EX. US-28 Calculation of Modes and Frequencies of a Bridge
This example demonstrates the input required for obtaining the modes and frequencies of the skewed bridge shown in the figure below. The structure consists of piers, pier-cap girders and a deck slab.
This problem is installed with the program by default to C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples\Sample Models\US\US-28 Calculation of Modes and Frequencies of a Bridge.std when you install the program.
Input File
STAAD SPACE FREQUENCIES OF VIBRATION OF A SKEWED BRIDGE
IGNORE LIST
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 4 0 0; 3 6.5 0 0; 4 9 0 0; 5 11.5 0 0; 6 15.5 0 0;
11 -1 10 0 25 16.5 10 0
REPEAT ALL 3 4 0 14
MEMBER INCI
1 1 13 ; 2 2 15 ; 3 3 17 ; 4 4 19 ; 5 5 21 ; 6 6 23
26 26 34 ; 27 27 36 ; 28 28 38 ; 29 29 40 ; 30 30 42 ; 31 31 44
47 47 55 ; 48 48 57 ; 49 49 59 ; 50 50 61 ; 51 51 63 ; 52 52 65
68 68 76 ; 69 69 78 ; 70 70 80 ; 71 71 82 ; 72 72 84 ; 73 73 86
101 11 12 114
202 32 33 215
303 53 54 316
404 74 75 417
DEFINE MESH
A JOINT 11
B JOINT 25
C JOINT 46
D JOINT 32
E JOINT 67
F JOINT 53
G JOINT 88
H JOINT 74
GENERATE ELEMENT
MESH ABCD 14 12
MESH DCEF 14 12
MESH FEGH 14 12
START GROUP DEFINITION
MEMBER
_GIRDERS 101 TO 114 202 TO 215 303 TO 316 404 TO 417
_PIERS 1 TO 6 26 TO 31 47 TO 52 68 TO 73
ELEMENT
_P1 447 TO 450 454 TO 457 461 TO 464 468 TO 471
_P2 531 TO 534 538 TO 541 545 TO 548 552 TO 555
_P3 615 TO 618 622 TO 625 629 TO 632 636 TO 639
_P4 713 TO 716 720 TO 723 727 TO 730 734 TO 737
_P5 783 TO 786 790 TO 793 797 TO 800 804 TO 807
_P6 881 TO 884 888 TO 891 895 TO 898 902 TO 905
END GROUP DEFINITION
MEMBER PROPERTY
_GIRDERS PRIS YD 0.6 ZD 0.6
_PIERS PRIS YD 1.0
ELEMENT PROPERTY
YRA 9 11 TH 0.375
UNIT KNS MMS
DEFINE MATERIAL START
ISOTROPIC CONCRETE
E 21.0
POISSON 0.17
DENSITY 2.36158e-008
ALPHA 5e-006
DAMP 0.05
G 9.25
TYPE CONCRETE
STRENGTH FCU 0.0275
END DEFINE MATERIAL
CONSTANTS
MATERIAL CONCRETE ALL
SUPPORTS
1 TO 6 26 TO 31 47 TO 52 68 TO 73 FIXED
CUT OFF MODE SHAPE 65
UNIT KGS METER
LOAD 1 FREQUENCY CALCULATION
SELFWEIGHT X 1.0
SELFWEIGHT Y 1.0
SELFWEIGHT Z 1.0
* PERMANENT WEIGHTS ON DECK
ELEMENT LOAD
YRA 9 11 PR GX 200
YRA 9 11 PR GY 200
YRA 9 11 PR GZ 200
* VEHICLES ON SPANS - ONLY Y & Z EFFECT CONSIDERED
ELEMENT LOAD
_P1 PR GY 700
_P2 PR GY 700
_P3 PR GY 700
_P4 PR GY 700
_P5 PR GY 700
_P6 PR GY 700
_P1 PR GZ 700
_P2 PR GZ 700
_P3 PR GZ 700
_P4 PR GZ 700
_P5 PR GZ 700
_P6 PR GZ 700
MODAL CALCULATION REQUESTED
PERFORM ANALYSIS
