omernecaticora.files.wordpress.com€¦ · 1 answers chapter 1 1–1. a) d1 22.6 mm b) d2 15.96 mm...
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1
Answers
Chapter 1 1–1. a) 1 22.6 mmd b) 2 15.96 mmd
1–2. a) 35.7 MPa AB
b) 42.4 MPa BC
1–3. 112.9 kNP 1–4. a) 81.5 M PaAB b) 18 .11 M P aBC
1–5. 25.2 mmsd
1–6. a) 35.7 m AB a
b) 5.34 MPa
1–7. a) 101.6 MPa BD
b) 21.7 MPa CE
1–8. a) 4.27 M PaDE b) 2.13 M PaDE
1–9. 33.1 kNP
1–10. 2285 mmBEA
1–11. 98.3 M PaCG 1–12. 6 2238.1 10 mAEA
1–13. 4.97 MPa CD
1–14. a) 17.86 kNP b) 41.4 MPa BC
1–15. 5.93 MPa
1–16. 9.22 kNP 1–17. 67.9 kNP 1–18. 60.2 mmd 1–19. 63.3 mmd
1–20. 178.6 mmL 1–21. 277 mma 1–22. a) 3.33 MPa b) 525 mmb
1–23. a) 69 MPa b) 40.6 MPa 1–24. a) 11.45 mmd b) 134.9 MPab c) 90.0 MPab 1–25. allow 8.31 kNP 1–26. a) 25.9 mmd b) 271 MPa b
1–27. a) 80.8 MPa
b) 127.0 MPa b
c) 203 MPa b
1–28. a) 3.97 MPa b) 202 mmb c) 20.8 MPab 1–29. 480 kPa 277 kPa 1–30. a) 6.25 kNP b) 289 kPa 1–31. 489 kPa 489 kPa
1–32. a) 13.95 kNP b) 620 kPa
1–33. 337 kNP 1–34. 37.1 MPa 17.28 MPa
1–35. a) max| | 54.1MPa
b) max 27.0 MPa
1–36. a) 706 kNP
b) 45 c) 18.00 MPa
d) max 36.0 MPa (compression)
1–37. F.S. 3.60 1–38. 27.8 mmw 1–39. a) F.S. 3.97 b) 16.27 mma 1–40. a) 313.47 10 ma b) 314.61 10 mb
1–41. 2168.1 mmABA
1–42. 15.08 kNQ
1–43. 146.8 mmL 1–44. F.S. 3.40 1–45. 10.25 kNP 1–46. a) F.S. 2.92 b) 40.3 mmb
c) 97.2 mmc
1–47. 20.8 mmd
1–48. F.S. 2.50 1–49. 38 mma 195.6 mmb 1–50. Actual factor of safety is the smaller value F.S. 3.15 1–51. 1.683 kNP 1–52. 2.06 kNP 1–53. 13.7 kNP
2 Answers
1–54. 19.6 kNP 1–55. 3.72 kNP 1–56. 3.97 kNP 1–57. 2.78 kNUP F.S. 1.69 1–58. a) 362 kgm b) F.S. 1.718
1–59. 2 14.93 mmd
1–60. a) 94.7 MPaAB b) 64.4 MPaBC 1–61. a) 55.3 MPa b) 144.9 MPab c) 72.4 MPab
1–62. 195.3 MPaCD
1–63. 292 mmL 1–64. a) F.S. 4.67 b) F.S. 3.19 c) F.S. 2.52 1–65. F.S. 3.45 1–66. F.S. 2.42 1–67. a) 5.57 mmd b) 38.9 MPa b
c) 35.0 MPa b
1–68. min all all/4 L d
1–69. 22.8 32.1 1–70. a) opt 27.9 b) F.S. 3.26
Chapter 2 2–1. a) all 2.45 kNP b) 50.0 mm
2–2. a) 5.32 mmd b) 1.750 mL 2–3. a) 81.8 MPa b) . . 1.712F S 2–4. a) 9.82 kNP b) 500 MPa
2–5. a) 2.6 mm b) 26.5 MPa 2–6. a) 0.546 mmd b) 36.3 MPa
2–7. 73.7 GPaE
2–8. a) 17.25 MPa b) 2.82 mmt 2–9. min 4.07 mmd min 0.91 mL 2–10. a) 1.458 mL b) 14.91 mma
2–11. 9.21 mmd
2–12. 0.631 mmd
2–13. 1.988 kNP
2–14. 5 mmd 2–15. 4.47 mmC 2–16. 21.5 kNP
2–17. a) tube 67.9 MPa rod 55.6 MPa b) tube 0.2425 mm
rod 0.1325 mm
2–18. 16.52 mmBCA 2–19. a) 32.8 kNQ b) 0.0728 mm AB
2–20. a) 0.01819 mmA b) 0.0919 mmB
2–21. a) 2.83 mmAB b) 3.27 mmBC 2–22. 50.4 kNP
2–23. Member AB: 2.11 mmAB
Member AD: 2.03 mm AD
2–24. 147.3 kNACF 2–25. 0.0531 mmE 2–26. a) 0.0302 mmBE b) 0.01783 mmCF 2–27. 14.74 kNP
2–28. a) 80.4 m E b) 209 mF
c) 390 m G
2–29. 2
6
gh
E
2–30. 21
2
gL
E
1
2F W
2–31. 12ln td
d
2–32. ln (1 ) t
2–33. a) 65.1 MPaa b) 0.279 mm
2–34. a) 287 kNP b) 140.0 MPa b
2–35. 59.5 MPas 8.627 MPac 2–36. a) 140.6 MPab b) 93.75 MPaa 2–37. a) 15 mmh b) 288 kNP 2–38. a) 116.3 MPas 40.7 MPaa b) 0.145 mm 2–39. 707.6 NP
Answers 3
2–40. a) 0.0762 mm b) 30.5 MPaAB 38.1 MPaEF 2–41. a) 58.6 kNAR 50.6 kNDR b) 339.2 10 mmBC 2–42. a) 35.97 kNAR 27.97 kNDR b) 35.83 10 mmBC
2–43. 1
10AT P 1
5BT P
3
10CT P 2
5DT P
2–44. a) 933 NBEP 1036.7 NCP b) 1.98 mmD 2–45. a) 9.73 kNCDP b) 2.02 mmC
2–46. a) 4 kNBCF 1.6 kNDEF b) 0.056 mmA 2–47. Stress in steel 8.04 MPas Stress in concrete 0.21 MPac 2–48. a) 80.53 CT b) 0.261 mm 2–49. 8.15 MPaa
2–50. 56.2 MPaa
2–51. 142.6 kNP 2–52. a) 98.3 MPa b) 38.3 MPa 2–53. a) 44.4 MPaAB 100.0 MPaBC b) 0.500 mmB 2–54. a) 40 MPaAB 90.1 MPaBC b) 0.32 mmB 2–55. a) 36.8 MPas b) 250.147 mmfL
2–56. a) 21.4 CT b) 3.68 MPab 2–57. 5.70 kNP 2–58. a) hot 94.1 CT b) exact 0.45027mL 2–59. a) 172.8 kNP b) 0.236 mmb 2–60. a) 116.2 MPaa b) 0.363 mma 2–61. a) 0.0358 mmL b) 0.00258 mmW c) 0.0003437 mmt d) 20.00825 mmA 2–62. a) 0.205 mmy
b) 0.00955 mmx 2–63. 205 MPaE 0.455v 70.3 MPaG 2–64. 408 kNF
2–65. a) 0.652 mm b) 0.0235 mmod c) 0.001173 mmt 2–66. a) 10.20 μmAB b) 2.40 μmBC c) 8.91μmAC 2–67. a) 63 MPay
b) 213.50 mmA c) 3540 mmV 2–68. tan 1.99551 2–69. a) 0.13 mmy b) 0.0146 mmx
2–70. a) 34292 NF b) 102876 NP
2–71. 2
( )1
x x yE
vv
2
( )1
y y xE
vv
( )1z x yv
v
2–72. 1( )z x y zv v
E
21[(1 ) (1 ) ]x x yv v v
E
21[(1 ) (1 ) ]y y xv v v
E
2–73. a) 1
2 xv b) 1
2 xv
2–74. a) 0x v b) 021z
E
v
2–75. a) 262 mmb b) 21.4 mma 2–76. 10.26 MPaG 2–77. 0.45 mm 2–78. min 56.3 mmb min 20.5 mma
2–79. 1.091 mm
2–80. 30.2 kNP 2–81. 42.9 mma 160.7 mmb 2–82. P 75.0 kN 40.0 mma 2–83. a) 6242 10e 318.40 mmV b) 6519 10e 339.4 mmV 2–84. a) 30.275 mmV
b) 30.275mmV 2–85. a) 615 10 md b) 9 3530 10 mv
c) 0
0
100% 0.03%
4 Answers
2–86. a) 0.0746 mmh 3143.9 mmV b) 0.0306 mmh 3521 mmV 2–87. P 16.46 kN 2–88. 2 1/ 3.00R R
2–89. a) 9 6
EGk
G E
b) 3 2
6 2
k Gv
k G
2–90. 1 1
3 2
G
E
2–91. a) 0.0303 mmx b) 40.6 MPax 5.48 MPay
2–92. a) 44.6 MPax 0y 3.45 MPaz b) 0.0129 mmy
2–93. a) max 69.5 MPa b) max 66.7 MPa 2–94. a) 58.7 kNP b) 69.75 kNP 2–95. a) 11.4 mmfr b) 28.8 kNP
2–96. 36.7 mmt 2–97. a) 92.3 kNP 0.791 mm b) 180.0 kNP 1.714 mm 2–98. max 189.6 MPa
2–99. a) 2max 96.4 N/mm
b) 2max 138.2 N/mm
2–100. 23.9 kNP 2–101. max 176.7 kNP 3.84 mmm
2–102. max 176.7 kNP 3.16 mmp
2–103. a) 310.5 kN m perm 0.705 mm
b) 310.5 kN m perm 4.205 mm
2–104. 310.5 kNmP a) 7.81 mmp b) 10.81 mmp
2–105. max 13.97 kNQ 1 3.39 mm 2–106. max 10.12 kNQ 1 2.46 mm 2–107. a) 23.9 kNP b) 250 MPaAD c) 0
2–108. a) 23.9 kNP b) 250 MPaAD final 0.310 mm
2–109. a) 0.292 mmC b) 250 MPaAC 307 MPaBC c) 0.0272 mmp
2–110. a) 990 kNP b) 250 MPaAC 316 MPaCB c) 0.031 mmp
2–111. a) 492.71 kNP b) 2 571.4 MPa 316 MPaCB c) 0.217 mmp
2–112. a) 0.816 mmm b) 2 466 MPa c) 0.116 mmp
2–113. a) 250 MPaAD 124.3 MPa BE b) 0.622 mmB
2–114. 250 MPaBE a) 233 MPa AD b) 1.322 mmB
2–115. a) , res 4.70MPaAD , res 19.34 MPaBE b) , 0.0967 mmB P
2–116. a) 250 MPa b) res 108 MPa 2–117. 248 MPaAC 0.174 mmC 2–118. a) , res 92.9 MPaAC , 0.1138 mmC P 2–119. 2,res 66 MPa 2–120. 1,res 102.9 MPa 2,res 123.5 MPa 2–121. a) 2 493 CYT b) 2 965 CT 2–122. a) , 0.1042 mmC p
b) , res 65.2 MPaAC
, res 65.2 MPaCB
2–123. a) , 0.00788 mmC p
b) , res 6.06 MPaAC
, res 6.06 MPaCB
2–124. 31 mmd 2–125. a) tot 0.1549 mm
b) 0.1019 mmB
