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Application Examples (U.K.)
Example Problem No. 11
Dynamic analysis (Response Spectrum) is performed for a steel structure. Results of a static and dynamic analysis are combined. The combined results are then used for steel design.
Actual input is shown in bold lettering followed by explanation.
STAAD PLANE RESPONSE SPECTRUM ANALYSIS
Every input has to start with the word STAAD. The word PLANE signifies that the structure is a plane frame structure and the geometry is defined through X and Y axes.
UNIT METER KNS
Specifies the unit to be used.
JOINT COORDINATES
1 0.0 0.0 0.0 ; 2 6.0 0.0 0.0
3 0.0 3.0 0.0 ; 4 6.0 3.0 0.0
5 0.0 6.0 0.0 ; 6 6.0 6.0 0.0
Joint number followed by X, Y and Z coordinates are provided above. Since this is a plane structure, the Z coordinates are all the same, in this case, zeros. Semicolon signs (;) are used as line separators to allow for input of multiple sets of data on one line.
MEMBER INCIDENCES
1 1 3 ; 2 2 4 ; 3 3 5 ; 4 4 6
5 3 4 ; 6 5 6
Defines the members by the joints they are connected to.
MEMBER PROPERTIES BRITISH
1 TO 4 TA ST UC254X254X73
5 TA ST UB305X165X54
6 TA ST UB203X133X30
Properties for all members are assigned from the British steel table. The word ST stands for standard single section.
SUPPORTS
1 2 FIXED
Fixed supports are specified at joints 1 and 2.
UNIT MMS
CONSTANTS
E 210.0 ALL
POISSON STEEL ALL
DEN 76.977E-09 ALL
Material constants such as E (modulus of elasticity), Poisson’s ratio and DENsity are specified above. Length unit is changed from METER to MMS to facilitate the input.
CUT OFF MODE SHAPE 2
The number of mode shapes to be considered in dynamic analysis is set to 2. Without the above command, this will be set to the default which can be found in section 5 of the Technical Reference Manual.
* LOAD 1 WILL BE STATIC LOAD
UNIT METER
LOAD 1 DEAD AND LIVE LOADS
Load case 1 is initiated followed by a title. Prior to this, the length unit is changed to METER for specifying distributed member loads. A line starting with an asterisk (*) mark indicates a comment line.
SELFWEIGHT Y -1.0
The above command indicates that the selfweight of the structure acting in the global Y direction is part of this load case. The factor of -1.0 is meant to indicate that the load acts opposite to the positive direction of global Y, hence downwards.
MEMBER LOADS
5 CON GY -25.0 1.8
5 CON GY -37.5 3.0
5 CON GY -25.0 4.2
5 6 UNI Y -22.5
Load 1 contains member loads also. GY indicates that the load is in the global Y direction while Y indicates local Y direction. The word UNI stands for uniformly distributed load while CON stands for concentrated load. GY is followed by the value of the load and the distance at which it is applied.
* NEXT LOAD WILL BE RESPONSE SPECTRUM LOAD
* WITH MASSES PROVIDED IN TERMS OF LOAD.
LOAD 2 SEISMIC LOADING
The two lines which begin with the asterisk are comment lines which tell us the purpose of the next load case. Load case 2 is then initiated along with an optional title. This will be a dynamic load case. Permanent masses will be provided in the form of loads. These masses (in terms of loads) will be considered for the eigensolution. Internally, the program converts these loads to masses, hence it is best to specify them as absolute values (without a negative sign). Also, the direction (X, Y, Z etc.) of the loads will correspond to the dynamic degrees of freedom in which the masses are capable of vibrating. In a PLANE frame, only X and Y directions need to be considered. In a SPACE frame, masses (loads) should be provided in all three (X, Y and Z) directions if they are active along all three. The user has the freedom to restrict one or more directions.
SELFWEIGHT X 1.0
SELFWEIGHT Y 1.0
The above commands indicate that the selfweight of the structure acting in the global X and Y directions with a factor of 1.0 is taken into consideration for the mass matrix.
MEMBER LOADS
5 CON GX 25.0 1.8
5 CON GY 25.0 1.8
5 CON GX 37.5 3.0
5 CON GY 37.5 3.0
5 CON GX 25.0 4.2
5 CON GY 25.0 4.2
The mass matrix will also consist of terms derived from the above member loads. GX and GY indicate that the load, and hence the resulting mass, is capable of vibration along the global X and Y directions. The word CON stands for concentrated load. Concentrated forces of 25, 37.5, and 25 kNs are located at 1.8m, 3.0m and 4.2m from the start of member 5.