FINISHSTAAD Output File
PAGE NO. 1 **************************************************** * * * STAAD.Pro 2023 * * Version 23.00.02.*** * * Proprietary Program of * * Bentley Systems, Inc. * * Date= DEC 15, 2023 * * Time= 16: 0:49 * * * * Licensed to: Bentley Systems Inc * **************************************************** 1. STAAD SPACE FREQUENCIES OF VIBRATION OF A SKEWED BRIDGE INPUT FILE: D:\Documentation\STAAD.Pro\_Automated_Py\output\2023-12-15\SPro_Output_Input_Files\Sample .. .STD 2. IGNORE LIST 3. UNIT METER KN 4. JOINT COORDINATES 5. 1 0 0 0; 2 4 0 0; 3 6.5 0 0; 4 9 0 0; 5 11.5 0 0; 6 15.5 0 0 6. 11 -1 10 0 25 16.5 10 0 7. REPEAT ALL 3 4 0 14 8. MEMBER INCI 9. 1 1 13 ; 2 2 15 ; 3 3 17 ; 4 4 19 ; 5 5 21 ; 6 6 23 10. 26 26 34 ; 27 27 36 ; 28 28 38 ; 29 29 40 ; 30 30 42 ; 31 31 44 11. 47 47 55 ; 48 48 57 ; 49 49 59 ; 50 50 61 ; 51 51 63 ; 52 52 65 12. 68 68 76 ; 69 69 78 ; 70 70 80 ; 71 71 82 ; 72 72 84 ; 73 73 86 13. 101 11 12 114 14. 202 32 33 215 15. 303 53 54 316 16. 404 74 75 417 17. DEFINE MESH 18. A JOINT 11 19. B JOINT 25 20. C JOINT 46 21. D JOINT 32 22. E JOINT 67 23. F JOINT 53 24. G JOINT 88 25. H JOINT 74 26. GENERATE ELEMENT 27. MESH ABCD 14 12 28. MESH DCEF 14 12 29. MESH FEGH 14 12 30. START GROUP DEFINITION 31. MEMBER 32. _GIRDERS 101 TO 114 202 TO 215 303 TO 316 404 TO 417 33. _PIERS 1 TO 6 26 TO 31 47 TO 52 68 TO 73 34. ELEMENT 35. _P1 447 TO 450 454 TO 457 461 TO 464 468 TO 471 36. _P2 531 TO 534 538 TO 541 545 TO 548 552 TO 555 37. _P3 615 TO 618 622 TO 625 629 TO 632 636 TO 639 38. _P4 713 TO 716 720 TO 723 727 TO 730 734 TO 737 FREQUENCIES OF VIBRATION OF A SKEWED BRIDGE -- PAGE NO. 2 39. _P5 783 TO 786 790 TO 793 797 TO 800 804 TO 807 40. _P6 881 TO 884 888 TO 891 895 TO 898 902 TO 905 41. END GROUP DEFINITION 42. MEMBER PROPERTY 43. _GIRDERS PRIS YD 0.6 ZD 0.6 44. _PIERS PRIS YD 1.0 45. ELEMENT PROPERTY 46. YRA 9 11 TH 0.375 47. UNIT KNS MMS 48. DEFINE MATERIAL START 49. ISOTROPIC CONCRETE 50. E 21.0 51. POISSON 0.17 52. DENSITY 2.36158E-008 53. ALPHA 5E-006 54. DAMP 0.05 55. G 9.25 56. TYPE CONCRETE 57. STRENGTH FCU 0.0275 58. END DEFINE MATERIAL 59. CONSTANTS 60. MATERIAL CONCRETE ALL 61. SUPPORTS 62. 