Exercise Solution Answers Only
Exercise Solution Answers Only
Exercise Solution Answers Only
Answers to problems with a number set in straight type are given on this and the following pages. Answers to problems
with a number set in italic and red are not listed.
AN-1
AN-2 Answers to Problems
2.54 (a) 298.3 MPa. (b) 238.3 MPa. 2.C1 Prob. 2.126: (a) 11.90 3 1023 in. T . (b) 5.66 3 1023 in. c.
2.55 (a) 21.48C. (b) 3.67 MPa. 2.C3 Prob. 2.60: (a) 2116.2 MPa. (b) 0.363 mm.
2.56 5.70 kN. 2.C5 r 5 0.25 in.: 3.89 kips;
2.58 (a) 201.68F. (b) 18.0107 in. r 5 0.75 in.: 2.78 kips.
2.59 (a) 52.3 kips. (b) 9.91 3 1023in. 2.C6 (a) 20.40083. (b) 20.10100. (c) 20.00405.
2.61 29 3 103 psi; 10.03 3 103 psi; 0.444.
2.63 0.399.
2.64 (a) 0.0358 mm. (b) 20.00258 mm. (c) 20.000344 mm.
CHAPTER 3
(d) 20.00825 mm 2. 3.1 641 N?m.
2.66 94.9 kips. 3.2 87.3 MPa.
2.67 (a) 20.0724 mm. (b) 20.01531 mm. 3.3 (a) 5.17 kN?m. (b) 87.2 MPa.
2.68 (a) 0.00312 in. (b) 0.00426 in. (c) 0.00505 in. 3.4 (a) 7.55 ksi. (b) 7.64 ksi.
2.69 (a) 352 3 1026 in. (b) 82.8 3 1026 in. (c) 307 3 1026 in. 3.6 (a) 70.7 MPa. (b) 35.4 MPa. (c) 6.25%.
2.70 (a) 263.0 MPa. (b) 213.50 mm 2. (c) 2540 mm3. 3.7 (a) 19.21 kip?in. (b) 2.01 in.
2.77 a 5 42.9 mm; b 5 160.7 mm. 3.9 (a) 8.35 ksi. (b) 5.94 ksi.
2.78 75.0 kN; 40.0 mm. 3.10 (a) 1.292 in. (b) 1.597 in.
2.79 (a) 10.42 in. (b) 0.813 in. 3.11 (a) shaft CD. (b) 85.8 MPa.
2.80 t 5 62.5 psi; G 5 156.3 psi. 3.13 (a) 77.6 MPa. (b) 62.8 MPa. (c) 20.9 MPa.
2.81 16.67 MPa. 3.15 9.16 kip?in.
2.82 19.00 3 103 kNym 3.16 (a) 1.503 in. (b) 1.853 in.
2.83 (a) 588 3 1026 in. (b) 33.2 3 1023 in 3. (c) 0.0294%. 3.18 (a) d AB 5 52.9 mm. (b) dBC 5 33.3 mm.
2.84 (a) 20.0746 mm; 2143.9 mm3. 3.20 3.18 kN?m.
(b) 20.0306 mm; 2521 mm 3. 3.21 (a) 59.6 mm. (b) 43.9 mm.
2.85 (a) 193.2 3 1026; 1.214 3 1023 in 3. 3.22 (a) 72.5 MPa. (b) 68.7 MPa.
(b) 396 3 1026; 2.49 3 1023 in 3. 3.23 1.189 kip?in.
2.88 3.00. 3.25 4.30 kip?in.
2.91 (a) 0.0303 mm. (b) sx 5 40.6 MPa, sy 5 sz 5 5.48 MPa. 3.27 73.6 N?m.
2.92 (a) sx 5 44.6 MPa; sy 5 0; sz 5 3.45 MPa. (b) 20.0129 mm. 3.28 (a) d AB 5 38.6 mm. (b) dCD 5 52.3 mm. (c) 75.5 mm.
2.93 (a) 58.3 kN. (b) 64.3 kN. 3.29 1.0; 1.025; 1.120; 1.200; 1.0.
2.94 (a) 87.0 MPa. (b) 75.2 MPa. (c) 73.9 MPa. 3.31 11.87 mm.
2.97 (a) 11.4 mm. (b) 28.8 kN. 3.32 9.38 ksi.
2.98 36.7 mm. 3.33 (a) 1.3908. (b) 1.4828.
2.99 (a) 12.02 kips. (b) 108.0%. 3.35 (a) 1.3848. (b) 3.228.
2.100 23.9 kips. 3.37 (a) 14.438. (b) 46.98.
2.101 (a) 15.90 kips; 0.1745 in. (b) 15.90 kips; 0.274 in. 3.38 6.028.
2.102 (a) 44.2 kips; 0.0356 in. (b) 44.2 kips; 0.1606 in. 3.40 1.1408.
2.105 176.7 kN; 3.84 mm. 3.41 3.778.
2.106 176.7 kN; 3.16 mm. 3.42 3.788.
2.107 (a) 0.292 mm. (b) sAC 5 250 MPa; sBC 5 2307 MPa. 3.44 53.88.
(c) 0.0272 mm. 3.45 36.1 mm.
2.108 (a) 990kN. (b) sAC 5 250 MPa; sBC 5 2316 MPa. 3.46 0.837 in.
(c) 0.0313 mm. 3.47 1.089 in.
2.111 (a) 112.1 kips. (b) 50 ksi in low-strength steel; 3.48 62.9 mm.
82.9 ksi in high-strength steel. (c) 0.00906 in. 3.49 42.0 mm.
2.112 (a) 0.0309 in. (b) 64.0 ksi. (c) 0.00387 in. 3.50 22.5 mm.
2.113 (a) sAD 5 250 MPa. (b) sBE 5 124.3 MPa. (c) 0.622 mm T. 3.53 (a) 4.72 ksi. (b) 7.08 ksi. (c) 4.358.
2.114 (a) sAD 5 233 MPa; sBE 5 250 MPa. (b) 1.322 mm T. 3.54 7.378.
2.115 (a) sAD 5 24.70 MPa; sBE 5 19.34 MPa. (b) 0.0967 mm T. 3.56 (a) TA 5 1090 N?m; TC 5 310 N?m.
2.116 (a) 236.0 ksi. (b) 15.84 ksi. (b) 47.4 MPa. (c) 28.8 MPa.
2.117 (a) sAC 5 2150.0 MPa; sCB 5 2250 MPa. 3.57 tAB 5 68.9 MPa; tCD 5 14.70 MPa.
(b) 20.1069 mm S. 3.59 12.24 MPa.
2.118 (a) sAC 5 56.5 MPa; sCB 5 9.41 MPa. (b) 0.0424 mm S. 3.61 0.241 in.
2.121 (a) 9158F. (b) 17598F. 3.63 Ty2ptr 12 at r 1.
2.122 (a) 0.1042 mm. (b) sAC 5 sCB 5 265.2 MPa. 3.64 (a) 9.51 ksi. (b) 4.76 ksi.
