Answers to Selected Even-Numbered Problems

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1 Answers to Selected Even-Numbered Problems NOTE TO INSTRUCTORS CONSIDERING ADOPTION: Additional content (e.g., FBDs, shear and moment diagrams, etc.) is in the process of being added to this document. The answers reported here, along with the solutions manual, are currently being accuracy checked by several professors. This document, as well as the solutions manual, will be updated and completed by early summer, 009. PowerPoint slides with embedded animations are also available. We are happy to receive any questions you might have on the book or the supplements. For statics, please contact Mike Plesha at: If you would like a copy of the solutions manual to aid your adoption decision, then please contact the editor, Bill Stenquist, at: Thank you for your consideration. The Authors Chapter 1 1. Answers given in problem statement. 1.4 (a) l D 5:4 m; (b) m D 53:4 kg; (c) F D 11:4 kn; (d) I mass D :60 N m s. 1.6 (a) l D 5:0 ft; (b) m D 4:46 slug; (c) F D 0:1 lb; (d) M D 91 in: lb: 1.8 (a) p D 3:63 lb=in: ; (b) E D 9:010 6 lb=in: ; (c) I area = 5.65 in: 4 ; (d) I mass =109 in: lb s m D 0:115 kg: 1.1 g theory D 9:787 m=s : 1.14 F D : N: 1.16 (a) D 65:7 kn=m 3, D 6: kg=m 3 ; (b) D 0:9 kn=m 3, D : kg=m 3 ; (c) D 0:314 kn=m 3, D 3:0 kg=m 3 ; (d) D 1:4 kn=m 3, D : kg=m :17 lb. 1.0 (a) D 0:61 rad; (b) D 0:0188 mrad; (c) D 66 ı ; (d) D 0:0146 ı. Chapter. (a) ER D 55 36:0 ı ; (b) ER D 1:10 14 ı..4 (a) ER D 6:3 71:6 ı ; (b) ER D 7:1 56:3 ı ; (c) ER D 16:97 45:0 ı ; (d) ER D 45:0 ı..6 D 16:0 ı or 104 ı..8 F D 1:60 kn, D 90 ı..10 (a) ı ; (b) ı ; (c) P D 607 N; (d) D 0 ı, P D 304 N..1 D 60 ı, F 1 D 46 N..14 (a) j EF a j D 5:9 lb, j EF b j D 96:6 lb; (b) j EF a j D 9:9 lb; j EF b j D 11 lb..16 ˇ D 90 ı, F OC 0 D 00 lb..18 ER D. 18 O{ C 35 O / kn..0 EF D 1:60 O kn.. (a) ER D. 304 O{ C 00 O / N; (b) ER D. 53:6 O{ 33 O / N; (c) P D 607 N; (d) D 0 ı, P D 304 N..4 D 60 ı, F 1 D 46 N, EF 1 D. 13 O{ C 13 O / N. 1 Last modified: March 19, 009

2 .6 (a) Er AB D.4 O{ 3 O / m; (b) Er BA D. 4 O{ C 3 O / m; (c) Ou AB D 4 5 O{ 3 5 O ; (d) Ou BA D 4 5 O{ C 3 5 EF AB D.9:6 O{ 7: O / kn; (f) EF BA D. 9:6 O{ 7: O / kn. O ; (e).8 ER D. 93:6 O{ C 541 O / N, j ERj D 549 N, ER D :8 ı..30 F =F 1 D 1:50..3 D 33:7 ı, R D 6:4 kn..34 (a) Not safe; (b) Not safe; (c) Safe..36 R x D 100 N, R y D 00 N, R t D 13:4 N, R n D 33 N..38 (a) R x D 13 N, R y D 51:7 N; (b) R t D 187 N, R n D 114 N..40 Er AB D. 0 O{ C 48 O / mm, x B D 165 mm, y B D 48 mm..4 Er AC D. 50 O{ C 10 O / mm, x C D 135 mm, y C D 10 mm..44 Er OA D.95 O{ C 56 O / mm; Er OB D.68 O{ C 9 O / mm; Er OC D.17 O{ C 160 O / mm; x B D 68 mm; y B D 9 mm:.46 EF D. 4:59 O{ C 6:8 O C 1:6 k/ O lb, EQ D.39:8 O{ C 30:0 O 33:4 k/ O lb, EP D.50:0 O{ 70:7 O C 50:0 k/ O lb, ER D.85: O{ 13:9 O C 9: k/ O lb..48 EP D. 1:33 O{ C 0:766 O C 1:9 O k/ kn, EQ D. :67 O{ C :67 O C 1:33 O k/ kn, EF D.:1 O{ C 1:50 O C 1:50 O k/ kn, ER D. 1:87 O{ C 4:93 O C 4:1 O k/ kn..50 EF D.1:5 O{ 14:5 O C16:1 O k/ N where x D 60 ı ; y D 15 ı ; D 50 ı ; EP D.49:4 O{C53:0 O C19:4 O k/ N where x D 48:8 ı ; y D 45 ı ; D 75 ı ; ER D.61:9 O{C38:5 O C35:5 O k/ N where x D 40:3 ı ; y D 61:6 ı ; D 64:0 ı..5 r BA D 4:16 km..54 (a) x D cos 1.sin h cos v /, y D cos 1.cos h cos v /, D cos 1.sin v / D.90 ı v /; (b) x D 75:5 ı ; y D 64:3 ı ; D 30 ı :.56 h D 33:7 ı ; v D 59:0 ı..58 EF B D. 44:4 O{ C 77:8 O 44:4 O k/ lb; EF E D.44:4 O{ 77:8 O C 44:4 O k/ lb..60.x E ; y E ; E / D.80; 60; 10/ mm, EF EG D. 47:1 O{ C 5:9 O C 70:6 O k/ N..6 (a) F B =F A D 1:51; (b) Spokes on side B are more severely loaded; (c) Essay-type answer..64 (a) 18 ı ; (b) A k D 4:33 lb, A? D 5:50 lb; (c) EA k D.4:04 O{ C 0:578 O 1:44 O k/lb, EA? D.1:96 O{ :58 O C 4:44 O k/lb..66 d D 5:77 cm, D 41:4 ı..68 D 4:70 ı, ˇ D 9:43 ı, a D 1: in:, b D 1:0 in:..70 F k D 67:4 N, F? D 73:9 N, The bead slides toward C..7 Answer given in problem statement..74 F D 1:4 kip, EF D. 0:640 O{ 0:05 O C 1:7 O k/ kip..76 5:83 N..78 F k D 37:5 lb, F? D 14:0 lb:.80 W D 45:0 N..8 F k D 1:71 N, F? D 60:0 N, The bead slides toward A..84 v D.1:15/s :7 mm..88 1:0 in:.90 (a) and (b) 350 O k Nmm..9 (a). 10 O{ O 6 k/ O mm ; (b).10 O{ C O C6 k/ O mm ; (c) Essay-type answer; (d) Answer given in problem statement..94 Essay-type answer..96 (a) Yes; (b) EM O D O{ C O / in.lb:.98 (a) Essay-type answer; (b) Ou D 0:19 O{ C 0:19 O C 0:96 O k; (c) 364 cm..100 Ev n D. :9 O{ 7:87 O 6:30 k/ O km/s, Ev t D. 3:6 O{ 1:95 O 4:11 k/ O km/s, jev n j D 10:5 km=s; jev t j D 5:8 km=s. Last modified: March 19, 009