1 TO 6 26 TO 31 47 TO 52 68 TO 73 FIXED 63. CUT OFF MODE SHAPE 65 64. UNIT KGS METER 65. LOAD 1 FREQUENCY CALCULATION 66. SELFWEIGHT X 1.0 67. SELFWEIGHT Y 1.0 68. SELFWEIGHT Z 1.0 69. * PERMANENT WEIGHTS ON DECK 70. ELEMENT LOAD 71. YRA 9 11 PR GX 200 72. YRA 9 11 PR GY 200 73. YRA 9 11 PR GZ 200 74. * VEHICLES ON SPANS - ONLY Y & Z EFFECT CONSIDERED 75. ELEMENT LOAD 76. _P1 PR GY 700 77. _P2 PR GY 700 78. _P3 PR GY 700 79. _P4 PR GY 700 80. _P5 PR GY 700 81. _P6 PR GY 700 82. _P1 PR GZ 700 83. _P2 PR GZ 700 84. _P3 PR GZ 700 85. _P4 PR GZ 700 86. _P5 PR GZ 700 87. _P6 PR GZ 700 88. MODAL CALCULATION REQUESTED 89. PERFORM ANALYSIS FREQUENCIES OF VIBRATION OF A SKEWED BRIDGE -- PAGE NO. 3 P R O B L E M S T A T I S T I C S ----------------------------------- NUMBER OF JOINTS 579 NUMBER OF MEMBERS 80 NUMBER OF PLATES 504 NUMBER OF SOLIDS 0 NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 24 Using 64-bit analysis engine. SOLVER USED IS THE IN-CORE ADVANCED MATH SOLVER TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 3330 TOTAL LOAD COMBINATION CASES = 0 SO FAR. ** WARNING: PRESSURE LOADS ON ELEMENTS OTHER THAN PLATE ELEMENTS ARE IGNORED. ELEM.NO. 101 ** WARNING: PRESSURE LOADS ON ELEMENTS OTHER THAN PLATE ELEMENTS ARE IGNORED. ELEM.NO. 101 ** WARNING: PRESSURE LOADS ON ELEMENTS OTHER THAN PLATE ELEMENTS ARE IGNORED. ELEM.NO. 101 ***NOTE: MASSES DEFINED UNDER LOAD# 1 WILL FORM THE FINAL MASS MATRIX FOR DYNAMIC ANALYSIS. EIGEN METHOD : SUBSPACE ------------------------- NUMBER OF MODES REQUESTED = 65 NUMBER OF EXISTING MASSES IN THE MODEL = 1665 NUMBER OF MODES THAT WILL BE USED = 65 *** EIGENSOLUTION : ADVANCED METHOD *** FREQUENCIES OF VIBRATION OF A SKEWED BRIDGE -- PAGE NO. 4 CALCULATED FREQUENCIES FOR LOAD CASE 1 MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC) 1 1.648 0.60681 2 2.622 0.38132 3 2.906 0.34409 4 3.783 0.26436 5 4.108 0.24345 6 4.423 0.22608 7 4.561 0.21927 8 4.725 0.21162 9 5.080 0.19684 10 7.277 0.13742 11 7.328 0.13647 12 7.454 0.13416 13 10.418 0.09599 14 10.818 0.09244 15 11.260 0.08881 16 11.377 0.08790 17 11.672 0.08567 18 11.945 0.08372 19 12.028 0.08314 20 12.209 0.08191 21 12.619 0.07925 22 13.823 0.07234 23 14.807 0.06754 24 14.920 0.06702 25 15.294 0.06539 26 17.489 0.05718 27 17.664 0.05661 28 17.937 0.05575 29 19.923 0.05019 30 20.116 0.04971 31 20.724 0.04825 32 20.817 0.04804 33 21.024 0.04756 34 21.340 0.04686 35 21.633 0.04623 36 22.002 0.04545 37 22.290 0.04486 38 23.393 0.04275 39 23.738 0.04213 40 24.235 0.04126 41 24.881 0.04019 42 25.690 0.03893 43 26.275 0.03806 44 26.700 0.03745 45 27.124 0.03687 46 27.610 0.03622 47 28.063 0.03563 48 29.272 0.03416 49 29.866 0.03348 50 30.118 0.03320 51 31.309 0.03194 FREQUENCIES OF VIBRATION OF A SKEWED BRIDGE -- PAGE NO. 5 CALCULATED FREQUENCIES FOR LOAD CASE 1 MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC) 52 31.832 0.03142 53 32.014 0.03124 54 32.312 0.03095 55 32.906 0.03039 56 33.204 0.03012 57 34.467 0.02901 58 35.270 0.02835 59 35.522 0.02815 60 35.766 0.02796 61 36.318 0.02753 62 36.919 0.02709 63 38.921 0.02569 64 39.189 0.02552 65 39.905 0.02506 MODAL WEIGHT (MODAL MASS TIMES g) IN KGS GENERALIZED MODE X Y Z WEIGHT 1 1.291934E+02 1.123418E+00 1.185768E+06 1.205497E+06 2 1.089784E+06 2.961298E+00 2.290601E+02 1.083499E+06 3 2.111306E-01 2.767724E+03 2.799804E+00 5.416754E+05 4 1.488365E+00 3.916563E+04 6.302102E+00 1.988939E+05 5 2.650657E-01 4.869465E+02 5.916391E+02 1.348431E+05 6 5.553985E+02 7.047738E+02 2.743600E+02 8.887365E+04 7 1.872127E+01 3.523236E+05 3.255370E+00 7.402632E+04 8 5.441681E+00 2.711803E+05 8.530684E+00 7.667142E+04 9 5.838996E+03 1.713501E+03 2.233780E+03 6.923635E+04 10 4.436158E+00 1.508718E+03 4.951104E-01 4.324923E+04 11 4.522846E+00 6.614279E+02 1.224734E+00 4.305570E+04 12 2.322126E-01 4.156161E+02 7.878947E-01 3.944772E+04 13 3.968726E+01 2.882564E+00 6.818221E+03 1.532777E+05 14 2.085091E-01 1.298117E+02 1.097372E+02 7.154577E+04 15 2.752974E-02 4.303212E+03 1.232103E+02 4.541365E+04 16 7.726809E+00 7.931786E+01 1.710543E+02 5.083780E+04 17 9.187165E+00 2.295488E+00 5.600056E-01 5.231609E+04 18 1.289274E+02 1.227798E+01 1.533801E+02 8.841806E+04 19 3.797408E-01 3.151484E+01 4.203883E+00 4.601297E+04 20 9.958856E+00 7.524730E+01 1.835670E+01 7.466321E+04 21 8.006146E-01 2.974809E+00 4.620779E+00 7.378575E+04 22 1.242891E+02 1.356224E-01 1.727536E+00 4.087678E+05 23 6.938982E+00 4.623798E+01 8.257328E+01 6.864460E+04 24 4.653175E-01 1.849773E+02 6.876842E+00 5.597259E+04 25 8.352727E+00 1.093998E+01 2.047659E+02 4.884299E+04 26 3.879229E-01 2.187085E+03 5.145218E-03 2.890765E+04 27 8.086885E+00 3.229583E+02 9.429697E-01 3.202062E+04 FREQUENCIES OF VIBRATION OF A SKEWED BRIDGE -- PAGE NO. 6 28 2.443751E+00 1.315502E+04 2.609740E-01 2.997395E+04 29 6.642359E+02 6.512258E+03 5.785467E+01 3.489561E+04 30 3.896515E+01 4.236802E+04 5.583570E+00 3.273818E+04 31 2.124308E+02 2.362562E+02 6.791406E-01 2.856038E+04 32 2.501307E+01 4.154716E+04 1.610248E-03 3.529900E+04 33 9.944393E+00 2.188227E+03 7.002218E-01 3.488091E+04 34 1.354775E+01 1.273812E+02 9.929674E+00 3.662762E+04 35 2.684736E+00 5.035591E+03 2.202823E+00 4.255654E+04 36 3.584198E-01 7.349881E+00 1.032835E+00 5.119778E+04 37 1.674724E+00 2.647461E+04 8.112263E-01 4.340583E+04 38 1.234580E+00 8.274586E+01 