2.123 (a) 0.00788 mm. (b) sAC 5 sCB 5 26.06 MPa. 3.65 (a) 46.9 MPa. (b) 23.5 MPa.
2.125 1.219 in. 3.66 (a) 0.893 in. (b) 0.709 in.
2.127 4.678C. 3.67 (a) 20.1 mm. (b) 15.94 mm.
2.128 (a) 9.53 kips. (b) 1.254 3 1023 in. 3.68 25.6 kW.
2.130 (steel) 2 15.80 ksi; (concrete) 2 1.962 ksi. 3.69 2.64 mm.
2.131 (a) 9.73 kN. (b) 2.02 mm d. 3.71 (a) 51.7 kW. (b) 6.178.
2.133 0.01870 in. 3.73 (a) 47.5 MPa. (b) 30.4 mm.
2.135 (a) A sYyµg. (b) E AyL. 3.76 (a) 4.08 ksi. (b) 6.79 ksi.
Answers to Problems AN-3
3.77 (a) 0.799 in. (b) 0.947 in. 3.162 (a) 0.347 in. (b) 37.28.
3.78 (a) 16.02 Hz. (b) 27.2 Hz. 3.C2 Prob. 3.44: 2.218.
3.79 1917 rpm. 3.C5 (a) 23.282%. (b) 20.853%.
3.80 50.0 kW. (c) 20.138%. (d) 20.00554%.
3.81 36.1 mm. 3.C6 (a) 21.883%. (b) 20.484%.
3.84 10.8 mm. (c) 20.078%. (d) 20.00313%.
3.86 (a) 5.36 ksi. (b) 5.02 ksi.
3.87 63.5 kW.
CHAPTER 4
3.88 42.6 Hz.
3.89 (a) 2.61 ksi. (b) 2.01 ksi. 4.1 (a) 261.6 MPa. (b) 91.7 MPa.
3.90 (a) 203 N?m. (b) 165.8 N?m. 4.2 (a) 22.38 ksi. (b) 20.650 ksi.
3.92 (a) 9.64 kN?m. (b) 9.91 kN?m. 4.3 80.2 kN?m.
3.93 2230 lb?in. 4.4 24.8 kN?m.
3.94 (a) 18.86 ksi; 1.500 in. (b) 21.0 ksi; 0.916 in. 4.5 (a) 1.405 kip?in. (b) 3.19 kip?in.
3.95 (a) 113.3 MPa; 15.00 mm. 4.6 (a) 239.3 MPa. (b) 26.2 MPa.
(b) 145.0 MPa; 6.90 mm. 4.9 214.71 ksi; 8.82 ksi.
3.98 (a) 6.728. (b) 18.718. 4.10 210.38 ksi; 15.40 ksi.
3.99 (a) 2.478. (b) 4.348. 4.11 2102.4 MPa; 73.2 MPa.
3.100 (a) 977 N?m. (b) 8.61 mm. 4.12 61.3 kN.
3.101 (a) 52.1 kip?in. (b) 80.8 kip?in. 4.15 20.4 kip?in.
3.102 tmax 5 145.0 MPa; f 5 19.708. 4.16 106.1 N?m.
3.104 (a) 8.17 mm. (b) 42.18. 4.18 4.63 kip?in.
3.106 (a) 8.028. (b) 14.89 kN?m. 4.19 3.79 kN?m.
3.107 (a) 11.71 kN?m; 3.448. (b) 14.12 kN?m; 4.818. 4.21 (a) 96.5 MPa. (b) 20.5 N?m.
3.110 (a) 5.24 kip?in. (b) 6.888. 4.22 (a) 0.602 mm. (b) 0.203 N?m.
3.111 (a) 1.322 kip?in. (b) 12.60 ksi. 4.23 (a) 145.0 ksi. (b) 384 lb?in.
3.112 2.32 kN?m. 4.24 (a) s 5 75.0 MPa, r 5 26.7 m.
3.113 2.26 kN?m. (b) s 5 125.0 MPa, r 5 9.60 m.
3.114 5.63 ksi. 4.25 (a) 9.17 kN?m (b) 10.24 kN?m.
3.115 14.628. 4.26 (a) 45.1 kip?in. (b) 49.7 kip?in.
3.118 68.0 MPa at inner surface. 4.29 (a) (8y9) h 0. (b) 0.949.
3.119 20.28. 4.30 (a) 1007 in. (b) 3470 in. (c) 0.013208.
3.120 (a) c 0 5 0.1500c. (b) T0 5 0.221tyc 3. 4.31 (a) 139.1 m. (b) 480m.
3.121 0.0505 in. 4.32 (a) [(sx)max y2 rc](y 2 2 c2). (b) 2 (sx)max cy2r.
3.122 68.2 in. 4.33 1.240 kN?m.
3.123 (a) 189.2 N?m; 9.058. (b) 228 N?m; 7.918. 4.34 887 N?m.
3.124 (a) 74.0 MPa; 9.568. (b) 61.5 MPa; 6.958. 4.37 689 kip?in.
3.127 5.07 MPa. 4.38 335 kip?in.
3.128 59.2 MPa. 4.39 (a) 256.0 MPa. (b) 66.4 MPa.
3.129 0.944. 4.40 (a) 256.0 MPa. (b) 68.4 MPa.
3.131 0.198. 4.41 (a) 21.979 ksi. (b) 16.48 ksi.
3.132 0.883. 4.43 8.70 m.
3.133 (a) 1.193 in. (b) 1.170 in. (c) 0.878 in. 4.44 8.59 m.
3.135 (a) 157.0 kN?m. (b) 8.708. 4.45 625 ft.
3.136 (a) 7.52 ksi. (b) 4.618. 4.47 3.87 kip?ft.
3.137 (a) 1007 N?m. (b) 9.278. 4.48 2.88 kip?ft.
3.138 (a) 4.55 ksi. (b) 2.98 ksi. (c) 2.568. 4.49 (a) 212 MPa. (b) 215.59 MPa.
3.139 (a) 5.82 ksi. (b) 2.91 ksi. 4.50 (a) 210 MPa. (b) 214.08 MPa.
3.142 (a) 16.85 N?m. 4.54 (a) 1674 mm 2. (b) 90.8 kN?m.
3.143 8.45 N?m. 4.55 (a) sA 5 6.86 ksi; sB 5 6.17 ksi; sS 5 4.11 ksi. (b) 151.9 ft.
3.144 ta 5 4.73 MPa, tb 5 9.46 MPa. 4.57 (a) 222.5 ksi. (b) 17.78 ksi.
3.146 0.894 in. 4.59 (a) 6.15 MPa. (b) 28.69 MPa.
3.147 (a) 12.76 MPa. (b) 5.40 kN?m. 4.61 (a) 219 MPa. (b) 176.0 MPa.
3.149 (a) 3cyt. (b) 3c 2yt2. 4.63 (a) 6.79 kip?in. (b) 5.59 kip?in.