3 .10 6:57 mm..104 (a) and (b) 3.4 Nm :8 kn P 4:6 kn..108 (a) ER D. :9 O{ C :7 O 1:45 k/ O kn; (b) ET D.:9 O{/ kn..110 P? D. 0:970/P, P k D.0:43/ P..11 P k D 7:66 kn, P? D 6:43 kn, EP k D. 3:48 O{ 3:48 O 5:87 k/ O kn, EP? D.3:48 O{ C 3:48 O 4:13 k/ O kn..114 (a) x D 107 ı, y D 114 ı ; (b) 0:50 O{ C 0:693 O C 0:500 k. O.116 Answers given in problem statement. Chapter 3 3. R C D R D D 31:8 lb. 3.4 (a) T 1 D 51 lb, R D 141 lb; (b) T D 149 lb, R D 141 lb. 3.6 (a) F D 17:9 N; R A D 17:9 N; R B D 98:1 N; R D 5: N (b) Block A may move with constant velocity but it will not accelerate. (c) Block B will accelerate to the right. 3.8 T AB D 5:13 kn, T AC D 0:340 kn F AB D 1580 lb, T AC D 1500 lb. 3.1 (a) T AB D 175 N; (b) T CD D T CE D 109 N; (c) Essay-type answer (a) Answer provided in problem description; (b) F D T cos ; (c) Essay-type answer T ACB D 60 N; T CDE D 4530 N: 3.18 m D 547 kg. 3.0 T CD D 840 N, T BA D 6840 N, T CB D 7890 N, W D 110 N. 3. (a) System (a): T D W, system (b): T D 1 W, system (c): 1 W, system (d): 1 3 W, system (e): 1 3 W, system (f): 1 4 W ; (b) Essay-type answer. 3.4 W D 18 lb. 3.6 T BH D 540 lb; T HE D 540 lb; T BC D 717 lb; T EF D 586 lb; W A D 3 lb; W G D 369 lb; W D D 108 lb: 3 Last modified: March 19, 009

4 3.8 D 46:8 ı, T D 86: N W 1 D 3:6 N, W D 11:3 N. 3.3 D 30 ı ; intermediate answer: F BD D.5 lb/.cos 30ı Csin 30 ı / cos 30 ı cos sin 30 ı sin T AC D 3460 lb, T AE D 6000 lb, T AG D 440 lb, ı D 6:00 in: 3.36 (a) L AB D 94:3 cm; L AD D 10 cm; (b) x D 104 cm; y D 46:7 cm (a) 10:0 N, 8:00 N; (b) 7:00 N, 5:00 N k D 167 lb=in., L 0 D 1:0 in: 3.4 F 1 D 18 lb, F D 335 lb, F 3 D 18 lb ı D 3:4 mm (a) ı D 1:17 in:; (b) ı D 1:99 in: q.5 mm/ C. mm ı/ p 9mm 3.48 (a) F D. N=mm/. mm ı/ C.0:3 N=mm/ı; (b) Answer not provided; (c) q.5 mm/ C. mm ı/ F max D 0:600 N; (d) Essay-type answer m D D 91:7 kg. 3.5 W D 500 N (a) W D 3k 3.56 P D 800 lb P D 800 lb P D 1450 lb. 1 r p r Cd d; (b) d D 16:9 in: 3.6 (a) F AE D 40 lb, F AC D 10 lb, F AD D 10 lb; (b) F EB D 10 lb F AB D F AC D 780 lb, R D 800 lb W D 400 N, R 1 D 300 N, R D 13:7 N, ER 1 D. 7: O{ C18 O C04 O k/ N, ER D. 1:8 O{ C:7 O 4:13 O k/ N P D 107 N, ER D.3:0 O{ C 4:6 O 107 O k/n F ED D 80 lb, F EF D 360 lb, F FB D 10 lb, F EA D 380 lb, F F C D 10 lb, 60 lb must be added to traffic light E. 3.7 Essay-type answer T AE D 44:6 lb, T AD D 69:6 lb, T DF D 19 lb, T DG D 74 lb, T ABCD D 100 lb. 4 Last modified: March 19, 009

