V. Cantilever Beam End Displacement 2

To find the displacement at the free end and normal stresses at mid-span of a cantilever beam modeled with solid elements.

Hand Calculation

 φL2 = TL/(c2ab3G)

where
 a = long side of the cross section = 3 in b = short side of the cross section = 2 in c2 = 0.1958 for a/b = 1.5 G = E/[2(1+ν)] = 10(10)3/(2(1+0.3)] = 3,846 ksi

 φL2 = 2000(15)//[0.1958(3)(2)33.846(10)6] = 0.00166 rad

δL3 = ML2/(2EI) = 2500(15)2/[2(10)(10)7(4.5)] = 0.00625 in

 δbend = PL3/(3EI) = 1000(15)3/{3[10(10)6](4.5)} = 0.025 in

 δshear = 12/5*(1+ν)PL/AE = 12/5*(1+0.3)(1000)(15)/[(6)10(10)6] = 0.00078 in

 δL4 = δbend + δshear = 0.025 + 0.00078 = 0.02578 in

Stress at midspan due to Load 1:

σa = P/A = 1200/6 = 200 psi

Stress at midspan due to Load 3:

σb = My/I = 2500(1.5)/4.5 = 833.33 psi

Stress at midspan due to Load 4:

σb = My/I = 7.5(1000)(1.5)/4.5 = 2,500 psi

Comparison

Table 1. Comparison of results
Maximum Displacement, δ (in) LC1 0.00030 0.00033 10% The theoretical results from classical Beam theory was compared with the results from the model with Solid Elements - hence the difference in results.
LC3 0.00625 0.00621 0.6%
LC4 0.02578 0.02537 1.6%
Maximum Rotation, φ (rad) LC2 0.00166 0.00149 10.2%
Normal Stress at Midspan* (psi) LC1 200.0 200.004 none
LC3 833.3 833.325 none
LC4 2,500 2,630.409 5.2%
Note: (*) Stresses computed at Node no. 32 of solid no. 10.

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\05 Solids\Cantilever Beam End Displacement 2.STD is typically installed with the program.