2–126. a) 31.6 kNP b) 0.025 mm
2–127. 3
3 3Pl P
lAE AE
2–128. 4.67 CT
2–129. 1.84 mmBD 2.88 mmDE
Answers 5
2–130. a) 57.1 MPaa
b) 85.7 MPab
2–131. 75.4 CT 2–132. a) 0.0754 mmAB b) 0.1028 mmBC c) 0.1220 mmAC 2–133. 16.67 MPaG
2–134. 319.00 10 kN/mk
2–135. a) YAm
g
b) EAk
L
Chapter 3 3–1. a) 53.4 MPa b) 53.9 MPa 3–2. a) 5.17 kN mT b) 87.2 MPa 3–3. max 78.8 MPa 3–4. 446.7 N mT 3–5. a) 6
max 54.6 10 Pa (i.e.) 54.6 MPa b) 1 43.6 mmc 3–6. a) 125.7 N mT b) 181.4 N mT 3–7. a) 2.08 kNT b) 50 mmsd 3–8. 2.08 kN mT 3–9. a) max 56.6 MPa
b) max 36.6 MPa
3–10. 39.8 mmd 3–11. a) shaft CD b) 85.8 MPa 3–12. a) shaft CD b) 87.6 MPa 3–13. a) 81.2 MPaAB b) 64.5 MPaBC c) 23.0 MPaCD 3–14. 44.4 mmd 3–15. 35.8 mmABd 42.4 mmBCd 3–16. 754 N mT 3–17. a) 50.3 mmABd b) 63.4 mmBCd 3–18. a) 1 15.18 mmd b) all 132.5 N mT
3–19. all 3.18 kN mT 3–20. all 3.37 kN mT 3–21. 441.7 NmCT 3–22. a) 37 mmBCd b) 31.2 mmEFd
3–23. a) 45.1 mmABd b) 65.0 mmCDd 3–24. 1.129 kN mT 3–25. a) 72.5 MPa b) 68.7 MPa 3–26. a) 59.6 mmd b) 43.9 mmd 3–27. a) max 55.0 MPa
b) max 45.3 MPa c) max 47.7 MPa
3–28. a) 20.1 mmABd
b) 26.9 mmCDd c) 36.6 mmEFd
3–29. a) 2 2
1 2 all
22
c cT
w gc
(hollow shaft)
b) 212
0 2
1T T c
w w c
3–30. max 1 22
0 1 2
1 ( / )
1 ( / )
c c
c c
1 2/c c 1.0 0.95 0.75 0.5 0.0
max 0/ 1.0 1.025 1.120 1.200 1.0
3–31. a) 4.21 b) 5.25
3–32. a) 199.5 N mT b) 10.40
3–33. a) 0 2.19 kN mT b) 9.11s 3–34. 64.7 MPa 3–35. a) / 1.384B C b) / 3.22B D
3–36. a) 8.54BC b) 2.11BD
3–37. a) 14.43B b) 46.9C
3–38. 6.02A
3–39. 1.624AD 3–40. a) 1508 N mT b) 1.624A 3–41. 3.82A 3–42. 73.6 N mT
3–43. 4 2
1 11A
AT l
GJ n n
3–44. 22.4A 3–45. 62.9 mmd 3–46. 42.1 mmd 3–47. a) 82.1 mmd b) 109.4 mmd
6 Answers
3–48. 22.5 mmd
3–49. 31.2 mmd 3–50. 35.2 mmd 3–51. a) 73.6 MPa b) 34.4 MPa c) 5.07
3–52. all 4.13
3–53. a) max 34.37 MPa b) max 50.82 MPa c) 4.53 3–54. all 7.27 3–55. 74.4 MPaAB 19.2 MPaCD 3–56. 15.9 MPaAB 53 MPaCD 3–57. a) 43.1 MPaAB
b) 48.5 MPaCD
3–58. 4.12 kN mT
3–59. 12.24 MPa
3–60. a) 2 1/2
2
(1 )
1s
h
T n
T n
b)
2
2
1
1s
h
T n
T n
3–61. 4
7
12
TL
Gc
3–62. 6 mmd
3–63. a) max 212
T
tr
b) / 2 21 2
1 1
4B CT
Gt r r
3–64. a) 46.9 MPa b) 23.5 MPa 3–65. a) 65 MPa b) 32.5 MPa 3–66. 6.69 mmd
3–67. 2 58.2 mmd 3–68. 2.64 mmt
3–69. 25.6 kWP 3–70. a) 612.21 10 WP b) 8.48 3–71. a) 51.7 kWP b) 6.17
3–72. a) 18.80 kWP b) 24.3 MPam
3–73. a) max 47.5 MPa b) 2 30.4 mmd 3–74. a) 20.3 mmABd b) 24 mmCDd 3–75. a) 29.66 MPaAB b) 49.44 MPaCD 3–76. 15.00 mmABd 20.4 mmCDd 27.6 mmEFd
3–77. all 7.11 kWP 3–78. 4.90 Hzf 3–79. a) 15.45 HzABf b) 21.95 HzABf 3–80. 50.0 kWP 3–81. 74.0 mmd 3–82. 2 24.9 mmd 3–83. 33.5 Hzf or 2010 rpm
3–84. 669 kWP 3–85. 584 kWP 3–86. 10.8 mmr
3–87. 42.6 Hzf
3–88. 63.5 kWP 3–89. 28.8 kWP 3–90. a) 18.3 MPa b) 13.6 MPa 3–91. a) 203 N mT b) 165.8 N mT
3–92. 21.2 N mT
3–93. a) 1197 N mT b) 1240.7 N mT 3–94. a) 113.3 MPam 15.00 mmE b) 145.0 MPam 6.90 mmY 3–95. 13.32 mmY 3–96. 314 MPaY
3–97. a) 2.18 b) 3.74 3–98. a) 7.614 b) 18.5 3–99. a) 6.72 b) 18.71 3–100. a) 5.4 kN mT b) 8.6 kN mT 3–101. a) 977 N mT b) 8.61 mmY
3–102. a) 8.17 mmY b) 42.1 3–103. YT T (plastic region with elastic core) max 125 MPa 27.9 3–104. max 145MPa 19.75
3–105. a) 1.126 Y
b) 1.587 Y
c) 2.15 Y
3–106. a) max 11.71kN m 3.44Y b) 4.81 14.12 kN mT 3–107. a) 8.02 b) 14.89 kN mPT 3–108. a) 10.63 mmYt b) 65.3 mmx 3–109. a) 4745 N mT b) 58.33 mmx 3–110. 73.4 N mT
Answers 7
3–111. a) 142 N mT b) 27.5 3–112. 2.32 kN mT
3–113. 2.26 kN mT
3–114. resmaximum 59 MPa 3–115. 31.1 3–116. a) 33.5 MPa at 16 mm
b) perm 1.032
3–117. 1 3.10 4.04Y
3–118. 68.0 MPa at inner surface. 3–119. perm 20.2
3–120. a) 0 0.150c c b) 30 0.221 YT c
3–121. a) 1.3 kN mT 0.87 b) 1.055 kN mT 0.902 3–122. a) max 30.77 MPa 0.535 b) max 37.9 MPa 0.684 3–123. a) max 40.1 MPa 0.653
b) max 50.9 MPa 0.917
3–124. a) 2.25 kN mT 0.815
b) 1.770 kN mT 0.901
3–125. a) 30.6 mmb b) 30.6 mmb c) 22.5 mmb 3–126. a) 29.4 mmb b) 28.9 mmb c) 21.7 mmb 3–127. max 59.2 MPa
3–128. max 5.07 MPa
3–129. 0.944A
B
3–130. 0.737A
B
3–131. 1.356A
B
T
T
3–132. 1.198B
A
3–133. a) 382 mmL b) 283 mmL c) 429 mmL 3–134. a) 639 N mT b) 603 N mT c) 807 N mT
3–135. a) max 59.9 MPa b) 8.45 3–136. a) 70.8 N mT b) 8.77
3–137. a) 31.44 MPaf
b) 20.57 MPaw c) 5.1 3–138. a) 1009 N mT b) 9.07
3–139. 18.67 MPa 3–140. 8.47 MPa 3–141. 4.73 MPaa 9.46 MPab
3–142. At point a, 44.2 MPa At point b, 27.6 MPa 3–143. 16.85 N mT
3–144. 10.58 kN mT 3–145. 30.6 mmd 3–146. 15.8 mmd
3–147. a) 0 1e
T Tt
b)
% red
0.1 10%
0.5 50%
0.9 90%
e
t
3–148. a) 12.76 MPa
b) 1 5.40 kN mT
3–149. a) 2
ave2
11
4m m
t
c
2
2
1
11
4 m
t
c
b) 2
ave2
11
4m m
t
c
3–150. a) 3b
a
c
t
b) 2
2
3b
a
c
t
3–151. max 89.7 MPa 3–152. 12.5 mmd 3–153. 67 kNT 3–154. 12.22A
3–155. a) 1105 N mAT 295 N mCT b) 45.0 MPaAB c) 27.4 MPaBC
3–156. 2 2
( )
4B A
A B
TL c c
Gtc c
3–157. max 2
Gd
La
3–158. 36.1mmd
8 Answers
3–159. 2
1
1.221d
d
3–160. At point a: 52.5 MPa At point b: 31.5 MPa 3–161. 2 39.3 MPa
Chapter 4 4–1. a) 30.7 MPaA b) 19.4 MPaB 4–2. a) 61.6 MPaA
b) 91.7 MPaB
4–3. a) Mc
I 109 N mM
b) 319 N mM 4–4. 2.38 kN mzM
4–5. 129.6 kN mxM 4–6. 34.2 kN myM
4–7. all 29.5 kN mM 4–8. all 9548 N mM
4–9. top 81.8 MPa bot 67.8 MPa
4–10. top 102.4 MPa (compression)
bot 73.2 MPa (tension)
4–11. top 79.8 MPa (compression) bot 118.2 MPa (tension) 4–12. 58.8 kNF 4–13. 61.3 kNF 4–14. 9.51 kNF 4–15. 106.1 N mM 4–16. 187.6 N mM 4–17. all 4.5 kNmM 4–18. all 2.12 kN mM 4–19. 177.8 kN mM 4–20. all 3.79 kN mM
4–21. 498.8 MPam 4–22. a) 965 MPa b) 20.5 N mM 4–23. a) 0.602 mmt b) 0.203 N mM 4–24. a) 75.0 MPa 26.7 m
b) 125.0 MPa 9.60 m
4–25. max 3
6M
a
4
1 12M
Ea
max 3
8.49M
a
4
1 12M
Ea
4–26. 0.950k
4–27. 08
9h h 0.949k
4–28. a) 2d
b b) 3
d
b
4–29. a) 95.9 mm b) 0.0478 4–30. a) 24 m b) 82.75 m c) 0.01380 4–31. a) 139.6 m b) 481 m
4–32. a) 2 2max( )( )
2x
y y cc
b) maxmax
( )( )
2x
yc
4–33. 1.092 kN mM 4–34. 887 N mM 4–35. 1.411 kN mM 4–36. 1.578 kN mM 4–37. 35.2 kN mM 4–38. 20.74 kNmM 4–39. a) 66.2 MPaa
b) 112.4 MPas
4–40. a) 56.9 MPaa
b) 111.9 MPas
4–41. a) 19.2 MPaw b) 123.8 MPas 4–42. a) 20.1 MPaw b) 135.3 MPas 4–43. 39.8 m
4–44. 43.7 m
4–45. 118 m 4–46. 108.7 m 4–47. a) 212 MPa b) 15.59 MPa
4–48. a) 210 MPa b) 14.08 MPa 4–49. 11.73 kN mM 4–50. 9.50 kN mM 4–51. 40.7 kN mM 4–52. 2.24 kNmM
Answers 9
4–53. 1 c s
s c
