MECHANICS OF MATERIALS EIGHTH EDITION PDF

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78572_fm_ptg01_hr_i-v.qxd 1/24/12 5:45 PM Page iii INSTRUCTOR'S SOLUTIONS MANUAL TO ACCOMPANY MECHANICS OF MATERIALS EIGHTH EDITION JAMES M. GERE BARRY J. GOODNO Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States 78572_fm_ptg01_hr_i-v.qxd 1/24/12 5:4...

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INSTRUCTOR'S SOLUTIONS MANUAL TO ACCOMPANY

MECHANICS OF MATERIALS EIGHTH EDITION

JAMES M. GERE BARRY J. GOODNO

Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States

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Contents

1. Tension, Compression, and Shear

1

2. Axially Loaded Members 117 3. Torsion

283

4. Shear Forces and Bending Moments 385 5. Stresses in Beams (Basic Topics) 435 6. Stresses in Beams (Advanced Topics) 557 7. Analysis of Stress and Strain 637 8. Applications of Plane Stress (Pressure Vessels, Beams, and Combined Loadings) 725 9. Deflections of Beams 793 10. Statically Indeterminate Beams 885 11. Columns

943

12. Review of Centroids and Moments of Inertia 1025 Answers to Problems 1057 Appendix A: FE Exam Review Problems 1083

v

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Answers to Problems CHAPTER 1 1.2-1 1.2-2

1.2-3

1.2-4 1.2-5 1.2-6 1.2-7 1.2-8 1.2-9 1.2-10 1.2-11

1.2-12 1.2-13

1.2-14 1.2-15

1.2-16

(a) Ay  5 lb, By  5 lb, Cx  50 lb, Cy  0; (b) N  50 lb, V  5 lb, M  75 ft-lb (a) MA  0, Cy  236 N, Dy  75.6 N; (b) N  0, V  70 N, M  36.7 Nm; (c) MA  0, Cy  236 N, Dy  75.6 N; N  0, V  70 N, M  36.7 Nm (a) Ax  12.55 lb, Ay  15 lb, Cy  104.3 lb, Dx  11.45 lb, Dy  19.83 lb; (b) ResultantB  19.56 lb; (c) Ax  42.7 lb, Ay  37.2 lb, MA  522 lb-ft, Dx  18.67 lb, Dy  32.3 lb, ResultantB  56.6 lb (a) R3x  40 N, R3y  25 N, R5x  20 N; (b) F11  0, F13  28.3 N (a) Ax  0, Ay  1.0 kip, Ey  5 kips; (b) FFE  1.898 kips (a) Fx  0, Fy  12.0 kN, Dy  6.0 kN; (b) FFE  0 (a) Bx  0.8 P, Bz  2.0 P, Oz  1.25 P; (b) FAC  0.960 P (a) Ax  1.25P, By  0, Bz  P; (b) FAB  1.601P (a) Ay  4.67P, Az  4.0P; (b) FAB  8.33P (a) Az  0, Bx  3.75 kN; (b) FAB  6.73 kN (a) TA  11,000 lb-in.; (b) T(L1/2)  TA  11,000 lb-in., T (L1  L2/2)  T2  10,000 lb-in. (a) TA  1225 Nm; (b) T(L1/2)  62.5 Nm, T (L1  L2/2)  T2  1100 Nm (a) Ax  540 lb, Ay  55.6 lb, MA  4320 lb-ft, Cy  55.6 lb; (b) N  55.6 lb, V  506 lb, M  2374 lb-ft (a) Ax  280 N, Ay  8.89 N, MA  1120 Nm, Dy  151.1 N; (b) ResultantB  280 N (a) Ax  30 lb, Ay  140 lb, Cx  30 lb, Cy  60 lb; (b) N  23.3 lb, V  20 lb, M  33.3 lb-ft (a) Ax  10.98 kN, Ay  29.0 kN, Ex  8.05 kN, Ey  22 kN; (b) ResultantC  23.4 kN