STAAD SPACE : A CANTILEVER BEAM WITH SOLID ELEMENTS
START JOB INFORMATION
ENGINEER DATE 17-Sep-18
END JOB INFORMATION
INPUT WIDTH 72
UNIT INCHES POUND
JOINT COORDINATES
1 0 0 0; 2 0.75 0 0; 3 1.5 0 0; 4 2.25 0 0; 5 3 0 0; 6 3.75 0 0;
7 4.5 0 0; 8 5.25 0 0; 9 6 0 0; 10 6.75 0 0; 11 7.5 0 0; 12 8.25 0 0;
13 9 0 0; 14 9.75 0 0; 15 10.5 0 0; 16 11.25 0 0; 17 12 0 0;
18 12.75 0 0; 19 13.5 0 0; 20 14.25 0 0; 21 15 0 0; 22 0 0 0.5;
23 0.75 0 0.5; 24 1.5 0 0.5; 25 2.25 0 0.5; 26 3 0 0.5; 27 3.75 0 0.5;
28 4.5 0 0.5; 29 5.25 0 0.5; 30 6 0 0.5; 31 6.75 0 0.5; 32 7.5 0 0.5;
33 8.25 0 0.5; 34 9 0 0.5; 35 9.75 0 0.5; 36 10.5 0 0.5; 37 11.25 0 0.5;
38 12 0 0.5; 39 12.75 0 0.5; 40 13.5 0 0.5; 41 14.25 0 0.5; 42 15 0 0.5;
43 0 0 1; 44 0.75 0 1; 45 1.5 0 1; 46 2.25 0 1; 47 3 0 1; 48 3.75 0 1;
49 4.5 0 1; 50 5.25 0 1; 51 6 0 1; 52 6.75 0 1; 53 7.5 0 1; 54 8.25 0 1;
55 9 0 1; 56 9.75 0 1; 57 10.5 0 1; 58 11.25 0 1; 59 12 0 1;
60 12.75 0 1; 61 13.5 0 1; 62 14.25 0 1; 63 15 0 1; 64 0 0 1.5;
65 0.75 0 1.5; 66 1.5 0 1.5; 67 2.25 0 1.5; 68 3 0 1.5; 69 3.75 0 1.5;
70 4.5 0 1.5; 71 5.25 0 1.5; 72 6 0 1.5; 73 6.75 0 1.5; 74 7.5 0 1.5;
75 8.25 0 1.5; 76 9 0 1.5; 77 9.75 0 1.5; 78 10.5 0 1.5; 79 11.25 0 1.5;
80 12 0 1.5; 81 12.75 0 1.5; 82 13.5 0 1.5; 83 14.25 0 1.5; 84 15 0 1.5;
85 0 0 2; 86 0.75 0 2; 87 1.5 0 2; 88 2.25 0 2; 89 3 0 2; 90 3.75 0 2;
91 4.5 0 2; 92 5.25 0 2; 93 6 0 2; 94 6.75 0 2; 95 7.5 0 2; 96 8.25 0 2;
97 9 0 2; 98 9.75 0 2; 99 10.5 0 2; 100 11.25 0 2; 101 12 0 2;
102 12.75 0 2; 103 13.5 0 2; 104 14.25 0 2; 105 15 0 2; 106 0 0.75 0;
107 0.75 0.75 0; 108 1.5 0.75 0; 109 2.25 0.75 0; 110 3 0.75 0;
111 3.75 0.75 0; 112 4.5 0.75 0; 113 5.25 0.75 0; 114 6 0.75 0;
115 6.75 0.75 0; 116 7.5 0.75 0; 117 8.25 0.75 0; 118 9 0.75 0;
119 9.75 0.75 0; 120 10.5 0.75 0; 121 11.25 0.75 0; 122 12 0.75 0;
123 12.75 0.75 0; 124 13.5 0.75 0; 125 14.25 0.75 0; 126 15 0.75 0;
127 0 0.75 0.5; 128 0.75 0.75 0.5; 129 1.5 0.75 0.5; 130 2.25 0.75 0.5;
131 3 0.75 0.5; 132 3.75 0.75 0.5; 133 4.5 0.75 0.5; 134 5.25 0.75 0.5;
135 6 0.75 0.5; 136 6.75 0.75 0.5; 137 7.5 0.75 0.5; 138 8.25 0.75 0.5;
139 9 0.75 0.5; 140 9.75 0.75 0.5; 141 10.5 0.75 0.5;
142 11.25 0.75 0.5; 143 12 0.75 0.5; 144 12.75 0.75 0.5;
145 13.5 0.75 0.5; 146 14.25 0.75 0.5; 147 15 0.75 0.5; 148 0 0.75 1;
149 0.75 0.75 1; 150 1.5 0.75 1; 151 2.25 0.75 1; 152 3 0.75 1;
153 3.75 0.75 1; 154 4.5 0.75 1; 155 5.25 0.75 1; 156 6 0.75 1;
157 6.75 0.75 1; 158 7.5 0.75 1; 159 8.25 0.75 1; 160 9 0.75 1;
161 9.75 0.75 1; 162 10.5 0.75 1; 163 11.25 0.75 1; 164 12 0.75 1;
165 12.75 0.75 1; 166 13.5 0.75 1; 167 14.25 0.75 1; 168 15 0.75 1;
169 0 0.75 1.5; 170 0.75 0.75 1.5; 171 1.5 0.75 1.5; 172 2.25 0.75 1.5;
173 3 0.75 1.5; 174 3.75 0.75 1.5; 175 4.5 0.75 1.5; 176 5.25 0.75 1.5;
177 6 0.75 1.5; 178 6.75 0.75 1.5; 179 7.5 0.75 1.5; 180 8.25 0.75 1.5;
181 9 0.75 1.5; 182 9.75 0.75 1.5; 183 10.5 0.75 1.5;
184 11.25 0.75 1.5; 185 12 0.75 1.5; 186 12.75 0.75 1.5;
187 13.5 0.75 1.5; 188 14.25 0.75 1.5; 189 15 0.75 1.5; 190 0 0.75 2;
191 0.75 0.75 2; 192 1.5 0.75 2; 193 2.25 0.75 2; 194 3 0.75 2;
195 3.75 0.75 2; 196 4.5 0.75 2; 197 5.25 0.75 2; 198 6 0.75 2;
199 6.75 0.75 2; 200 7.5 0.75 2; 201 8.25 0.75 2; 202 9 0.75 2;
203 9.75 0.75 2; 204 10.5 0.75 2; 205 11.25 0.75 2; 206 12 0.75 2;
207 12.75 0.75 2; 208 13.5 0.75 2; 209 14.25 0.75 2; 210 15 0.75 2;
211 0 1.5 0; 212 0.75 1.5 0; 213 1.5 1.5 0; 214 2.25 1.5 0; 215 3 1.5 0;
216 3.75 1.5 0; 217 4.5 1.5 0; 218 5.25 1.5 0; 219 6 1.5 0;
220 6.75 1.5 0; 221 7.5 1.5 0; 222 8.25 1.5 0; 223 9 1.5 0;
224 9.75 1.5 0; 225 10.5 1.5 0; 226 11.25 1.5 0; 227 12 1.5 0;
228 12.75 1.5 0; 229 13.5 1.5 0; 230 14.25 1.5 0; 231 15 1.5 0;
232 0 1.5 0.5; 233 0.75 1.5 0.5; 234 1.5 1.5 0.5; 235 2.25 1.5 0.5;
236 3 1.5 0.5; 237 3.75 1.5 0.5; 238 4.5 1.5 0.5; 239 5.25 1.5 0.5;
240 6 1.5 0.5; 241 6.75 1.5 0.5; 242 7.5 1.5 0.5; 243 8.25 1.5 0.5;
244 9 1.5 0.5; 245 9.75 1.5 0.5; 246 10.5 1.5 0.5; 247 11.25 1.5 0.5;
248 12 1.5 0.5; 249 12.75 1.5 0.5; 250 13.5 1.5 0.5; 251 14.25 1.5 0.5;
252 15 1.5 0.5; 253 0 1.5 1; 254 0.75 1.5 1; 255 1.5 1.5 1;
256 2.25 1.5 1; 257 3 1.5 1; 258 3.75 1.5 1; 259 4.5 1.5 1;
260 5.25 1.5 1; 261 6 1.5 1; 262 6.75 1.5 1; 263 7.5 1.5 1;
264 8.25 1.5 1; 265 9 1.5 1; 266 9.75 1.5 1; 267 10.5 1.5 1;
268 11.25 1.5 1; 269 12 1.5 1; 270 12.75 1.5 1; 271 13.5 1.5 1;
272 14.25 1.5 1; 273 15 1.5 1; 274 0 1.5 1.5; 275 0.75 1.5 1.5;