dx
E
E
4–54. a) 21674 mmsA b) 90.8 kN mM 4–55. a) 62.3 MPaa
62.3 MPab
62.3 MPas
b) 33.7 m
4–56. a) 13.37 MPaa
60.1 MPab
80.1 MPas
b) 52.4 m
4–57. a) 159.4 MPa b) 129.7 MPa 4–58. a) 54.1 MPaa b) 130.2 MPas
4–59. a) 6.15 MPat b) 8.69 MPac
4–60. 2
4 t cr
c t
E EE
E E
4–61. a) 704 N mM b) 580 N mM 4–62. a) max 38.3 MPa
b) max 46.6 MPa
4–63. a) 128 N mM b) 142 N mM 4–64. a) max 219 MPa
b) max 176 MPa
4–65. a) 147 MPa b) 119 MPa 4–66. a) 1.25 kN m b) 1.53 kN mM 4–67. a) 38.4 N mYM b) 52.8 N mM
4–68. a) 57.6 N mYM b) 83.2 N mM
4–69. a) 2 11.6 mmYy b) 3.9 m 4–70. a) 2 2 mmYy b) 0.67 m 4–71. a) 2.40 kN mYM
b) 3.41 kN mM 4–72. a) 1.778 kN mM b) 2.60 kN mM 4–73. a) 19.44 kN mYM
b) 28.1 kN mM 4–74. a) 10.08 kN mYM b) 16.12 kN mM 4–75. a) 2 16.67 mmy b) 48.5 kN mM 4–76. a) 2 16.67 mmy b) 45.3 kNmM
4–77. a) 29.2 kN mpM b) 1.500k
4–78. a) 16.20 kN mpM b) 1.607k
4–79. a) 51.6 kNpM b) 1.437k
4–80. a) 46.9 kNmpM b) 1.363k
4–81. 1.866 kN mpM
4–82. 19.01 kN mpM
4–83. 911 N mpM
4–84. 48.6 kN mpM
4–85. 2250 N mpM
4–86. 21.918 kN mpM
4–87. res 120.0 MPa
4–88. res 145.7 MPa 4–89. a) 215.35 MPa b) res 730.7 MPa 4–90. a) 204.5 MPa b) res 109 MPa 4–91. a) res 106.7 MPa
b) 0 31.15 mm, 0, 31.15 mmy c) 24.1 m
4–92. a) res 102.3 MPa b) 0 37.9 mm, 0, 37.9 mmy
c) Ey
48.9 m
4–93. 2
2
1 1 3 11 1
2 3R Y Y
4–94. a) 0.70711 Y b) 6.09R Y
4–95. a) 292 MPaY b) thickness of elastic core 2
7.01 mmYy
4–96. a) 4.69 m b) 7.29 kN mM
4–97. a) 300 MPam b) 1.175 kNmM
4–98. 2 1
3mn Mc
n I
4–99. a) 71.0 MPaA b) 80.2 MPaB 4–100. a) 37.5 MPa b) 38.4 MPaA 4–101. a) 102.8 MPaA
b) 80.6 MPaB
10 Answers
4–102. a) 112.7 MPaA
b) 96.0 MPaB
4–103. a) 130.2 MPaA
b) 110.0 MPaB
4–104. a) 8.33 MPaA b) 15.97 MPaA 4.86 MPaB
4–105. a) 8.3 MPa b) 13.2 MPaA 7.6 MPaB 4–106. a) 1163 NP b) 842 NP 4–107. a) 139.3 MPa b) 152.3 MPa 4–108. 14.40 kNP 4–109. 16.04 mmd 4–110. a) 3.2 MPa b) 5.26 MPa c) 4.3 MPa d) 8.2 MPa e) 6.4 MPa 4–111. 0.500h d
4–112. 10.8 mmh 4–113. a) 2.54 kNP b) 3.89 mmy
4–114. a) 40.3 kNP b) 6.30 mmy 4–115. a) 69.6 kNP b) Neutral axis lies 50 8.10 41.9 mm from left edge. 4–116. a) 1125 kNP b) 817 kNP 4–117. a) 24.15 N/mm or 4.15 MPaA b) 213.77 N/mm or 13.77 MPaB c) Neutral axis lies 60.26 mm below centroid or 95 60.26 34.74 above point A. 34.74 mm from point .A 4–118. 62.13 mm 114.03 mmy 4–119. a) 47.6 MPaA
b) 49.4 MPaB c) 9.80 mm below top of section
4–120. 1
4AP
A
1
2BP
A
2
5AP
A
2
3BP
A
3
7AP
A
3
5BP
A
4
9AP
A
4
3BP
A
4–121. 9.00 kNP
4–122. a) 30.0 mmd b) 94.5 kNP
4–123. a) 5.00 mmd b) 243 kNP 4–124. 190.32 kNP 247.17 kNQ 4–125. 39.54 kNP 210.27 kNQ 4–126. a) 75 mmd b) 40 MPaA
4–127. a) 2.80 MPaA
b) 0.452 MPaB c) 2.80 MPaD
4–128. a) 3.37 MPaA
b) 18.60 MPaB c) 3.37 MPaD
4–129. a) 6.02 MPaA b) 0.9 MPaB c) 6.02 MPaD 4–130. a) 2.05 MPaA b) 0.684 MPaB c) 2.73 MPaD 4–131. a) 29.3 MPaA
b) 144.8 MPaB c) 125.9 MPaD
4–132. a) 127.5 MPaA b) 47.4 MPaB c) 127.5 MPaD 4–133. a) 65.8 MPaA b) 164.5 MPaB c) 65.8 MPaD 4–134. a) 57.8 MPaA
b) 56.8 MPaB c) =25.9 MPaD
4–135. a) 9.59 b) 77.5 MPaD
4–136. a) 57.3 b) 75.1 MPaE
4–137. a) 19.52 b) 95.0 MPaE 4–138. a) 10.03 b) 54.2 MPaE
4–139. a) 18.21 b) 80.9 MPaD 4–140. a) 32.9 b) 61.4 MPaE
4–141. 16.6 MPaA 4–142. 72.1 MPaA 4–143. 113.0 MPaA
4–144. a) 31.5 MPaA 10.39 MPaB
b) 94.0 mm above point A.
Answers 11
4–145. a) 22.9 MPaA 8.96 MPaB
b) 56.0 mm to the right of point B. 4–146. a) 633 kPaA b) 233 kPaB c) Point G lies 146.2 mm from point A 4–147. a) 53.1 b) 700 kPaA 100 kPaB
133.3kPaC 967 kPaD
4–148. 36.8 mma 4–149. 17.11 mma 4–150. 0 733 N mM
4–151. 0 1.323 kN mM
4–152. 0 3.42 kNmM 4–153. 0 3.42 kNmM 4–154. 0 900 N mM 4–155. 4.70 4–156. The neutral axis passes through corner A of the diagonal AD.
4–157. 2
z yzA y
y z yz
I z I yM
I I I
4–158. 2
2
y yzA z
y z yz
I y IM
I I I
4–159. a) 2 2
1A A
z x
x zx z
r r
b) 0A by equation from part (a).
4–160. a) 1/6 /6
x z
b h
b) 0 /6Ez x b 0 /6Fx z h 4–161. a) 4.07 MPaA b) 38.2 MPaA 4–162. 39.2 MPaA 29.9 MPaB 4–163. 60.9 mma 4–164. 148.6 MPaA
4–165. 12.49MPa 5.22 MPa 4–166. a) % error 34.4% a) 34.4 % b) 6.0 % c) 0.6 % 4–167. a) 154.4 MPaA
b) 75.2 MPaB
4–168. 73.2 mma
4–169. 1 kNP 4–170. 1.945 kNP 4–171. a) 172.4 MPaA
b) 53.2 MPaB
4–172. a) 131.5 MPaA
b) 34.7 MPaB
4–173. 6.5 mme 4–174. a) 22.9 MPaA b) 21.2 MPaB c) 4 MPaC 4–175. a) 45.2 MPaA
b) 17.40 MPaB
4–176. a) 43.3 MPaA
b) 14.43 MPaB
4–177. 107.8 N mM
4–178. a) 111.8 MPaA b) 68.3 MPaB 4–179. a) 3.5 MPaA b) 0.6 MPaB 4–180. a) 32.5 MPaA
b) 34.2 MPaB
4–181. a) 26.4 MPaA b) 26.9 MPaB 4–182. a) 62.1 MPaA b) 15.3 MPaB 4–183. a) 63.9 MPaA
b) 52.6 MPaB
4–184. 84.7 MPaA
4–185. a) 47.46 MPaA b) 23.86 MPaB 4–186. 38.06 mma
4–187. 31 2
32 4
1 2 3
lnbb b
AR
rr r
r r r
4–188. 2 21
2R r r c
4–189. 2
1
211 22
2 1 1 2 1 2
( )
( ) ln ( )rr
h b bR
r b r b h b b
4–190. 2 2
1
12
ln 1r rh r
hR
4–191. 1
1
1 lnrrM R
Ae R r
0.54 ksir
12 Answers
4–192. 5.28 kN mM 4–193. a) max 1066.6 MPa b) 53.6 N mM 4–194. 210.9 NmM 4–195. a) 46.9 MPas
b) 18.94 MPaa c) 55.4 m
4–196. 9242 N m,
9838.6 N m,
656.29 kN
x
z
M
M
P
14.99 mmx 14.08 mmz 60 MPaD 4–197. a) 82.4 MPaA
b) 36.6 MPaB
4–198. a) 46.6 b) 79.6 MPaD
4–199. a) 112.5 MPa
b) 1 M
EI 12.80 m
4–200. a) 2AP
at
b) 2B
P
at
c) 2CP
at
4–201. a) 56.7 kN mM b) 20 m
4–202. a) 57.8 MPaA b) 56.8 MPaB c) 25.9 MPaC
4–203. a) 11
2A 1B
1C 11
2D
b) 14
3
Chapter 5 5–1. Pb
VL
PbxM
L
PaV
L
( )Pa L xM
L
2
PabM
L
5–2. 2
LV w x
( )2
wM x L x
2
max 8
wLM
5–3. V wx
2
2
wxM
V wa
2
aM wa x
5–4. 2
0
2
w xV
L
30
6
w xM
L
0max| |
2
w LV
20
max| |6
w LM
5–5. V P M Px 0V M Pa V P ( )M P L x
5–6. 1( 2 )
2V w L a
1( 2 )
2M w L a x
2
LV w x
21[( 2 ) ( ) ]
2M w L a x x a
( 2 )
2
wV L a
1( 2 )( )
2M w L a L x
2 2
max 8 2
L aM w
5–7. a) 2.15 kNV b) 150 N mM 5–8. a) 300 NV b) 67.5 N mM
5–9. a) max
40.0kNV
b) max
40.0kN mM
5–10. a) max
72.0kNV
b) max
96.0 kN mM
5–11. a) Maximum | | 8 kNV b) Maximum | | 1.92 kNmM
5–12. a) max| | 85.0 NV
b) max| | 21.25 N mM
5–13. a) Maximum | | 18 kNV b) Maximum | | 12.15 kN mM 5–14. a) Maximum | | 0.9 kN 900 NV
b) Maximum | | 112.5 N mM
5–15. 7.13 MPa
Answers 13
5–16. 10.89 MPa 5–17. 27.7 MPa 5–18. 139.2 MPa 5–19. 75.8 MPa 5–20. 129.5 MPa
5–21. 38.7 MPa 5–22. 116.2 MPa
5–23. 99.5 MPam
5–24. 135.9 MPa
5–25. 63.3 MPa 5–26. 2 kNV 6 kNV 6 kNV 2 kNV 2 kN mCM