1.2-17 1.2-18

1.2-19 1.2-20

1.2-21

1.2-22

1.2-23

1.2-24 1.2-25 1.2-26 1.3-1 1.3-2 1.3-3

1.3-4 1.3-5

(a) Ay  1250 lb, Ex  0, Ey  1750 lb; (b) N  1750 lb, V  500 lb, M  575 lb-ft (a) Ax  320 N, Ay  240 N, Cy  192 N, Ey  192 N; (b) N  312 N, V  57.9 N, M  289 Nm; (c) ResultantC  400 N (a) Ax  28.9 lb, Ay  50.0 lb, Bx  65.0 lb; (b) Fcable  71.6 lb (a) Ax  10 kN, Ay  2.17 kN, Cy  9.83 kN, Ey  1.333 kN; (b) ResultantD  12.68 kN (a) Ox  48.3 lb, Oy  40 lb, Oz  12.94 lb, MOx  331 lb-in., MOy  690 lb-in., MOz  338 lb-in.; (b) N  40 lb, V  50 lb, T  690 lb-in., M  473 lb-in. (a) Ay  120 N, Az  60 N, MAx  70 Nm, MAy  142.5 Nm, MAz  180 Nm, Dx  60 N, Dy  120 N, Dz  30 N; (b) N  120 N, V  41.3 N, T  142.5 Nm, M  180.7 Nm (a) Ax  5.77 lb, Ay  47.3 lb, Az  2.31 lb, MAz  200 lb-in.; (b) TDC  3.81 lb, TEC  6.79 lb Cx  120 N, Cy  160 N, Cz  506 N, Dz  466 N, Hy  320 N, Hz  499 N Ay  57.2 lb, Bx  44.2 lb (to the left), By  112.4 lb, Cx  28.8 lb, Cy  5.88 lb (a) HB  104.6 N, VB  516 N, VF  336 N; (b) N  646 N, V  176.8 N, M  44.9 kNm (a) sAB  1443 psi; (b) P2  1487.5 lbs; (c) tBC  0.5 in. (a) s  130.2 MPa; (b)   4.652 * 104 (a) RB  lb (cantilever), 191.3 lb (V-brakes); sC  144 psi (cantilever), 306 psi (V-brakes); (b) scable  26,946 psi (both) (a) s  3.101 * 104; (b) d  0.1526 mm; (c) Pmax  89.5 kN (a) sC  2.46 ksi; (b) xC  19.56 in., yC  19.56 in.

1057

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Answers to Problems

(a) st  132.7 MPa; (b) amax  34.4 (a) s1  34.4 ksi, s2  30.6 ksi; (b) d1new  3.18  102 in.; (c) s1  19.6 ksi, s2  18.78 ksi, s3  22.7 ksi 1.3-8 sC  5.21 MPa 1.3-9 (a) T  184 lb, s  10.8 ksi; (b) cable  5  104 1.3-10 (a) T  819 N, s  74.5 MPa; (b) cable  4.923  104 1.3-6 1.3-7

5877 48,975 1.3-11 (a) T  £ 4679 ≥ lb; (b) s  £ 38,992 ≥ psi; 7159 59,658 4278 35,650 6461 53,842 (c) T  § ¥ psi ¥ lb, s  § 27,842 3341 35,650 4278 (a) sx  gv2(L2  x2)/2g; (b) smax  gv2L2/2g (a) TAB  1620 lb, TBC  1536 lb, TCD  1640 lb; (b) sAB  13,501 psi, sBC  12,799 psi, sCD  13,667 psi 1.3-14 (a) TAQ  TBQ  50.5 kN; (b) s  166 MPa 1.4-1 (a) Lmax  11,800 ft; (b) Lmax  13,500 ft 1.4-2 (a) Lmax  7143 m; (b) Lmax  8209 m 1.4-3 % elongation  6.5, 24.0, 39.0; % reduction  8.1, 37.9, 74.9; Brittle, ductile, ductile 1.4-4 11.9  103 m; 12.7  103 m; 6.1  103 m; 6.5  103 m; 23.9  103 m 1.4-5 s  52.3 ksi 1.4-6 spl ⬇ 47 MPa, Slope ⬇ 2.4 GPa, s g ⬇ 53 MPa; Brittle 1.4-7 spl ⬇ 65,000 psi, Slope ⬇ 30  106 psi, s Y ⬇ 69,000 psi, sU ⬇ 113,000 psi; Elongation  6%, Reduction  31% 1.5-1 0.13 in. longer 1.5-2 4.0 mm longer 1.5-3 (a) dpset  1.596 in.; (b) sB  30 ksi 1.5-4 (a) dpset  4.28 mm; (b) sB  65.6 MPa 1.5-5 (b) 0.71 in.; (c) 0.58 in.; (d) 49 ksi 1.6-1 Pmax  157 k 1.6-2 P  27.4 kN (tension) 1.6-3 P  15.708 kips 1.6-4 (a) P  74.1 kN; (b) d   # L  0.469 mm