276 1.5 1.5 1.5; 277 2.25 1.5 1.5; 278 3 1.5 1.5; 279 3.75 1.5 1.5;
280 4.5 1.5 1.5; 281 5.25 1.5 1.5; 282 6 1.5 1.5; 283 6.75 1.5 1.5;
284 7.5 1.5 1.5; 285 8.25 1.5 1.5; 286 9 1.5 1.5; 287 9.75 1.5 1.5;
288 10.5 1.5 1.5; 289 11.25 1.5 1.5; 290 12 1.5 1.5; 291 12.75 1.5 1.5;
292 13.5 1.5 1.5; 293 14.25 1.5 1.5; 294 15 1.5 1.5; 295 0 1.5 2;
296 0.75 1.5 2; 297 1.5 1.5 2; 298 2.25 1.5 2; 299 3 1.5 2;
300 3.75 1.5 2; 301 4.5 1.5 2; 302 5.25 1.5 2; 303 6 1.5 2;
304 6.75 1.5 2; 305 7.5 1.5 2; 306 8.25 1.5 2; 307 9 1.5 2;
308 9.75 1.5 2; 309 10.5 1.5 2; 310 11.25 1.5 2; 311 12 1.5 2;
312 12.75 1.5 2; 313 13.5 1.5 2; 314 14.25 1.5 2; 315 15 1.5 2;
316 0 2.25 0; 317 0.75 2.25 0; 318 1.5 2.25 0; 319 2.25 2.25 0;
320 3 2.25 0; 321 3.75 2.25 0; 322 4.5 2.25 0; 323 5.25 2.25 0;
324 6 2.25 0; 325 6.75 2.25 0; 326 7.5 2.25 0; 327 8.25 2.25 0;
328 9 2.25 0; 329 9.75 2.25 0; 330 10.5 2.25 0; 331 11.25 2.25 0;
332 12 2.25 0; 333 12.75 2.25 0; 334 13.5 2.25 0; 335 14.25 2.25 0;
336 15 2.25 0; 337 0 2.25 0.5; 338 0.75 2.25 0.5; 339 1.5 2.25 0.5;
340 2.25 2.25 0.5; 341 3 2.25 0.5; 342 3.75 2.25 0.5; 343 4.5 2.25 0.5;
344 5.25 2.25 0.5; 345 6 2.25 0.5; 346 6.75 2.25 0.5; 347 7.5 2.25 0.5;
348 8.25 2.25 0.5; 349 9 2.25 0.5; 350 9.75 2.25 0.5; 351 10.5 2.25 0.5;
352 11.25 2.25 0.5; 353 12 2.25 0.5; 354 12.75 2.25 0.5;
355 13.5 2.25 0.5; 356 14.25 2.25 0.5; 357 15 2.25 0.5; 358 0 2.25 1;
359 0.75 2.25 1; 360 1.5 2.25 1; 361 2.25 2.25 1; 362 3 2.25 1;
363 3.75 2.25 1; 364 4.5 2.25 1; 365 5.25 2.25 1; 366 6 2.25 1;
367 6.75 2.25 1; 368 7.5 2.25 1; 369 8.25 2.25 1; 370 9 2.25 1;
371 9.75 2.25 1; 372 10.5 2.25 1; 373 11.25 2.25 1; 374 12 2.25 1;
375 12.75 2.25 1; 376 13.5 2.25 1; 377 14.25 2.25 1; 378 15 2.25 1;
379 0 2.25 1.5; 380 0.75 2.25 1.5; 381 1.5 2.25 1.5; 382 2.25 2.25 1.5;
383 3 2.25 1.5; 384 3.75 2.25 1.5; 385 4.5 2.25 1.5; 386 5.25 2.25 1.5;
387 6 2.25 1.5; 388 6.75 2.25 1.5; 389 7.5 2.25 1.5; 390 8.25 2.25 1.5;
391 9 2.25 1.5; 392 9.75 2.25 1.5; 393 10.5 2.25 1.5;
394 11.25 2.25 1.5; 395 12 2.25 1.5; 396 12.75 2.25 1.5;
397 13.5 2.25 1.5; 398 14.25 2.25 1.5; 399 15 2.25 1.5; 400 0 2.25 2;
401 0.75 2.25 2; 402 1.5 2.25 2; 403 2.25 2.25 2; 404 3 2.25 2;
405 3.75 2.25 2; 406 4.5 2.25 2; 407 5.25 2.25 2; 408 6 2.25 2;
409 6.75 2.25 2; 410 7.5 2.25 2; 411 8.25 2.25 2; 412 9 2.25 2;
413 9.75 2.25 2; 414 10.5 2.25 2; 415 11.25 2.25 2; 416 12 2.25 2;
417 12.75 2.25 2; 418 13.5 2.25 2; 419 14.25 2.25 2; 420 15 2.25 2;
421 0 3 0; 422 0.75 3 0; 423 1.5 3 0; 424 2.25 3 0; 425 3 3 0;
426 3.75 3 0; 427 4.5 3 0; 428 5.25 3 0; 429 6 3 0; 430 6.75 3 0;
431 7.5 3 0; 432 8.25 3 0; 433 9 3 0; 434 9.75 3 0; 435 10.5 3 0;
436 11.25 3 0; 437 12 3 0; 438 12.75 3 0; 439 13.5 3 0; 440 14.25 3 0;
441 15 3 0; 442 0 3 0.5; 443 0.75 3 0.5; 444 1.5 3 0.5; 445 2.25 3 0.5;
446 3 3 0.5; 447 3.75 3 0.5; 448 4.5 3 0.5; 449 5.25 3 0.5; 450 6 3 0.5;
451 6.75 3 0.5; 452 7.5 3 0.5; 453 8.25 3 0.5; 454 9 3 0.5;
455 9.75 3 0.5; 456 10.5 3 0.5; 457 11.25 3 0.5; 458 12 3 0.5;
459 12.75 3 0.5; 460 13.5 3 0.5; 461 14.25 3 0.5; 462 15 3 0.5;
463 0 3 1; 464 0.75 3 1; 465 1.5 3 1; 466 2.25 3 1; 467 3 3 1;
468 3.75 3 1; 469 4.5 3 1; 470 5.25 3 1; 471 6 3 1; 472 6.75 3 1;
473 7.5 3 1; 474 8.25 3 1; 475 9 3 1; 476 9.75 3 1; 477 10.5 3 1;
478 11.25 3 1; 479 12 3 1; 480 12.75 3 1; 481 13.5 3 1; 482 14.25 3 1;
483 15 3 1; 484 0 3 1.5; 485 0.75 3 1.5; 486 1.5 3 1.5; 487 2.25 3 1.5;
488 3 3 1.5; 489 3.75 3 1.5; 490 4.5 3 1.5; 491 5.25 3 1.5; 492 6 3 1.5;
493 6.75 3 1.5; 494 7.5 3 1.5; 495 8.25 3 1.5; 496 9 3 1.5;
497 9.75 3 1.5; 498 10.5 3 1.5; 499 11.25 3 1.5; 500 12 3 1.5;
501 12.75 3 1.5; 502 13.5 3 1.5; 503 14.25 3 1.5; 504 15 3 1.5;
505 0 3 2; 506 0.75 3 2; 507 1.5 3 2; 508 2.25 3 2; 509 3 3 2;
510 3.75 3 2; 511 4.5 3 2; 512 5.25 3 2; 513 6 3 2; 514 6.75 3 2;
515 7.5 3 2; 516 8.25 3 2; 517 9 3 2; 518 9.75 3 2; 519 10.5 3 2;
520 11.25 3 2; 521 12 3 2; 522 12.75 3 2; 523 13.5 3 2; 524 14.25 3 2;
525 15 3 2;
*
* SINCE SOLID-ONLY MODELS HAVE NO ROTATIONAL DOF AT THEIR NODES, ADD
* DUMMY MEMBERS TO CREATE THOSE DEGREES OF FREEDOM.
*
MEMBER INCIDENCES
1001 525 273; 1002 105 273; 1003 21 273; 1004 441 273;
ELEMENT INCIDENCES SOLID
1 22 127 106 1 23 128 107 2; 2 23 128 107 2 24 129 108 3;
3 24 129 108 3 25 130 109 4; 4 25 130 109 4 26 131 110 5;
5 26 131 110 5 27 132 111 6; 6 27 132 111 6 28 133 112 7;
7 28 133 112 7 29 134 113 8; 8 29 134 113 8 30 135 114 9;