4 kN mDM 2 kN mEM max 14.29 MPa
5–27. a) 10.67 kNW b) max 9.52 MPa
5–28. a) 0.93 ma b) 29.6 MPam 5–29. a) 1.33 ma b) 56.3 MPa
5–30. a) 866 mma b) max 99.2 MPa
5–31. a) 819 mma b) max 89.5 MPa
5–32. a) 33.3 mmb b) 6.66 mmb 5–33. 24.8 mmd
5–34. PbV
L
B
PbaM
L
PaV
L
max| |
PabM
L
5–35. 2
wLV wx
2( )2
wM Lx x
2
max| |8
wLM
5–36. 2
2
wxM
2
2Bwa
M
V wa 2
aM wa x
5–37. 2
0
2
w xV
L
30
6
w xM
L
5–38. to :A B V P to : 0B C V to :C D V P M Px PaM ( )M P L x
5–39. 2 2
max 8 2
L aM w
5–40. a) Maximum 2.15 kNV b) Maximum 150 N mM
5–41. a) Maximum 300 NV
b) Maximum 67.5 N mM
5–42. a) Maximum 40.0 kNV
b) Maximum 40.0 kN mM
5–43. a) max| | 72.0 kNV b) max| | 96.0 kN mM
5–44. a) max| | 6.75 kNV
b) max| | 6.51 kN mM
5–45. a) max
6.00 kNV
b) max
6.00 kN mM
5–46. 7.13 MPa
5–47. 10.89 MPa 5–48. 139.2MPa
5–49. 75.8 MPa
5–50. a) 2
00
w xV w x
L
2 30 0
2 3
w x w xM
L
20
max 6
w LM
b) 2
0 03
2 4
w x w xV
L
2 3
0 0
4 4
w x w xM
L
20
max| |27
w LM
5–51. a) 2 20
1( 3 )/
6V w L x L
30
1( / )
6M w Lx x L
b) 2max 00.0642M w L
5–52. a) 0 cosw L x
VL
2
02
sinw L x
ML
b) 2
0max 2
w LM
14 Answers
5–53. 3
0 2
4 1
3 3
dM xw L x
dx L
4
2 20 2
4 1 1 3
3 2 12 4
xM w Lx x L
L
2max 0
3| |
4M w L
5–54. 73.5 MPa 5–55. 30.3 MPa
5–56. 64.9 MPa
5–57. 136.4 MPam
5–58. 67.3 kN mEM 68.5 MPam
5–59. 86.9 MPa 5–60. a) 0CM equilibrium
b) 2
03(1.5 )
mw L
a
5–61. 62.2 MPa
5–62. 42.83 MPa 5–63. 500 NP 250 NQ
max| | 1150 NV max| | 221 N mM
5–64. b) max 62.5 MPa
5–65. 173.2 mmh 5–66. 394 mmh
5–67. 323 mmh 5–68. 146 mmb 5–69. 203 mmh 5–70. 48.0 mmb 5–71. Lightest wide flange beam W530 66 @ 66 kg/m 5–72. Lightest wide flange beam W610 101 @ 101 kg/m 5–73. Lightest acceptable wide flange beam: W530 66 5–74. W530 92 | 2080 Use W530 92 5–75. Lightest S-section: S460 81.4 5–76. Lightest S-shape S510 98.2 5–77. Lightest S-section S510 98.3 5–78. Lightest S-section S310 47.3 @ 47.3 kg/m
5–79. Lightest angle is L102 76 12.7 min 12.7 mmt 5–80. Lightest channel section: C180 14.6 5–81. 263 mmb 5–82. 9 mmt
5–83. W530 92 5–84. Lightest wide flange section: W 610 101
5–85. 30.1 kNP 5–86. 15.1 kNP 5–87. 176.8 kN/mw 5–88. 108.8 kN/mw 5–89. a) 2.085 ml b) W 410 46.1 5–90. a) 3.35 ml b) Use W360 44. 5–91. a) W410 60 b) W530 66 c) Use W410 38.8 5–92. a) 1.485 kN/mw b) 1.935 ma 5–93. a) 4.01 kNP b) 3.27 ma
5–94. W690 125 5–95. Increase 33.8% 5–96. 383 mmh
5–97. 336 mmh
5–98. a) dMV
dx
2 3
30 0 0
2 6 6
w x w x wM x a
a a
b) 20
5
6CM w a
5–99. a) dMV
dx
2 20 0
1 1
2 2M w x w x a
b) 20
3
2CM w a
5–100. a) dMV
dx
3
2 30 0 0
6 2 6
w x w wM x a x a
a a
b) 20
2
3CM w a
Answers 15
5–101. a) dMV
dx
20 0
10
1 3
2 415
2 04
M w x a w ax
w a x a
b) 20
1
2EM w a
5–102. a) 0 01.25 2V P P x a P x a
1 11.25 2M Px P x a P x a b) 0.750 EM Pa
5–103. a) 10 0 0
10
3
3
V w a w x w x a
w x a
22
0 0 03 /2 /2M w ax w x w x a
2
0 3 /2w x a
b) 205 / 2EM w a
5–104. a) 0V P x a
1 0M P x a Pa x a b) M Pa
5–105. 3
2M Pa
5–106. a) 0
0
1.5 3 0.8
3 3.2 kN
V x x
x
2 1
1
0.75 3 0.8
3 3.2 kN m
M x x
x
b) max
600 N mM
5–107. a) 0 0
0
40 48 1.5 60 3.0
60 3.6 kN
V x x
x
1 1
1
40 48 1.5 60 3.0
60 3.6 kN m
M x x x
x
b) max 60 kN mM
5–108. 1 1
0 0
62.5 25 0.6 25 2.4
40 0.6 40 2.4 kN
V x x
x x
2 2
1 1
62.5 12.5 0.6 12.5 2.4
40 0.6 40 2.4 kN m
M x x x
x x
47.625 kN mM
5–109. 0 0
0
40 48 1.5 60 3.0
60 3.6 kN
V x x
x
1 1
1
40 48 1.5 60 3.0
60 3.6 kN m
M x x x
x
max 60 kN mM 5–110. a) 050 125 0.3V x
0 0125 0.7 100 1.2 kNx x 150 125 0.3M x x
1 1125 0.7 100 1.2 kN mx x b) 125.0MPa
5–111. a) 0
0 0
0
30 24 0.75
24 1.5 24 2.25
66 3 kN
V x
x x
x
1
1 1
1
30 24 0.75
24 1.5 24 2.25
66 3 kN m
M x x
x x
x
b) 87.7 MPa
5–112. a) 1.9375 mM b) 45.3 MPa
5–113. a) max
3.625mM b) 60.6 MPa
5–114. 1.8 mx W 410 60 5–115. 1.964 mx W 410 60 5–116. a) 2.09375 mDx
0.87211 kN mDM b) 130 mmh 5–117. 6.2342Dx , 1.7658 m a) 1.7658 mx b) 120 mmh 5–118. 2 1
2 0
3 2
3 1
16.67 45 1.35
16.67 1.35 16 1.8
5.56 22.5 1.35
5.56 1.35 16 1.8
V x x
x x
M x x
x x
5–119. 2
2
69 50 5.56
5.56 1.8 kN
V x x
x
2 3
3
69 25 1.852
1.852 1.8 kNm
M x x x
x
5–120. 0 289 120 2 6 3 kNV x x
1
3
89 120 2
2 3 kN m
M x x
x
16 Answers
5–121. 1 016 1.2 12 47.6 1.2V x x
2 18 1.2 12 47.6 1.2M x x x
5–122. a) 1
0
10.2 3 2 2
3 3.5 kN
V x x
x
b) 2 2
1
10.2 1.5 2
3 3.5 kN m
M x x x
x
83.8 MPa
5–123. a) 0 1
1
5 45 2 20 2
20 5 kN
V x x
x
1 2
2
5 45 2 10 2
10 5 kN m
M x x x
x
b) max 40.0 MPa 5–124. 1
1 0
17.235 30 12 0.45
18 1.05 1.2 1.05 kN
V x x
x x
2 2
2 1
17.235 15 6 0.45
9 1.05 1.2 1.05 kNm
M x x x
x x
6.87 MPa 5–125. 0
1
70 165 0.75
20 1.5 kN
V x x
x
2 1
2
35 165 0.75
10 1.5 kNm
M x x
x
123.2 MPa
5–126. a) 02
, 02
x Lh h x
L
b) 60 kNP
5–127. a) 2 3
0 3
3 4L x xh h
L
b) 0 225 kN/mw
5–128. a) 1/2
all
3 ( )wx L xh
b
1/2
0 1x x
h hL L
b) 733.3 kN/mw 5–129. a) 1/2
0 ( / )h h x L b) 82.5 kNP
5–130. a) 3/2
0x
h hL
b) 0 167.7 mmh
5–131. a) 1/2
02
1.659 sin2
x xh h
L L
b) 0 197.6 mmh
5–132. 1.800 ml
5–133. 1.900 ml
5–134. 1 1.824 ml 2 1.216 ml 5–135. 1 1.52 ml 2 0.76 ml
5–136. 1/3
0
d y
d L
5.09 kNP
5–137. 2/3
0y
d dL
0 50.3 mmd
5–138. 2
0 1x
b bL
57 N/mmw
5–139. a) 0 1x
b bL
b) 20.8 mmh
5–140. a) 155.2 MPa b) 143.3 MPa 5–141. 193.8 kNP 5–142. a) 190.7 MPa b) 149.6 MPa 5–143. a) 2.68 ml b) 365.3 mmb 5–144. a) 152.6 MPa b) 133.6 MPa 5–145. a) 4.49 ml b) 211 mmb 5–146. 1/3
0 (2 / )d d x L 1/3
0[2( )/ ]d d L x L
5–147. 1/3
0 4 1x x
d dL L
5–148. a) 0.24 mmx b) 149.3 kN/mw
5–149. a) 0.240 mmx b) 150.0 MPam
5–150. a) 750 mmmx b) 52.8 kNP 5–151. 0.400 mmx 134.4 kNP 5–152. a) max| | 120 kNV b) max| | 108 kNmM 5–153. 17.19 MPa
5–154. a) 0CM equilibrium
b) 2
03(1.5 )
mw L
a
5–155. a) 0(2 / sin( /2 )V Lw x L 2
0(4 / )[1 cos( /2 )]M L w x L
b) 2 20max
4 /M w L
5–156. 73.5 MPa
Answers 17
5–157. 50.9 MPa 5–158. min 169 mma 5–159. W 250 28.4 @ 28.4 kg/m
5–160. 7.32 kNP 5–161. a) 1.950 mx b) 137.3 MPa
5–162. a) 2 3
0 3
3 4L x xh h
L
b) 0 225 kN/mw
5–163. 01.5d d
Chapter 6 6–1. a) 1.387 kNV b) max 380 kPa 6–2. a) nail 155.8 NF b) max 329 kPa 6–3. 738 NV
6–4. 747 NV
6–5. 193.5 kNV 6–6. 217 kNV 6–7. bolt 78.9 MPa 6–8. 56.2 kNV 6–9. max 50 MPa 244 N/mm 6–10. a) max 920 kPa b) 765 kPaa
6–11. a) 17.63 MPa b) 13.01 MPa
6–12. a) max 21.05 MPa b) 15.85 MPa 6–13. 120.3 kNV
6–14. 114.0 kNV
6–15. 360.8 mmh 6–16. 88.9 mmb
6–17. a) 2m
m
h
L
b) 225 mmh 61.7 mmb