1.6-5 1.6-6 1.6-7

1.6-8

1.7-1 1.7-2 1.7-3 1.7-4

1.7-5 1.7-6

1.3-12 1.3-13

shortening;

Af  A A

 0.081%,

¢V1  V1f  Vol 1  207 mm3;

1.7-7 1.7-8 1.7-9 1.7-10 1.7-11 1.7-12 1.7-13

1.7-14

1.7-15

d  1.56  104 in., P  2.154 kips (a) E  104 GPa; (b)  0.34 (a) dBC inner  8  104 in.; (b) brass  0.34; (c) tAB  2.732  104 in., dAB inner  1.366  104 in. (a) L1  12.66 mm; L2  5.06 mm; L3  3.8 mm; (b) Vol1  21,548 mm3; Vol2  21,601 mm3; Vol3  21,610 mm3 sb  7.04 ksi, tave  10.756 ksi sb  139.86 MPa; Pult  144.45 kN (a) t  12.732 ksi; (b) sbf  20 ksi, sbg  26.667 ksi (a) Bx  252.8 N, Ax  Bx, Ay  1150.1 N; (b) Aresultant  1178 N; (c) t  5.86 MPa, sbshoe  7.36 MPa (a) tmax  2979 psi; (b) sbmax  936 psi T1  13.176 kN, T2  10.772 kN, t1ave  25.888 MPa, t2ave  21.166 MPa, sb1  9.15 MPa, sb2  7.48 MPa (a) Resultant  1097 lb; (b) sb  4999 psi; (c) tnut  2793 psi, tpl  609 psi G  2.5 MPa (a) gaver  0.004; (b) V  89.6 k (a) gaver  0.50; (b) d  4.92 mm (a) sb  69.5 ksi, sbrg  39.1 ksi, tf  21 ksi; (b) sb  60.4 ksi, sbrg  34 ksi, tf  18.3 ksi taver  42.9 MPa (a) Ax  0, Ay  170 lb, MA  4585 in.-lb; (b) Bx  253.6 lb, By  160 lb, Bres  299.8 lb, Cx  Bx ; (c) tB  3054 psi, tC  1653 psi; (d) sbB  4797 psi, sbC  3246 psi For a bicycle wih L/R  1.8: (a) T  1440 N; (b) taver  147 MPa P b P (a) t  ; (b) d  ln 2prh 2p hG d

(a) t1  2.95 MPa , t4  0; (b) sb1  1.985 MPa, sb4  0; (c) sb4  41 MPa; (d) t  10.62 MPa; (e) s3  75.1 MPa 1.7-17 (a) Ox  12.68 lb, Oy  1.294 lb, Ores  12.74 lb; (b) tO  519 psi, sbO  816 psi; (c) t  362 psi 1.7-18 (a) Fx  153.9 N, s  3.06 MPa; (b) tave  1.96 MPa; (c) sb  1.924 MPa 1.7-19 (a) P  395 lb; (b) Cx  374 lb, Cy  237 lb, Cres  443 lb; (c) t  18.04 ksi, sbC  4.72 ksi 1.8-1 Pallow  3140 lb 1.7-16

(c) d3  65.4 mm

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Answers to Problems

1.8-2 1.8-3 1.8-4

1.8-5 1.8-6 1.8-7 1.8-8 1.8-9 1.8-10 1.8-11 1.8-12 1.8-13 1.8-14 1.8-15 1.8-16 1.9-1 1.9-2 1.9-3 1.9-4 1.9-5 1.9-6 1.9-7 1.9-8 1.9-9 1.9-10 1.9-11 1.9-12 1.9-13