3.150 (b) 0.25% , 1.000%, 4.00%. 4.64 (a) 4.71 ksi. (b) 5.72 ksi.
3.151 637 kip?in. 4.65 (a) 147.0 MPa. (b) 119.0 MPa.
3.153 12.228. 4.67 (a) 38.4 N?m. (b) 52.8 N?m.
3.155 1.285 in. 4.68 (a) 57.6 N?m. (b) 83.2 N?m.
3.156 (a) 73.7 MPa. (b) 34.4 MPa. (c) 5.068. 4.69 2460 lb?in.
3.157 4.12 kN?m. 4.71 (a) 5.87 mm. (b) 2.09 m.
3.158 (a) 18.80 kW. (b) 24.3 MPa. 4.72 (a) 21.9 mm. (b) 7.81 m.
3.160 7.34 kip?ft. 4.75 (a) 1759 kip?in. (b) 2650 kip?in.
AN-4 Answers to Problems
4.77 (a) 29.2 kN?m. (b) 1.500. 4.170 (a) 282.4 MPa. (b) 36.6 MPa.
4.78 (a) 27.5 kN?m. (b) 1.443. 4.171 (a) 3.06 ksi. (b) 22.81 ksi. (c) 0.529 ksi.
4.79 (a) 2840 kip?in. (b) 1.611. 4.173 13.80 kN?m.
4.80 (a) 4820 kip?in. (b) 1.443. 4.174 8.49 kN?m.
4.81 1.866 kN?m. 4.175 (a) 16.05 ksi. (b) 29.84 ksi.
4.82 19.01 kN?m. 4.177 (a) 41.8 MPa. (b) 220.4 MPa.
4.84 22.8 kip?in. 4.178 27.2 mm.
4.86 212 kip?in. 4.179 107.8 N?m.
4.87 120 MPa. 4.180 (a) 232.5 MPa. (b) 34.2 MPa.
4.88 106.4 MPa. 4.181 (a) 23.65 ksi. (b) 3.72 ksi.
4.91 (a) 106.7 MPa. (b) y0 5 231.2 mm, 0, 31.2 mm. (c) 24.1 m. 4.183 (a) 25.96 ksi. (b) 3.61 ksi.
4.92 (a) 13.36 ksi. (b) y 0 5 21.517 in., 0, 1.517 in. (c) 168.8 ft. 4.184 (a) 26.71 ksi. (b) 3.24 ksi.
4.94 (a) 0.707rY. (b) 6.09rY. 4.185 (a) 63.9 MPa. (b) 252.6 MPa.
4.96 (a) 4.69 m. (b) 7.29 kN?m. 4.191 20.536 ksi.
4.99 (a) 2102.8 MPa. (b) 80.6 MPa. 4.192 67.8 MPa; 281.8 MPa
4.100 (a) 2212 psi. (b) 2637 psi. (c) 21061 psi. 4.194 (a) smax 5 6 M ya 3, 1yr 5 12MyEa 4.
4.101 (a) 22Pypr 2. (b) 25Pypr 2. (b) smax 5 8.49 Mya 3, 1yr 5 12MyEa 4.
4.103 (a) 237.8 MPa. (b) 238.6 MPa. 4.195 48.6 kN?m.
4.105 (a) 288 lb. (b) 209 lb. 4.196 (a) 46.9 MPa. (b) 18.94 MPa. (c) 55.4 m.
4.106 1.994 kN. 4.198 (a) 220.9 ksi. (b) 222.8 ksi.
4.107 14.40 kN. 4.199 60.9 mm.
4.108 16.04 mm. 4.201 (a) 56.7 kN?m. (b) 20.0 mm.
4.109 43.0 kips. 4.202 P 5 75.6 kips T; Q 5 87.1 kips T.
4.110 0.500d. 4.203 (a) sA 5 2½ s; sB 5 s1; sC 5 2s1; sD 5 ½ s1. (b) 4y3 r1.
4.113 7.86 kips T; 9.15 kips c. 4.C1 a 5 4 mm: sa 5 50.6 MPa, ss 5 107.9 MPa.
4.114 5.32 kips T; 10.79 kips c. a 5 14 mm: sa 5 89.7 MPa, ss 5 71.8 MPa.
4.115 (a) 47.6 MPa. (b) 249.4 MPa. (c) 9.80 mm below top of (a) 1 11.6 MPa. (b) 6.61 mm.
section. 4.C2 yY 5 65 mm, M 5 52.6 kN.m, r 5 43.3; yY 5 45 mm,
4.116 (a) 2Py2at. (b) 22Pyat. (c) 2Py2at. M 5 55.6 kN?m, r 5 30.0 m.
4.117 (a) 1125 kN. (b) 817 kN. 4.C3 b 5 308: sA 5 27.83 ksi, sB 5 25.27 ksi,
4.121 (a) 30.0 mm. (b) 94.5 kN. sC 5 7.19 ksi, sD 5 5.91 ksi;
4.122 (a) 5.00 mm. (b) 243 kN. b 5 1208: sA 5 1.557 ksi, sB 5 6.01 ksi,
4.124 P 5 44.2 kips; Q 5 57.3 kips. sC 5 22.67 ksi, sD 5 24.89 ksi.
4.125 (a) 152.3 kips. (b) x 5 0.59 in. (c) 300 m. 4.C4 r 1yh 5 0.529 for 50% increase in smax .
4.127 (a) 23.37 MPa. (b) 218.60 MPa. (c) 3.37 MPa. 4.C5 Prob. 4.10: 2102.4 MPa; 73.2 MPa.
4.128 (a) 9.86 ksi. (b) 22.64 ksi. (c) 29.86 ksi. 4.C6 yY 5 0.8 in.: 76.9 kip?in., 552 in.;
4.129 (a) 229.3 MPa. (b) 2144.8 MPa. (c) 2125.9 MPa. yY 5 0.2 in.: 95.5 kip?in., 138.1 in.
4.130 (a) 0.321 ksi. (b) 20.107 ksi. (c) 0.427 ksi. 4.C7 a 5 0.2 in.: 2 7.27 ksi, a 5 0.8 in.: 2 6.61 ksi.
4.133 (a) 57.8 MPa. (b) 256.8 MPa. (c) 25.9 MPa. For a 5 0.625 in., s 5 2 6.51 ksi.
4.134 (a) 57.48. (b) 75.7 MPa.
4.135 (a) 18.298. (b) 13.74 ksi.
CHAPTER 5
4.137 (a) 10.038. (b) 54.2 MPa.
4.138 (a) 27.58. (b) 5.07 ksi. 5.1 (b) V 5 w(Ly2 2 x); M 5 wx(L 2 x)y2.
4.139 (a) 32.98. (b) 61.4 MPa. Pb
5.2 (b) A to B: V 5 ; M 5 PbxyL.
4.141 113.0 MPa. L
4.143 10.46 ksi. B to C: V 5 PayL; M 5 Pa (L 2 x)yL.