1.831619E-02 1.919433E+04 39 1.177019E-02 3.952054E+02 4.526474E-01 1.820400E+04 40 2.510682E-03 2.913923E+01 2.643008E-04 4.236454E+05 41 1.752055E+00 1.750469E+03 1.098303E+01 4.948152E+04 42 3.172853E-01 5.576266E+04 1.029036E-01 7.029313E+04 43 4.088524E+00 7.230284E+02 1.647904E+00 7.840900E+04 44 6.792844E-03 6.810530E+02 2.323051E-02 7.748353E+04 45 1.286032E-02 2.969021E+02 6.276731E-04 1.698166E+05 46 3.915110E-01 1.842050E+03 1.016859E-02 2.296592E+04 47 1.222720E+01 2.250049E+00 1.763239E+00 1.408108E+04 48 5.796924E-03 4.479735E+03 7.592468E-02 2.885324E+04 49 3.062960E+00 1.622740E+01 2.516519E-01 4.734347E+04 50 5.381654E-01 2.109875E-02 3.715996E+00 4.275013E+04 51 6.988027E-03 1.414464E+02 1.037723E-01 2.721877E+04 52 3.120314E-01 2.679203E+00 8.601323E-01 4.346363E+04 53 7.712285E-01 1.227296E+03 2.159809E-01 3.644744E+04 54 1.092693E+01 6.309261E+01 4.335824E+00 4.837668E+04 55 4.389927E-01 2.654929E+02 5.449158E+00 2.579368E+04 56 1.697410E-01 8.013763E+02 1.519167E-02 3.565397E+04 57 5.812394E-01 1.003674E+02 1.297763E+00 3.819235E+04 58 6.155775E+00 1.623267E+03 1.175780E+01 4.182908E+04 59 3.892790E+00 1.515229E+01 1.764828E+01 3.953446E+04 60 7.019893E+00 5.144657E+02 4.912786E+01 5.200588E+04 61 5.075761E+01 1.707431E+03 3.625510E+01 1.190568E+04 62 2.640553E+01 3.154571E+03 1.681321E+01 1.455738E+04 63 1.733228E-01 5.382845E+02 4.096147E-01 7.325642E+04 64 1.024425E-01 3.773902E+03 1.746056E-01 6.231664E+04 65 7.508947E+00 2.059276E+03 1.501086E+01 3.298603E+04 FREQUENCIES OF VIBRATION OF A SKEWED BRIDGE -- PAGE NO. 7 MASS PARTICIPATION FACTORS MASS PARTICIPATION FACTORS IN PERCENT -------------------------------------- MODE X Y Z SUMM-X SUMM-Y SUMM-Z 1 0.01 0.00 99.04 0.012 0.000 99.042 2 99.14 0.00 0.02 99.152 0.000 99.061 3 0.00 0.23 0.00 99.152 0.232 99.061 4 0.00 3.27 0.00 99.152 3.503 99.062 5 0.00 0.04 0.05 99.152 3.544 99.111 6 0.05 0.06 0.02 99.202 3.602 99.134 7 0.00 29.43 0.00 99.204 33.030 99.134 8 0.00 22.65 0.00 99.205 55.681 99.135 9 0.53 0.14 0.19 99.736 55.824 99.322 10 0.00 0.13 0.00 99.736 55.950 99.322 11 0.00 0.06 0.00 99.737 56.005 99.322 12 0.00 0.03 0.00 99.737 56.040 99.322 13 0.00 0.00 0.57 99.740 56.040 99.891 14 0.00 0.01 0.01 99.740 56.051 99.901 15 0.00 0.36 0.01 99.740 56.411 99.911 16 0.00 0.01 0.01 99.741 56.417 99.925 17 0.00 0.00 0.00 99.742 56.417 99.925 18 0.01 0.00 0.01 99.754 56.418 99.938 19 0.00 0.00 0.00 99.754 56.421 99.938 20 0.00 0.01 0.00 99.754 56.427 99.940 21 0.00 0.00 