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226 STRENGTH OF MATERIALS. (d) In this case /= 5, and the maximum bending moment is M: Hence, from formula T4, wr ST %ST ^, , ,„ %ST , 8X120,000X280.466 Therefore, W = w I = ). — ' , ,^^ , iti^tt. 20,290 72 ; A=bd=^\. lb. Ans. Ifc (599) {a) According to formula 72, 420 X 5 X 6,319 /= A r\ or r = 1^ = j/|^ == 4/3 = 1.732. Ans. Scale of forces 1=960 lb. Scale of distance 1=8' PiG.se. (d) From the table of Moments of Inertia, 7=—^ d^' ^^ Dividing, bd = 24'°'" 12'' 36 ; ^ = 6' and b = 4'. Ans. = 3.
STRENGTH OF MATERIALS. 227 Tzd' {c) As above, r=>|/^=/iL = /|=^. Ans. i)d (600) Using formula 69, pd—^^tS, we have t = ^. Using a factor of safety of 0, ^, 4/5 ^ epd 6X100X8 _, . ^^=^'^^^^ ir= 4X20,000 =-^^- ^"^- (601) The graphic solution is shown in Fig. 52. The uniform load is divided into 14 equal parts, and lines drawn through the center of gravity of each part. These loads are laid off on the line through the left reaction, the pole P chosen, and the rays drawn. The polygon b c d e f a is then drawn in the usual manner. The shear diagram is drawn as shown. The maximum shear is either t T ox r v ^=- 540 lb. The maximum moment is shown by the polygon to be at /"r vertically above the point ?/, where the shear line crosses the shear axis. The pole distance /*7 is 1,440 1b. to the scale of forces, and the intercept/"^ is 14 inches to the scale of distances. Hence, the bending moment is 20,160 in. -lb. (602) From formula 74, Any ^=-p*- = 20,160. 5. = 9,000;/= 8. _,, / 20,160X8 _ ^- =^^-^^' ^^^"'r= 9,000 But, — = ^^. . z=i —bd"^ for a rectangle. c ^d 6 Hence, i^^' = 17.92, ot bd' = 107.52. number of beams will fulfil this condition. Assuming d=iQ', b— — -^ — = 3', nearly. Assuming d=h\ b = — ^ — = 4.3'. (603) Using the factor of safety of 10, in formula 71, y~ 10 Id 108x2.5
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( W v. 5 Copyright, 1897, by The Co
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Arithmetic, - CONTENTS Algebra, Log
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i ARITHMETIC. of tens. 1 + 8 + 7 +
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4 ARITHMETIC. and the difference (4
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ARITHMETIC. (c) 217 Multiply any tw
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8 ARITHMETIC. 72 in the dividend an
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10 ARITHMETIC. (70 X 50 X 24 X 20).
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12 ARITHMETIC, The 5 in the dividen
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14 ARITHMETIC. (22) (a) 576) 589824
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16 ARITHMETIC. (33) To reduce a fra
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18 ARITHMETIC. 3 3 (e) 15-r-7-43-=
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20 ARITHMETIC. (41) ,9| + 50i + 41+
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22 ARITHMETIC. (45) The man evident
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24 ARITHMETIC. • u s o e 3 2 o 93
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26 ARITHMETIC. {b) Here again the p
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28 ARITHMETIC. 64) 1.000000(. 01562
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30 ARITHMETIC. (66) In subtraction
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38 ARITHMETIC. (6) .875 — 5-=? Re
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84 ARITHMETIC. {c) First perform th
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36 ARITHMETIC. Reducing 387 387 to
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38 ARITHMETIC. nominator of the fra
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40 ARITHMETIC. (d) Base = percentag
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42 ARITHMETIC. Another method of so
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44 ARITHMETIC. (89) Here we have gi
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46 ARITHMETIC. 24 ) 13750 gr. 20 )
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48 ARITHMETIC. (98) Reduce the grai
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50 ARITHMETIC. contained times in 3
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gal.