9 30 135 114 9 31 136 115 10; 10 31 136 115 10 32 137 116 11;
11 32 137 116 11 33 138 117 12; 12 33 138 117 12 34 139 118 13;
13 34 139 118 13 35 140 119 14; 14 35 140 119 14 36 141 120 15;
15 36 141 120 15 37 142 121 16; 16 37 142 121 16 38 143 122 17;
17 38 143 122 17 39 144 123 18; 18 39 144 123 18 40 145 124 19;
19 40 145 124 19 41 146 125 20; 20 41 146 125 20 42 147 126 21;
21 43 148 127 22 44 149 128 23; 22 44 149 128 23 45 150 129 24;
23 45 150 129 24 46 151 130 25; 24 46 151 130 25 47 152 131 26;
25 47 152 131 26 48 153 132 27; 26 48 153 132 27 49 154 133 28;
27 49 154 133 28 50 155 134 29; 28 50 155 134 29 51 156 135 30;
29 51 156 135 30 52 157 136 31; 30 52 157 136 31 53 158 137 32;
31 53 158 137 32 54 159 138 33; 32 54 159 138 33 55 160 139 34;
33 55 160 139 34 56 161 140 35; 34 56 161 140 35 57 162 141 36;
35 57 162 141 36 58 163 142 37; 36 58 163 142 37 59 164 143 38;
37 59 164 143 38 60 165 144 39; 38 60 165 144 39 61 166 145 40;
39 61 166 145 40 62 167 146 41; 40 62 167 146 41 63 168 147 42;
41 64 169 148 43 65 170 149 44; 42 65 170 149 44 66 171 150 45;
43 66 171 150 45 67 172 151 46; 44 67 172 151 46 68 173 152 47;
45 68 173 152 47 69 174 153 48; 46 69 174 153 48 70 175 154 49;
47 70 175 154 49 71 176 155 50; 48 71 176 155 50 72 177 156 51;
49 72 177 156 51 73 178 157 52; 50 73 178 157 52 74 179 158 53;
51 74 179 158 53 75 180 159 54; 52 75 180 159 54 76 181 160 55;
53 76 181 160 55 77 182 161 56; 54 77 182 161 56 78 183 162 57;
55 78 183 162 57 79 184 163 58; 56 79 184 163 58 80 185 164 59;
57 80 185 164 59 81 186 165 60; 58 81 186 165 60 82 187 166 61;
59 82 187 166 61 83 188 167 62; 60 83 188 167 62 84 189 168 63;
61 85 190 169 64 86 191 170 65; 62 86 191 170 65 87 192 171 66;
63 87 192 171 66 88 193 172 67; 64 88 193 172 67 89 194 173 68;
65 89 194 173 68 90 195 174 69; 66 90 195 174 69 91 196 175 70;
67 91 196 175 70 92 197 176 71; 68 92 197 176 71 93 198 177 72;
69 93 198 177 72 94 199 178 73; 70 94 199 178 73 95 200 179 74;
71 95 200 179 74 96 201 180 75; 72 96 201 180 75 97 202 181 76;
73 97 202 181 76 98 203 182 77; 74 98 203 182 77 99 204 183 78;
75 99 204 183 78 100 205 184 79; 76 100 205 184 79 101 206 185 80;
77 101 206 185 80 102 207 186 81; 78 102 207 186 81 103 208 187 82;
79 103 208 187 82 104 209 188 83; 80 104 209 188 83 105 210 189 84;
81 127 232 211 106 128 233 212 107; 82 128 233 212 107 129 234 213 108;
83 129 234 213 108 130 235 214 109; 84 130 235 214 109 131 236 215 110;
85 131 236 215 110 132 237 216 111; 86 132 237 216 111 133 238 217 112;
87 133 238 217 112 134 239 218 113; 88 134 239 218 113 135 240 219 114;
89 135 240 219 114 136 241 220 115; 90 136 241 220 115 137 242 221 116;
91 137 242 221 116 138 243 222 117; 92 138 243 222 117 139 244 223 118;
93 139 244 223 118 140 245 224 119; 94 140 245 224 119 141 246 225 120;
95 141 246 225 120 142 247 226 121; 96 142 247 226 121 143 248 227 122;
97 143 248 227 122 144 249 228 123; 98 144 249 228 123 145 250 229 124;
99 145 250 229 124 146 251 230 125; 100 146 251 230 125 147 252 231 126;
101 148 253 232 127 149 254 233 128;
102 149 254 233 128 150 255 234 129;
103 150 255 234 129 151 256 235 130;
104 151 256 235 130 152 257 236 131;
105 152 257 236 131 153 258 237 132;
106 153 258 237 132 154 259 238 133;
107 154 259 238 133 155 260 239 134;
108 155 260 239 134 156 261 240 135;
109 156 261 240 135 157 262 241 136;
110 157 262 241 136 158 263 242 137;
111 158 263 242 137 159 264 243 138;
112 159 264 243 138 160 265 244 139;
113 160 265 244 139 161 266 245 140;
114 161 266 245 140 162 267 246 141;
115 162 267 246 141 163 268 247 142;
116 163 268 247 142 164 269 248 143;
117 164 269 248 143 165 270 249 144;
118 165 270 249 144 166 271 250 145;
119 166 271 250 145 167 272 251 146;
120 167 272 251 146 168 273 252 147;
121 169 274 253 148 170 275 254 149;
122 170 275 254 149 171 276 255 150;
123 171 276 255 150 172 277 256 151;
124 172 277 256 151 173 278 257 152;
125 173 278 257 152 174 279 258 153;
126 174 279 258 153 175 280 259 154;
127 175 280 259 154 176 281 260 155;
128 176 281 260 155 177 282 261 156;
129 177 282 261 156 178 283 262 157;
130 178 283 262 157 179 284 263 158;
131 179 284 263 158 180 285 264 159;
132 180 285 264 159 181 286 265 160;
133 181 286 265 160 182 287 266 161;
134 182 287 266 161 183 288 267 162;
135 183 288 267 162 184 289 268 163;