0.00 99.755 56.428 99.940 22 0.01 0.00 0.00 99.766 56.428 99.940 23 0.00 0.00 0.01 99.766 56.431 99.947 24 0.00 0.02 0.00 99.767 56.447 99.948 25 0.00 0.00 0.02 99.767 56.448 99.965 26 0.00 0.18 0.00 99.767 56.630 99.965 27 0.00 0.03 0.00 99.768 56.657 99.965 28 0.00 1.10 0.00 99.768 57.756 99.965 29 0.06 0.54 0.00 99.829 58.300 99.970 30 0.00 3.54 0.00 99.832 61.839 99.970 31 0.02 0.02 0.00 99.852 61.859 99.971 32 0.00 3.47 0.00 99.854 65.329 99.971 33 0.00 0.18 0.00 99.855 65.512 99.971 34 0.00 0.01 0.00 99.856 65.522 99.971 35 0.00 0.42 0.00 99.856 65.943 99.972 36 0.00 0.00 0.00 99.856 65.944 99.972 37 0.00 2.21 0.00 99.856 68.155 99.972 38 0.00 0.01 0.00 99.857 68.162 99.972 39 0.00 0.03 0.00 99.857 68.195 99.972 40 0.00 0.00 0.00 99.857 68.197 99.972 41 0.00 0.15 0.00 99.857 68.343 99.973 42 0.00 4.66 0.00 99.857 73.001 99.973 43 0.00 0.06 0.00 99.857 73.061 99.973 44 0.00 0.06 0.00 99.857 73.118 99.973 45 0.00 0.02 0.00 99.857 73.143 99.973 46 0.00 0.15 0.00 99.857 73.297 99.973 47 0.00 0.00 0.00 99.858 73.297 99.973 48 0.00 0.37 0.00 99.858 73.671 99.973 49 0.00 0.00 0.00 99.859 73.673 99.973 50 0.00 0.00 0.00 99.859 73.673 99.973 51 0.00 0.01 0.00 99.859 73.685 99.973 52 0.00 0.00 0.00 99.859 73.685 99.973 53 0.00 0.10 0.00 99.859 73.787 99.973 54 0.00 0.01 0.00 99.860 73.793 99.974 55 0.00 0.02 0.00 99.860 73.815 99.974 56 0.00 0.07 0.00 99.860 73.882 99.974 FREQUENCIES OF VIBRATION OF A SKEWED BRIDGE -- PAGE NO. 8 MASS PARTICIPATION FACTORS IN PERCENT -------------------------------------- MODE X Y Z SUMM-X SUMM-Y SUMM-Z 57 0.00 0.01 0.00 99.860 73.890 99.974 58 0.00 0.14 0.00 99.860 74.026 99.975 59 0.00 0.00 0.00 99.861 74.027 99.977 60 0.00 0.04 0.00 99.861 74.070 99.981 61 0.00 0.14 0.00 99.866 74.212 99.984 62 0.00 0.26 0.00 99.868 74.476 99.985 63 0.00 0.04 0.00 99.868 74.521 99.985 64 0.00 0.32 0.00 99.868 74.836 99.985 65 0.00 0.17 0.00 99.869 75.008 99.987 90. FINISH FREQUENCIES OF VIBRATION OF A SKEWED BRIDGE -- PAGE NO. 9 *********** END OF THE STAAD.Pro RUN *********** **** DATE= DEC 15,2023 TIME= 16: 0:52 **** ************************************************************ * For technical assistance on STAAD.Pro, please visit * * http://www.bentley.com/en/support/ * * * * Details about additional assistance from * * Bentley and Partners can be found at program menu * * Help->Technical Support * * * * Copyright (c) Bentley Systems, Inc. * * http://www.bentley.com * ************************************************************