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54 ARITHMETIC. (108) In multiplicat
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56 ARITHMETIC. Since there are 24 g
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58 ARITHMETIC. There are 100 lb. in
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60 ARITHMETIC. 62 is contained in 1
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63 ARITHMETIC. (121) (a) 106' = 106
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64 ARITHMETIC. (^) .4044* = .4044 X
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6G ARITHMETIC. Since there are 2 de
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68 ARITHMETIC. (128) {a) .0133' =.0
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70 ARITHMETIC (130^ (a) 1 1 20 _8 2
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72 ARITHMETIC. in the root. Write i
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74 ARITHMETIC. (^) 9 -/QO.OO'OO'OO
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76 ARITHMETIC. correction. This, mu
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78 ARITHMETIC. found by division sh
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80 ARITHMETIC. (137) {a) 1 1 f .0 6
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82 ARITHMETIC. (138^ {a) In this ex
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84 ARITHMETIC. (^)
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86 ARITHMETIC. {b) f 6 = VTa 2 4/G.
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88 8 8 ARITHMETIC.
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90 ARITHMETIC. 40,000 144)40000.0(2
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92 ARITHMETIC. (163) 2 ft. 5 in. =
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94 ARITHMETIC. (164) Taking the tim
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96 ALGEBRA. (171) See Arts. 352 and
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98 ALGEBRA. In this case, where we
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100 ALGEBRA. By Art. 482, the signs
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102 ALGEBRA. (189) Applying the met
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104 ALGEBRA. (196) {a) ^+_;/ + ^-(^
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106 ALGEBRA- (201 ) The subtraction
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108 ALGEBRA. Canceling the factors
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110 ALGEBRA. (208) (a) Writing the
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112 ALGEBRA. 20j^(4^+5)-12.r(3:r-7)
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ALGEBRA. (QUESTIONS 218-257.) (218)
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ALGEBRA. 117 Clearing of fractions,
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ALGEBRA. 119 Transposing, — A:X*
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Completing the square, ALGEBRA. 131
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Extracting ALGEBRA. 123
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(d) Completing the square, Extracti
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ALGEBRA. 127 (238) (a) i/| by Art.
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(242) ALGEBRA. 139 Let X = the whol
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(246) Then,-^ X ALGEBRA. 131 Let X
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ALGEBRA. 133 y+5-{x-o) = 6. (1) But
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ALGEBRA. 136 (266) Let X — the nu
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LOGARITHMS. (QUESTIONS 258-272.) (2
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l^OGARITHMS. 139 .6602 -3 — 1.980
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LOGARITHMS. 141 {l>) .76'"._ Log .7
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LOGARITHMS. 143 (271) Substituting
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140 GEOMETRY AND TRIGONOMETRY. in t
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148 GEOMETRY AND TRIGONOMETRY. 3 (2
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150 GEOMETRY AND TRIGONOMETRY. (302
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154 GEOMETRY AND TRIGONOMETRY. draw
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158 GEOMETRY AND TRIGONOMETRY. {d)
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1G4 GEOMETRY AND TRIGONOMETRY. (354
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166 ELEMENTARY MECHANICS. per min.
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168 ELEMENTARY MECHANICS. replaced,
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170 ELEMENTARY MECHANICS. (384) (a)
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172 ELEMENTARY MECHANICS. (389) See
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174 ELEMENTARY MECHANICS. (398) 1 h
Page 188 and 189: 176 ELEMENTARY MECHANICS (412) Use
Page 190 and 191: 178 ELEMENTARY MECHANICS. (421) See
Page 192 and 193: 180 ELEMENTARY MECHANICS. a distanc
Page 194 and 195: 182 ELEMENTARY MECHANICS. (433) See
Page 196 and 197: 184 ELEMENTARY MECHANICS. (d) Using
Page 198 and 199: 186 ELEMENTARY MECHANICS. (452) (a)
Page 200 and 201: 188 HYDROMECHANICS. (457) (a) Area
Page 202 and 203: 190 HYDROMECHANICS. Pressure due to
Page 204 and 205: 192 HYDROMECHANICS. (47 1 ) (a) 36
Page 206 and 207: 194 HYDROMECHANICS. 5' X 7854 (479)
Page 208 and 209: 196 HYDROMECHANICS. (d) See Art. 10
Page 210 and 211: 198 HYDROMECHANICS. Pressure per sq
Page 212 and 213: aOO HYDROMECHANICS. For z;„ = 4,/
Page 214 and 215: 202 PNEUMATICS. (509) Substituting
Page 216 and 217: 204 PNEUMATICS. (519) 8.47 = origin
Page 218 and 219: 206 PNEUMATICS. (537) (a) 30 — 17
Page 220 and 221: 208 PNE-aMATlCS. (548) CO' — 50'
Page 222 and 223: 210 STRENGTH OF MATERIALS. P- p-^^.