1.9-14 1.9-15

Tmax  33.4 kN.m Pallow  607 lb (a) Pallow  8.74 kN; (b) Pallow  8.69 kN; (c) Pallow  21.2 kN, Pallow  8.69 kN (shear controls) P  294 k (a) F  1.171 kN; (b) Shear: Fa  2.86 kN Wmax  5110 lb (a) FA  22T, FB  2T, FC  T; (b) Shear at A: Wmax  66.5 kN Pa  10.21 kips Cult  5739 N: Pmax  445 N Wmax  0.305 kips Shear in rivets in CG & CD controls: Pallow  45.8 kN (a) Pa  sa (0.587d 2); (b) Pa  21.6 kips Pallow  96.5 kN Pmax  11.98 psf (a) Pallow  sc (pd 2/4) 21  (R/L)2; (b) Pallow  9.77 kN (a) dmin  3.75 in; (b) dmin  4.01 in. (a) dmin  164.6 mm; (b) dmin  170.9 mm (a) dmin  0.704 in.; (b) dmin  0.711 in. dmin  63.3 mm dpin  1.029 in. (b) Amin  435 mm2 dmin  0.372 in. dmin  5.96 mm n  11.6, or 12 bolts (d2)min  131 mm Ac  1.189 in.2 (a) tmin  18.8 mm, use t  20 mm; (b) Dmin  297 mm (a) sDF  10.38 ksi  s allow, sbF  378 psi  sba; (b) new sBC  25 ksi, so increase rod BC to 14-in. diameter; required 5 diameter of washer  1  in.  1.312 in. 16 (a) dm  24.7 mm; (b) Pmax  49.4 kN u  arccos 1/ 23  54.7

CHAPTER 2 4W 6W ; (b) d  5k 5k

2.2-1

(a) d 

2.2-2

(a) d  12.5 mm; (b) n  5.8

da Es da Es 30   ; (b)   1.651; ds Ea 11 ds C Ea La Ea (c)  1.5  0.55; Ls Es Es (d) E 1   17,647 ksi (cast iron or copper 1.7 alloy) (see App. I)

2.2-3

(a)

2.2-4 2.2-5 2.2-6

h  13.4 mm h  L  prmaxd 2/4k (a) x  102.6 mm; (b) x  205 mm; (c) Pmax  12.51 N; (d) uinit  1.325; (e) P  20.4 N 26P (a) d4  ; 3k

2.2-7

(b) d4  2.2-8 2.2-9 2.2-10 2.2-11 2.2-12 2.2-13

1059

104P 15 , ratio   3.75 45k 4

(a) dB  1.827 mm; (b) Pmax  390 kN; (c) dBx  6.71 mm, Pmax  106.1 kN Pmax  72.3 lb (a) x  134.7 mm; (b) k1  0.204 N/mm; (c) b  74.1 mm; (d) k3  0.638 N/mm (a) tc,min  0.021 in.; (b) dr  0.031 in.; (c) hmin  0.051 in. dA  0.200 mm, dD  0.880 mm L1 P 27 (a) dD  (28f2  9f1); (b)  16 L2 16 d1 365L (c)  1.225; (d) x  d2 236

(a) u  35.1, d  44.6 mm, RA  25 N, RC  25 N; (b) u  43.3, d  8.19 mm, RA  31.5 N, RC  18.5 N, MA  1.882 Nm 2.2-15 (a) u  35.1, d  1.782 in., RA  5 lb, RC  5 lb; (b) u  43.3, d  0.327 in., RA  6.3 lb, RC  3.71 lb , MA  1.252 lb-ft 2.3-1 (a) d  0.0276 in.; (b) dB  1.074 in. 2.3-2 (a) d  0.675 mm; (b) Pmax  267 kN 2.3-3 (a) d  0.01125 in. (elongation); (b) So new value of P3 is 1690 lb, an increase of 390 lb. (c) AAB  0.78 in.2 7PL 2.3-4 (a) d  ; (b) d  0.5 mm; (c) Lslot  244 mm 6Ebt 2.2-14

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Answers to Problems

7PL ; (b) d  0.021 in.; (c) Lslot  10 in. 6Ebt

2.3-5

(a) d 

2.3-6 2.3-7

(a) dAC  3.72 mm; (b) P0  44.2 kN (a) da  0.0589 in.; (b) db  0.0501 in.; dc dc (c)  0.58,  0.681 da db