6–18. a) 2
m
m
h
L
b) 320 mmh 97.7 mmb
6–19. 645 kNP 6–20. 179.6 kNP
6–21. a) 31.0 MPaa b) 23.2 MPab
6–22. a) 10.8 MPaa b) 17.3 MPaa
6–23. 32.7 MPam
6–24. 19.5 MPa 6–25. a) 2t c b) 1.333k
6–26. a) 1,
2my h i.e., at mid-height
b) 31.500
2k
6–27. a) 2 mt t at neutral axis where
maximum occurs. b) 2.00k
6–28. a) 3
4my
h b) 1.125k
6–29. 4.28 kNV
6–30. 4.63 kNV
6–31. a) 379 kPaA b) 0B
6–32. 40.1 mms 6–33. a) 239 NAF b) 549 NBF
6–34. a) 12.27 MPaa b) 58.9 MPaC 6–35. a) 36.5 MPaa b) 34.5 MPab 6–36. a) 41.4 MPaa b) 41.4 MPab
6–37. 33.7 MPaa 75.0 MPab
43.5 MPac
6–38. 6.07 MPa; 9.1 MPa;
27.6 MPa; 56.9 MPaa b
c d
6–39. 16.7 MPa; 16.7 MPa,
60 MPa, 0a b
c d
6–40. a) 18.23 MPaa b) 14.59 MPab c) 46.2 MPac
6–41. 0a 29.1 N/mmb 224.12 N/mmc 248.8 N/mmd 256.3 N/mmc 6–42. 28.7 MPaa 19.55 MPab 4.57 MPac 7.5 MPad 0e 6–43. bolt 83.3 MPa 6–44. bolt 20.6 MPa
6–45. bolt 9.05 mmd
6–46. 255 kNq 6–47. a) 14.1 MPam b) 12.5 MPaB 6–48. a) 23.2 MPaA b) 35.2 MPaM
18 Answers
6–49. 10.76 MPaa 0b
11.21 MPac 22.0 MPad
9.35 MPae
6–50. a) CVQ
It 5.56 mmt
b) 1.4 MPaE 6–51. 37.4 mma 6–52. a) 2.08k b) 2.10k 6–53. a) 2.25k b) 2.12k
6–54. a) sinP
m
V
r t
b) 2m
V
A
6–55. q
t
VQ
It
6–56. a) 29.92 N/mm b) 2
max 9.97 N/mm 6–57. a) 26.65 N/mm b) 2
max 10.90 N/mm
6–58. a) bolt 23.3 MPa b) 109.7 kPac
6–59. a) bolt 6.73 MPa b) 1.515 MPa
6–60. a) 21
22 Y Y
Y
yH b c y
y
b) 2
231
4xyY Y
P y
by y
6–61. 2 23( )
6( )
b ae
a b h
6–62. 1.250e a 6–63. 0.345e a 6–64. 0.714e a 6–65. a) 23.2 mme b) 0A D F G 1 8.2 MPa
2 12.4 MPa 3 20.6 MPa 25.2 MPaH 4 3 20.6 MPa 5 2 12.4 MPa 6 1 8.2 MPa
6–66. a) 66.7 mme 0A G
b) 6.7 MPaB 24.4 MPaD 31.1 MPaH 6–67. a) 10.22 mme b) 0 41.1 MPa 68.5 MPa 13.71 MPa 77.7 MPa 81.1 MPa
6–68. a) 9.12 mme b) 0 50.6 MPa 33.8 MPa 67.5 MPa 16.88 MPa 84.4 MPa 88.6 MPa 6–69. 30.35 mme 6–70. 20.2 mme 6–71. 6.14 mme 6–72. 12.25 mme 6–73. 1.273e a 6–74. 2e a 6–75. 59.3 mme 6–76. 57.1 mme 6–77. 0 and 40.0 mmb b
6–78. 75.0 mma
6–79. 0qdz qdy P
6–80. a) 2
5y a 27
20mP
ta
2
3z a
m1
4
P
ta
3
4
P
ta
b) 2
5y a
2
3z a
6–81. a) 43.76 MPaV b) max 65.9 MPa
6–82. a) 77.16 MPaV b) max 106.6 MPa
6–83. a) 2 kNV 0 38.2 NmM b) 17.3 MPa 6–84. a) 2 kNV 0 38.2 NmM b) 42.3 MPa 6–85. 1 2 (150 )[0.0172 0.0003415 ]x x 6–86. 4 2
1 2 8.6917 2.2812 10 y
6–87. 3
(2 )(0.750 0.500 )P a y y a
ta
6–88. 3
( )(3.00 1.000 )P a x x a
ta
6–89. 1304 NV 6–90. bolt 68.8 MPa
6–91. a) max 8.97 MPa b) 8.15 MPaa
6–92. 87.3 mmb
6–93. a) 8.75 MPaa b) 15 MPab 6–94. 20 MPamm
6–95. a) 146.1kN m b) 19.99 MPaa
Answers 19
6–96. a) 50.9 MPa A b) 62.4 MPam
6–97. 266 kN/mq 848 kN/mmq
6–98. 2 23( )
6( )
b ae
a b h
6–99. 10.97 mme 6–100. 40 mmb
Chapter 7 7–1. 49.2 MPa 2.41 MPa 7–2. 32.9 MPa 71.0 MPa 7–3. 14.19 MPa 15.19 MPa 7–4. 0.546 MPa 59.2 MPa 7–5. a) 37.0 , 53.0p b) max 13.60 MPa min 86.4 MPa
7–6. a) 18.43 ,108.43p b) max 154 MPa min 14 MPa 7–7. a) 14.04 ,104.04p b) max 70 MPa min 49 MPa 7–8. a) 18.4 ,108.4p b) max 33.0 MPa min 3.00 MPa 7–9. a) 8.0 , 98.0s b) max 36.4 MPa 50.0 MPa
7–10. a) 26.57 , 63.43s b) max 70 MPa c) 84 MPa 7–11. a) 30.96 , 59.04s b) max 59.5 MPa c) 10.5 MPa 7–12. a) 26.6 , 63.4s max 15.00 MPa b) 18.00 MPa 7–13. a) 24.0 MPax 1.5 MPax y 104.0 MPay
b) 19.5 MPax 60.7 MPax y
60.5 MPay
7–14. a) 63.1 MPax 26.6 MPax y 91.1 MPay
b) 37.4 MPax 63.4 MPax y
65.4 MPay
7–15. a) 56.2 MPa x 38.2 MPax y 86.2 MPay
b) 45.2 MPax 53.8 MPax y
75.2 MPay
7–16. a) 16.8 MPax 1.05 MPax y 72.8 MPay
b) 13.7 MPax 42.5 MPax y
42.4 MPay
7–17. a) 3.64 MPax y b) 2.1 MPax
7–18. a) 0.250 MPax y b) 2.43 MPax 7–19. 25.4 MPaw 9.5 MPaw 7–20. 3.90 kNP 7–21. a) 47.9 MPaw b) 102.7 MPaw
7–22. a) 14.34 b) 117.3 MPa
7–23. 180.76 MPaa 4.76 MPab max 92.76 MPa 7–24. 38.5 MPaa 12.3 MPab max 25.4 MPa 7–25. max 12.18 MPa min 48.7 MPa
max 30.5 MPa
7–26. a) max 18.67 MPa min 158.5 MPa
b) 18.9 and 108.9°p
max 88.6 MPa
7–27. a) 53 MPaxy b) ave 7.5 MPa 89.5 MPaa 74.5 MPab 7–28. 205 MPay
7–29. 15 MPa 135 MPax 7–30. a) 2.89 MPaxy
b) 12.77 MPaa 1.226 MPab
7–31. a) 37.03B 52.97A b) min 86.4 MPa max 13.6 MPa c) 8.0d 98.0e max 36.4 MPa
d) 50.0 MPa
20 Answers
7–32. a) 13.29a 76.72b b) max 37.9 MPa min 149.9 MPa c) 31.7d 121.7e max 93.9 MPa d) 56 MPa 7–33. 59.04d 30.96e max 59.5 MPa 10.5 MPa 7–34. a) 26.6d 63.4e max (in-plane) 15.00 MPa
b) 18.00 MPa 7–35. a) 24.0 MPax 1.5 MPax y
104.0 MPay
b) 19.5 MPax 60.7 MPax y 60.5 MPay
7–36. a) 24.0 MPax 1.5 MPax y
104.0 MPay
b) 19.5 MPax 60.7 MPax y 60.5 MPay
7–37. a) 56.2 MPax 38.2 MPax y
86.2 MPay
b) 45.2 MPax 53.8 MPax y 75.2 MPay
7–38. a) 16.8 MPax 1.05 MPax y
72.8 MPay
b) 13.7 MPax 42.3 MPax y 42.4 MPay
7–39. a) 3.6 MPax y b) 2.1 MPax 7–40. a) 0.25 MPax y b) 2.43 MPax 7–41. 25.4 MPaw 9.5 MPaw 7–42. 3.90 kNP 7–43. a) 47.9 MPaw b) 102.7 MPaw
7–44. a) 14.3 b) 117.3 MPa 7–45. 180.76 MPaa 4.76 MPab max 92.76 MPa 7–46. 38.5 MPaa 12.3 MPab 7–47. max 12.18 MPa
min 48.74 MPa
max 30.46 MPa
7–48. a) 18.9a , 108.9b 158.5 MPaa 18.67 MPab
b) max 88.6 MPa
7–49. a) 2 53 MPaxy b) 74.5 MPab 7–50. 205 MPay
7–51. Thus 15 MPa 135 MPax 7–52. a) 2.89 MPaxy
b) 12.77 MPaa 1.23 MPab
7–53. 8.66 MPaxy 17 MPaa
3 MPab
7–54. 33.69a 123.69b 168 MPaa 14 MPab 7–55. 24.6 , 114.6a b 72.91 MPaa 27.09 MPab
7–56. 1
2p 0 0 cos a
0 0 cos b
7–57. 30 60b a
03a 03b
7–58. U V 45 97.64 7–59. 16.524 110.085 7–60. 5.15 132.02 7–61. 120 MPa 120 MPaxy
7–62. 141.4 MPa 141.4 MPaxy
7–63. a) 33.69a 123.69b b) max ave 126 MPaR c) max(in-plane) 45.5 MPaR
7–64. cos 22 2
sin 2
x y x yx
xy
cos 2 sin 22
x yx y xy
7–65. a) 2 2
x y x yOK b) max minxy x y
7–66. a) max 50 MPa b) max 62.5 MPa 7–67. a) max 55 MPa b) max 50 MPa
Answers 21
7–68. a) max 94.3 MPa b) max 105.3 MPa
7–69. a) max 100 MPa b) max 110 MPa
7–70. a) max 39 MPa b) max 45 MPa c) max 39 MPa 7–71. a) max 39 MPa b) max 54 MPa c) max 42 MPa 7–72. a) max 85 MPa b) max 85 MPa c) max 95 MPa
7–73. a) max 97.5 MPa b) max 85 MPa c) max 120 MPa
7–74. Case (1) 56.88 MPay
Case (2) 130 MPaU 7–75. Case (1) 8.8 MPay
Case (2) 52.12 MPay
max 52 MPa O.K. 7–76. a) 42 MPaxy b) 78.7 MPaxy
7–77. a) 40 MPaxy b) 72 MPaxy
7–78. 40 MPay 130 MPay
7–79. 40 MPa 40 MPaxz
7–80. a) 45.7 MPay b) max 92.9 MPa
7–81. a) . . 1.228F S b) . . 1.098F S
c) 2 2
329.24 MPa > 325 MPaa b a b