4.144 (a) sA 5 31.5 MPa; sB 5 210.39 MPa. 5.3 (b) V 5 w 0Ly2 2 w0 x2y2L; M 5
(b) 94.0 mm above point A. 2 w 0L2y3 1 w 0Lxy2 2 w 0x 3y6L
4.145 (a) 17.11 mm. 5.4 (b) V 5 w(L 2 x); M 5 wy2 (L 2 x)2.
4.146 0.1638 in. 5.5 (b) (0 , x , a): V 5 2P; M 5 Px. (a , x , 2a): V 5 2P;
4.147 53.9 kips. M 5 22Px 1 Pa.
4.150 29.1 kip?in. 5.6 (b) A to B: V 5 w(a 2 x); M 5 w(ax 2 x 2y2).
4.151 29.1 kip?in. B to C: V 5 0; M 5 wa 2y2.
4.152 733 N?m. C to D: V 5 w(L 2 x 2 a); M 5 w[a(L 2 x) 2 (L 2 x)2y2].
4.153 1.323 kN?m. 5.7 (a) 3.00 kN. (b) 0.800 kN?m.
4.155 900 N?m. 5.8 (a) 150.0 lb. (b) 1500 lb?in.
4.161 (a) 277.3 MPa. (b) 255.7 MPa. 5.9 (a) 62.5 kN. (b) 47.6 kN?m.
4.162 sA 5 265.1 MPa; sB 5 39.7 MPa. 5.11 (a) 3.45 kN. (b) 1125 N?m.
4.163 (a) 12.19 ksi. (b) 11.15 ksi. 5.12 (a) 2000 lb. (b) 19200 lb?in.
4.164 sA 5 10.77 ksi; sB 5 23.22 ksi. 5.13 (a) 900 N. (b) 112.5 N?m.
4.167 655 lb. 5.15 10.89 MPa.
4.169 73.2 mm. 5.16 950 psi.
Answers to Problems AN-5
5.18 139.2 MPa. 5.96 W27 3 84.
5.20 9.90 ksi. 5.97 123.2%.
5.21 14.17 ksi. 5.98 (a) V 5 2w0 x 1 w0 Kx 2 al1; M 5 w 0x2y2 1 (w0y2) kx 2 al 2.
5.23 0 V 0 max 5 342 N; 0M 0 max 5 51.6 N?m; s 5 17.19 MPa. (b) 23 w0 a2y2.
5.25 10.34 ksi. 5.100 (a) V 5 2w 0x 1 w0 x2y2a 2 (w 0y2a)kx 2 al2;
5.26 0 V 0 max 5 6.00 kN; 0M 0 max 5 4.00 kN?m; smax 5 14.29 MPa. M 5 2w0x 2y2 1 w0x 3y6a 2 (w0y6a)kx 2 al 3.
5.27 (a) 10.67 kN. (b) 9.52 MPa. (b) 25 w 0 a2y6.
5.29 (a) 866 mm. (b) 99.2 MPa. 5.102 (a) V 5 2w 0 kx 2 al1 23w0 ay4 1 (15 w 0 ay4)kx 2 2al 0;
5.30 (a) 819 mm. (b) 89.5 MPa. M 5 2(w0y2)kx 2 al2 2 3w0 axy4 1
5.31 (a) 3.09 ft. (b) 12.95 ksi. (15 w0 ay4)kx22al1.
5.32 1.021 in. (b) 2w0 a2y2.
5.33 (a) 33.3 mm. (b) 6.66 mm. 5.103 (a) V 5 1.25 P 2 Pkx2al 0 2 Pkx 2 2al 0;
5.34 See 5.1. M 5 1.25 Px 2 Pkx 2 al1 2 Pkx 2 2al1.
5.35 See 5.2. (b) 0.750 Pa.
5.36 See 5.3. 5.104 (a) V 5 2Py2 2 Pkx 2 al 0; M 5 Pxy2 2 Pkx 2 al1 1
5.37 See 5.4. Pa 1 Pakx 2 al 0.
5.38 See 5.5. (b) 3 Pay2.
5.39 See 5.6. 5.105 (a) V 5 2Pkx 2 al 0; M 5 2Pkx 2 al1 2 Pakx2al 0. (b) 2Pa.
5.40 See 5.7. 5.106 (a) V 5 40 2 48kx 2 1.5l0 2 60kx 2 3.0l 0 1 60kx 2 3.6l 0 kN;
5.41 See 5.8. M 5 40x 2 48kx 2 1.5l1 2 60kx 2 3.0l1 1
5.42 See 5.9. 60kx 2 3.6l1 kN?m.
5.43 See 5.10. (b) 60.0 kN?m.
5.46 See 5.15. 5.107 (a) V 5 23 1 9.75kx 2 3l 0 2 6kx 2 7l 0 2 6kx 2 11l 0 kips;
5.47 See 5.16. M 5 23x 1 9.75kx 2 3l1 2 6kx 2 7l1 2 6kx 2 11l1 kip?ft.
5.48 See 5.18. (b) 21.0 kip?ft.
5.49 See 5.20. 5.108 (a) V 5 62.5 2 25kx 2 0.6l1 1 25kx 2 2.4l1 2
5.52 (a) V 5 (w0Lyp) cos(pxyL); M 5 (w0L2yp2) sin (pxyL). 40kx 2 0.6l 0 2 40kx 2 2.4l 0 kN;
(b) w 0L2yp2. M 5 62.5x 2 12.5kx 2 0.6l2 1 12.5kx 2 2.4l2 2
5.53 (a) V 5 w 0 (L 2 2 3x2)y6L; M 5 w 0(Lx 2 x 3yL)y6. 40kx 2 0.6l1 2 40kx 2 2.4l1 kN?m
(b) 0.0642 w0L2. (b) 47.6 kN?m.
5.54 0 V 0 max 5 15.75 kips; 0 M 0 max 5 27.8 kip?ft; s 5 13.58 ksi. 5.109 (a) V 5 13 2 3x 1 3kx 2 3l1 2 8kx 2 7l 0 2 3kx 2 11l1 kips;
5.55 0 V 0 max 5 16.80 kN; 0 M 0 max 5 8.82 kN?m; s 5 73.5 MPa. M 5 13x 2 1.5x 2 1 1.5kx 2 3l2 2 8kx 2 7l1 2
5.56 0 V 0 max 5 20.7 kN; 0 M 0 max 5 9.75 kN?m; s 5 60.2 MPa. 1.5kx 2 11l 2 kip?ft.
5.58 0 V 0 max 5 1400 lb; 0 M 0 max 5 19.20 kip?in; s 5 6.34 ksi. (b) 41.5 kip?ft.