5 3.76 D 19:1 ı, T AB D 153 N F D 90:1 N ı 1 D 10:0 mm, ı D 10:0 mm. 3.8 T AB D 9:33 kn, T AC D 9:33 kn, T AD D 16:0 kn, T AE D 8:00 kn T AB D 8:40 kn, T AD D 8:00 kn, T AC D 9:33 kn, T AE D 8:00 kn The bead slides toward B T AC D 1650 lb, T BC D 106 lb, T CD D 330 lb, F CE D 1400 lb, F CF D 1400 lb, P D 106 lb. Chapter 4 Note: Throughout Ch. 4, unless otherwise stated, answers for two-dimensional problems are reported using positive values for counterclockwise moments and negative values for clockwise moments. Answers for three-dimensional problems are reported using positive values for moments that act in the positive coordinate directions and negative values for moments that act in the negative coordinate directions. 4. (a) d D 6:00 in:, M B D 150 in:lb; (b) M B D 150 in:lb; (c) M B D 150 in:lb; (d) M B D 150 in:lb; (e) EM B D 150 k O in.lb. 4.4 (a) d D 14:1 mm, M B D 4:4 Nmm; (b) M B D 4:4 Nmm; (c) M B D 4:4 Nmm; (d) M B D 4:4 Nmm; (e) EM B D 4:4 O k Nmm. 4.6 (a) F D 0:1 lb; (b) F D 56:1 lb; (c) k D 13:0 lb=in. 4.8 F D 640 lb, D 140 ı (a) M A D 30:0 knm; (b) M A D 35:0 knm; (c) M A D 38:0 knm. 4.1 (a) Q D 10:0 kn; (b) W D 5:00 kn, D 53:1 ı F D 100 N (a) EM B D.3570 O{ C 86 O 3000 O k/ in.lb; (b) EM O D.8030 O{ C 514 O 3000 O k/ in.lb (a) EM A D. 700 O{ C 700 O / Nmm; (b) EM B D.9;600 O / Nmm. 4.0 (a) EM B D O{ 880 k/ O ftlb; (b) EM A D. 300 O{ C 190 O 880 k/ O ftlb; (c) EM O D O{ C 7680 O 880 k/ O ftlb. 4. F D 1:75 kn. 4.4 (a) F D 40 N, (b) EM O D 91 O{ Nm; (c) Essay-type answer. 4.6 (a) M AB D 1900 Nmm, EF D.3:85 O{ C 9:3 O k/ N; (b) M AB D 47 Nmm; (c) M AB D F D 9:6 lb F D 115 N. Twisting occurs at both fittings on pipe OA. 4.3 (a) EM A D.:9 O{ C 10:3 O C :9 k/ O N mm, M AB D 8:00 N mm; (b) EM B D.1:0 O{ 6:00 k/ O N mm, M AB D 8:00 Nmm; (c) Essay-type answer M OB D 1:5 Nm (a) EM A D.9830 O{ C1940 O C7770 O k/ Nmm, M a D Nmm; (b) EM O D O{ Nmm, M a D Nmm EF D.35:8 O C 17:9 O k/ lb, M GH D 537 in.lb EQ D.6 O{ C 6 O C 3 O k/ lb, M BC D 90 in.lb. 4.4 M a D 17;400 ftlb, D 90 ı M D 144 in.lb: 4.46 (a) Q D 10 N; (b) The answer does not change (a) M D 96:6 Nmm; (b) M D 96:6 Nmm EM D.00 O{ 600 O k/ Nm: 4.5 d D 1:9 m (a) EM D. 800 O{ 00 O / Nm; (b) Essay-type answer. 5 Last modified: March 19, 009

6 4.56 The forces F are resolved into horizontal and vertical components as shown. The two vertical forces F cos 30 ı constitute one couple. The two horizontal forces F sin 30 ı and the horizontal force F constitute another couple EF A D.4 lb/. 0:976 O{ C 0:484 O 0:179 O k/, EF B D EF A D.4 lb/.0:976 O{ 0:484 O C 0:179 O k/; Additional result: the moment of the couple about line a is M a D 91 in:lb Force systems (a) and (d) are equivalent, and force systems (b) and (c) are equivalent. 4.6 For force system (b), F D kip and P D 4 kip; for force system (c), there are no values for F and P such that force systems (a) and (c) will be equivalent; for force system (d), F D 5 kip and P D 1 kip F Rx D 1490 lb, F Ry D 10 lb, M R 5110 in.lb F Rx D 0:500 kn, F Ry D 3:87 kn, :58 m to the right of the bearing at C (a) EF R D O k/ N, EM RO D.6:94 O{ 1:0 O / Nm; (b) EF R D O k/ N,.x; y/ D. 3:86 mm; 6:67 mm/: 4.70 (a) EF R D. 5:00 O{ C 50:0 O 10:0 O k/ nn, EM RB D.10 O{ 60:0 O k/ nnm; (b) EF R D. 5:00 O{ C 50:0 O 10:0 O k/ nn, EM RO D.0 O{ C 800 O C 3890 O k/ nnm. 4.7 (a) EF R D.10:0 O / kn, EM RA D.5:0 O{ C 4:00 O C 0:0 O k/ knm; (b) F Rx D 0, F Ry D 10:0 kn, F R D 0, M RAx D 5:0 knm, M RAy D 4:00 knm, M RA D 0:0 knm EF R D F O k, EM R D 3P r O k,.x; y/ D.0; r/ EF R D.:00 O{ C 3:00 O 4:00 O k/ N, EM RA D.9:00 O{ C 8:00 O 4:00 O k/ Nm EF R D F. O C k/, O EM R D F a 1. O C k/, O.x; y/ D. 1 a; b/ EM R D.150 O{ C 104 O 00 O k/ Nm: 4.8 (a) M a D 56 Nm; (b) Ou D 0:530 O{ C 0:66 O C 0:530 O k F D 300 lb P D 10 lb, Q D 5 lb, R D 0, S D 0 lb, M D D 10 in:lb (a) F Rx D 0:880 lb, F Ry D 0:660 lb, M O D 0:55 in. lb; (b) F Rx D 0:880 lb, F Ry D 0:660 lb, y D 0:67 in: 4.90 (a) F Rx D 0, F Ry D 0, F R D 1800 lb, M Ax D 8700 ftlb, M Ay D 0, M A D 6;700 ftlb; (b) F Rx D 0, F Ry D 0, F R D 1800 lb, x D 1: ft, D 7:83 ft. 4.9 EF R D. 30:0 O{ 10 O :5 O k/ lb, EM RO D. 990 O{ C 60:0 O C 1180 O k/ in.lb. Chapter 5 5. A D 3:5 N, B D 107 N. 5.4 F D 10 lb, B D 13 lb, A D 53:5 lb. 6 Last modified: March 19, 009