Page 224 and 225: 212 STRENGTH OF MATERIALS. Since 40
Page 226 and 227: 214 STRENGTH OF MATERIALS. drawn. P
Page 228 and 229: 21G STRENGTH OF MATERIALS. c \d of
Page 230 and 231: 218 STRENGTH OF MATERIALS. n o. I//
Page 232 and 233: 220 STRENGTH OF MATERIALS. Substitu
Page 234 and 235: 222 STRENGTH OF MATERIALS. (589) Su
Page 236 and 237: 224 STRENGTH OF MATERIALS. (597) {a
Page 240 and 241: 228 STRENGTH OF MATERIALS. (604) Us
Page 242 and 243: 230 STRENGTH OP MATERIALS. (609) Th
Page 244 and 245: 232 STRENGTH OF MATERIALS. moments
Page 246 and 247: 234 SURVEYING. adjacent sides of th
Page 248 and 249: 236 SURVEYING. (622) 1st. A B in Fi
Page 250 and 251: 238 SURVEYING. true bearing IS the
Page 252 and 253: 240 SURVEYING. A B, as the bearing
Page 254 and 255: Un SURVEYING. an angle of 15° 10'
Page 256 and 257: 244 SURVEYING. in dotted lines. In
Page 258 and 259: 246 SURVEYING. table of Radii and D
Page 260 and 261: 248 SURVEYING. ^^^ = 1.875'. The de
Page 262 and 263: . (690) 250 SURVEYING. sight to the
Page 264 and 265: 252 SURVEYING. and including that a
Page 266 and 267: 254 SURVEYING. horizontal lines 1 f
Page 269 and 270: (706) LAND SURVEYING (QUESTIONS 706
Page 271 and 272: LAND SURVEYING. 259 ture of A B is
Page 273 and 274: LAND SURVEYING. 261 -{-, in the col
Page 275 and 276: LAND SURVEYING. 263 is +8.86 chains
Page 277 and 278: a a *• o « .i Q a V Q + • hJ *
Page 279 and 280: LAND SURVEYING. 2G7
Page 281 and 282: RAILROAD LOCATION. (756) (QUESTIONS
Page 283 and 284: RAILROAD LOCATION. 271 second curve
Page 285 and 286: RAILROAD LOCATION. 273 in which;!'
Page 287 and 288: RAILROAD LOCATION. 275 Whence, we h
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RAILROAD LOCATION. 277 4.0827 ft.,
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point so determined by RAILROAD LOC
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282 RAILROAD CONSTRUCTION. (818) Th
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884 RAILROAD CONSTRUCTION. (833) Ap
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286 RAILROAD CONSTRUCTION. (859) Fi
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288 RAILROAD CONSTRUCTION. (864) (8
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RAILROAD CONSTRUCTION. (QUESTIONS 8
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RAILROAD CONSTRUCTION. 293 (896) Se
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RAILROAD CONSTRUCTION. 295 (a) The
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RAILROAD CONSTRUCTION. 207 (939) Se
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300 TRACK WORK. (962) (963) (964) (
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302 TRACK WORK. (994) See Art. 1687
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304 TRACK WORK. (1008) 8 ft. G in.
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306 RAILROAD STRUCTURES. (1039) See
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308 RAILROAD STRUCTURES. (1060) Fro
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3," ^ >;> :3 3>32> ^ >:> J> Oi?^ :>
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UNIVERSrTY OF ILLINOIS-URBANA 3 011
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