SPECTRUM CQC X 1.0 ACC DAMP 0.05 SCALE 9.806
0.03 1.00 ; 0.05 1.35
0.1 1.95 ; 0.2 2.80
0.5 2.80 ; 1.0 1.60
The above SPECTRUM command specifies that the modal responses be combined using the CQC method (alternatives being the SRSS method, ABS method, etc.). The spectrum effect is in the global X direction with a factor of 1.0. Since this spectrum is in terms of ACCeleration (the other possibility being displacement), the spectrum data is given as period vs. acceleration. Damping ratio of 0.05 (5%) and a scale factor of 9.806 are used. The scale factor is the quantity by which spectral accelerations (and spectral displacements) must be multiplied by before they are used in the calculations. The values of periods and the corresponding accelerations are given in the last 3 lines.
LOAD COMBINATION 3
1 0.75 2 0.75
LOAD COMBINATION 4
1 0.75 2 -0.75
In a response spectrum analysis, the sign of the forces cannot be determined, and hence are absolute numbers. Consequently, to account for the fact that the force could be positive or negative, it is necessary to create 2 load combination cases. That is what is being done above. Load combination case no. 3 consists of the sum of the static load case (1) with the positive direction of the dynamic load case (2). Load combination case no. 4 consists of the
sum of the static load case (1) with the negative direction of the dynamic load case (2). In both cases, the result is factored by 0.75.
PERFORM ANALYSIS PRINT MODE SHAPES
This command instructs the program to proceed with the analysis. The PRINT command instructs the program to print mode shape values.
PRINT ANALYSIS RESULTS
Displacements, reactions and member forces are recorded in the output file using the above command.
LOAD LIST 1 3 4
PARAMETER
CODE BRITISH
SELECT ALL
A steel design in the form of a member selection is performed based on the rules of the British code. Only the member forces resulting from load cases 1, 3 and 4 will be considered for these calculations.
FINISH
This command terminates the STAAD run.
****************************************************
* *
* STAAD.Pro *
* Version Bld *
* Proprietary Program of *
* Research Engineers, Intl. *
* Date= *
* Time= *
* *
* USER ID: *
****************************************************
1. STAAD PLANE RESPONSE SPECTRUM ANALYSIS
2. UNIT METER KNS
3. JOINT COORDINATES
4. 1 0.0 0.0 0.0 ; 2 6.0 0.0 0.0
5. 3 0.0 3.0 0.0 ; 4 6.0 3.0 0.0
6. 5 0.0 6.0 0.0 ; 6 6.0 6.0 0.0
7. MEMBER INCIDENCES
8. 1 1 3 ; 2 2 4 ; 3 3 5 ; 4 4 6
9. 5 3 4 ; 6 5 6
10. MEMBER PROPERTIES BRITISH
11. 1 TO 4 TA ST UC254X254X73
12. 5 TA ST UB305X165X54
13. 6 TA ST UB203X133X30
14. SUPPORTS
15. 1 2 FIXED
16. UNIT MMS
17. CONSTANTS
18. E 210.0 ALL
19. POISSON STEEL ALL
20. DEN 76.977E-09 ALL
21. CUT OFF MODE SHAPE 2
22. * LOAD 1 WILL BE STATIC LOAD
23. UNIT METER
24. LOAD 1 DEAD AND LIVE LOADS
25. SELFWEIGHT Y -1.0
26. MEMBER LOADS
27. 5 CON GY -25.0 1.8
28. 5 CON GY -37.5 3.0
29. 5 CON GY -25.0 4.2
30. 5 6 UNI Y -22.5
31. * NEXT LOAD WILL BE RESPONSE SPECTRUM LOAD
32. * WITH MASSES PROVIDED IN TERMS OF LOAD.
