Appendix B - bud21932_appB_1039-1043 09/21/2006 08:32 PM...

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Answers to Selected Problems Appendix B 1039 B–1 Chapter 1 1–5 (a) 1368 cars/h, (b) loss of throughput ± 12%, (c) increase in speed ± 5.5% 1–8 (a) e 1 = 0 . 006 067 977, e 2 = 0 . 009 489 743, e = 0 . 015 557 720, (b) e 1 =− 0 . 003 932 023, e 2 =− 0 . 000 510 257, e =− 0 . 004 442 280 1–11 (a) σ = 13 . 1MPa , (b) σ = 70 MPa , (c) y = 15.5 mm, (d) θ = 5 . 18 B–2 Chapter 2 2–9 E = 30 Mpsi, S y = 45 . 5 kpsi , S ut = 85 . 5 kpsi, area reduction = 45.8 percent 2–15 ¯ S ut = 125 . 2 kpsi , ˆ σ S ut = 1 . 9 kpsi 2–17 (a) u R . = 34 . 5in · lbf/in 3 , (b) u T . = 66 . 7 ( 10 3 ) in · lbf/in 3 2–22 Steel, Titanium, Aluminum, and Composites B–3 Chapter 3 3–4 (a) V ( x ) =− 1 . 43 40 ± x 4 ² 0 + 30 ± x 8 ² 0 + 71 . 43 ± x 14 ² 0 60 ± x 18 ² 0 lbf M ( x ) =− 1 . 43 x 40 ± x 4 ² 1 + 30 ± x 8 ² 1 + 71 . 43 ± x 14 ² 1 60 ± x 18 ² 1 lbf · in 3–6 (a) M max = 253 lbf · in , (b) ( a / l ) = 0 . 207 , M = 214 lbf · in 3–8 (a) σ 1 = 14 2 = 4 3 = 0 p = 26 . 6 cw ; τ 1 = 5 ave = 9 s = 18 . 4 ccw (b) σ 1 = 18 . 6 2 = 6 . 4 3 = 0 p = 27 . 5 ccw ; τ 1 = 6 . 10 ave = 12 . 5 s = 17 . 5 cw (c) σ 1 = 26 . 2 2 = 7 . 78 3 = 0 p = 69 . 7 ccw ; τ 1 = 9 . 22 ave = 17 s = 24 . 7 ccw (d) σ 1 = 23 . 4 2 = 4 . 57 3 = 0 p = 61 . 0 cw ; τ 1 = 9 . 43 ave = 14 s = 16 . 0 cw 3–13 σ = 10 . 2 kpsi = 0 . 0245 in 1 = 0 . 000 340 , ν = 0 . 292 2 =− 0 . 000 099 3 d = 0 . 000 049 7 in 3–18 σ 1 = 30 MPa 2 = 10 MPa 3 =− 20 MPa , τ max = 25 MPa 3–22 (a) M max = 21 600 kip · in , (b) x max = 523 in from left or right supports 3–23 (a) σ A = 42 kpsi B = 18 . 5 kpsi C = 2 . 7 kpsi , σ D =− 52 . 7 kpsi 3–27 M max = 219 lbf · in = 17 . 8 kpsi , τ max = 3 . 4 kpsi, both models 3–33 The same 3–37 Two 1 16 -in-thick strips: T max = 31 . 25 lbf · in , θ = 0 . 200 rad , k t = 156 lbf · in/rad. One 1 8 -in-thick strip: T max = 62 . 5 lbf · in = 0 . 100 rad , k t = 625 lbf · in/rad 3–43 d C = 45 mm 3–48 σ max = 11 . 79 kpsi max = 7 . 05 kpsi 3–54 p i = 639 psi 3–58 r ) max = 3656 psi 3–66 δ max = 0 . 038 mm min = 0 . 0175 mm , p max = 147 . 5MPa , p min = 67 . 9MPa 3–70 For δ max , p = 33 . 75 kpsi ,(σ t ) o = 56 . 25 kpsi, t ) i =− 33 . 75 kpsi o = 0 . 001 10 in , δ i =− 0 . 000 398 in 3–73 σ i = 26 . 3 kpsi o =− 15 . 8 kpsi 3–78 σ i = 71 . 3 kpsi o =− 34 . 2 kpsi 3–81 p max = 399 F 1 / 3 MPa max = 399 F 1 / 3 MPa , τ max = 120 F 1 / 3 MPa B–4 Chapter 4 4–1 (a) k = ( 1 / k 1 + 1 / k 2 + 1 / k 3 ), (b) k = k 1 + k 2 + k 3 , (c) k = [1 / k 1 + 1 /( k 2 + k 3 ) ] 1 4–11 ² = 17 70 [ w/( 24 EI ) ] 2 l 7 4–12 σ max =− 20 . 4 kpsi, y B =− 0 . 908 in 4–15 y left =− 1 . 565 mm , y right =− 1 . 565 mm, y midspan = 0 . 5868 mm 4–18 y max =− 0 . 0130 in
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4–20 z A = 0 . 0368 in , z B
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Appendix B - bud21932_appB_1039-1043 09/21/2006 08:32 PM...

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