 . 5) + 1 . 5(4 . 5) 12 = 2 . 828 in Ans. I = 1 12 (6)(1 . 25) 3 + 7 . 5(3 . 625 2 . 828) 2 + 1 12 (1 . 5)(3) 3 + 4 . 5(2 . 828 1 . 5) 2 = 17 . 05 in 4 Ans. σ A = 10 000(2 . 828) 17 . 05 = 1659 psi Ans. σ B =− 10 000(3 2 . 828) 17 . 05 =− 101 psi Ans. σ C =− 10 000(1 . 422) 17 . 05 =− 834 psi Ans. (f) Let a = total area A = 1 . 5(3) 1(1 . 25) = 3 . 25 in 2 I = I a 2 I b = 1 12 (1 . 5)(3) 3 1 12 (1 . 25)(1) 3 = 3 . 271 in 4 Ans. σ A = 10 000(1 . 5) 3 . 271 = 4586 psi, σ D =− 4586 psi Ans. σ B = 10 000(0 . 5) 3 . 271 = 1529 psi, σ C =− 1529 psi 3-24 (a) The moment is maximum and constant between A and B M =− 50(20) =− 1000 lbf · in, I = 1 12 (0 . 5)(2) 3 = 0 . 3333 in
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Unformatted text preview: 4 ρ = ± ± ± ± E I M ± ± ± ± = 1 . 6(10 6 )(0 . 3333) 1000 = 533 . 3 in ( x , y ) = (30, − 533 . 3) in Ans. (b) The moment is maximum and constant between A and B M = 50(5) = 250 lbf · in, I = . 3333 in 4 ρ = 1 . 6(10 6 )(0 . 3333) 250 = 2133 in Ans. ( x , y ) = (20, 2133) in Ans. C B A b a b D c ± 1.5 c ± 1.5 1.5 a b A B C c 1 ± 1.422" c 2 ± 2.828"...
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