7 5.6 B D 4:9 N (force supported by one link), A x D 68:6 N, A y D 51:4 N. 5.8 d D 3:10 ft (a) A y D 3 F C 3 1 P, A x D 0, D y D 1 3 F C 3 P ; (b) A x D 0:19F C0:385P, A y D 3 F C 1 3 P, D D 0:385F C 0:770P ; (c) A y D F C P, D x D 0, M D D 3 1 L.F C P /; (d) A x D 0, A y D F C P, M A D 1 3 L.F C P /. 5.1 A y D 1:88 kn, E y D :1 kn, E x D :00 kn A x D 0, A y D 3:00 kip, P y D 1:00 kip C y D 11;300 lb, D y D 6170 lb A x D 0, B y D P, M A D P a. 5.0 Rollers B and C make contact, A y D 0, B y D 40:8 lb, C y D 31 lb, D y D Rollers A and C make contact, A y D 193 lb, B y D 0, C y D 198 lb, D y D (a) A D 498 lb; (b) Essay-type answer. 5.6 (a) > 75:5 ı ; (b) > 90:0 ı 5.8 Essay-type answer F x D 9:08 lb, F y D 4:8 lb, E y D 17:0 lb. 5.3 G D 4:66 N, N D 17:4 N, D 17:0 ı A x D 0, A y D 00 lb, T D 600 lb (a) A x D :59 kn, A y D 35: kn, B y D 54:8 kn; (b) A x D 7:59 kn, A y D 41: kn, B y D 59:5 kn T D 1:66 kip (tension in cable BCD), A x D 1:66 kip, A y D 0:55 kip T DE D :76 kip, F DF D :36 kip (a) Complete fixity, statically determinate; (b) T D 10:68F ; Additional results: C x D :000F, C y D 11:3F. 5.4 (a) Partial fixity, statically indeterminate; (b) The cable tension cannot be determined; Additional result: The equations of static equilibrium require F D 0. If F 0, then the equations of static equilibrium cannot be satisfied, and dynamic motion occurs F D 13:6 lb (a) D 4:58 ı ; (b) D 36:7 ı ; (c) Essay-type answer Essay-type answer 5.50 A x D 0, A y D F h 1 kl i F kl.k t C kl, C / y D.k t C kl /, M A D FL h 1 kl i k t C kl. 5.5 For structure (a), full fixity and statically determinate; for structure (b), full fixity and statically indeterminate; for structure (c), full fixity and statically determinate; for structure (d), partial fixity and statically determinate; for structure (e), full fixity and statically determinate; for structure (f), partial fixity and statically indeterminate D D 0:314 N, L D 1:34 N ı D :40 mm, D 1:49 ı (a) T EA D 1:33 kip, B x D 0, B y D 3:33 kip; (b) T EA D 1:3 kip, B x D 0, B y D 0:3 kip; (c) T EA D 15:9 kip, B x D 0, B y D 5:7 kip. 7 Last modified: March 19, 009

8 5.60 ABC is a 3-force member and BD is a -force member. 5.6 ABDE is a multiforce member and BC is a -force member force member force member ABCD is a multiforce member and DE is a -force member Multiforce member force member F AB D 318 kn to begin opening the dump when D 0 ı ; F AB D 0 when the center of gravity G of the dump and its contents is immediately above point O C x D 0:333 kn, C y D 0:667 kn, T AD D 1:5 kn, M Cx D 0, M Cy D :00 knm, M C D 3:33 knm (a) Partial fixity and statically determinate; (b) T D 7 lb, A x D 18:0 lb, A y D 9:00 lb, M Ax D 54:0 in.lb, M A D T AD D 50:75 kn. 5.8 (b), 0, 4, 1, 3; (a) 5.84 A x D 0, A y D 0, A D F, M Ax D F r, M Ay D 0, M A D P r. 8 Last modified: March 19, 009

9 5.86 F D 3:1 kn, C x D 3:00 kn, C y D :07 kn, C D 0:49 kn, M Cx D 0:343 knm, M Cy D 0:600 knm A D 5:77 kn, C D :89 kn, D y D 5:00 kn, D D 0, M Dy D 0, M D D 9:3 knm Essay-type answer; partial answer: the propellers rotate counterclockwise. 5.9 T D 163 N, C D 163 N, A D 83: N A x D 7:00 N, A y D 6:1 N, M A D 76 Ncm (a) F D 3:9 N; (b) F D 11:5 N; (c) F D 0:1 N For structure (a), full fixity and statically determinate; for structure (b), partial fixity and statically indeterminate; for structure (c), full fixity and statically indeterminate; for structure (d), partial fixity and statically determinate; for structure (e), partial fixity and statically determinate; for structure (f), full fixity and statically indeterminate (a) Essay-type answer; (b) T 1 D 15:7 lb, T D 1:5 lb, O x D 13:3 lb, O y D 11:5 lb, O D 19:4 lb (a) Full fixity and statically determinate; (b) A y D 0, A D 60:0 lb, B x D 40:0 lb, B D 40:0 lb, M Ay D 00 in.lb, M A D 80:0 in.lb. 9 Last modified: March 19, 009

