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 2024\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
FINISH
PAGE NO. 1
****************************************************
* *
* STAAD.Pro 2023 *
* Version 23.00.03.** *
* Proprietary Program of *
* Bentley Systems, Inc. *
* Date= JUL 4, 2024 *
* Time= 11:22:20 *
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* Licensed to: Bentley Systems Inc *
****************************************************
1. STAAD SPACE FREQUENCIES OF VIBRATION OF A SKEWED BRIDGE
INPUT FILE: D:\Documentation\STAAD.Pro\_Automated_Py\output\2024-07-04\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= JUL 4,2024 TIME= 11:22:23 ****
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