FORMULAS USEFUL IN CALCULATING WEIGHT OF …

1 TriangleArea = cd. s = (a + b + c)Example: a = 3 , b = 4 , c = 5 FORMULAS USEFUL IN CALCULATING WEIGHT OF CASTINGS Regular Polygonsn = Number of sides, s = Length of one side, r = Inside radius area = nsr Number of Sides area 5 s = r 6 s = r 7 s = r 8 s = r 9 s = r 10 s = r 11 s = r 12 s = r TrapeziumArea = [a (e + d) + bd + ce]Example: a = 10 , b = 3 , c = 5 , d = 6 , e = 8 area = [10 (8 + 6) + (3 6) + (5 8)] = 99 sq. in. Rectangle and Parallelogram area = abwhenc)(sb)(sa)(ssArea =6"25" 4"3"s=++= )-(64)(63)(66 area = = of a CircleExample: R = 5 , = 120 , C = , h = of arc L = R area = [LR C (R h)]Example: R = 5 , C = , h = , = 120 L = 5 120 = area = [( 5) (5 )] = sq.

2 = R = C Example: R = 3 area = 3 = SegmentArea = shExample: s = 3, h = 4 area = 3 4 = 8 EllipseArea = ab = abExample: a = 3, b = 4 area = 3 4 = of Circular Cross SectionArea of Surface = 4 Rr = RrArea of Surface = Dd = DdVolume = 2 Rr = Rr Volume = Dd = Dd FORMULAS USEFUL IN CALCULATING WEIGHT OF )( =2h)(RC360 RArea2 = = area of baseP = perimeter of baseLateral area = PsVolume = AhFrustum of a PyramidA = area of basea = area of topm = area of midsectionP = perimeter of basep = perimeter of topLateral area = s (P + p)Volume = h (A + a + 4 m)ConeVolume = r h = r h = d hFrustum of a ConeA = area of basea = area of topm = area of midsectionR = D 2.

3 R = d 2 area of Conical Surface = s (D + d) = s (D + d)Volume = h (R + Rr + r ) = h (R + Rr + r )Volume = 121h(D + Dd + d ) = h (D + Dd + d )m)4A(ah)aAA(ahVolume6131++=++= FORMULAS USEFUL IN CALCULATING WEIGHT OF CASTINGS)aAA(ahVolume31++=22hr r rsAreaConical+== = 4 r2 = r2 = d2 Volume = r3 = r3 Volume = d3 = d3 Segment of a SphereSpherical Surface = 2 rh = (c2 + 4 h2) = (c2 + 4 h2)Total Surface = (c2 + 8 rh) = (c2 + 8 rh)Volume = h2 (3 r - h) = h2 (3 r - h)orVolume = h (3 c2 + 4 h2) = h (3 c2 + 4 h2)Sector of a SphereTotal Surface = r (4 h + c) = r (4 h + c)Volume = r2h = r2hCylinderCylindrical Surface = dh = 2 rh = rhTotal Surface = 2 r (r + h) = r (r + h)Volume = r2h = d2h = d2hFORMULAS USEFUL IN CALCULATING WEIGHT OF USEFUL IN CALCULATING WEIGHT OF CASTINGSC ircle (the Greek letter Theta) = angle included between radii (pi) = , D = Diameter, R = Radius, C = Chord,h = Height of Arc, L = Length of = D2 = D2 = R2 Circle RingArea = (D2-d2), or (D-d) (D + d)Example: D = 10 , d = 3 area = (102 - 32) = sq.

4 Of a CircleArea = LRExample: L = , R = 5 Example: R = 5 , = 120 area 22 DnceCircumfere === Area2 nceCircumfere R 2 Diameter = == Area2 nceCircumfere D Radius21= ==h2h2C Radius22+ = ? sine R 2 h)-(Dh2 Chord ==222CR RhArc,ofHeight = L Arc, ofLength = = )in ( 21= R2C Sine21 = in. sq. = 22R RAreaor = =in. sq. = (SI) STRESS CONVERSION FACTORS0 to 100 ksi MPa ksi MPa 0 50 1 51 2 52 3 53 4 54 5 55 6 56 7 57 8 58 39 9 59 10 60 11 61 12 62 427. 5 13 63 14 64 15 65 16 66 17 67 18 68 19 69 20 70 21 71 22 72 23 73 24 74 25 75 26 76 27 77 28 78 537.

5 8 29 79 30 80 31 81 32 82 33 83 34 84 35 85 36 86 37 87 38 88 39 89 40 90 41 91 6 42 92 43 93 44 94 45 95 46 96 6 47 97 48 98 49 99 50 100 up stress to be converted in the boldface column. If in ksi (103 psi), read MPa in righthand column. If in MPa, read ksi in lefthand column. Conversion factors: 1 MPa = 1 MN/m2 (meganewton per square metre) or 1 N/mm2 (newton per square millimetre); 1 MPa = ksi, and 1 ksi = MPa. To convert ksi or MPa values above 400, use the supplemental table. Example: Convert 1320 MPa to ksi.