5.59 0 V 0 max 5 76.0 kN; 0 M 0 max 5 67.3 kN?m; s 5 68.5 MPa. 5.110 (a) V 5 30 224kx 2 0.75l 0 2 24kx 2 1.5l 0 2
5.60 0 V 0 max 5 48.0 kN; 0 M 0 max 5 12.00 kN?m; s 5 62.2 MPa. 24kx 2 2.25l 0 1 66kx 2 3l 0 kN;
5.61 0 V 0 max 5 30.0 lb; 0 M 0 max 5 24.0 lb?ft; s 5 6.95 ksi. M 5 30x 2 24kx 2 0.75l1 2 24kx 2 1.5l1 2
5.63 (a) 0 V 0 max 5 24.5 kips; 0 M 0 max 5 36.3 kip?ft; (b) 15.82 ksi. 24kx 2 2.25l1 1 66kx 2 3l1 kN?m.
5.64 0 V 0 max 5 1150 N; 0 M 0 max 5 221 N?m; P 5 500 N; Q 5 250 N. (b) 87.7 MPa.
5.65 h . 173.2 mm. 5.114 (a) 122.7 kip?ft at x 5 6.50 ft. (b) W16 3 40.
5.68 b . 6.20 in. 5.115 (a) 121.5 kip?ft at x 5 6.00 ft. (b) W16 3 40.
5.69 h . 203 mm. 5.118 0V 0 max 5 35.6 kN; 0 M 0 max 5 25.0 kN?m.
5.70 b . 48.0 mm. 5.119 0V 0 max 5 89.0 kN; 0 M 0 max 5 178.0 kN?m.
5.71 W21 3 62. 5.120 0V 0 max 5 15.30 kips; 0 M 0 max 5 38.0 kip?ft.
5.72 W27 3 84. 5.122 (a) 0 V 0 max 5 13.80 kN; 0 M 0 max 5 16.16 kN?m. (b) 83.8 MPa.
5.73 W530 3 92. 5.123 (a) 0 V 0 max 5 40.0 kN; 0M 0 max 5 30.0 kN?m. (b) 40.0 MPa.
5.74 W250 3 28.4. 5.124 (a) 0 V 0 max 5 3.84 kips; 0 M 0 max 5 3.80 kip?ft. (b) 0.951 ksi.
5.76 S15 3 42.9. 5.126 (a) h 5 h 0 [(xyL) (1 2 xyL)]1/2. (b) 4.44 kip?in.
5.77 S510 3 98.2. 5.127 (a) h 5 h 0 (xyL)1/2. (b) 20.0 kips.
5.79 9 mm. 5.128 (a) h 5 h 0 (xyL)3/2. (b) 167.7 mm.
5.80 C180 3 14.6. 5.130 (a) h 5 h 0 22x/L. (b) 60.0 kN.
5.81 C9 3 15. 5.132 l2 5 6.00 ft; l 2 5 4.00 ft.
5.82 3y8 in. 5.134 1.800 m.
5.83 W610 3 101. 5.135 1.900 m.
5.84 W24 3 68. 5.136 d 5 d 0 (2xyL)1/3 for 0 ≤ x ≤ Ly2;
5.85 176.8 kNym. d 5 d 0 [2 (L 2 x)yL]1/3 for Ly2 ≤ x ≤ L.
5.86 108.8 kNym. 5.139 (a) b 5 b 0 (1 2 xyL)2. (b) 160.0 lbyin.
5.89 (a) 1.485 kNym. (b) 1.935 m. 5.140 (a) 155.2 MPa. (b) 143.3 MPa.
5.91 (a) S15 3 42.9. (b) W27 3 84. 5.141 (a) 25.0 ksi. (b) 18.03 ksi.
5.92 (a) 6.49 ft. (b) W16 3 31. 5.143 193.8 kN.
5.94 383 mm. 5.144 (a) 152.6 MPa. (b) 133.6 MPa.
5.95 336 mm. 5.145 (a) 4.49 m. (b) 211. mm.
AN-6 Answers to Problems
5.147 (a) 11.16 ft. (b) 14.31 in. 6.59 (a) 0.888 ksi. (b) 1.453 ksi.
5.149 (a) 240 mm. (b) 150.0 MPa. 6.61 0.345a.
5.150 (a) 15.00 in. (b) 320 lbyin. 6.62 0.714a.
5.151 (a) 30.0 in. (b) 12.80 kips. 6.63 1.250a.
5.152 (a) 85.0 N. (b) 21.3 N?m. 6.64 3(b 2 2 a2)y[6(a 1 b) 1 h].
5.154 (a) 1.260 ft. (b) 7.24 ksi. 6.65 (a) 19.06 mm. (b) tA 5 0; (tB)AB 5 50.5 MPa;
5.156 0 V 0 max 5 200 kN; 0 M 0 max 5 300 kN?m; 136.4 MPa. (tB)BD 5 25.3 MPa; tc 5 59.0 MPa.
5.158 h . 14.27 in. 6.68 (a) 10.22 mm. (b) 0 at B and E; 41.1 MPa at A;
5.159 W27 3 84. 68.5 MPa just above D; 13.71 MPa just to the right of D;
5.161 (a) 225.6 kN?m at x 5 3.63 m. 77.7 MPa just below D; 81.8 MPa at center of DF.
(b) 60.6 MPa. 6.69 0.727 in.
5.163 (a) b 0 (1 2 xyL). (b) 20.8 mm. 6.70 20.2 mm.
5.C4 For x 5 13.5 ft: M1 5 131.25 kip?ft; 6.71 1.265 in.
M2 5 156.25 kip?ft; MC 5 150.0 kip?ft. 6.72 6.14 mm.
5.C6 Prob. 5.112: VA 5 29.5 kN, Mmax 5 28.3 kN?m, 6.75 2.37 in.
at 1.938 m from A. 6.76 21.7 mm.
6.77 40.0 mm.
6.78 3.75 in.
CHAPTER 6 6.81 (maximum) Pyat.
6.1 60.0 mm. 6.82 (maximum) 1.333 Pyat.
6.2 2.00 kN. 6.83 (a) 144.6 N?m. (b) 65.9 MPa.
6.3 326 lb. 6.84 (a) 144.6 N?m. (b) 106.6 MPa.
6.4 (a) 155.8 N. (b) 329 kPa. 6.87 (maximum) 0.428 ksi at B9.
6.5 193.5 kN. 6.88 (maximum) 1.287 ksi at C9.
6.7 10.56 ksi. 6.89 738 N.
6.9 (a) 8.97 MPa. (b) 8.15 MPa. 6.90 (a) 17.63 MPa. (b) 13.01 MPa.
6.11 (a) 13.15 ksi. (b) 11.16 ksi. 6.91 143.3 kips.
6.12 (a) 3.17 ksi. (b) 2.40 ksi. 6.93 189.6 lb.
6.13 114.0 kN. 6.94 (a) 41.4 MPa. (b) 41.4 MPa.
6.15 1733 lb. 6.96 53.9 kips.
6.17 (a) 84.2 kips. (b) 60.2 kips. 6.97 (a) 146.1 kNym. (b) 19.99 MPa.
6.18 87.3 mm. 6.99 40.0 mm.
6.19 (b) h 5 320 mm; b 5 97.7 mm. 6.100 0.433 in.
6.21 (a) 1.745 ksi. (b) 2.82 ksi. 6.C1 (a) h 5 173.2 mm. (b) h 5 379 mm.
