omernecaticora.files.wordpress.com€¦ · 1 Answers Chapter 1 1–1. a) d1 22.6 mm b) d2 15.96 mm 1–2. a) AB 35.7 MPa b) BC 42.4 MPa 1–3. P 112.9 kN 1–4. a) AB 81.5 MPa b)

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


65.4 MPay

7–15. a) 56.2 MPa x 38.2 MPax y 86.2 MPay


75.2 MPay

7–16. a) 16.8 MPax 1.05 MPax y 72.8 MPay


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


7–37. a) 56.2 MPax 38.2 MPax y

86.2 MPay


7–38. a) 16.8 MPax 1.05 MPax y

72.8 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

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omernecaticora.files.wordpress.com€¦ · 1 Answers Chapter 1 1–1. a) d1 22.6 mm b) d2 15.96 mm 1–2. a) AB 35.7 MPa b) BC 42.4 MPa 1–3. P 112.9 kN 1–4. a) AB 81.5 MPa b)