EX. UK-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\UK\UK-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 MMS
DEFINE MATERIAL START
ISOTROPIC CONCRETE
E 21.0
POISSON 0.17
DENSITY 2.4e-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 23.00.00.*** * * Proprietary Program of * * Bentley Systems, Inc. * * Date= MAY 4, 2023 * * Time= 13:11:54 * * * * Licensed to: Bentley Systems Inc * **************************************************** 1. STAAD SPACE FREQUENCIES OF VIBRATION OF A SKEWED BRIDGE INPUT FILE: D:\Documentation\STAAD.Pro\_Automated Py\output\2023-05-04\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 MMS 48. DEFINE MATERIAL START 49. ISOTROPIC CONCRETE 50. E 21.0 51. POISSON 0.17 52. DENSITY 2.4E-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 1.637 0.61071 2 2.604 0.38399 3 2.886 0.34652 4 3.760 0.26597 5 4.083 0.24494 6 4.396 0.22747 7 4.533 0.22062 8 4.696 0.21293 9 5.049 0.19806 10 7.232 0.13828 11 7.281 0.13734 12 7.407 0.13501 13 10.360 0.09653 14 10.758 0.09296 15 11.195 0.08932 16 11.310 0.08841 17 11.605 0.08617 18 11.872 0.08423 19 11.956 0.08364 20 12.134 0.08241 21 12.542 0.07974 22 13.727 0.07285 23 14.719 0.06794 24 14.831 0.06743 25 15.202 0.06578 26 17.387 0.05751 27 17.560 0.05695 28 17.828 0.05609 29 19.795 0.05052 30 19.988 0.05003 31 20.596 0.04855 32 20.688 0.04834 33 20.901 0.04785 34 21.212 0.04714 35 21.502 0.04651 36 21.873 0.04572 37 22.161 0.04512 38 23.248 0.04301 39 23.593 0.04239 40 24.075 0.04154 41 24.730 0.04044 42 25.535 0.03916 43 26.120 0.03828 44 26.537 0.03768 45 26.938 0.03712 46 27.433 0.03645 47 27.884 0.03586 48 29.090 0.03438 49 29.686 0.03369 50 29.927 0.03341 51 31.110 0.03214 FREQUENCIES OF VIBRATION OF A SKEWED BRIDGE -- PAGE NO. 5 CALCULATED FREQUENCIES FOR LOAD CASE 1 MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC) 52 31.643 0.03160 53 31.824 0.03142 54 32.121 0.03113 55 32.701 0.03058 56 33.002 0.03030 57 34.257 0.02919 58 35.053 0.02853 59 35.310 0.02832 60 35.548 0.02813 61 36.095 0.02770 62 36.688 0.02726 63 38.682 0.02585 64 38.951 0.02567 65 39.661 0.02521 MODAL WEIGHT (MODAL MASS TIMES g) IN KGS GENERALIZED MODE X Y Z WEIGHT 1 1.313672E+02 1.108398E+00 1.201129E+06 1.221103E+06 2 1.105162E+06 2.912622E+00 2.323269E+02 1.098762E+06 3 2.073649E-01 2.786898E+03 2.769101E+00 5.493268E+05 4 1.462758E+00 3.955818E+04 6.224106E+00 2.014392E+05 5 2.818490E-01 4.828385E+02 5.992502E+02 1.365709E+05 6 5.598604E+02 6.953900E+02 2.771716E+02 9.013609E+04 7 1.854187E+01 3.566982E+05 3.225212E+00 7.500848E+04 8 5.356242E+00 2.742697E+05 8.417095E+00 7.765617E+04 9 5.904817E+03 1.694393E+03 2.261244E+03 7.013562E+04 10 4.430377E+00 1.534484E+03 4.903639E-01 4.388408E+04 11 4.601393E+00 6.655514E+02 1.207885E+00 4.369367E+04 12 2.289314E-01 4.228225E+02 7.787098E-01 3.999065E+04 13 3.993157E+01 2.747181E+00 6.896335E+03 1.557242E+05 14 2.161567E-01 1.315486E+02 