6.22 (a) 31.0 MPa. (b) 23.2 MPa. 6.C2 (a) L 5 37.5 in.; b 5 1.250 in.
6.23 3.21 ksi. (b) L 5 70.3 in.; b 5 1.172 in.
6.24 32.7 MPa. (c) L 5 59.8 in.; b 5 1.396 in.
6.26 (a) Line at mid-height. (b) 2.00. 6.C4 (a) tmax 5 2.03 ksi; tB 5 1.800 ksi. (b) 194 psi.
6.28 (a) Line at mid-height. (b) 1.500. 6.C5 Prob. 6.66: (a) 2.67 in. (b) tB 5 0.917 ksi;
6.29 1.672 in. tD 5 3.36 ksi; tmax 5 4.28 ksi.
6.30 10.79 kN.
6.31 (a) 59.9 psi. (b) 79.8 psi.
CHAPTER 7
6.32 (a) 379 kPa. (b) 0.
6.35 (a) 95.2 MPa. (b) 112.8 MPa. 7.1 s 5 9.46 ksi; t 5 1.013 ksi.
6.36 (a) 101.6 MPa. (b) 79.9 MPa. 7.2 s 5 32.9 MPa; t 5 71.0 MPa.
6.37 ta 5 33.7 MPa; tb 5 75.0 MPa; tc 5 43.5 MPa. 7.3 s 5 10.93 ksi; t 5 0.536 ksi.
6.38 (a) 40.5 psi. (b) 55.2 psi. 7.4 s 5 20.521 MPa; t 5 56.4 MPa.
6.40 ta 5 0; tb 5 1.262 ksi; tc 5 3.30 ksi; 7.5 (a) 237.08, 53.08. (b) 213.60 MPa. (c) 286.4 MPa.
td 5 6.84 ksi; te 5 7.86 ksi. 7.7 (a) 2 26.68; 63.48. (b) 190.0 MPa, 210.00 MPa.
6.42 (a) 18.23 MPa. (b) 14.59 MPa. (c) 46.2 MPa. 7.9 (a) 8.08, 98.08. (b) 36.4 MPa. (c) 250.0 MPa.
6.43 7.19 ksi. 7.10 (a) 226.68, 63.48. (b) 5.00 ksi. (c) 6.00 ksi.
6.44 9.05 mm. 7.11 (a) 18.48, 108.48. (b) 100.0 MPa. (c) 90.0 MPa.
6.45 0.371 in. 7.12 (a) 231.08, 59.08 (b) 17.00 ksi. (c) 3.00 ksi.
6.46 83.3 MPa. 7.13 (a) sx9 5 22.40 ksi; tx9y9 5 0.1498 ksi; sy9 5 10.40 ksi.
6.48 ta 5 10.76 MPa; tb 5 0; tc 5 11.21 MPa; (b) sx9 5 1.951 ksi; tx9y9 5 6.07 ksi; sy9 5 6.05 ksi.
td 5 22.0 MPa; te 5 9.35 MPa. 7.15 (a) sx9 5 9.02 ksi; tx9y9 5 3.80 ksi; sy9 5 213.02 ksi.
6.49 (a) 50.9 MPa. (b) 62.4 MPa. (b) sx9 5 5.34 ksi; tx9y9 5 29.06 ksi; sy9 5 29.34 ksi.
6.51 1.4222 in. 7.17 (a) 217 psi. (b) 2125.0 psi.
6.52 10.53 ksi. 7.18 (a) 20.300 MPa. (b) 22.92 MPa.
6.56 (a) 6.73 MPa. (b) 1.515 MPa. 7.19 16.58 kN.
6.57 (a) 23.3 MPa. (b) 109.7 MPa. 7.21 (a) 18.48. (b) 16.67 ksi.
6.58 (a) 1.323 ksi. (b) 1.329 ksi. 7.23 (a) 18.98, 108.98, 18.67 MPa, 2158.5 MPa. (b) 88.6 MPa.
Answers to Problems AN-7
7.24 (a) 25.1 ksi, 20.661 ksi, 12.88 ksi. 7.129 Px9 5 115.0 m; Py9 5 285 m; gx9y9 5 25.72 m.
7.25 5.12 ksi, 21.640 ksi, 3.38 ksi. 7.131 Px9 5 36.7 m; Py9 5 283 m; gx9y9 5 227 m.
7.26 12.18 MPa, 248.7 MPa; 30.5 MPa. 7.132 Px9 5 2653 m; Py9 5 303 m; gx9y9 5 2829 m.
7.27 205 MPa. 7.133 Px9 5 115.0 m; Py9 5 285 m; gx9y9 5 25.72 m.
7.29 (a) 22.89 MPa. (b) 12.77 MPa, 1.226 MPa. 7.135 Px9 5 36.7 m; Py9 5 283 m; gx9y9 5 227 m.
7.53 (a) 28.66 MPa. (b) 17.00 MPa, 23.00 MPa. 7.136 (a) 233.78, 56.38; 2420 m, 100 m, 160 m.
7.55 33.88, 123.88; 168.6 MPa, 6.42 MPa. (b) 520 m. (c) 580 m.
7.56 08, 908; s0, 2s0. 7.137 (a) 230.18, 59.98; 2702 m, 2298 m, 500 m. (b) 403 m.
7.57 2308, 608; 223 t0, 23 t0. (c) 1202 m.
7.58 2120.0 MPa ≤ txy ≤ 120.0 MPa. 7.139 (a) 226.68, 64.48; 2150.0 m, 750 m, 2300 m. (b) 900 m.
7.59 2141.4 MPa ≤ txy ≤ 141.1 MPa. (c) 1050 m.
7.61 16.58 ≤ u ≤ 110.18. 7.140 (a) 7.88, 97.88; 56.6 m, 243 m, 0. (b) 186.8 m.(c) 243 m.
7.62 25.18 ≤ u ≤ 132.08. 7.141 (a) 121.08, 31.08; 513 m, 87.5 m, 0. (b) 425 m.(c) 513 m.
7.63 (a) 33.78, 123.78. (b) 18.00 ksi. (c) 6.50 ksi. 7.143 (a) 127.98, 37.98; 2383 m, 257.5 m, 0. (b) 325 m.(c) 383 m.
7.65 (b) 0 txy 0 5 2sx sy 2 smax smin. 7.146 (a) 2300 3 1026 in.yin. (b) 435 3 1026 in.yin., 2315 3
7.66 (a) 13.00 ksi. (b) 15.00 ksi. 1026 in.yin.; 750 3 1026 in.yin.
7.68 (a) 94.3 MPa. (b) 105.3 MPa. 7.149 (a) 30.08, 120.08; 560 3 1026 in.yin, 2140.0 3 1026 in.yin.
7.69 (a) 100.0 MPa. (b) 110.0 MPa. (b) 700 3 1026 in.yin.