2.3-8

2.3-9

Page 1060

2.4-8 2.4-9 2.4-10

(a) dmax  23.9 mm; (b) b  4.16 mm; (c) x  183.3 mm P y PL (a) d  ; (b) s(y)  a b ; 2EA A L (c) d 

y P y PL 2 a b, s(y)  c a 2  b d EA 3 A L L

(a) d2-4  0.024 mm; (b) Pmax  8.15 kN; (c) L2  9.16 mm 2.3-11 (a) R1  3P/2; (b) N1  3P/2 (tension), N2  P/2 (tension); (c) x  L/3; (d) d2  2PL/3EA; (e) b  1/11 2 2 2.3-12 (a) dc  W(L  h )/2EAL; (b) dB  WL/2EA; (c) b  3; WL (d) d   359 mm (in sea water); 2EA WL d  412 mm (in air) 2EA

d (x)  c

2.3-10

2.3-13 2.3-14 2.3-15 2.3-16 2.3-17 2.4-1 2.4-2 2.4-3 2.4-4

2.4-5 2.4-6 2.4-7

(a) RA  10.5 kN (to the left), RD  2.0 kN (to the right); (b) FBC  15.0 kN (compression) (b) sa  1610 psi (compression), ss  9350 psi (tension) (a) P  13.73 kN, R1  9.07 kN, R2  4.66 kN, s2  7 MPa; (b) dcap  190.9 mm, Axial Force Diagram: N(x)  R2 if x L2, N(x)  R1 if x  L2; Axial Displacement Diagram: R2 (x) d if x L2, d(x)  c EA2

2.4-11

2.4-12 2.4-13 2.4-14

(b) d  0.010 in. d  2PH/3Eb2 d  2WL/pd 2E (a) d  2.18 mm; (b) d  6.74 mm (b) d  11.14 ft (a) P  1330 lb; (b) Pallow  1300 lb (a) P  104 kN; (b) Pmax  116 kN (a) PB /P  3/11; (b) sB /sA  1/2; (c) Ratio  1 (a) If x L/2, RA  (3PL)/(2(x  3L)), RB  P(2x  3L)/(2(x  3L)). If x L/2, RA  (P(x  L))/(x  3L), RB  (2PL)/(x  3L). (b) If x L/2, d  PL(2x  3L)/[(x  3L)Epd 2]. If x L/2, d  8PL(x  L)/[3(x  3L)Epd 2]. (c) x  3L/10 or x  2L/3; (d) RB  rgpd 2L/8, RA  3 rgpd2L/32 (a) 41.7%; (b) sM  32.7 ksi, sO  51.4 ksi (a) d  1.91 mm; (b) d  1.36 mm; (c) d  2.74 mm (a) RA  2P/3, RE  5P/3; LP LP 5LP (b) dB   ; ,d  ,d  6EA C 6EA D 6EA 5LP (c) dmax  (to the right), dA  dE  0 6EA

2.4-15

(d) Pmax  12.37 kip

2.5-14

2.4-16 2.4-17 2.5-1 2.5-2 2.5-3 2.5-4

2.5-5 2.5-6

2.5-7 2.5-8 2.5-9 2.5-10 2.5-11 2.5-12 2.5-13

R2L 2 R1 + (x  L 2) d if x  L2; EA2 EA1

(c) q  1.552 kN/m (a) P1  PE1/(E1  E2); (b) e  b(E2  E1)/[2(E2  E1)]; (c) s1/s2  E1/E2 (a) Pallow  1504 N; (b) Pallow  820 N; (c) Pallow  703 N d2  0.338 in., L2  48.0 in. (a) Ax  41.2 kN, Ay  71.4 kN, Bx  329 kN, By  256 kN; (b) Pmax  233 kN (a) sc  10,000 psi, sD  12,500 psi; (b) dB  0.0198 in. Pmax  1800 N ss  3.22 ksi, sb  1.716 ksi, sc  1.93 ksi s  11,700 psi T  40.3C T  185F (a) T  24C, srod  57.6 MPa; (b) Clevis: sbc  42.4 MPa, Washer: sbw  74.1 MPa; (c) db  10.68 mm (a) sc  Ea ( TB)/4; (b) sc  Ea( TB)/[4(EA/kL  1)] (a) N  51.8 kN, max. sc  26.4 MPa, dC  0.314 mm; (b) N  31.2 kN, max. sc  15.91 MPa, dC  0.546 mm d  0.123 in. T  34C t  15.0 ksi Pallow  39.5 kN (a) TA  400 lb, TB  200 lb; (b) TA  454 lb, TB  92 lb; (c) T  153F (a) s  98 MPa; (b) T  35 C (a) s  957 psi; (b) Fk  3006 lbs (C); (c) s  2560 psi s  PL/6EA