136 184 289 268 163 185 290 269 164;
137 185 290 269 164 186 291 270 165;
138 186 291 270 165 187 292 271 166;
139 187 292 271 166 188 293 272 167;
140 188 293 272 167 189 294 273 168;
141 190 295 274 169 191 296 275 170;
142 191 296 275 170 192 297 276 171;
143 192 297 276 171 193 298 277 172;
144 193 298 277 172 194 299 278 173;
145 194 299 278 173 195 300 279 174;
146 195 300 279 174 196 301 280 175;
147 196 301 280 175 197 302 281 176;
148 197 302 281 176 198 303 282 177;
149 198 303 282 177 199 304 283 178;
150 199 304 283 178 200 305 284 179;
151 200 305 284 179 201 306 285 180;
152 201 306 285 180 202 307 286 181;
153 202 307 286 181 203 308 287 182;
154 203 308 287 182 204 309 288 183;
155 204 309 288 183 205 310 289 184;
156 205 310 289 184 206 311 290 185;
157 206 311 290 185 207 312 291 186;
158 207 312 291 186 208 313 292 187;
159 208 313 292 187 209 314 293 188;
160 209 314 293 188 210 315 294 189;
161 232 337 316 211 233 338 317 212;
162 233 338 317 212 234 339 318 213;
163 234 339 318 213 235 340 319 214;
164 235 340 319 214 236 341 320 215;
165 236 341 320 215 237 342 321 216;
166 237 342 321 216 238 343 322 217;
167 238 343 322 217 239 344 323 218;
168 239 344 323 218 240 345 324 219;
169 240 345 324 219 241 346 325 220;
170 241 346 325 220 242 347 326 221;
171 242 347 326 221 243 348 327 222;
172 243 348 327 222 244 349 328 223;
173 244 349 328 223 245 350 329 224;
174 245 350 329 224 246 351 330 225;
175 246 351 330 225 247 352 331 226;
176 247 352 331 226 248 353 332 227;
177 248 353 332 227 249 354 333 228;
178 249 354 333 228 250 355 334 229;
179 250 355 334 229 251 356 335 230;
180 251 356 335 230 252 357 336 231;
181 253 358 337 232 254 359 338 233;
182 254 359 338 233 255 360 339 234;
183 255 360 339 234 256 361 340 235;
184 256 361 340 235 257 362 341 236;
185 257 362 341 236 258 363 342 237;
186 258 363 342 237 259 364 343 238;
187 259 364 343 238 260 365 344 239;
188 260 365 344 239 261 366 345 240;
189 261 366 345 240 262 367 346 241;
190 262 367 346 241 263 368 347 242;
191 263 368 347 242 264 369 348 243;
192 264 369 348 243 265 370 349 244;
193 265 370 349 244 266 371 350 245;
194 266 371 350 245 267 372 351 246;
195 267 372 351 246 268 373 352 247;
196 268 373 352 247 269 374 353 248;
197 269 374 353 248 270 375 354 249;
198 270 375 354 249 271 376 355 250;
199 271 376 355 250 272 377 356 251;
200 272 377 356 251 273 378 357 252;
201 274 379 358 253 275 380 359 254;
202 275 380 359 254 276 381 360 255;
203 276 381 360 255 277 382 361 256;
204 277 382 361 256 278 383 362 257;
205 278 383 362 257 279 384 363 258;
206 279 384 363 258 280 385 364 259;
207 280 385 364 259 281 386 365 260;
208 281 386 365 260 282 387 366 261;
209 282 387 366 261 283 388 367 262;
210 283 388 367 262 284 389 368 263;
211 284 389 368 263 285 390 369 264;
212 285 390 369 264 286 391 370 265;
213 286 391 370 265 287 392 371 266;
214 287 392 371 266 288 393 372 267;
215 288 393 372 267 289 394 373 268;
216 289 394 373 268 290 395 374 269;
217 290 395 374 269 291 396 375 270;
218 291 396 375 270 292 397 376 271;
219 292 397 376 271 293 398 377 272;
220 293 398 377 272 294 399 378 273;
221 295 400 379 274 296 401 380 275;
222 296 401 380 275 297 402 381 276;
223 297 402 381 276 298 403 382 277;
224 298 403 382 277 299 404 383 278;
225 299 404 383 278 300 405 384 279;
226 300 405 384 279 301 406 385 280;
227 301 406 385 280 302 407 386 281;
228 302 407 386 281 303 408 387 282;
229 303 408 387 282 304 409 388 283;
230 304 409 388 283 305 410 389 284;
231 305 410 389 284 306 411 390 285;
232 306 411 390 285 307 412 391 286;
233 307 412 391 286 308 413 392 287;
234 308 413 392 287 309 414 393 288;
235 309 414 393 288 310 415 394 289;
236 310 415 394 289 311 416 395 290;
237 311 416 395 290 312 417 396 291;
238 312 417 396 291 313 418 397 292;
239 313 418 397 292 314 419 398 293;
240 314 419 398 293 315 420 399 294;
241 337 442 421 316 338 443 422 317;
242 338 443 422 317 339 444 423 318;
243 339 444 423 318 340 445 424 319;
244 340 445 424 319 341 446 425 320;
245 341 446 425 320 342 447 426 321;
246 342 447 426 321 343 448 427 322;
247 343 448 427 322 344 449 428 323;
248 344 449 428 323 345 450 429 324;
249 345 450 429 324 346 451 430 325;
250 346 451 430 325 347 452 431 326;
251 347 452 431 326 348 453 432 327;
252 348 453 432 327 349 454 433 328;
253 349 454 433 328 350 455 434 329;