7.70 (a) 91.0 MPa. (b) 91.0 MPa. (c) 108.0 MPa. 7.150 P 5 69.6 kips; Q 5 30.3 kips.
7.71 (a) 113.0 MPa. (b) 91.0 MPa. (c) 143.0 MPa. 7.151 P 5 34.8 kips; Q 5 38.4 kips.
7.73 (a) 18.5 ksi. (b) 13.00 ksi. (c) 11.00 ksi. 7.154 1.421 MPa.
7.74 (a) 66.00 ksi. (b) 611.24 ksi. 7.155 1.761 MPa.
7.75 660.0 MPa. 7.156 222.58, 67.58; 426 m, 2952 m, 2224 m.
7.77 2.00 ksi; 9.33 ksi. 7.157 232.18, 57.98; 270.9 MPa, 229.8 MPa.
7.79 240.0 MPa; 130.0 MPa. 7.158 24.76 ksi; 20.467 ksi.
7.80 (a) 45.7 MPa. (b) 92.9 MPa. 7.159 (a) 47.9 MPa. (b) 102.7 MPa.
7.81 (a) 1.228. (b) 1.098. (c) Yielding occurs. 7.161 uy2, (u 1 p)y2; s0 1 s0 cos u, s0 2s0 cos u.
7.82 (a) 1.083. (b) Yielding occurs. (c) Yielding occurs. 7.163 (a) 40.0 MPa. (b) 72.0 MPa.
7.83 (a) 1.287. (b) 1.018. (c) Yielding occurs. 7.164 (a) 1.286. (b) 1.018. (c) Yielding occurs.
7.84 (a) 1.119. (b) Yielding occurs. (c) Yielding occurs. 7.165 smax 5 45.1 MPa; tmax (in-plane) 5 9.40 MPa.
7.87 8.19 kip?in. 7.167 3.43 ksi (compression).
7.88 9.46 kip?in. 7.169 415 3 1026 in.yin.
7.89 Rupture will occur. 7.C1 Prob. 7.14: (a) 256.2 MPa, 86.2 MPa, 238.2 MPa.
7.90 Rupture will occur. (b) 245.2 MPa, 75.2 MPa, 53.8 MPa.
7.91 No Rupture. Prob. 7.16: (a) 24.0 MPa, 2104.0 MPa, 21.50 MPa.
7.92 Rupture will occur. (b) 219.51 MPa, 260.5 MPa, 260.7 MPa.
7.94 68.49 MPa. 7.C4 Prob. 7.93: Rupture occurs at t0 5 3.67 ksi.
7.95 50.0 MPa. 7.C6 Prob. 7.138: (a) 221.68, 68.48; 279m, 2599m, 160.0m.
7.96 196.9 N?m. (b) 877m. (c) 877m.
7.98 (a) 1.290 MPa. (b) 0.852 mm. 7.C7 Prob. 7.142: (a) 11.38, 101.38; 310m, 50.0m, 0.
7.100 5.49. (b) 260m. (b) 310m.
7.102 10.25 ksi; 5.12 ksi. 7.C8 Prob. 7.144: Px 5 253m; Py 5 307; gxy 5 2893.
7.103 2.94 MPa. Pa 5 727m; Pb 5 2167.2; gmax 5 2894.
7.104 12.76 m. Prob. 7.145: Px 5 725m; Py 5 275.0; gxy 5 173.2.
7.105 smax 5 113.7 MPa; tmax 5 56.8 MPa. Pa 5 734m; Pb 5 284.3; gmax 5 819.
7.106 smax 5 136.0 MPa; tmax 5 68.0 MPa.
7.108 smax 5 78.5 MPa; tmax 5 39.3 MPa. CHAPTER 8
7.109 251 psi.
7.111 0.307 in. 8.1 (a) 10.69 ksi. (b) 19.18 ksi. (c) Not acceptable.
7.112 3.29 MPa. 8.2 (a) 10.69 ksi. (b) 13.08 ksi. (c) Acceptable.
7.113 3.80 MPa. 8.3 (a) 94.6 MPa. (b) 93.9 MPa. (c) Acceptable.
7.114 (a) 44.2 MPa. (b) 15.39 MPa. 8.4 (a) 91.9 MPa. (b) 95.1 MPa. (c) Acceptable.
7.115 56.88. 8.5 (a) W 310 3 38.7. (b) 147.8 MPa; 18.18 MPa; 140.2 MPa.
7.117 (a) 3750 psi. (b) 1079 psi. 8.6 (a) W 690 3 125. (b) 118.2 MPa; 34.7 MPa; 122.3 MPa.
7.118 387 psi. 8.9 (a) 137.5 MPa. (b) 129.5 MPa.
7.120 (a) 3.15 ksi. (b) 1.9993 ksi. 8.11 (a) 17.90 ksi. (b) 17.08 ksi.
7.121 (a) 1.486 ksi. (b) 3.16 ksi. 8.12 (a) 19.39 ksi. (b) 20.7 ksi.
7.122 smax 5 68.6 MPa; tmax 5 34.3 MPa. 8.13 (a) 131.3 MPa. (b) 135.5 MPa.
7.124 smax 5 77.4 MPa; tmax 5 38.7 MPa. 8.15 41.2 mm.
7.126 (a) 5.64 ksi. (b) 282 psi. 8.19 873 lb.
7.127 (a) 2.28 ksi. (b) 228 psi. 8.20 1.578 in.
7.128 Px9 5 2653 m; Py9 5 303 m; gx9y9 5 2829 m. 8.22 (a) H : 6880 psi; K : 6760 psi. (b) H : 7420 psi; K : 7010 psi.
AN-8 Answers to Problems
10.62 (a) 26.6 kN. (b) 33.0 kN. 11.3 (a) 177.9 kJym3. (b) 712 kJym3. (c) 160.3 kJym3.
10.64 76.8 kips. 11.5 (a) 58.0 in ? lbyin 3. (b) 20.0 in ? kipyin 3.
10.65 76.3 kips. 11.6 (a) 1296 kJym3. (b) 90.0 MJym3.
10.66 1596 kN. 11.7 (a) 1.750 MJym3. (b) 71.2 MJym3.
10.68 173.5 kips. 11.9 (a) 176.2 in ? lb.
10.69 (a) 66.3 kN. (b) 243 kN. (b) uAB 5 11.72 in ? lbyin 3; uBC 5 5.65 in ? lbyin 3.
10.71 123.1 mm. 11.10 (a) 12.18 J. (b) u AB 5 15.83kJym3; uBC 5 38.6 kJym3.
10.72 6.53 in. 11.11 (a) 168.8 in ? lb.
10.74 1.615 in. (b) uCD 5 0.882 in ? lbyin 3; uEF 5 5.65 in ? lbyin 3.
10.75 22.3 mm. 11.12 0.846 J.
10.77 W200 3 46.1. 11.15 (a) 3.28. (b) 4.25.
10.78 W14 3 82. 11.17 102.7 in ? lb.
10.79 W10 3 54. 11.18 1.398 P 2lyEA.
10.80 (a) 30.1 mm. (b) 33.5 mm. 11.20 2.37 P 2lyEA.
