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. = 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.

2 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.

3 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. 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.

4 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. 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 1 565 277 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

5 627 286 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 1 296 139 189 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)

6 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 2 592 327 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.

7 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 . 8 9 191. 2 124 38 2 252 1 18 7. 6 122 380 250 1 5 6 . 67 18 120 378 248 1 55. 5 6 18 118 376 246 1 5 4 176 . 8 116 374 244 1 53.

8 33 173. 2 114 372 242 1 52 . 2 2 169. 6 112 370 240 1 16 6 .0 110 368 238 1 5 0 16 2 .4 108 7 36 6 236 10 6 36 4 234 1 55. 2 10 4 75. 5 362 232 14 6 . 67 1 51. 6 102 360 230 145. 5 6 14 8 .0 100 73. 358 228 98 72. 35 6 226 143. 33 14 0. 8 96 35 4 224 142 . 2 2 1 37. 2 94 352 222 1 33. 6 92 350 220 14 0 1 3 90 3 48 218 1 3 8 . 8 9 1 26 .4 88 3 46 216 1 1 2 2 . 8 86 3 4 4 214 1 3 6 . 67 119. 2 84 3 42 212 82 3 40 210 1 3 4 11 2 .0 80 338 208 7 8 336 206 1 32 . 2 2 10 4. 8 76 33 4 204 1 101. 2 74 332 202 1 3 0 9 7. 6 7 2 330 200 7 0 328 198 1 9 68 326 196 66 324 19 4 64 322 19 2 62 320 190 60 318 18 8 58 316 18 6 56 314 18 4 54 312 18 2 52 310 180 5 8.

9 0 50 308 178 48 30 6 176 46 30 4 174 4 47. 2 44 302 172 42 300 170 40 298 168 38 296 16 6 36 294 16 4 3 4 3 292 162 2 5. 6 32 290 160 30 3 4read known temperatures in bold face and corresponding temperatures in degrees fahrenheit will be found in the column to the left temperatures in celsius (centigrade) to the rightTEMPERATURE C F C F C 28 102 232 26 104 234 24 106 236 22 108 238 20 110 240 18 112 242 16 114 244 14 116 246 12 118 248 10 120 250 8 122 252 6 124 254 4 126 256 2 128 258 0 130 260 2 132 262 1 4 134 264 6 136 266 8 138 268 10 140 270 12 142 272 14 144 274 16 146 276 18 148 278 20 150 280 1 22 152 282 24 154 284 26 156 286 28 158 288 30 160 290 32 162 292 34 164 294 36 166 296 38 168

10 298 40 170 300 42 172 302 44 174 304 46 176 306 48 178 308 50 180 310 52 182 312 54 184 314 56 186 316 1 58 188 318 60 190 320 62 192 322 64 194 324 66 196 326 68 198 328 70 200 330 72 202 332 74 204 334 76 206 336 78 208 338 80 210 340 82 212 342 84 214 344 86 216 346 88 218 348 90 220 350 19 7. 6 92 222 352 17 94 224 354 96 226 356 98 228 358 100 230 360 known temperatures in bold face and corresponding temperatures in degrees fahrenheit will be found in the column to the left temperatures in celsius (centigrade) to the rightTEMPERATURE C F C F C 362 492 910 4 8 364 494 920 366 496 930 368 498 940 370 500 950 372 502 960 374 504 970 376 506 980 378 508 990 380 510 1000 382 512 1010 384 514 1020 386 516 1030 388 518 1040 390 520 1050 392 522 1060 394 524 1070 396 526 1080 398 528 1090 5 8 400 530 1100 402 532 1110 404 534 1120 406 536 1130 408 538 1140 410 540 1150 412 542 1160 414 544 1170 416 546 1180 6 418 548 1190 420 550 1200 422 560 1210 424 570 1220 426 580 1230 428