10 Chapter 6 6. T AB D 500 lb, T AC D 0, T BC D 65 lb, T BD D 375 lb, T CD D 65 lb, T CE D 0, T DE D 500 lb. 6.4 P D 300 lb. 6.6 P D 8000 lb. 6.8 T CE D 3:75 kn, T DF D 3:66 kn T AB D 4:00 kn, T AC D 0, T BC D 7:1 kn, T BD D 6:00 kn, T CD D 5:00 kn, T CE D 6:00 kn, T DE D 7:1 kn. 6.1 P D 10:0 kn P D 6:66 kn :9: :77: 6.0 T AB D F, T AE D p F, T CD D 0, T CE D 0, T DB D p F, T DE D F, T EB D F. 6. T AB D 5:66 kn, T AD D 4:00 kn, T BC D 7:07 kn, T BD D :4 kn, T BE D 3:00 kn, T BF D 4:47 kn, T CF D 5:00 kn, T DE D 3:00 kn, T EF D 3:00 kn. 6.4 (a) F G, DG; (b) T F G D 0, T DG D 0, T AC D 1:0 kn, T AB D 10:4 kn, T CB D 4:00 kn, T BD D 10:4 kn, T GH D 8:00 kn, T FH D 6:93 kn, T EG D 8:00 kn, T CE D 8:00 kn, T DE D 8:00 kn, T CD D 16:0 kn, T DF D 6:93 kn. 6.6 (a) BG, DI, EJ, DE, CD, CH ; (b) T BG D 0, T CH D 0, T AB D 3:00 kip, T AF D 5:0 kip, T BC D 3:00 kip, T CF D 7:1 kip, T F G D 6:00 kip, T C G D 5:00 kip, T GH D 3:00 kip; (c) T DI D 0, T EJ D 0, T DE D 0, T CD D 0, T CJ D 14:4 kip, T IJ D 9:00 kip, T CI D 10:0 kip, T HI D 3:00 kip. 6.8 T BD D 5:77P, T CD D 5:77P, T CE D 8:66P 6.30 (a) DE, HI, JK, LM, NO; (b) eliminate DE, HI, LM, essay-type answer; (c) T GH D 5 8 Q. 6.3 (a) HI, JK, LM ; (b) eliminate JK, essay-type answer; (c) T F G D :00 kn (a) Statically determinate; (b) T CD D 8:00 kip, T DE D 0, T AD D 10:4 kip, T DB D 10:4 kip (a) T J T D 40: kn; (b) T HJ D 30:0 kn, T IJ D 14:1 kn, T JK D 0, T JM D 0:563 kn, T JL D 0:796 kn (a) Statically indeterminate; (b) mechanism; (c) statically indeterminate; (d) statically determinate (a) For truss system (a): T AB D 1:41W, T BD D W, T DF D 1:41W, T AC D W, T CE D W, T EF D W, T BC D W, T CD D 0, T DE D W ; for truss system (b): T AB D 1:1W, T BD D 0:500W, T DF D 1:1W, T AC D 0:500W, T CE D 0:500W, T EF D 0:500W, T BC D W, T CD D 0, T DE D W ; (b) Essay-type answer; (c) Essay-type answer; (d) Essay-type answer. 6.4 (a) Partial fixity; (b) statically determinate; (c) T AB D 0, T AC D 0, T AD D 4:00 kn, T BC D 0:417 kn, T BD D :13 kn, T BE D 0:838 kn, T CD D :13 kn, T CE D 0:838 kn, T DE D 1:33 kn. 10 Last modified: March 19, 009

11 6.44 Answers to be provided Answers to be provided Answers to be provided FBDs to be provided. 6.5 Essay-type answer Horizontal force applied by the operator is Q D 0:8 lb, T AE D 6:67 lb, B x D 5:77 lb, B y D 13:3 lb, C x D 15:0 lb, C y D 13:3 lb Horizontal force applied by the operator is Q D 47:7 N, F BE D 63:0 N, A x D 55:7 N, A y D 10:7 N, C x D 103 N, C y D 10:7 N (b) F AD D 3390 lb; (a) 6.60 (b) T 1 D 83 N, T D 83 N; (c) from DE: A x D 60 N, A y D 5 N, from F G: A x D 60 N, A y D 5 N; (a) 6.6 (b) F CF D 7;00 lb; (a) 6.64 F FH D :5 N, F BF D 70:8 N. 11 Last modified: March 19, 009

12 6.66 (a) The structure is not a truss, essay-type answer; (b) T DG D :00 kn, T BE D 3:00 kn, T FH D 4:00 kn, T AD D 3:00 kn, T DE D 3:00 kn, T EF D 3:00 kn, T CF D 3:00 kn, B x D 3:00 kn, B y D 1:00 kn (a) Statically indeterminate; (b) QH and IQ, (c) F DG D p kn T BP D 813 lb, T BO D 813 lb, T CD D 100 lb. 6.7 T AD D 163 lb, T AB D 115 lb, T BE D 163 lb, T BD D 115 lb, T GI D 0, T HI D 85:0 lb, T EH D 184 lb, T DG D 184 lb, T EG D 35:0 lb (b) F AE D 55 lb; (a) 1 Last modified: March 19, 009

13 Chapter Nx; Ny/ D.0; 65:0/ mm Nx; Ny/ D.1:18; 1:18/ in Nx; Ny/ D.60:8; 30:0/ mm Nx; Ny; Ń/ D.:31; :1; 1:4/ in Nx; Ny/ D. 9 0 ; 9 0 / in Nx; Ny/ D. 6 5 ; 3 / mm Nx; Ny/ D ; Nx; Ny/ D.48:0; 16:0/ in Answer given in problem statement. 7.0 c 1 D b= p a, c D b=a 3,. Nx; Ny/ D. 1 5 a; 3 7 b/. R 1 in: 0 x p 1C9x 4 dx R 1 in: 0 R 1 in: 7. (a) Nx D p ; Ny D 0 x 3p R r1c 1 1C9x 4 in: dx 1C9x 4 R 1 in: p ; (b) Nx D 0 y1=3 13 y =3 dy r dx 0 1C9x 4 dx R 1 in: ; Ny D 0 1C 13 y =3 dy (c). Nx; Ny/ D.0:609; 0:366/ in. s s R r r x R x 1C p r p dx r 7.4 (a) Nx D x s r r x 1C p x dx r ; Ny D x s ; (b). Nx; Ny/ D.0; r/. x x 1C dx 1C dx R r r p r x 7.6 Nx D 11 8 R Nx; Ny; Ń/ D.133; 0; 0/ in Nx; Ny; Ń/ D.:98; 0; 0/ in. 7.3 m c D 680 g. R r r p r x r R 1 in: 0 y 1C 13 y =3 dy r R 1 in: ; 0 1C 13 y =3 dy Nx; Ny; Ń/ D.1:07; 0; 0:876/ in Nx; Ny/ D.1:46; 1:00/ m, mass of frame m D 44:6 kg, T D 639 N; B x D 553 N; B y D 118 N (a) Nx D R r= 0 x 0.r x /dxc R r r= x 0.r x /dx R r= 0 0.r x /dxc R r r= 0.r x /dx, Ny D 0; Ń D 0; (b) Nx D 5 56 r R a dx 0 (a) Nx D 0 h 1 x a R a dx ; (b) h x 16 5 a. a 7.4 R L 0 x 0 R. L x / =3 R x L dx (a) Nx D R L 0 0 R. L x / =3, Ny D 0; Ń D 0; (b) Nx D R x 14 L dx 7.44 (a) Ny D R 1 cm 0 1.1CxCx / 0 xœ1cx x dx R 1 cm 0 0 xœ1cx x dx ; (b) Nx D cm. 13 Last modified: March 19, 009