1.086174E+02 7.218063E+04 15 2.743077E-02 4.349509E+03 1.227626E+02 4.601683E+04 16 7.932399E+00 7.722762E+01 1.715499E+02 5.132691E+04 17 9.357269E+00 2.437766E+00 6.022200E-01 5.278384E+04 18 1.310402E+02 1.245065E+01 1.558885E+02 8.975814E+04 19 3.237358E-01 3.119274E+01 4.475092E+00 4.629568E+04 20 9.860828E+00 7.537996E+01 1.815535E+01 7.571097E+04 21 8.020853E-01 2.958744E+00 4.741305E+00 7.486690E+04 22 1.257488E+02 1.348115E-01 1.747276E+00 4.145462E+05 23 6.964422E+00 4.654827E+01 8.396615E+01 6.993260E+04 24 4.645357E-01 1.888568E+02 6.969984E+00 5.688589E+04 25 8.396620E+00 1.087438E+01 2.082024E+02 4.957080E+04 26 3.970981E-01 2.273349E+03 6.502642E-03 2.916350E+04 27 8.158171E+00 3.453441E+02 9.698586E-01 3.234756E+04 FREQUENCIES OF VIBRATION OF A SKEWED BRIDGE -- PAGE NO. 6 28 2.411181E+00 1.344046E+04 2.572347E-01 3.030211E+04 29 6.757432E+02 6.222985E+03 5.878092E+01 3.533053E+04 30 3.712278E+01 4.299742E+04 5.310814E+00 3.319031E+04 31 2.171634E+02 2.603085E+02 6.963874E-01 2.870320E+04 32 2.478604E+01 4.222519E+04 2.375592E-03 3.571038E+04 33 9.426945E+00 2.074711E+03 7.006805E-01 3.546272E+04 34 1.318033E+01 1.391960E+02 9.997939E+00 3.683261E+04 35 2.655567E+00 5.108468E+03 2.202262E+00 4.277587E+04 36 3.664638E-01 4.719298E+00 1.036419E+00 5.132263E+04 37 1.618305E+00 2.671420E+04 8.032944E-01 4.385049E+04 38 1.289408E+00 8.348047E+01 2.136199E-02 1.948813E+04 39 1.090681E-02 3.990261E+02 4.500325E-01 1.839953E+04 40 2.516875E-03 2.838393E+01 1.672893E-04 4.285791E+05 41 1.800354E+00 1.729541E+03 1.115900E+01 4.982347E+04 42 3.094704E-01 5.689236E+04 1.057619E-01 7.183174E+04 43 4.237560E+00 7.117003E+02 1.709904E+00 7.941099E+04 44 6.985981E-03 7.120621E+02 2.228543E-02 7.795531E+04 45 1.090046E-02 2.815537E+02 8.068273E-04 1.854435E+05 46 3.867976E-01 1.895886E+03 9.105723E-03 2.331780E+04 47 1.245474E+01 2.154164E+00 1.786947E+00 1.432475E+04 48 6.042358E-03 4.552571E+03 7.449196E-02 2.931614E+04 49 3.089849E+00 1.585498E+01 2.356090E-01 4.790401E+04 50 5.917700E-01 3.501022E-02 3.813271E+00 4.319210E+04 51 7.531865E-03 1.363633E+02 1.039786E-01 2.739737E+04 52 3.396939E-01 2.796655E+00 9.065380E-01 4.399495E+04 53 7.633919E-01 1.251482E+03 2.100451E-01 3.694608E+04 54 1.113975E+01 6.123655E+01 4.429348E+00 4.883033E+04 55 4.296741E-01 2.619401E+02 5.431140E+00 2.644050E+04 56 1.724619E-01 8.197998E+02 1.827260E-02 3.670345E+04 57 5.833701E-01 9.933417E+01 1.283571E+00 3.868065E+04 58 6.173715E+00 1.663166E+03 1.165825E+01 4.293976E+04 59 3.968332E+00 1.254915E+01 1.776702E+01 3.983809E+04 60 7.435025E+00 5.085940E+02 5.033208E+01 5.274970E+04 61 5.168555E+01 1.721488E+03 3.628858E+01 1.212435E+04 62 2.675386E+01 3.225244E+03 1.680691E+01 1.478013E+04 63 1.898740E-01 5.111631E+02 4.371451E-01 7.704926E+04 64 1.017851E-01 3.878617E+03 1.786230E-01 6.212678E+04 65 7.558339E+00 2.180679E+03 1.533813E+01 