254 350 455 434 329 351 456 435 330;
255 351 456 435 330 352 457 436 331;
256 352 457 436 331 353 458 437 332;
257 353 458 437 332 354 459 438 333;
258 354 459 438 333 355 460 439 334;
259 355 460 439 334 356 461 440 335;
260 356 461 440 335 357 462 441 336;
261 358 463 442 337 359 464 443 338;
262 359 464 443 338 360 465 444 339;
263 360 465 444 339 361 466 445 340;
264 361 466 445 340 362 467 446 341;
265 362 467 446 341 363 468 447 342;
266 363 468 447 342 364 469 448 343;
267 364 469 448 343 365 470 449 344;
268 365 470 449 344 366 471 450 345;
269 366 471 450 345 367 472 451 346;
270 367 472 451 346 368 473 452 347;
271 368 473 452 347 369 474 453 348;
272 369 474 453 348 370 475 454 349;
273 370 475 454 349 371 476 455 350;
274 371 476 455 350 372 477 456 351;
275 372 477 456 351 373 478 457 352;
276 373 478 457 352 374 479 458 353;
277 374 479 458 353 375 480 459 354;
278 375 480 459 354 376 481 460 355;
279 376 481 460 355 377 482 461 356;
280 377 482 461 356 378 483 462 357;
281 379 484 463 358 380 485 464 359;
282 380 485 464 359 381 486 465 360;
283 381 486 465 360 382 487 466 361;
284 382 487 466 361 383 488 467 362;
285 383 488 467 362 384 489 468 363;
286 384 489 468 363 385 490 469 364;
287 385 490 469 364 386 491 470 365;
288 386 491 470 365 387 492 471 366;
289 387 492 471 366 388 493 472 367;
290 388 493 472 367 389 494 473 368;
291 389 494 473 368 390 495 474 369;
292 390 495 474 369 391 496 475 370;
293 391 496 475 370 392 497 476 371;
294 392 497 476 371 393 498 477 372;
295 393 498 477 372 394 499 478 373;
296 394 499 478 373 395 500 479 374;
297 395 500 479 374 396 501 480 375;
298 396 501 480 375 397 502 481 376;
299 397 502 481 376 398 503 482 377;
300 398 503 482 377 399 504 483 378;
301 400 505 484 379 401 506 485 380;
302 401 506 485 380 402 507 486 381;
303 402 507 486 381 403 508 487 382;
304 403 508 487 382 404 509 488 383;
305 404 509 488 383 405 510 489 384;
306 405 510 489 384 406 511 490 385;
307 406 511 490 385 407 512 491 386;
308 407 512 491 386 408 513 492 387;
309 408 513 492 387 409 514 493 388;
310 409 514 493 388 410 515 494 389;
311 410 515 494 389 411 516 495 390;
312 411 516 495 390 412 517 496 391;
313 412 517 496 391 413 518 497 392;
314 413 518 497 392 414 519 498 393;
315 414 519 498 393 415 520 499 394;
316 415 520 499 394 416 521 500 395;
317 416 521 500 395 417 522 501 396;
318 417 522 501 396 418 523 502 397;
319 418 523 502 397 419 524 503 398;
320 419 524 503 398 420 525 504 399;
MEMBER PROPERTY AMERICAN
1001 TO 1004 PRIS YD 0.2
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 1e+07
POISSON 0.3
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 ALL
SUPPORTS
1 106 211 316 421 PINNED
22 127 232 337 442 PINNED
43 148 253 358 463 PINNED
64 169 274 379 484 PINNED
85 190 295 400 505 PINNED
21 FX -48
42 FX -48
63 FX -48
84 FX -48
105 FX -48
126 FX -48
147 FX -48
168 FX -48
189 FX -48
210 FX -48
231 FX -48
252 FX -48
273 FX -48
294 FX -48
315 FX -48
336 FX -48
357 FX -48
378 FX -48
399 FX -48
420 FX -48
441 FX -48
462 FX -48
483 FX -48
504 FX -48
525 FX -48
231 FY 1000
315 FY -1000
21 FX 133.33
42 FX 133.33
63 FX 133.33
84 FX 133.33
105 FX 133.33
126 FX 66.67
147 FX 66.67
168 FX 66.67
189 FX 66.67
210 FX 66.67
336 FX -66.67
357 FX -66.67
378 FX -66.67
399 FX -66.67
420 FX -66.67
441 FX -133.33
462 FX -133.33
483 FX -133.33
504 FX -133.33
525 FX -133.33
21 FY 40
42 FY 40
63 FY 40
84 FY 40
105 FY 40
126 FY 40
147 FY 40
168 FY 40
189 FY 40
210 FY 40
231 FY 40
252 FY 40
273 FY 40
294 FY 40
315 FY 40
336 FY 40
357 FY 40
378 FY 40
399 FY 40
420 FY 40
441 FY 40
462 FY 40
483 FY 40
504 FY 40
525 FY 40
PERFORM ANALYSIS
PRINT JOINT DISPLACEMENTS LIST 21 42 63 84 105 126 147 168 189 210 -
231 252 273 294 315 336 357 378 399 420 441 462 483 504 525
PRINT JOINT DISPLACEMENTS LIST 21 105 273 441 525
PRINT JOINT DISPLACEMENTS LIST 21 42 63 84 105 126 147 168 189 210 -
231 252 273 294 315 336 357 378 399 420 441 462 483 504 525
PRINT JOINT DISPLACEMENTS LIST 21 42 63 84 105 126 147 168 189 210 -
231 252 273 294 315 336 357 378 399 420 441 462 483 504 525
PRINT ELEMENT JOINT STRESSES SOLID LIST 10
*PRINT ELEMENT JOINT STRESSES SOLID LIST 10 TO 70 BY 20
*PRINT ELEMENT JOINT STRESSES SOLID LIST 90 TO 150 BY 20
*PRINT ELEMENT JOINT STRESSES SOLID LIST 170 TO 230 BY 20
*PRINT ELEMENT JOINT STRESSES SOLID LIST 250 TO 310 BY 20
FINISH