14 7.46 V D 83 mm 3, A D 6 mm V D 1: mm 3, A D 1: mm V D 8h 3, A D h.11 C 8 p /. 7.5 V D 19:8 in. 3, W c D 0:118 lb (a) V D 37 mm 3 ; (b) A outside D 34:610 3 mm ; (c) A inside D 1:10 3 mm V D 7 1 R3, A D 4.11 C p 5/R (a) w D :78 lb=in. for 0 x 36 in:; (b) w D 1:85 lb=in. for 0 x 18 in:, w D 3:70 lb=in. for 18 in: x 36 in:; (c) w D 1:85 lb=in. C.0:0514 lb=in. /x for 0 x 36 in:, (d) w D 1:85 lb=in. C.0:103 lb=in. /x for 0 x 18 in:, w D 5:56 lb=in..0:109 lb=in. /x for 18 in: x 36 in: 7.60 A x D 0, A y D 33:3 lb, B y D 66:7 lb. 7.6 A x D 0, A y D 49:1 kn, M A D 98:1 knm (a) Nx D 1:0 in:; (b) & (c) A x D 0, A y D : lb, B y D 77:8 lb (a) Nx D 1:67 m; (b) & (c) A x D 0, A y D 49:1 kn, M A D 81:8 knm (a) a D 800 N=m, b D 0, c D 8:00 N=m 3 ; (b) d D 800 N=m, f D 0 m. 7.7 A x D 0, A y D 4:00 kn, B y D 16:0 kn A x D 0, A y D 40:0 kip, B y D 40:0 kip A x D 0, A y D 6:08 kip, B y D 4:9 kip C x D 0, C y D 1:0 kn, M C D 4 knm A x D 0, A y D 80 kip, C y D 80 kip. 7.8 A x D 0, A y D w 1 a C w.l a/, M A D 1 w 1 a C 1 w.l a / a D 0:54 kn=m, b D 1:1 kn=m, c D 0:0556 kn=m 3, F D 3:0 kn, Nx D 4:05 m A x D 0, A y D 0, A D W, M Ax D WR T D d T D 39:0 lb D 0:35 rad D 13:5 ı (a) T D 40:7 lb; (b) T D 33 lb T B D 414 N, T C D 87 N, T D D 684 N F EG D 381 lb Nx; Ny/ D.0; 0:/ mm Nx; Ny/ D ; 1/ m Nx; Ny; Ń/ D.34:7; 0; 0/ mm (a) Let o D 0:00 g=mm 3, i D 0:003 g=mm 3, Nx D Ń D 0; (b). Nx; Ny; Ń/ D.3:0; 0; 0/ mm Nx D 4 3 m. R 1 cm 0 x.1cx Nx D / dx R, (b) Nx D 5 1 cm 0.1Cx / dx 8 cm (a) Nx D R km 1 km xp 1C4x R km 1 km V D 4 3 r3, A D 4r V D 4360 cm 3, A D 867 cm. /, M Ay D WR, M A D 0. R 6 mm 0 xf i. 6 1 x/ C o Œ.3C 6 1 x/. 1 6 x/ g dx R 6 mm 0 f i. 6 1 x/ C o Œ.3C 6 1 x/. 1 6 x/ g dx R km p, Ny D 1 km xp 1C4x p ; (b). Nx; Ny/ D.0:801; 1:48/ km. 1C4x 1C4x R km 1 km A x D 0, A y D 1700 lb, B y D 1300 lb B y D 640 lb, C x D 0, C y D 1460 lb where pin C is located 6 ft from the left-hand end of the beam. 7.1 A x D 0, A y D :17 kn, C y D 3:83 kn where roller C is located m from the right-hand end of the beam A x D 46:8 lb, A y D 81 lb, C x D 187 lb d D 1:5 mm., Ny D 0, 14 Last modified: March 19, 009