(Yielding occurs) 7–82. a) (No yielding) . . 1.083F S b) max2 340 MPa > 325 MPa (Yielding occurs) c) max2 380 MPa 325 MPa (Yielding occurs) 7–83. a) (No yielding) . . 1.286F S b) (No yielding) . . 1.018F S c) 2 2
224 MPa 210 MPa
a b a b
(Yielding occurs)
7–84. a) (No yielding) . . 1.119F S b) max2 224 MPa 210 MPa (Yielding occurs) c) max2 237.1 210 MPa (Yielding occurs) 7–85. 708 N mT
7–86. 818 N mT
7–87. 717 N mT 7–88. 828 N mT 7–89. Rupture will occur. 7–90. Rupture will occur. 7–91. No rupture. 7–92. Rupture will occur. 7–93. 0 25.5 MPa 7–94. 0 8.49 MPa 7–95. 196.9 N mT
7–96. 0 50.0 MPa
7–97. a) 56 MPaa b) 0 46.7 MPa c) 0 62.2 MPa 7–98. 72.7 MPa max 36.4 MPa
7–99. . . 5.04F S 7–100. 2.94 MPa 7–101. min 7.74 mmt
7–102. a) 1.290 MPap b) 0.0852 mmd 7–103. a) max 95.7 MPa b) 1.699 mmd 7–104. max 89.0 MPa max 44.5 MPa
7–105. 12.55 mmt 7–106. max 136.0 MPa max 68.0 MPa
7–107. 1.676 MPap 7–108. max 78.5 MPa max 39.3 MPa
7–109. 14.3 mh 7–110. max 105.8 MPa max 52.9 MPa 7–111. a) 42 MPa b) 34.5 MPa 7–112. a) 33.2 MPaw b) 9.55 MPaw
7–113. 2.17 MPap
7–114. 22.0 27.0°
and 63.0 117.0°
22 Answers
7–115. a) 44.2 MPaw b) 15.39 MPaw
7–116. 56.8
7–117. 2.95 MPap 7–118. 3.41 MPap 7–119. a) 419 kPap b) 558 kPap 7–120. max 45.1 MPa
max (in-plane) 9.40 MPa
7–121. max 45.1 MPa
max (in-plane) 7.49 MPa
7–122. max 68.6 MPa max 34.3 MPa
7–123. 17.06 kN mT 7–124. a) 26.585 15.081 cos 70
21.4 MPax
b) 14.17 MPax y
7–125. a) 11.00 MPax b) 21.5 MPax y
7–126. a) 35.1 MPas b) 1.67 MPap 7–127. a) 14 MPas b) 1.33 MPap 7–128. 670x 50y 474x y
7–129. 36.7x 283y 227x y
7–130. 653x 303y 829x y
7–131. 450x 200y 375x y
7–132. 670x 50y 474 mx y
7–133. 36.7x 283y 227x y
7–134. 653x 303y 829x y
7–135. 450x 200y 375x y
7–136. 33.67b 56.31a a) 100a 420b b) max (in-plane) 520
c) max 580
7–137. 30.13b 59.87a a) 298a 702b b) max (in-plane) 403 500c
c) max 1202
7–138. a) 21.58a 68.42b 278.6a 598.6b b) (max, in-plane) 877
c) 160.0c max 877
7–139. a) 26.565b 64.435a 750a 150b b) max (in-plane) 900 300c
c) max 1050
7–140. 97.76a 7.76b a) 243.4a 56.6b b) max (in-plane) 186.8
c) max 243.4
7–141. 30.96a 120.96b a) 512.5a 87.5b b) max (in-plane) 425
c) max 512.5
7–142. 11.31a 101.31b a) 310a 50b b) max (in-plane) 260
c) max 310
7–143. a) 37.87a 127.87b 57.5a 382.5b b) max (in-plane) 2 325R
c) max 382.5
7–144. 253x
7–145. 6max 415 10 mm/mm
7–146. a) 3 300 b) 435a 315b max (in-plane) 750
7–147. a) 120.0a 6560 10 mm/mma
6140.0 10 mm/mmb
b) 6max (in-plane) 700 10 mm/mm
7–148. max, min ave R
7–149. ave 1 2 33 7–150. 12.2 kNmT 7–151. 9.9 kNmT
Answers 23
7–152. 1.421 MPap
7–153. 1.761 MPap
7–154. a) 22.5a 426a 952b 224c
b) 426a 22.5a
7–155. a) 29.8 MPaa 70.9 MPab b) 29.8 MPaa 70.9 MPab
7–156. 375 kNP 163.5 kNxQ 7–157. 300 kNP 261.5 kNxQ 7–158. min 9.52 MPa max 41.7 MPa 7–159. 31.5 10 N mxM 31.125 10 N myM 32.7 10 N mzM
7–160. a) 18.4 b) 116.6 MPaP
A
7–161. 0 and 90°p max 0
min 0
7–162. a) max 39 MPa b) max 45 MPa c) max 39 MPa 7–163. 45 8.13 45 98.13 7–164. a) (No yielding) . . 1.286F S b) (No yielding) . . 1.018F S c) 2 2
224 MPa 210 MPa
a b a b
(Yielding occurs) 7–165. 13.144 MPaxy 77.4 MPa, 32.3 MPaa b
0z max 38.7 MPa
7–166. 67.305 MPay max 73.1 MPa
max 51.9 MPa
7–167. 1 2.74 MPa (tension) 2 21.9 MPa (compression) 7–168. a) 6495 10a
6105 10b
b) 6max(in-plane) 390 10
c) 6max 795 10
7–169. a) 734a 84.3b
b) max (in-plane) 819
Chapter 8 8–1. a) 36.3 MPam b) max 74.3 MPa c) W250 101 is acceptable. 8–2. a) 36.3 MPam b) max 31.4 MPa c) W250 101 is acceptable. 8–3. a) 94.6 MPam b) max 93.9 MPa c) W920 449 is acceptable. 8–4. a) 91.9 MPam b) max 95.1 MPa c) W920 449 is acceptable. 8–5. a) Use W690 125. b) 128.2 MPam 47.3 MPam max 124.0 MPa 8–6. a) Use W360 32.9 b) 146.1 MPam 27.6 MPam max 118.4 MPa 8–7. a) Use W690 125. b) 118.2 MPam 34.7 MPam
max 122.3 MPa
8–8. a) Use W310 38.7. b) 147.8 MPam 18.18 MPam
max 140.2 MPa
8–9. a) 134.3 MPam b) max 132.4 MPa
8–10. a) 137.5 MPam b) max 129.5 MPa
max 123.4 MPa
8–11. a) 131.3 MPam b) max 135.5 MPa 8–12. a) 111.6 MPam b) max 106.6 MPa
8–13. a) 119.9 MPam b) max 110.9 MPa
max 103.7 MPa
8–14. a) 126.0 MPam b) max 115.9 MPa
max 105.1 MPa
24 Answers
8–15. 2 3.710 kNP 8–16. 38.8 mmd 8–17. 41.8 mmd 8–18. 37.3 mmod
8–19. 21.7 mmBCd 33.4 mmCDd
8–20. max 44.4 MPa max 48.0 MPa
8–21. 2
2 2( cos )
3Kc
M Vc TJ
8–22. a) 44.98 MPaH 44.26 MPaK b) 48.50 MPaH 45.83 MPak 8–23. a) 58.8 mmd b) 47.8 mmd 8–24. a) 51.4 mmd b) 41.8 mmd 8–25. 41.3 mmd 8–26. 44.8 mmd 8–27. 37.0 mmd
8–28. 43.9 mmd
8–29. 46.5 md 8–30. 45.9 mmd 8–31. a) 116.3 MPa 0 b) 4.47 MPa 13.42 MPa c) 125.2 MPa 0 8–32. a) 129.7 MPa 0 b) 8.94 MPa 6.71 MPa c) 111.8 MPa 0 8–33. 2.08 MPax 0xy
2.72 MPax 0xy
0.320 MPax 0.500 MPaxy
8–34. a) 32.5 MPax 14.06 MPaxy
b) 126.2 MPax 0xy
8–35. a) 37.9 MPa 14.06 MPa b) 131.6 MPa 0
8–36. a) 16.24 MPa 14.06 MPa b) 110.0 MPa 0
8–37. a) 49.1 MPaH 31.3 MPaN b) 26.1 MPaK 31.03 MPaK 8–38. 14.98 MPa 17.29 MPa 8–39. 29.55 MPa 6.23 MPa 8–40. a) 79.6 MPa 7.96 MPa b) 0 13.26 MPa 8–41. 131 MPaH 43.7 MPaH
8–42. a) 4.3 MPaa 93.4 MPab
12.1 , 102.1a b b) max 48.9 MPa
8–43. a) max 30.0 MPa min 30.0 MPa
max 30.0 MPa
b) max 7.02 MPa min 96.0 MPa
max 51.5 MPa
8–44. a) 21.4 MPaa 52.9 MPab 33.3a 123.3b b) max 37.2 MPa 8–45. a) 15.8 MPa 7.1 MPa b) 40.7 MPa 5.3 MPa c) 65.6 MPa 0 8–46. a) 24.1 MPa 7.1 MPa b) 53.7 MPa 5.3 MPa c) 83.3 MPa 0 8–47. a) 18.39 MPa 0.391 MPa b) 21.3 MPa 0.293 MPa c) 24.1 MPa 0
8–48. a) 7.98 MPa 0.391 MPa b) 5.11 MPa 0.293 MPa c) 2.25 MPa 0
8–49. 30.1 MPaa 0.62 MPab
8.2a 81.8b max 15.37 MPa
8–50. 0.12 MPaa 51.4 MPab
2.8 92.8a b
max 25.8 MPa 8–51. 9.94 MPaa 26.54 MPab max 18.24 MPa
8–52. 0.94 MPaa 17.54 MPab max 9.24 MPa 8–53. 86.5 MPa 0 57.0 MPa 9.47 MPa 8–54. 42.2 MPa 2.83 MPa 12.74 MPa 0 8–55. max 29.8 MPa min 0.09 MPa max 14.92 MPa 8–56. max 11.41 MPa min 30.2 MPa max 20.8 MPa
Answers 25
8–57. max 12.94 MPa
min 1.33 MPa max 7.13 MPa
8–58. max 1.99 MPa min 50.5 MPa
max 26.2 MPa
8–59. a) all 51.0 kNP b) all 39.4 kNP
8–60. a) 6 cos sinPl
bh h b
b) 1tanb
h
8–61. max 12.2 MPa min 12.2 MPa
max 12.2 MPa
8–62. a) max 87.1 MPa min 2.1 MPa 8.9 , 81.1p max 44.6 MPa b) 43.06 MPa max 43.1 MPa min 43.1 MPa 45P max 43.1 MPa
8–63. 31 MPaa 26 MPab 8–64. max 2.72 MPa min 249.4 MPa max 126 MPa 8–65. a) Use W 250 22.3 b) 156.31 MPam 33.6 MPam max 155.08 MPa 8–66. 41.2 mmd
8–67.