   JOINT DISPLACEMENT (INCH RADIANS)    STRUCTURE TYPE = SPACE
------------------
JOINT  LOAD   X-TRANS   Y-TRANS   Z-TRANS   X-ROTAN   Y-ROTAN   Z-ROTAN
21    1   -0.00033  -0.00002  -0.00001   0.00000   0.00002  -0.00003
42    1   -0.00031  -0.00002  -0.00001   0.00000   0.00000   0.00000
63    1   -0.00031  -0.00002   0.00000   0.00000   0.00000   0.00000
84    1   -0.00031  -0.00002   0.00001   0.00000   0.00000   0.00000
105    1   -0.00033  -0.00002   0.00001  -0.00000  -0.00002  -0.00003
126    1   -0.00030  -0.00001  -0.00001   0.00000   0.00000   0.00000
147    1   -0.00029  -0.00001  -0.00000   0.00000   0.00000   0.00000
168    1   -0.00029  -0.00001   0.00000   0.00000   0.00000   0.00000
189    1   -0.00029  -0.00001   0.00000   0.00000   0.00000   0.00000
210    1   -0.00030  -0.00001   0.00001   0.00000   0.00000   0.00000
231    1   -0.00030   0.00000  -0.00001   0.00000   0.00000   0.00000
252    1   -0.00029   0.00000  -0.00000   0.00000   0.00000   0.00000
273    1   -0.00029   0.00000   0.00000   0.00000   0.00000   0.00000
294    1   -0.00029   0.00000   0.00000   0.00000   0.00000   0.00000
315    1   -0.00030   0.00000   0.00001   0.00000   0.00000   0.00000
336    1   -0.00030   0.00001  -0.00001   0.00000   0.00000   0.00000
357    1   -0.00029   0.00001  -0.00000   0.00000   0.00000   0.00000
378    1   -0.00029   0.00001   0.00000   0.00000   0.00000   0.00000
399    1   -0.00029   0.00001   0.00000   0.00000   0.00000   0.00000
420    1   -0.00030   0.00001   0.00001   0.00000   0.00000   0.00000
441    1   -0.00033   0.00002  -0.00001  -0.00000   0.00002   0.00003
462    1   -0.00031   0.00002  -0.00001   0.00000   0.00000   0.00000
483    1   -0.00031   0.00002   0.00000   0.00000   0.00000   0.00000
504    1   -0.00031   0.00002   0.00001   0.00000   0.00000   0.00000
525    1   -0.00033   0.00002   0.00001   0.00000  -0.00002   0.00003
************** END OF LATEST ANALYSIS RESULT **************
508. PRINT JOINT DISPLACEMENTS LIST 21 105 273 441 525
JOINT    DISPLACE LIST     21
: A CANTILEVER BEAM WITH SOLID ELEMENTS                  -- PAGE NO.   12
JOINT DISPLACEMENT (INCH RADIANS)    STRUCTURE TYPE = SPACE
------------------
JOINT  LOAD   X-TRANS   Y-TRANS   Z-TRANS   X-ROTAN   Y-ROTAN   Z-ROTAN
21    2   -0.00002   0.00149  -0.00224   0.00149   0.00001  -0.00001
105    2    0.00002  -0.00149  -0.00224   0.00149   0.00001   0.00001
273    2    0.00000   0.00000   0.00000   0.00149   0.00000   0.00000
441    2    0.00002   0.00149   0.00224   0.00149  -0.00001  -0.00001
525    2   -0.00002  -0.00149   0.00224   0.00149  -0.00001   0.00001
************** END OF LATEST ANALYSIS RESULT **************
510. PRINT JOINT DISPLACEMENTS LIST 21 42 63 84 105 126 147 168 189 210 -
JOINT    DISPLACE LIST     21
511. 231 252 273 294 315 336 357 378 399 420 441 462 483 504 525
: A CANTILEVER BEAM WITH SOLID ELEMENTS                  -- PAGE NO.   13
JOINT DISPLACEMENT (INCH RADIANS)    STRUCTURE TYPE = SPACE
------------------
JOINT  LOAD   X-TRANS   Y-TRANS   Z-TRANS   X-ROTAN   Y-ROTAN   Z-ROTAN
21    3    0.00132   0.00621   0.00004  -0.00002   0.00000   0.00088
42    3    0.00125   0.00621   0.00002   0.00000   0.00000   0.00000
63    3    0.00125   0.00621   0.00000   0.00000   0.00000   0.00000
84    3    0.00125   0.00621  -0.00002   0.00000   0.00000   0.00000
105    3    0.00132   0.00621  -0.00004   0.00002   0.00000   0.00088
126    3    0.00061   0.00619   0.00001   0.00000   0.00000   0.00000
147    3    0.00060   0.00619   0.00001   0.00000   0.00000   0.00000
168    3    0.00060   0.00619   0.00000   0.00000   0.00000   0.00000
189    3    0.00060   0.00619  -0.00001   0.00000   0.00000   0.00000
210    3    0.00061   0.00619  -0.00001   0.00000   0.00000   0.00000
231    3    0.00000   0.00618   0.00000   0.00000   0.00000   0.00000
252    3    0.00000   0.00618   0.00000   0.00000   0.00000   0.00000
273    3    0.00000   0.00619   0.00000   0.00000   0.00000   0.00088
294    3    0.00000   0.00618   0.00000   0.00000   0.00000   0.00000
315    3    0.00000   0.00618   0.00000   0.00000   0.00000   0.00000
336    3   -0.00061   0.00619  -0.00001   0.00000   0.00000   0.00000
357    3   -0.00060   0.00619  -0.00001   0.00000   0.00000   0.00000
378    3   -0.00060   0.00619   0.00000   0.00000   0.00000   0.00000
399    3   -0.00060   0.00619   0.00001   0.00000   0.00000   0.00000
420    3   -0.00061   0.00619   0.00001   0.00000   0.00000   0.00000
441    3   -0.00132   0.00621  -0.00004  -0.00002   0.00000   0.00088
462    3   -0.00125   0.00621  -0.00002   0.00000   0.00000   0.00000
483    3   -0.00125   0.00621   0.00000   0.00000   0.00000   0.00000
504    3   -0.00125   0.00621   0.00002   0.00000   0.00000   0.00000
525    3   -0.00132   0.00621   0.00004   0.00002   0.00000   0.00088
************** END OF LATEST ANALYSIS RESULT **************
513. PRINT JOINT DISPLACEMENTS LIST 21 42 63 84 105 126 147 168 189 210 -
JOINT    DISPLACE LIST     21
514. 231 252 273 294 315 336 357 378 399 420 441 462 483 504 525
: A CANTILEVER BEAM WITH SOLID ELEMENTS                  -- PAGE NO.   14
JOINT DISPLACEMENT (INCH RADIANS)    STRUCTURE TYPE = SPACE
------------------
JOINT  LOAD   X-TRANS   Y-TRANS   Z-TRANS   X-ROTAN   Y-ROTAN   Z-ROTAN
21    4    0.00372   0.02537  -0.00001   0.00003   0.00000   0.00248
42    4    0.00373   0.02536  -0.00001   0.00000   0.00000   0.00000
63    4    0.00373   0.02535   0.00000   0.00000   0.00000   0.00000
84    4    0.00373   0.02536   0.00001   0.00000   0.00000   0.00000
105    4    0.00372   0.02537   0.00001  -0.00003   0.00000   0.00248