15 Chapter 8 8. N H D 34:7 lb, V H D 197 lb, M H D 1180 in.lb, N J D 480 lb, V J D 0, M J D N E D 00 lb, V E D 346 lb, M E D 0, N F D 00 lb, V F D 346 lb, M F D 8310 in.lb 8.6 N F D 3:0 kn, V F D 4:7 kn, M F D 0, N G D 3:0 kn, V G D 4:7 kn, M G D 10:7 kn m, N H D 0:800 kn, V H D 1:07 kn, M H D 10:7 knm, N I D 0:800 kn, V I D 1:07 kn, M I D 13:3 knm. 8.8 N F D 11: kn, V F D 1:60 kn, M F D 0, N G D 11: kn, V G D 1:60 kn, M G D 4:00 kn m, N H D 8:80 kn, V H D 1:60 kn, M H D 4:00 knm, N I D 8:80 kn, V I D 1:60 kn, M I D N D D 0, V D D 100 lb, M D D 0, N E D 0, V E D 100 lb, M E D 150 in.lb, N F D 70:7 lb, V F D 70:7 lb, M F D 56 in.lb. 8.1 N H D :00 kn, V H D :00 kn, M H D 0, N I D :00 kn, V I D :00 kn, M I D 5:60 knm: 8.14 N L D :00 kn, V L D :00 kn, M L D 3:0 knm, N O D :00 kn, V O D :00 kn, M O D N R D 5:83 kn, V R D 0 kn, M R D 0, N A D 4:00 kn, V A D 0, M A D 4:0 knm N H D 400 lb, V H D 693 lb, M H D 1390 ftlb, N I D 400 lb, V I D 693 lb, M I D N L D 46 lb, V L D 653 lb, M L D 1600 ftlb, N M D 0, V M D 800 lb, M M D Essay-type answer. 8.4 V Ax D 0, V Ay D 150 lb, N A D 0, M Ax D 400 in.lb, M Ay D 0, M A D 3600 in.lb. 8.6 N Bx D 0, V By D 0, V B D 10 N, M Bx D 8:40 Nm, M By D 1:6 Nm, M B D V Dx D 0, N Dy D 0, V D D 10 N, M Dx D 13:8 Nm, M Dy D 14:4 Nm, M D D V D :50 kn, M D.:50 kn/x for 0 x 3 m; V D 7:50 kn, M D.7:50 kn/.4 m x/ for 3 m x 4 m. 8.3 (a) V D P, M D P x for 0 x 3 1 L; V D 0, M D 3 1 PL for 1 3 L x 3 L; V D P, M D P.L x/ for 3 L x L; (b) Essay-type answer V D 15 lb, M D.15 lb/ x for 0 x 8 ft; V D 15 lb, M D. 15 lb/.16 ft x/ for 8 ft x 16 ft V D 1000 lb, M D lb/.0 ft x/ V D. 8:00 kn=m/ x, M D. 4:00 kn=m/ x V D 100 N.600 N=m/ x C.50 N=m / x, M D.100 N/ x.300 N=m/ x C.16:7 N=m / x Essay-type answer V D 3:00 N, M D 8:00 N mm C.3:00 N/ x for 0 x mm; V D 1:00 N, M D.1:00 N/ x for mm x 4 mm; V D :00 N, M D 1 Nmm C.:00 N/ x for 4 mm x 6 mm V D 3:00 N, M D 8:00 Nmm C.3:00 N/ x for 0 x mm; V D 0, M D 0 for mm x 6 mm: 8.48 Essay-type answer V D 100 lb=ft.6:00 ft x/ C 1000 lb, M D 50 lb=ftœ.1:0 ft/x x C.1000 lb/ x for 0 x 6 ft; V D 100 lb=ft.6:00 ft x/ 1000 lb, M D 50 lb=ftœ.1:0 ft/x x C.1000 lb/.1 ft x/ for 6 ft x 1 ft. 8.5 V D 1000 N, M D.1000 N/ x for 0 x 1 m; V D 100 N, M D.100 N/.9:00 m C x/ for 1 m x m; V D 1100 N, M D.1100 N/.3:00 m x/ for m x 3 m V D.0:0 kip=in./ x, M D.0:101 kip=in./x for 0 x 0 in:; V D 10:0 kip C.0:0 kip=in./ x, M D 00 in. lb.10:0 kip/ x C.0:101 kip=in./x for 0 in: x 79 in:; V D. 0:0 kip=in./.99:0 in: x/, M D.0:101 kip=in./.99:0 in: x/ for 79 in: x 99 in: 8.56 V D. 8:00 kn=m/ x, M D. 4:00 kn=m/ x V D 60 kn.8:00 kn=m/ x. 1 3 kn=m / x, M D 19 knm C.60:0 kn/ x.4 kn=m/ x. 1 9 kn=m / x V D 4000 lb.15:0 lb=ft/œ.40:0 ft/x x, M D.4000 lb/ x.5:00 lb=ft /Œ.60 ft/x x 3, M max D 15;400 ftlb at x D 8:45 ft. 8.6 V D 1 6 w 0 L w 0.x 1 L x /, M D w 0. L 6 x 1 x C 1 3L x3 /, M max D.0:0160/w 0 L at x D.0:11/L and M max D. 0:0160/w 0 L at x D.0:789/L V D P, M D 3 PL C P x for 0 x L ; V D P, M D 1 PL C P.x 1 L/ for L x L V D. 5:0 lb=ft / x 5, M D. 3 lb=ft / x 3 for 0 x 4 ft; V D 1800 lb.5:0 lb=ft / x, M D 700 ftlb C.1800 lb/ x. 5 3 lb=ft / x 3 for 4 ft x 1 ft V D. 1:00 kn=m/ x, M D. 0:500 kn=m/ x for 0 x 1:3 m; V D 6:86 kn.1:00 kn=m/.x 1:30 m/, M D 7: knm.5:56 kn/ x.0:500 kn=m/ x for 1:3 m x 4 m; V D 14:0 kn.1:00 kn=m/.x 4:00 m/, M D 5:0 knm.10:0 kn/ x.0:500 kn=m/ x for 4 m x 5:5 m. 15 Last modified: March 19, 009