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Answers to Problems

2.5-15

2.5-16

2.5-17 2.5-18 2.5-19 2.5-20 2.5-21 2.5-22 2.5-23 2.5-24 2.5-25 2.6-1 2.6-2 2.6-3 2.6-4 2.6-5 2.6-6

2.6-7 2.6-8

2.6-9

2.6-10

(a) P1  231 k, RA  55.2 k, RB  55.2 k; (b) P2  145.1 k, RA  55.2 k, RB  55.2 k; (c)For P1, tmax  13.39 ksi, for P2, tmax  19.44 ksi; (d) T  65.8F, RA  0, RB  0; (e) RA  55.2 k, RB  55.2 k (a) RA  [s  a T(L1  L2)]/[(L1/EA1)  (L2/EA2)  (L/k3)], RD  RA; (b) dB  a T(L1)  RA(L1/EA1), dC  a T(L1  L2)  RA[(L1/EA1)  L2/EA2)] TB  660 lb, TC  780 lb Pallow  1.8 MN (a) sp  0.196 ksi, sr  3.42 ksi; (b) sb  2.74 ksi, tc  0.285 ksi sp  25.0 MPa sp  2400 psi (a) PB  25.4 kN, Ps  PB; (b) Sreqd  25.7 mm; (c) dfinal  0.35 mm (a) Fx  0.174 k; (b) F1  0.174 k; (c) Lf  12.01 in.; (d) T  141.9F sa  500 MPa (tension), sc  10 MPa (compression) (a) Fk  0.174 k; (b) Ft  0.174 k; (c) Lf  11.99 in.; (d) T  141.6F Pmax  42,600 lb dmin  6.81 mm Pmax  24,000 lb (a) Tmax  46C; (b) T   9.93C (a) tmax  10,800 psi; (b) Tmax  49.9F; (c) T  75.9F (a) sx  84 MPa; (b) tmax  42 MPa; (c) On rotated x face: sx1  42 MPa, tx1y1  42 MPa; On rotated y face: sy1  42 MPa, (d) On rotated x face: sx1  71.7 MPa, txlyl  29.7 MPa On rotated y face: sy1  12.3 MPa (a) smax  18,000 psi; (b) tmax  9000 psi (a) Element A: sx  105 MPa (compression), Element B: tmax  52.5 MPa; (b) u  33.1 sAC (a) tmaxAC   1.859 ksi, 2 sAB  7.42 ksi, tmaxAB  2 sBC  9.41 ksi; tmaxDC  2 (b) Pmax  36.5 kip (a) (1) sx  945 kPa; (2) su  807 kPa, tu  334 kPa; (3) su  472 kPa, tu  472 kPa, smax  945 kPa, tmax  472 kPa; (b) smax  378 kPa, tmax  189 kPa