1/22 2max
1/22 2 2
y z
y z
cM M
J
M M T
8–68. 46.4 mmd 8–69. a) 74.9 MPa 0 b) 2.78 MPa 7.22 MPa 8–70. a) 20.4 MPa 14.34 MPa b) 21.5 MPa 19.98 MPa
8–71. 3max (2 4 /3)/ P R r r
8–72. 55.0 MPaa 55.0 MPab 45b max 55.0 MPa 8–73. 20.2 MPa 2.82 MPa 8–74. 25.2 MPaa 0.87 MPab
max 13.06 MPa
8–75. max 65.5 MPa min 21.8 MPa max 43.7 MPa
8–76. a) 7.50 MPa b) 11.25 MPa c) 56.3 13.52 MPa
Chapter 9
9–1. a) 2
(3 )6
Pxy L x
EI
b) 3
3BPL
yEI
c) 2
2BPL
EI
9–2. a) 2 20 ( 2 )2
My x Lx L
EI
20 ( )2
My L x
EI
b) 2
0
2AM L
yEI
c) 0A
w L
EI
9–3. a) 4 3 4( 4 3 )24
wy x L x L
EI
b) 4
8AwL
yEI
c) 3
6AwL
EI
9–4. a) 0
3 2 4 51 1 1
6 12 120
wy
EIL
L x Lx x
b) 4
011
120Bw L
yEI
c) 3
01
8Bw L
EI
9–5. a) 4 3 2 2( 4 4 )24
wy x Lx L x
EI
b) 4
24BwL
yEI
c) 0B
26 Answers
9–6. a) 4 3(3 16 )72
wy x ax
EI
b) 410
9Bwa
yEI
c) 34
3Bwa
EI
9–7. a)
3 4 2 2 31 1 1 1
10 24 20 120
wy
EI
Lx x L x L x
b) 413
1920MwL
yEI
c) 3
120BwL
EI
9–8. a) 0
2 3 5 41 1 1
48 120 80
wy
EIL
L x x L x
b) 4
02 256L
w Ly
EI
c) 3
0
120Bw L
EI
9–9. a) 32.77 10 radA
b) 1.156 mmCy 9–10. a) 36.43 10 radA
b) 5.6 mmy
9–11. a) 0.423mx L 2
00.06415mM L
yEI
b) 0 45.3 kN mM
9–12. 0.5193mx L
400.00652mw L
yEI
7.61 mmmy
9–13. 9.2 mmCy
9–14. a) 38.18 10 radA
b) 11.78 mmCy
9–15. 6.28 mmCy
9–16. a) 2 31 1 1
2 2 6
Py ax aLx a
EI
b) 1.976 mmCy
9–17. a) 2 4 502
6 4 2
1 1
24 30
1 1
120 24
wy L x Lx
EIL
x L x
b) 4
0
40B
w Ly
EI
9–18. a) 6 502
3 3 5
1 1
90 30
1 1
18 30
wy x Lx
EIL
L x L x
b) 3
01
30Aw L
EI
c) 4
061
5760Cw L
yEI
9–19. 03
2AM
RL
9–20. 3
8BR wL
9–21. 011
40AR w L
9–22. 011
40BR w L
9–23. 9.75 kNBR
9–24. 14.44 kNAR
9–25. 09
8BM
RL
01
8AM M
0
7
16CM M
0
9
16CM M
9–26. 5
16BR P
7
16AR P
3
16AM PL
5
32CM PL
0BM
9–27. 7
128AR wL
20.02734CM wL
0.07031BM wL
20.02884mM wL
9–28. 021
160AR w L
019
160BR w L
200.0354BM w L
200.0317mM w L
Answers 27
9–29. 17
64BR wL
41
1024CwL
yEI
9–30. 41
128AR wL
419
6144CwL
yEI
9–31. 05
6BM
RL
207
486DM L
yEI
9–32. 14
27AR P
320
2187DPL
yEI
9–33. 4
AwL
R
200.05208AM w L
2
00.03125CM w L
9–34. 1
2BR wL 21
12AM wL
2[6 ( ) ] / 12M w x L x L
9–35. a)
0
3 2 2 2
6
3 (3 )
My
EIL
x L x a b L x
b) 2 20 (3 )6AM
b LEIL
c) 0 ( )3CM ab
y b aEIL
9–36. a)
3 3 2 2
6
{ ( ) }
Py
EIL
bx L x a b L b x
b) 2 2( )6APb
L bEIL
c) 2 2
3CPa b
yEIL
9–37. a) 35
2BPa
yEI
b) 349
6CPa
yEI
c) 315
DPa
yEI
9–38. a) 39
4BPa
yEI
b) 319
6CPa
yEI
c) 39
4DPa
yEI
9–39. a) 2
05
4AM a
yEI
b) 2
01
4CM a
yEI
c) 01
4DM a
EI
9–40. a) 33
4APa
yEI
b) 31
12CPa
yEI
c) 21
12DPa
EI
9–41. a) 3 4 4
4 3
1 1 1
6 24 24
1 53
24 6
wy ax x x a
EI
x a a x
b) 423
24Cwa
yEI
9–42. a)
44 4 3
3 3
24
2
13
16
wy
EI
Lx x x L Lx
L x L L x
b) 4
768BwL
yEI
c) 45
256DwL
yEI
9–43. a) 5
50
4 2 3
4
96 962
240 200
53 /5760
Ly w x x
Lx L x
L x EIL
b) 4
03
1280Cw L
yEI
9–44. a) 5
50
4 2 3
4
16 322
40 40
15 /960
Ly w x x
Lx L x
L x EIL
b) 4
03
640Cw L
yEI
28 Answers
9–45. a) 32.49 10 radA
b) 1.078 mmCy
9–46. a) 30.873 10 radA
b) 1.641 mmCy
9–47. a) 35.40 10 radA
b) 3.06 mmCy
9–48. a) 39.51 10 radA
b) 5.80 mmCy
9–49. a) 09
8AM
RL
b) 2
0
128CM L
yEI
9–50. a) 5
16BR P
b) 37
168CPL
yEI
9–51. a) 03
4 D
MR
L
b) 2
011
512 B
M Ly
EI
9–52. a) 2
3DR P
b) 35
486BPL
yEI
9–53. a) 11.546 kNCR b) 4.18 mmBy
9–54. a) 24.1 kNAR b) 2.5 mmCy
9–55. a) 34.5 kNAR b) 1.35 mmCy
9–56. a) 41.25 kNER b) 0.705 mmCy
9–57. a) 20
27AR P 4
27AM PL
b) 35
1296CPL
yEI
9–58. a) 3
32AwL
R 25
192AwL
M
b) 4
768BwL
yEI
9–59. 0.8570 mmx 1.401 mmmy
9–60. 2.855 mmx 1.648 mmmy
9–61. 0.942 mmx 3.07 mmmy
9–62. 0.991 mmx 5.80 mmmy
9–63. a) 0.177 mmBy b) 0.895 mmCy
9–64. a) 33.82 10 rad.A
b) 5.84 mmCy
9–65. 2
APL
EI
317
24APL
yEI
9–66. 25
8CPL
EI
37
16CPL
yEI
9–67. 313
6Bwa
EI
429
24Bwa
yEI
9–68. 3
48BwL
EI
4
384BwL
yEI
9–69. a) 31
486CPL
yEI
b) 21
81APL
EI
9–70. a) 35
162CPL
yEI
b) 21
9APL
EI
9–71. a) 38
243CPL
yEI
b) 219
162APL
EI
9–72. a) 41
384CwL
yEI
b) 0A
9–73. 3= 6.32 10 radC
= 5.55 mmCy
9–74. 35.58 10 radB
= 2.51 mmBy
9–75. 311.76 10 radC
8.57 mmCy 9–76. 311.34 10 radB
5.66 mmBy
Answers 29
9–77. a) 30.601 10 radA
b) 3.67 mmCy
9–78. a) 32.58 10 radA
b) 2.70 mmCy
9–79. 7
8CR P 3
8AR P 4
4DR P
9–80. 03C
MR
L 0
2AM
RL
05
2BM
RL
9–81. a) 41
128AR wL
b) 23
128BR wL
27
128BM wL
9–82. a) 2 203
3( )
2A
MR L a
L
b) 2 203
3( )
2B
MR L a
L
2 202
( 3 )2
BM
M L aL
9–83. 1
2BR wL
21
12BM wL
9–84. 03
2BM
RL
01
4BM M
9–85. 121.5 N/mw
9–86. a) 0.00605 radA b) 1.43 mmBy
9–87. 5.94 mmCy 6.75 mmCy
9–88. a) 10.54 mmBy b) 23.4 mmDy
9–89. 23.9 kNCR 96.1 kNAR 96.1 kNBR
9–90. 43.9 kNP
9–91. 5.63 kNP
9–92. a) 8.265 kNBR b) 4.235 kNER
9–93. 8.28 mmAy
9–94. 9.31 mmCy
9–95. a) 2
2APL
EI
b) 3
3APL
yEI
9–96. a) 0A
M L
EI
b) 2
0
2A
M Ly
EI
9–97. a) 3
0
24A
w L
EI
b) 4
0
30Aw L
yEI
9–98. a) 3
6AwL
EI
b) 4
8AwL
yEI
9–99. a) 23
2BPa
EI
311
6BPa
yEI
b) 2
CPa
EI
3
2CPa
yEI
9–100. a) 0B 2
01
4BM L
yEI
b) 01
2CM L
EI
201
8CM L
yEI
9–101. 35.88 10 radD 9.14 mmDy
9–102. a) 37.15 10 radA
b) 17.67 mmAy
9–103. 34.566 10 radC 1.878 mmCy
9–104. a) 32.55 10 radA
b) 6.25 mmCy
9–105. a) 211
24CPL
EI b)
311
36CPL
yEI
9–106. 2
025
12AM a
yEI
011
6AM a
EI
9–107. 33.11 10C 3.15 mCy
9–108. a) 33.43 10 radA
b) 6.66 mmAy
9–109. a) 21
16APL
EI
b) 31
48CPL
yEI
9–110. a) 25
32APL
EI b)
319
384CPL
yEI
30 Answers
9–111. a) 2
(3 2 )12Awa
L aEI
b) 2
2 2(3 2 )48Awa
y L aEI
9–112. a) 3
05
192A
w L
EI
b) 4
0
120c
w Ly
EI
9–113. a) 01( 2 )
2AM
L aEI
b) 2 201( 4 )
8CM
y L aEI
9–114. a) 2
32APL
EI
b) 3
128CPL
yEI
9–115. a) 25
8APa
EI
b) 33
4CPa
yEI
9–116. a) 211
6APa
EI
b) 335
18CPa
yEI
9–117. a) 35.21 10 radA
b) 21.2 mmCy
9–118. a) 34.71 10 radA
b) 5.84 mmCy
9–119. a) 34.50 10 radA
b) 8.26 mmCy
9–120. a) 33.125 10 radB
b) 1.016 mmCy 9–121. 3.84 kN/mw
9–122. 3.55 kNP 9–123. 0.211a L
9–124. 0.223 La
9–125. a) 2
03
64DM L
yEI
b) 05
32AM L
EI
9–126. a) 34
243DPL
yEI
b) 24
81DPL
EI
9–127. a) 4
05
768D
w Ly
EI
b) 3
07
360A
w L
EI
9–128. a) 45
768DwL
yEI
b) 33
128AwL
EI
9–129. a) 38.74 10 radA
b) 15.10 mmDy
9–130. a) 37.48 10 rad.A
b) 5.35 mmDy
9–131. a) 35.18 10 radA
b) 5 mmEy 9–132. a) 39.51 10 radA
b) 5.80 mmCy
9–133. a) 21
48APL
EI
b) 33
32DPL
yEI
9–134. a) 0 ( 3 )3AM
L aEI
b) 0 (2 3 )6AM a
y L aEI
9–135. a) 32.61 10 radC
b) 4.7 mmCy
9–136. a) 32.99 10 radB
b) 8.75 mmDy
9–137. a) 35.83 10 radD
b) 0.39 mmAy
9–138. a) 33.61 10 radB
b) 0.960 mmAy
Answers 31
9–139. a) 317
972DPL
yEI
b) 319
972EPL
yEI
9–140. a) 39
256AwL
EI
b) 37
256BwL
EI
c) 45
512CwL
yEI
9–141. 3
0.01792KPL
yEI
0.544Kx L
9–142. is 0.519my L from A .
4
3 06.52 10m
w Ly
EI
9–143. 15.17 mmKy 2.81 mKx
9–144. 1.545 mKx 5.2 mmKy 9–145. 1.841 mmKy
9–146. 2.9 mmKy
9–147. 00.275BR w L
9–148. 5
16AR P
9–149. 7
128AR wL
9–150. 09
8AM
RL
9–151. 3
4BR wL 1
6AR wL 5
12CR wL
9–152. 02B
MR
L
04
3AM
RL
02
3CM
RL
9–153. 65.24 kNAR
9–154. 40.7 kNBR 105.5 kN mAM 55.6 kN mDM 55 kN mEM 0BM
9–155. 3
48
7
EIk
L
9–156. 3
144EI
kL
9–157. a) 0
5 4 4 5
120
(2 5 10 7 )
wy
EIL
x Lx L x L
b) 4
07
120A
w Ly
EI
c) 3
0
12A
w L
EI
9–158. 0.21132mx L
2
0| | 0.0160375mM L
yEI
6.09 mL
9–159. a) 6 2 40
3 3 5 2
( 15
25 11 )/360
y w x L x
L x L x EIL
b) 3
011
360Aw L
EI
c) 4
00.00916Cw L
yEI
9–160. 1
2A BR R P
1
8AM PL
1
8BM PL 1
8CM PL
9–161. a) 0.01015 radA b) 4.4 mmBy
9–162. a) 30.712 10 radA
b) 1.068 mmBy
9–163. a) 10.86 kNAR 1.942 kN mAM b) 1.144 kNDR 0.286 kN mDM
9–164. 121.5 N/mw
9–165. a) 35.20 10 radA
b) 10.85 mmAy
9–166. a) 34.71 10A
b) 2.94 mmAy c) 5.6 mmCy
9–167. a) (2 3 )
6CPa L a
EI
b) 2 ( )
3CPa L a
yEI
9–168. a) 6.87 mmBy b) 46.3 kNBR
32 Answers
Chapter 10 10–1. crP kL
10–2. cr /P K L
10–3. crK
PL
10–4. cr2
9
kLP
10–5. 2
cr 2
kaP
l
10–6. > 4.91 kN/mk 10–7. 45 kNP
10–8. cr8K
PL
10–9. cr 81.2 NP 10–10. cr 305 kNP
10–11. a) 6.25% b) cr 17.17 kNP 10–12. a) 7.48 mmt b) cr 58.8 kNP cr 84.8 kNP
10–13. cr,
cr,
1.421a
b
P
P
10–14. 14.10 mmc cr 61.4 kNP
cr 64.3 kNP
10–15. . . 2.81F S 10–16. all 93.0 kNP all 448 kNP
10–17. all 303 kNP 10–18. all 1338 kNP 10–19. . . 2.44F S 10–20. all 4.00 kNP 10–21. 319 kgm 79.8 kgm
319 kgm 653 kgm
10–22. a) . . 2.55F S b) 2 28.3 mmd 3 14.14 mmd
4 16.72 mmd 5 20.0 mmd
10–23. a) 1.96 mBCL 0.49 mCDL b) all 23.1 kNP 10–24. all 8.61 kNP 10–25. 12.01 mL 10–26. all 143.7 kNP 10–27. 657 mmL
10–28. a) / 1/2b d b) 28.3 mmd 14.15 mmb
10–29. a) max 1.658 mmy b) max 78.9 MPa
10–30. a) 4.32 mmmy b) max 44.4 MPa
10–31. a) 8.3 mmmy b) max 85 MPa 10–32. a) 1.552 mme b) max 47.8 MPa
10–33. a) max 1.658 mmy b) max 78.9 MPaM 10–34. a) 6.31 mme b) max 68.6 MPa
10–35. a) cr 58.89 kNP b) max 105.0 MPa 10–36. a) 370 kNP b) max 104.6 MPa
10–37. a) 224 kNP b) max 63.3 MPa
10–38. a) 300.6 kNP b) max 52.3 MPa 10–39. a) 235 kNP b) max 149.6 MPa
10–40. a) 151.6 kNP b) max 109.5 MPa
10–41. 37.2 CT 10–42. 5.81 mmd 10–43. a) all 171.6 kNP b) Ratio 0.628 10–44. a) all 266.9 kNP b) Ratio 0.415 10–45. a) all 189 kNP b) all 229 kNP
10–46. a) all 147 kNP b) all 174 kNP
10–47. 2.16 mL 10–48. 1.302 mL
10–49. a) 2
cr 2e
EIP
L
4.54 mL
b) 2.41 mL 10–50. a) 8.31 mL b) 2.54 mL 10–51. The lightest section with max 110 MPa is 56 mm.d 10–52. The lightest section with max 110 MPa is 64 mm.d 10–53. Use W200 26.6.