16 8.70 V max D 4P at x D 0, M max D 10P d at x D V max D 45:0 N just to the left of x D 30 mm, M max D 1130 Nmm at x D 30 mm V max D 10:0 lb just to the right of x D 17 in:, M max D 16:0 in.lb at x D 4 in: 8.76 Beam 1: Shear diagram (b), Moment diagram (g); Beam : Shear diagram (a), Moment diagram (g); Beam 3: Shear diagram (d), Moment diagram (f) N F D 6:19 kip, V F D 0:940 kip, M F D 0, N G D 6:19 kip, V G D 0:940 kip, M G D 4:00 kipft N E D 833 N, V E D 833 N, M E D 0, N F D 1180 N, V F D 0, M F D 69:0 N m, N G D 833 N, V G D 833 N, M G D V D 1:0 kn.0:750 kn=m / x, M D.1:0 kn/ x.0:50 kn=m / x 3 for 0 x 4 m; V D 36:0 kn.1:0 kn=m/ x C.0:750 kn=m / x, M D 3:0 knm C.36:0 kn/ x.6:00 kn=m/ x C.0:50 kn=m / x 3 for 4 m x 8 m V D 1:0 kn.0:750 kn=m / x, M D.1:0 kn/ x.0:50 kn=m / x 3 for 0 x 4 m; V D 36:0 kn.1:0 kn=m/ x C.0:750 kn=m / x, M D 3:0 knm C.36:0 kn/ x.6:00 kn=m/ x C.0:50 kn=m / x 3 for 4 m x 8 m V D 60:0 N, M D 1;000 Nmm C.60:0 N/ x V D 60:0 N, M D 1;000 Nmm C.60:0 N/ x for 0 x 150 mm; V D 40 N, M D 48;000 Nmm C.40 N/ x for 150 mm x 00 mm V max D 1750 lb for 15 ft x 0 ft, M max D 8750 ftlb at x D 15 ft. 8.9 (a) V D 4:00 kn. 1 3 kn=m / x ; (b) M D. 4:00 kn/ x. 1 9 kn=m / x 3 ; (c) V max D 9:00 kn at x D 3 m, M max D 15:0 knm at x D 3 m (a) M D. :00 kip=ft/ x ; (b) V D 56:0 kip.8:00 kip=ft/ x C. 3 1 kip=ft / x ; (c) V max D 0:0 kip at x D 6 ft, M max D 7:0 ftkip at x D 6 ft (a) M D 13 knm.17:0 kn/ x C.0:500 kn=m/ x ; (b) V D 16:0 kn.4:00 kn=m/ x C. 1 3 kn=m / x ; (c) V max D 16:0 kn at x D 0, M max D 48:0 knm at x D 6 m. Chapter 9 9. N D 5:1 lb, F D 10:3 lb, the box remains at rest on the ramp : D tan h D 60:0 cm The dam will not slide or tip when the reservoir is completely full. 9.1 The dam will not tip and will fail by sliding N D 1: lb, F D 8: lb P D 47:4 N (a) min D 0:89; (b) The answer to Part (a) will change, essay-type answer; (c) The answer to Part (a) does not change, essay-type answer. 9.0 s D 0: P D 0:900 lb will cause all books to slide. 9.4 s D 0: Q D 7:70 lb. 9.8 P D 10:6 N P D 7 kn. 9.3 s D The truck is not capable of pulling the dumpster (a) P D 4:56 N; (b) T CD D 6:58 N, essay-type answer (a), (b), & (c) P D 73:0 lb M A D 3:1 Nm. 9.4 M A D 575 in.lb. 16 Last modified: March 19, 009

17 9.44 (a) P D 14:1 N; (b) P D 4:54 N W D 35:3 lb W B D 53:8 lb, surface C will stick while motion is impending at A and B D 0: D 0:0943, the normal and friction forces between the dam and foundation are located 0:730 m to the left of point A P D 1:60 lb, the roll of paper will tip P D 56: lb, slip is impending at E and there is no slip at B and C T 0 D 57:4 lb. Chapter Essay-type answer I x D 568 a 4, I y D 38 a I x D 0:0404 in. 4, I y D 0:0570 in I x D 1 1, I y D 1 1 hb Answer provided in problem statement I y D 16 r4 0, J O D 8 r4 o, essay-type answer J A D 4 r4 o Essay-type answer (a) I x D :74 mm 4 ; (b) I y D 11:0 mm (a) I x D 0:305 mm 4 ; (b) I y D 1:60 mm (a) I x D 0:500 in. 4 ; (b) I y D 0:375 in c 1 D b= p a, c D b=a 3, I x D 1 10 ab I x D 0:305 mm I x D 4: mm 4, I y D 4: mm 4, k x D 105 mm, k y D 33:1 mm I x D 117 in. 4, essay-type answer k x D 3:1 in: For the rectangular cross section: I x D 108 in. 4, I y D 108 in. 4 ; For the I cross section: I x D 48 in. 4, I y D 76:0 in I x D 4: mm 4, I y D 1: mm I x D 37:6 in. 4, I y D 10:9 in (a) I x1 D 180 mm 4 ; (b) I x D 550 mm (a) d D 4:00 in:; (b) I x D 18 in. 4 ; (c) I y D 704 in (a) d D :00 mm; (b) I x D 88:0 mm 4 ; (c) I y D 48:0 mm (a) d D 65:0 mm; (b) I x D 1: mm 4 ; (c) I y D 1: mm Answer provided in problem statement I y D 1 4 mr where m D r t I y D m. 1 4 R C 1 3 L / where m D R L I D 3 5 m. 1 4 R C L / where m D 1 3 R L I y D 3 5 m. 1 3 a C h / where m D 4 3 abh Essay-type answer (a) I x D 1 R r= 0 0.r x / dx C I x D 4:810 5 slugin. R r r= 0.r x / dx; (b) I x D r Last modified: March 19, 009

18 10.64 I y D 1 3 ma where m D 1 ha (a) I y D R L 0 where m D LR (a) I x D R L 0 t 0. x L I y D 1: kgcm. 4 R4 Œ. x L /4=3. x L /4 dx C R L 0 R x Œ. x L /=3. x L / dx; (b) I y D m L C7689 R I x D 5 56 mr where m D 7 1 R I D 7 16 mr where m D 7 1 R I O D 0:017 slugft, essay-type answer I y D 1 3 m.a C b / I B D 0;700 kgmm I A D 9:410 4 slugin I x D 0:497 slugin I B D 0:0778 kgm I x D 1:61 slugin I D 0:619 slugin I y D 3:53 slugin I y D 5: slugft J O D 4.r4 o r 4 i / (a) I y D R 4 m 0 x. p x q Rx 3 / L q1 C R L dx; (b) I x D 0 9 mr where m D 3 4 t 0 RL 1 C R L. 1 4 x/ dx; (b) I y D 0:6 m c 1 D 6, c D 1 3, c 3 D 1; (a) I y D R 9 in: 0 x (a) I y D R 1 in: 0 x.x 1/ dx; (b) I y D 0:0667 in I x D : mm 4, I y D 3:510 5 mm (a) d D 1:183 in:; (b) I x D 5:56 in I D 3 10 mr where m D 1 3 r h I x D 1700 kgmm : I D 3040 kgmm : I x D 0:0113 kgmm : I x D 1 R h 0 1 x dx C I y D 1: kgm : R h h x dx (a) I x D 1: mm 4 ; (b) I x D 5: kgmm I x D 13:3 slugin I D 16:7 slugin x p x/ dx; (b) Iy D 86 in Last modified: March 19, 009

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