10.83 L89 3 64 3 12.7. 11.21 0.233 P 2lyEA.
10.84 56.1 kips. 11.23 6.68 kip ? in.
10.86 (a) PD 5 433 kN; PL 5 321 kN. 11.24 W2 L5y40 EI.
(b) PD 5 896 kN; PL 5 664 kN. 11.25 (P 2 a2y6 EI) (a 1 L).
10.87 W310 3 74. 11.27 (M02y6 EIL2) (a 3 1 b3).
10.88 5y16 in. 11.28 89.5 in ? lb.
10.89 76.7 kN. 11.30 1048 J.
10.91 (a) 18.26 kips. (b) 14.20 kips. 11.31 670 J.
10.92 (a) 21.1 kips. (b) 18.01 kips. 11.33 12.70 J.
10.93 (a) 329 kN. (b) 280 kN. 11.37 (a) No yield. (b) Yield occurs.
10.95 (a) 0.698 in. (b) 2.11 in. 11.39 (a) 2.33. (b) 2.02.
10.97 16.44 ft. 11.40 (2M 20 L y Ebd 3) (1 1 3Ed2y10GL 2).
10.99 5.48 m. 11.41 (Q 2y4pGL) ln (R 2 y R1).
10.100 4.81 m. 11.42 24.7 mm.
10.101 1.021 m. 11.43 25.5 ftysec.
10.102 1.175 m. 11.44 9.12 lb.
10.103 83.4 mm. 11.45 841 mm.
10.104 87.2 mm. 11.48 11.09 ftys.
10.105 12.00 mm. 11.50 (a) 7.54 kN. (b) 41.3 MPa. (c) 3.18 mm.
10.106 15.00 mm. 11.51 (a) 9.60 kN. (b) 32.4 MPa. (c) 2.50 mm.
10.107 140.0 mm. 11.52 (a) 15.63 mm. (b) 83.8 N?m. (c) 208 MPa.
10.109 1.882 in. 11.53 (a) 7.11 mm. (b) 140.1 MPa.
10.110 1.735 in. 11.54 (a) 0.903 in. (b) 511 lb?in. (c) 21.3 ksi.
10.111 t 5 ¼ in. 11.56 (b) 7.12.
10.113 W14 3 145. 11.57 (b) 0.152.
10.114 W14 3 68. 11.58 Pa 2b 2y3EI T.
10.116 W250 3 58. 11.59 Pa 2 (a 1 L)y3EI .
10.117 (a) 647 lb. (b) 0.651 in. (c) 58.8%. 11.61 M0 (L 1 3a)y3EI c.
10.118 k . 4.91 kNym. 11.62 3PL 3y16 EI T.
10.120 (a) 47.28. (b) 1.582 kips. 11.63 3Pa 3y4 EI T.
10.121 2.44. 11.65 M0Ly16 EI c.
10.123 DT 5 p2b 2y12L2 a. 11.66 59.8 mm T.
10.125 107.7 kN. 11.67 32.4 in.
10.126 W250 3 67. 11.68 3.128.
10.128 (a) 0.0987 in. (b) 0.787 in. 11.72 2.38PlyEA S.
10.C1 r 5 8 mm: 9.07 kN. r 5 16 mm: 70.4 kN. 11.73 0.650 in. T.
10.C2 b 5 1.0 in.: 3.85 kips. b 5 1.375 in.: 6.07 kips. 11.75 0.366 in. T.
10.C3 h 5 5.0 m: 9819 kg. h 5 7.0 m: 13,255 kg. 11.76 1.111 mm T.
10.C4 P 5 35 kips: (a) 0.086 in.; (b) 4.69 ksi. 11.77 (a) and (b) P 2L 3y6 EI 1 PM0L2y2EI 1 M02Ly2 EI.
P 5 55 kips: (a) 0.146 in.; (b) 7.65 ksi. 11.78 (a) and (b) P 2L 3y48 EI 1 M0PL 2y8EI 1 M02 Ly2 EI.
10.C6 Prob. 10.113: Pall 5 282.6 kips. 11.80 (a) and (b) 5 M02Ly4 EI.
Prob. 10.114: Pall 5 139.9 kips. 11.82 (a) and (b) M02 Ly2 EI.
11.83 0.0443wL 4yEI T.
11.85 wL 4y768 EI c.
CHAPTER 11
11.86 7wL 3y48 EI a.
11.1 (a) 43.1 in ? lbyin 3. (b) 72.8 in ? lbyin 3. 11.88 wL 3y384 EI a.
(c) 172.4 in ? lbyin 3. 11.89 (Paby6EIL2) (3La 1 2a2 1 2b 2) c.
11.2 (a) 21.6 kJym 3. (b) 336 kJym3, (c) 163.0 kJym3. 11.90 M0Ly6 EI c.
Answers to Problems AN-11
11.91 0.329 in. T. 11.119 0.652P.
11.93 5.12 mm T. 11.121 2Py3.
11.94 7.25 mm T. 11.123 136.6 J.
11.95 7.07 3 1023 rad c. 11.124 1.767 in ? kip.
11.96 3.80 mm T. 11.126 4.76 kg.
11.97 2.07 3 1023 rad a. 11.129 2.558.
11.99 xC 5 0, yC 5 2.80 PLyEA T. 11.130 11.57 mm T.
11.101 0.1613 in. T. 11.134 0.807 in . T.
11.102 0.01034 in. d . 11.C2 (a) a 5 15 in.: sD 5 17.19 ksi, sC 5 21.0 ksi;
11.103 0.1459 mm T. a 545 in.: sD 5 36.2 ksi, sC 5 14.74 ksi.
11.105 (a) PL 3y6EI T. (b) 0.1443 PL 3yEI. (b) a 5 18.34 in., s 5 20.67 ksi.
11.106 pPR 3y2 EI T. 11.C3 (a) L 5 200 mm: h 5 2.27 mm;
11.107 (a) PR 3y2 EI S. (b) pPR 3y4 EI T. L 5 800 mm: h 5 1.076 mm.
11.109 5PL 3y6EI. (b) L 5 440 mm: h 5 3.23 mm.
11.111 5Py16 c. 11.C4 a 5 300 mm: 1.795 mm, 179.46 MPa;
11.112 3M0y2L c. a 5 600 mm: 2.87 mm, 179.59 MPa.
11.113 3M0 b(L 1 a) y2L 3 c. 11.C5 a 5 2 m: (a) 30.0 J; (b) 7.57 mm, 60.8 J.
11.114 7wLy128 c. a 5 4 m: (a) 21.9 J; (b) 8.87 mm, 83.4 J.
11.117 Py(1 1 2 cos 3 f). 11.C6 a 5 20 in: (a) 13.26 in.; (b) 99.5 kip ? in.; (c) 803 lb.
11.118 7Py8. a 5 50 in: (a) 9.46 in.; (b) 93.7 kip ? in.; (c) 996 lb.