10–54. Use W200 35.9.
Answers 33
10–55. . . 3.02F S 10–56. . . 3.09F S 10–57. a) all 220 kNP b) all 841 kNP
10–58. a) all 431.3 kNP b) all 437.9 kNP 10–59. a) all 114.7 kNP b) all 208 kNP 10–60. a) all 1530 kNP b) all 638 kNP
10–61. all 412.2 kNP 10–62. a) 231 mmL b) 376 mmL c) 714 mmL 10–63. all 44.4 kNP 10–64. all 35.9 kNP
10–65. all 382 kNP 10–66. all 899 kNP
10–67. all 1596 kNP
10–68. all 831kNP 10–69. all 160.4 kNP
10–70. all 107.7 kNP
10–71. 44.9 mmb 10–72. Since allP must be greater than 120 kN,
use 9 mm.t
10–73. 22.3 mmb
10–74. 123.1 mmd
10–75. 143 mmd 10–76. a) 34kN: Use 4 boards.P b) 17 kN: Use 3 boards.P
10–77. Use W250 67. 10–78. Use W200 46.1. 10–79. Use W360 122 10–80. Use 9 mmt 10–81. all 531.7 kNP 10–82. a) 30.1 mmd b) 33.5 mmd 10–83. Use 89 64 12.7 mm.L 10–84. Use 89 64 12.7.L
10–85. a) 433 kNDP 321 kNLP b) 896 kNDP 664 kNLP
10–86. 262.3 kNLP 10–87. Use W310 74.
10–88. Use 8 mmt 10–89. 76.7 kNP 10–90. 55.2 kNP 10–91. a) 329 kNP b) 280 kNP 10–92. a) 1060 kNP b) 678 kNP 10–93. a) all 82.6 kNP b) all 64.8 kNP 10–94. a) all 94.7 kNP b) all 81.1 kNP 10–95. 35.3 kNP 10–96. 28.4 kNP 10–97. a) 11.89 mmxe b) 6.56 mmxe
10–98. 7.78 mme 10–99. 1.016 mL 10–100. 1.159 mL 10–101. 5.48 mL 10–102. 4.81 mL 10–103. 70.9 mmd 10–104. 81.5 mmd 10–105. Use 12 mm.t
10–106. Use 15 mm.t
10–107. 48.2 mmd 10–108. 44.3 mmd 10–109. a) 1.84 mme b) 18.5 mme 10–110. a) 16.1 mme b) 41 mme 10–111. 140 mmb 10–112. 140 mmb 10–113. Use W360 216 10–114. Use W360 101 10–115. Use W250 58. 10–116. Use W200 59.
10–117. 2
cr 2
kaP
l
10–118. 9.68 mmd 10–119. a) cr 1516 NP b) 14.1 mmd c) 49.2%
10–120. 2 2
212
bT
L
10–121. ,all 2.77 kNACT
10–122. 5.37 kNP
10–123. all 311.2 kNP
34 Answers
10–124. . . 2.27F S 10–125. a) 4.84 mmmy b) max 135.7 MPa
10–126. Use W250 80 10–127. a) all 26.6 kNP b) all 33.0 kNP
10–128. Use W200 52
Chapter 11 11–1. a) 3177.9 kJ/mYu
b) 3712 kJ/mYu
c) 3160.3 kJ/mYu
11–2. a) 33.33 MJ/mYu b) 3444.4 kJ/mYu c) 355.8 kJ/mYu
11–3. a) 3306.3 kJ/mYu b) 3506.3 kJ/mYu c) 31.225 MJ/mYu
11–4. a) 321.6 kJ/mYu
b) 3336 kJ/mYu
c) 3163.0 kJ/mYu
11–5. a) 31296 kJ/mYu b) modulus of toughness 390 MJ/m
11–6. a) 3400 kJ/mYu b) modulus of toughness 3137.7 MJ/m
11–7. a) 6 21.575 10 N/mYU b) modulus of toughness 363.65 MJ/m
11–8. 3150 kJ/mYu modulus of toughness 363 MJ/m 11–9. a) 23.7 JU b) 3In , 75.8 kJ/mAB u
3In , 31.0 kJ/mBC u
11–10. a) 44.0 JU b) 31.4 JU 11–11. a) 25.77 JU b) 30.0077 J/mu 30.062 J/mu 11–12. 136.6 JU 11–13. 0.846 JU
11–14. 13.73 mmd 11–15. a) . . 3.28F S b) . . 4.25F S 11–16. 10.06 JU
11–17. 2
min4
P LU
EA
11–18. 2
1.398P l
UEA
11–19. 2
3.81P l
UEA
11–20. 2
0.233P l
UEA
11–21. 2
2.37P l
UEA
11–22. 1015 JU 11–23. 900 JU
11–24. 2 5
40
w LU
EI
11–25. 2 5
240
w LU
EI
11–26. 2 3 30
2
( )
6
M a bU
EIL
11–27. 2 2
(3 4 )6
P aU L a
EI
11–28. 1048JU
11–29. 670 JU 11–30. 93.4 JU 11–31. 28.3 JU
11–32. max 15U
uV
11–33. 254.9 kJU 11–34. 14.70 JU
11–35. 2
min
7
48
T LU
GJ
11–36. a) . . 2.28F S b) . . 1.99F S 11–37. 70.4 125.4 MPay
11–38. 2.65 MPa < < 122.65 MPaz
11–39. a) (No yield.) b) (Yield occurs.)
11–40. 2 20
3 2
2 31
10
M L E dU
GEbd L
Answers 35
11–41. 2
2
14
RQU ln
GL R
11–42. a) 79.8 kNP b) max 254 MPa c) 1.523 mm 11–43. 24.7 mmd 11–44. 4.76 kgm
11–45. 5.63 kgm
11–46. 285 mmh 11–47. 200 mmh 11–48. a) 21.0 kNmP
b) 172.1 MPam c) 8.61 mmmy
11–49. a) 7.66 kNmP
b) 316 MPam c) 23.5 mmmy
11–50. 0 2.55 m/sv 11–51. 0 3.68 m/sv 11–52. a) 15.63 mmmy
b) | | 83.8 N mmM c) 208 MPam
11–53. a) 23.6 mmmy
b) | | 64.4 N mmM c) 157.6 MPam
11–54. a) 34.01 10 mEy
b) 212.3 MPam 11–55. a) 318.6 mmmy b) 3.63 kNmP c) 36.25 MPam
11–56. a) 21 1m st
st
hy y
y
b) Impact factor 7.12
11–57. relative error 0.152 0.1662my
h
11–58. 2 ( )
3DPa a L
EI
11–59. 2 2
3DPa b
EI
11–60. 0 ( 3 )3DM
L aEI
11–61. 3 3
02
( )
3D
M a b
EIL
11–62. 33
4CPa
EI
11–63. 33
16CPL
EI
11–64. 03
16AM L
EI
11–65. 01
16DM L
EI
11–66. 5.28B
11–67. 59.8 mmA
11–68. 386 mmL 11–69. 2.55
11–70. 24
TL
G� ds
t
11–71. 3.375BP
yEA
11–72. 5.34mm
11–73. 31.14 10 m 11–74. 0.00919 mm 11–75. 1.030 mm
11–76. 1.111 mmD
11–77. a) 2 22 3
0 0
6 2 2
PM L M LP LU
EI EI EI
b) 2 22 3
0 0
6 2 2
M PL M LP LU
EI EI EI
11–78. a) 2 22 3
0 0
48 8 2
PM L M LP LU
EI EI EI
b) 2 22 3
0 0
48 8 2
M PL M LP LU
EI EI EI
11–79. a) 2 22 3
0 0
96 16 6
PM L M LP LU
EI EI EI
b) 2 22 3
0 0
96 16 6
M PL M LP LU
EI EI EI
36 Answers
11–80. a) 2
2oM L
UEI
b) 2
2oM L
UEI
11–81. a) 2 2
48
P LU
EI
b) 2 31
384ADP L
UEI
2 31
48
P LU
EI
11–82. a) 2 37
24
P LU
EI
b) 2 313
48ABP L
UEI
2 37
24
P LU
EI
11–83. 35
48DPL
EI
11–84. 4
0.0443DwL
EI
11–85. 23
8DPL
EI
11–86. 37
48DwL
EI
11–87. 4
128DwL
EI
11–88. 3
96DPL
EI
11–89. 3
192DwL
EI
11–90. 2
48DPL
EI
11–91. 6o
BM L
EI
11–92. 8.75 mA 11–93. 21.6 mmB
11–94. 0.6
3
05.265kN m
MM
Q
3.80 mmD
11–95. 7.25 mmB
11–96. 5.12 mmB
11–97. 2.1 mmC
11–98. 33.73 10 radA
11–99. 2CPl
xEA
3.80CPl
yEA
11–100. 0Cx 2.80CP
yEA
11–101. 0.1459 mmB
11–102. 0.0468 mmB
11–103. 0.00537 mP 11–104. 3.7 mmQ
11–105. a) 32
3CPl
EI
b) 2
6CPl
EI
11–106. a) 35
3PPl
EI
b) 22
DPl
EI
11–107. a) 3
DPl
EI
b) 23
2CPl
EI
11–108. a) 3
6PPL
EI
b) 3
0.1443QPL
EI
11–109. a) 3
2QPR
EI
b) 3
4PPR
EI
11–110. 3
2
PR
EI
11–111. 03
2AM
RL
03
12
M M x
11–112. 5
16BR P
5
32CM PL
3
16AM PL
0BM
11–113. 7
128AR wL
20.02734 CM wL
20.02884mM wL
27
/2 /2128
M wLx w L L
Answers 37
11–114. 03
3 ( )
2A
M b L aR
L
0AM
0
3
( )3
2DM ab L a
ML
003
( )3
2DM ab L a
M ML
002
( )3
2BM b L a
M ML
3 00 03 ( ) /2M M b L a x L M L a
11–115. 02
3AM
RL
04
3CM
RL
02BM
RL
11–116. 14
27AR P
0.1728DM PL
0.1481BM PL
114
/327
M Px P x L
11–117. 31 2cos
BCP
F
11–118. 3
4BCF P
11–119. 7
8BCF P
11–120. 0.652BCF P
11–121. 2
3ABF P
11–122. 7
12ABF P
11–123. a) 12.18 JU
b) 315.83 kJ/mABu 338.6 kJ/mBCu
11–124. max45
8
Uu
V
11–125. 41.6 NW 11–126. 59.8 JU 11–127. 2m sty
11–128. 11.57 mm 11–129. 3.96A 11–130. 1.030 mm
11–131. 3 2
21 1.5
3CPL Ea
EI GL
11–132. 2
6DPL
EI
11–133. 0.0160 mC
11–134. 1
6AR wL
5
12CR wL
3
4BR wL