126    4    0.00184   0.02535  -0.00000   0.00000   0.00000   0.00000
147    4    0.00185   0.02534  -0.00000   0.00000   0.00000   0.00000
168    4    0.00185   0.02534   0.00000   0.00000   0.00000   0.00000
189    4    0.00185   0.02534   0.00000   0.00000   0.00000   0.00000
210    4    0.00184   0.02535   0.00000   0.00000   0.00000   0.00000
231    4    0.00000   0.02534   0.00000   0.00000   0.00000   0.00000
252    4    0.00000   0.02533   0.00000   0.00000   0.00000   0.00000
273    4    0.00000   0.02533   0.00000   0.00000   0.00000   0.00248
294    4    0.00000   0.02533   0.00000   0.00000   0.00000   0.00000
315    4    0.00000   0.02534   0.00000   0.00000   0.00000   0.00000
336    4   -0.00184   0.02535   0.00000   0.00000   0.00000   0.00000
357    4   -0.00185   0.02534   0.00000   0.00000   0.00000   0.00000
378    4   -0.00185   0.02534   0.00000   0.00000   0.00000   0.00000
399    4   -0.00185   0.02534  -0.00000   0.00000   0.00000   0.00000
420    4   -0.00184   0.02535  -0.00000   0.00000   0.00000   0.00000
441    4   -0.00372   0.02537   0.00001   0.00003   0.00000   0.00248
462    4   -0.00373   0.02536   0.00001   0.00000   0.00000   0.00000
483    4   -0.00373   0.02535   0.00000   0.00000   0.00000   0.00000
504    4   -0.00373   0.02536  -0.00001   0.00000   0.00000   0.00000
525    4   -0.00372   0.02537  -0.00001  -0.00003   0.00000   0.00248
************** END OF LATEST ANALYSIS RESULT **************
516. PRINT ELEMENT JOINT STRESSES SOLID LIST 10
ELEMENT  JOINT    STRESSES SOLID
: A CANTILEVER BEAM WITH SOLID ELEMENTS                  -- PAGE NO.   15
ELEMENT STRESSES        UNITS= POUNINCH
-------------------------------------------------------------------------------
NODE/           NORMAL STRESSES               SHEAR STRESSES
ELEMENT LOAD CENTER      SXX       SYY       SZZ       SXY       SYZ       SZX
-------------------------------------------------------------------------------
10    1     31   -200.005    -0.003     0.000     0.001     0.000    -0.001
10    1    136   -199.999    -0.003     0.001     0.001    -0.000    -0.000
10    1    115   -200.000    -0.003     0.002     0.001    -0.000    -0.000
10    1     10   -200.007    -0.003    -0.000     0.001    -0.000    -0.001
10    1     32   -200.004    -0.001     0.001     0.001    -0.000    -0.000
10    1    137   -199.999    -0.001     0.000     0.001     0.000    -0.001
10    1    116   -200.000    -0.002     0.000     0.001     0.000    -0.000
10    1     11   -200.007    -0.002     0.001     0.001     0.000    -0.001
10    1 CENTER   -200.003    -0.002     0.001     0.001    -0.000    -0.000
S1=      0.001   S2=     -0.002   S3=   -200.003   SE=    200.002
DC=      -0.000    -0.017     1.000     0.000     1.000     0.017
10    2     31      0.006    -0.006    -0.008   137.619     0.001  -279.913
10    2    136      0.006    -0.004    -0.004   137.618     0.003   -53.160
10    2    115      0.006    -0.009    -0.006   390.964     0.002   -53.159
10    2     10      0.007    -0.010    -0.009   390.962    -0.000  -279.913
10    2     32      0.005     0.004     0.008   137.619     0.000  -279.913
10    2    137      0.002     0.002     0.003   137.618    -0.002   -53.160
10    2    116      0.006     0.007     0.005   390.963    -0.001   -53.159
10    2     11      0.011     0.009     0.010   390.962     0.001  -279.914
10    2 CENTER      0.006    -0.001    -0.000   264.291     0.001  -166.536
S1=    312.387   S2=      0.000   S3=   -312.382   SE=    541.066
DC=       0.707     0.598    -0.377     0.000     0.533     0.846
: A CANTILEVER BEAM WITH SOLID ELEMENTS                  -- PAGE NO.   16
ELEMENT STRESSES        UNITS= POUNINCH
-------------------------------------------------------------------------------
NODE/           NORMAL STRESSES               SHEAR STRESSES
ELEMENT LOAD CENTER      SXX       SYY       SZZ       SXY       SYZ       SZX
-------------------------------------------------------------------------------
10    3     31    833.325    -0.002    -0.000     0.000     0.000     0.000
10    3    136    416.662    -0.002    -0.000    -0.000     0.000     0.000
10    3    115    416.662    -0.002    -0.001     0.000     0.000     0.000
10    3     10    833.325    -0.002    -0.000     0.000     0.000     0.000
10    3     32    833.325     0.000     0.000     0.000     0.000     0.000
10    3    137    416.662     0.001     0.000    -0.000    -0.000     0.000
10    3    116    416.662     0.001     0.000     0.000    -0.000     0.000
10    3     11    833.325     0.001     0.000    -0.000     0.000     0.000
10    3 CENTER    624.994    -0.001    -0.000     0.000     0.000     0.000
S1=    624.994   S2=     -0.000   S3=     -0.001   SE=    624.994
DC=       1.000     0.000     0.000     0.000     0.000     1.000
10    4     31   2619.592   -45.597   -52.800   101.363     2.404    -4.541
10    4    136   1317.907   -34.780   -27.561   101.362     2.404    -2.110
10    4    115   1317.908   -34.781   -27.562   115.768    -2.403     2.697
10    4     10   2619.594   -45.598   -52.801   115.768    -2.404    -9.349
10    4     32   2630.409    45.589    52.800   101.363    -2.404    -4.541
10    4    137   1307.089    34.772    27.558   101.363    -2.404    -2.110
10    4    116   1307.091    34.773    27.559   115.768     2.404     2.698
10    4     11   2630.412    45.590    52.800   115.767     2.404    -9.349
10    4 CENTER   1968.750    -0.004    -0.001   108.565     0.000    -3.326
S1=   1974.724   S2=     -0.001   S3=     -5.978   SE=   1977.721
DC=       0.998     0.055    -0.002    -0.000     0.031     1.000