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 2024\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
FINISH
PAGE NO. 1
****************************************************
* *
* STAAD.Pro 2023 *
* Version 23.00.03.** *
* Proprietary Program of *
* Bentley Systems, Inc. *
* Date= JUL 4, 2024 *
* Time= 11:28: 8 *
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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 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= JUL 4,2024 TIME= 11:28:11 ****
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