3.321933E+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 99.043 2 99.14 0.00 0.02 99.153 0.000 99.063 3 0.00 0.23 0.00 99.154 0.230 99.063 4 0.00 3.26 0.00 99.154 3.492 99.063 5 0.00 0.04 0.05 99.154 3.532 99.113 6 0.05 0.06 0.02 99.204 3.589 99.136 7 0.00 29.41 0.00 99.206 33.002 99.136 8 0.00 22.62 0.00 99.206 55.618 99.137 9 0.53 0.14 0.19 99.736 55.758 99.323 10 0.00 0.13 0.00 99.736 55.884 99.323 11 0.00 0.05 0.00 99.737 55.939 99.323 12 0.00 0.03 0.00 99.737 55.974 99.323 13 0.00 0.00 0.57 99.740 55.974 99.892 14 0.00 0.01 0.01 99.740 55.985 99.901 15 0.00 0.36 0.01 99.740 56.344 99.911 16 0.00 0.01 0.01 99.741 56.350 99.925 17 0.00 0.00 0.00 99.742 56.350 99.925 18 0.01 0.00 0.01 99.753 56.351 99.938 19 0.00 0.00 0.00 99.754 56.354 99.938 20 0.00 0.01 0.00 99.754 56.360 99.940 21 0.00 0.00 0.00 99.754 56.360 99.940 22 0.01 0.00 0.00 99.766 56.360 99.940 23 0.00 0.00 0.01 99.766 56.364 99.947 24 0.00 0.02 0.00 99.766 56.380 99.948 25 0.00 0.00 0.02 99.767 56.381 99.965 26 0.00 0.19 0.00 99.767 56.568 99.965 27 0.00 0.03 0.00 99.768 56.597 99.965 28 0.00 1.11 0.00 99.768 57.705 99.965 29 0.06 0.51 0.00 99.829 58.218 99.970 30 0.00 3.55 0.00 99.832 61.763 99.970 31 0.02 0.02 0.00 99.852 61.785 99.971 32 0.00 3.48 0.00 99.854 65.267 99.971 33 0.00 0.17 0.00 99.855 65.438 99.971 34 0.00 0.01 0.00 99.856 65.449 99.971 35 0.00 0.42 0.00 99.856 65.871 99.972 36 0.00 0.00 0.00 99.856 65.871 99.972 37 0.00 2.20 0.00 99.856 68.074 99.972 38 0.00 0.01 0.00 99.856 68.081 99.972 39 0.00 0.03 0.00 99.856 68.114 99.972 40 0.00 0.00 0.00 99.856 68.116 99.972 41 0.00 0.14 0.00 99.857 68.259 99.973 42 0.00 4.69 0.00 99.857 72.950 99.973 43 0.00 0.06 0.00 99.857 73.008 99.973 44 0.00 0.06 0.00 99.857 73.067 99.973 45 0.00 0.02 0.00 99.857 73.090 99.973 46 0.00 0.16 0.00 99.857 73.247 99.973 47 0.00 0.00 0.00 99.858 73.247 99.973 48 0.00 0.38 0.00 99.858 73.622 99.973 49 0.00 0.00 0.00 99.858 73.624 99.973 50 0.00 0.00 0.00 99.858 73.624 99.973 51 0.00 0.01 0.00 99.858 73.635 99.973 52 0.00 0.00 0.00 99.858 73.635 99.973 53 0.00 0.10 0.00 99.859 73.738 99.973 54 0.00 0.01 0.00 99.860 73.743 99.974 55 0.00 0.02 0.00 99.860 73.765 99.974 56 0.00 0.07 0.00 99.860 73.833 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 73.841 99.974 58 0.00 0.14 0.00 99.860 73.978 99.975 59 0.00 0.00 0.00 99.861 73.979 99.977 60 0.00 0.04 0.00 99.861 74.021 99.981 61 0.00 0.14 0.00 99.866 74.163 99.984 62 0.00 0.27 0.00 99.868 74.429 99.985 63 0.00 0.04 0.00 99.868 74.471 99.985 64 0.00 0.32 0.00 99.868 74.791 99.985 65 0.00 0.18 0.00 99.869 74.971 99.987 90. FINISH FREQUENCIES OF VIBRATION OF A SKEWED BRIDGE -- PAGE NO. 9 *********** END OF THE STAAD.Pro RUN *********** **** DATE= MAY 4,2023 TIME= 13:11:57 **** ************************************************************ * 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 * ************************************************************