2.6-11 2.6-12

2.6-13 2.6-14 2.6-15 2.6-16 2.6-17 2.6-18 2.6-19

2.7-1 2.7-2 2.7-3 2.7-4 2.7-5 2.7-6 2.7-7 2.7-8

2.7-9

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(a) tpq  11.54 psi; (b) spq  1700 psi, s(pq  p/2)  784 psi; (c) Pmax  14,688 lb (a) Tmax  31.3C; (b) spq  21.0 MPa (compression), tpq  30 MPa (CCW); (c) b  0.62 NAC  5.77 kips; dmin  1.08 in. (a) su  0.57 MPa, tu  1.58 MPa; (b) a  33.3; (c) a  26.6 (a) u  35.26, t0  7070 psi; (b) smax  15,000 psi, tmax  7500 psi su1  54.9 MPa, su2  18.3 MPa, tu  31.7 MPa smax  10,000 psi, tmax  5000 psi (a) u  30.96; (b) Pmax  1.53 kN (a) tu  348 psi, u  20.1; (b) sx1  950 psi, sy1  127.6 psi; (c) kmax  15,625 lb/in.; (d) Lmax  1.736 ft; (e) Tmax  92.8F (a) U  23P2L/12EA; (b) U  125 in.-lb (a) U  5P2L/4pEd 2; (b) U  1.036 J U  5040 in.-lb (c) U  P2L/2EA  PQL/2EA  Q2L/4EA Aluminum: 171 psi, 1740 in. (a) U  P2L/EA; (b) dB  2PL/EA (a) U1  0.0375 in.-lb; (b) U2  2.57 in.-lb; (c) U3  2.22 in.-lb (a) U  5kd 2; (b) d  W/10k; (c) F1  3W/10, F2  3W/20, F3  W/10 b2 P 2L (a) U  ln ; 2Et(b2  b1) b1 (b) d 

b2 PL ln Et(b2  b1) b1

(a) P1  270 kN; (b) d  1.321 mm; (c) U  243 J 2.7-11 (a) x  2s, P  2(k1  k2)s; (b) U1  (2k1  k2)s2 2.7-12 (a) U  6.55 J; (b) dC  168.8 mm 2.8-1 (a) dmax  0.0361 in.; (b) smax  22,600 psi; (c) Impact factor  113 2.8-2 (a) dmax  6.33 mm; (b) smax  359 MPa; (c) Impact factor  160 2.8-3 (a) dmax  0.0312 in.; (b) smax  26,000 psi; (c) Impact factor  130 2.8-4 (a) dmax  215 mm; (b) Impact factor  3.9 2.8-5 (a) dmax  9.21 in.; (b) Impact factor  4.6 2.8-6 v  13.1 m/s 2.8-7 hmax  8.55 in. 2.8-8 Lmin  9.25 m 2.7-10

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2.8-9 2.8-10 2.8-11 2.8-12 2.8-13 2.8-14 2.10-1 2.10-2 2.10-3 2.10-4 2.10-5 2.10-6 2.10-7 2.11-2 2.11-3 2.11-4 2.11-5 2.11-6 2.12-1 2.12-2 2.12-3 2.12-4 2.12-5 2.12-6 2.12-7 2.12-8 2.12-9 2.12-10 2.12-11

1/19/12

10:47 AM

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Answers to Problems

Lmin  500 in. Vmax  5.40 m/s dmax  11.0 in. L  25.5 m (a) Impact factor  1  (1  2EA/W)1/ 2; (b) 10 smax  33.3 MPa (a) smax ⬇ 6.2 ksi and 6.9 ksi; (b) smax ⬇ 11.0 ksi and 9.0 ksi (a) smax ⬇ 26 MPa and 29 MPa; (b) smax ⬇ 25 MPa and 22 MPa Pmax  stbt/3 smax ⬇ 46 MPa smax ⬇ 6100 psi (a) No, it makes it weaker: P1  25.1 kN, P2 ⬇ 14.4 kN; (b) d0 ⬇ 15.1 mm dmax ⬇ 0.51 in. (a) dC  1.67 mm; (b) dC  5.13 mm; (c) dC  11.88 mm (b) P  17.7 k For P  30 kN: d  6.2 mm; for P  40 kN: d  12.0 mm For P  24 k: d  0.18 in.; for P  40 k: d  0.68 in. For P  3.2 kN: dB  4.85 mm; for P  4.8 kN: dB  17.3 mm PY  PP  2sY A sin u PP  201 kN (a) PP  5sY A PP  2sY A(1  sin a) PP  47.9 k PP  82.5 kN PP  20.4 k (a) PY  sY A, dY  3sY L/2E; (b) PP  4sY A/3, dP  3sY L/E (a) PY  sY A, dY  sY L/E; (b) PP  5sY A/4, dP  2sY L/E (a) WY  28.8 kN, dY  125 mm; (b) WP  48 kN, dP  225 mm (a) PY  70.1 k, dY  0.01862 in.; (b) PP  104.3 k, dP  0.0286 in.

CHAPTER 3 3.2-1 3.2-2 3.2-3 3.2-4 3.2-5

(a) dmax  0.413 in.; (b) Lmin  21.8 in. (a) Lmin  162.9 mm; (b) dmax  68.8 mm (a) g1  267  106 r...