6 Solu-tion: 1000 MPa = ksi (from the small table), and 320 MPa = ksi (from the large table). Then, = = to 300 ksi MPa ksi MPa 200 1 379 250 1 724 201 1 386 251 1 731 202 1 393 252 1 737 203 1 400 253 1 744 204 1 407 254 1 751 205 1 413 255 1 758 206 1 420 256 1 765 207 1 427 257 1 772 208 1 434 258 1 779 209 1 441 259 1 786 210 1 448 260 1 793 211 1 455 261 1 800 212 1 462 262 1 806 213 1 469 263 1 813 214 1 475 264 1 820 215 1 482 265 1 827 216 1 489 266 1 834 217 1 496 267 1 841 218 1 503 268 1 848 219 1 510 269 1 855 220 1 517 270 1 862 221 1 524 271 1 868 222 1 531 272 1 875 223 1 538 273 1 882 224 1 544 274 1 889 225 1 551 275 1 896 226 1 558 276 1 903 227 1

7 565 277 1 910 228 1 572 278 1 917 229 1 579 279 1 924 230 1 586 280 1 931 231 1 593 281 1 937 232 1 600 282 1 944 233 1 606 283 1 951 234 1 613 284 1 958 235 1 620 285 1 965 236 1 627 286 1 972 237 1 634 287 1 979 238 1 641 288 1 986 239 1 648 289 1 993 240 1 655 290 1 999 3 241 1 662 291 2 006 242 1 669 292 2 013 243 1 675 293 2 020 244 1 682 294 2 027 245 1 689 295 2 034 246 1 696 296 2 041 247 1 703 297 2 048 248 1 710 298 2 055 249 1 717 299 2 062 250 1 724 300 2 068100 to 200 ksi MPa ksi MPa 100 150 1 034 101 151 1 041 102 152 1 048 103 153 1 054 104 154 1 062 105 155 1 069 106 156 1 076 107 157 1 082 108 158 1 089 109 159 1 096 110 160 1 103 111 161 1 110 112 162 1 117 113 163 1 124 114 164 1 131 115 165 1 138 116 166 1 145 117 167 1 151 118 168 1 158 119 169 1 165 120 170 1 172 121 171 1 179 122 172 1 186 123 173 1 193 124 174 1 200 125 175 1 207 126 176 1 213 127 177 1 220 128 178 1 227 129 179 1 234 130 180 1 241 131 181 1 248 132 182 1 255 133 183 1 262 134 184 1 269 135 185 1 276 136 186 1 282 137 187 1 289 138 188 1 296 139

8 189 1 303 140 190 1 310 141 191 1 317 142 192 1 324 143 193 1 331 144 194 1 338 145 195 1 344 146 1 007 196 1 351 147 1 014 197 1 358 148 1 020 198 1 365 149 1 027 199 1 372 150 1 034 200 1 379 ENGLISH/METRIC (SI) STRESS CONVERSION to 400 ksi MPa ksi MPa 300 2 068 350 2 413 301 2 075 351 2 420 302 2 082 352 2 427 303 2 089 353 2 434 304 2 096 354 2 441 305 2 103 355 2 448 306 2 110 356 2 455 307 2 117 357 2 461 308 2 124 358 2 468 309 2 130 359 2 475 310 2 137 360 2 482 311 2 144 361 2 489 312 2 151 362 2 496 313 2 158 363 2 503 314 2 165 364 2 510 315 2 172 365 2 517 316 2 179 366 2 523 317 2 186 367 2 530 318 2 193 368 2 537 319 2 199 369 2 544 320 2 206 370 2 551 321 2 213 371 2 558 322 2 220 372 2 565 323 2 227 373 2 572 4 9 324 2 234 374 2 579 325 2 241 375 2 585 326 2 248 376 2

9 592 327 2 255 377 2 599 47. 5 7 328 2 261 378 2 606 329 2 268 379 2 613 330 2 275 380 2 620 331 2 282 381 2 627 332 2 289 382 2 634 333 2 296 383 2,641 334 2 303 384 2 648 335 2 310 385 2 654 336 2 317 386 2 661 337 2 324 387 2 668 338 2 330 388 2 675 339 2 337 389 2 682 340 2 344 390 2 689 341 2 351 391 2 696 342 2 358 392 2 703 343 2 365 393 2 710 344 2 372 394 2 717 345 2 379 395 2 723 346 2 386 396 2 730 347 2 392 397 2 737 348 2 399 398 2 744 349 2 406 399 2 751 350 2 413 400 2 758500 to 5000 ksi MPa 500 3447 600 4137 700 4826 800 5516 900 6205 1000 6895 2000 13 790 3000 20 684 4000 27 579 5000 34 474 Source: Anton deS.

10 Brasunas. University of Missouri-RollaMID-JUNE 1979 METAL PROGRESSENGLISH/METRIC (SI) STRESS CONVERSION C F C F 418 .. 288 17 2 52 .4 158 10 5. 5 416 .. 286 15 6 10 414 .. 284 15 4 103. 412 .. 282 152 10 2 . 2 410 .. 280 150 408 .. 278 148 406 .. 276 146 404 .. 274 0 2 27. 2 14 4 9 402 272 142 400 270 2 140 398 268 138 396 266 136 39 4 264 13 4 39 2 262 132 390 260 130 38 8 258 19 8 .4 128 38 6 256 16 0 19 4. 8 126 8 38 4 254 1 5 8.