33. LOAD 2 SEISMIC LOADING
34. SELFWEIGHT X 1.0
35. SELFWEIGHT Y 1.0
36. MEMBER LOADS
37. 5 CON GX 25.0 1.8
38. 5 CON GY 25.0 1.8
39. 5 CON GX 37.5 3.0
40. 5 CON GY 37.5 3.0
41. 5 CON GX 25.0 4.2
42. 5 CON GY 25.0 4.2
43. SPECTRUM CQC X 1.0 ACC DAMP 0.05 SCALE 9.806
44. 0.03 1.00 ; 0.05 1.35
45. 0.1 1.95 ; 0.2 2.80
46. 0.5 2.80 ; 1.0 1.60
47. LOAD COMBINATION 3
48. 1 0.75 2 0.75
49. LOAD COMBINATION 4
50. 1 0.75 2 -0.75
51. PERFORM ANALYSIS PRINT MODE SHAPES
P R O B L E M S T A T I S T I C S
-----------------------------------
NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 6/ 6/ 2
ORIGINAL/FINAL BAND-WIDTH= 2/ 2/ 9 DOF
TOTAL PRIMARY LOAD CASES = 2, TOTAL DEGREES OF FREEDOM = 12
SIZE OF STIFFNESS MATRIX = 1 DOUBLE KILO-WORDS
REQRD/AVAIL. DISK SPACE = 12.0/ 38897.1 MB
NUMBER OF MODES REQUESTED = 2
NUMBER OF EXISTING MASSES IN THE MODEL = 8
NUMBER OF MODES THAT WILL BE USED = 2
CALCULATED FREQUENCIES FOR LOAD CASE 2
MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC) ACCURACY
1 5.179 0.19308 2.209E-10
2 19.437 0.05145 6.482E-08
The following Frequencies are estimates that were calculated. These are for
information only and will not be used. Remaining values are either above
the cut off mode/freq values or are of low accuracy. To use these
frequencies, rerun with a higher cutoff mode (or mode + freq) value.
CALCULATED FREQUENCIES FOR LOAD CASE 2
MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC) ACCURACY
3 50.784 0.01969 2.891E-10
4 57.172 0.01749 3.977E-10
MODE SHAPES
-----------
JOINT MODE X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN
1 1 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00
2 1 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00
3 1 0.58328 0.00218 0.00000 0.000E+00 0.000E+00 -3.863E-03
4 1 0.58328 -0.00218 0.00000 0.000E+00 0.000E+00 -3.863E-03
5 1 1.00000 0.00251 0.00000 0.000E+00 0.000E+00 -2.797E-03
6 1 1.00000 -0.00251 0.00000 0.000E+00 0.000E+00 -2.797E-03
MODE SHAPES
-----------
JOINT MODE X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN
1 2 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00
2 2 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00
3 2 -0.07067 0.00282 0.00000 0.000E+00 0.000E+00 -2.798E-03
4 2 -0.07067 -0.00282 0.00000 0.000E+00 0.000E+00 -2.798E-03
5 2 1.00000 0.00400 0.00000 0.000E+00 0.000E+00 -9.742E-03
6 2 1.00000 -0.00400 0.00000 0.000E+00 0.000E+00 -9.742E-03
RESPONSE LOAD CASE 2
CQC MODAL COMBINATION METHOD USED.
DYNAMIC WEIGHT X Y Z 9.889183E+01 9.889183E+01 0.000000E+00 KNS
MISSING WEIGHT X Y Z -3.077453E-04 -9.889183E+01 0.000000E+00 KNS
MODAL WEIGHT X Y Z 9.889152E+01 6.308759E-36 0.000000E+00 KNS
MODE ACCELERATION-G DAMPING
---- -------------- -------
1 2.74097 0.05000
2 1.36730 0.05000
PARTICIPATION FACTORS
MASS PARTICIPATION FACTORS IN PERCENT BASE SHEAR IN KNS
-------------------------------------- ------------------
MODE X Y Z SUMM-X SUMM-Y SUMM-Z X Y Z
1 98.20 0.00 0.00 98.197 0.000 0.000 266.17 0.00 0.00
2 1.80 0.00 0.00 100.000 0.000 0.000 2.44 0.00 0.00
---------------------------
TOTAL SRSS SHEAR 266.18 0.00 0.00
TOTAL 10PCT SHEAR 266.18 0.00 0.00
TOTAL ABS SHEAR 268.61 0.00 0.00
TOTAL CQC SHEAR 266.18 0.00 0.00
52. PRINT ANALYSIS RESULTS
JOINT DISPLACEMENT (CM RADIANS) STRUCTURE TYPE = PLANE
------------------
JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN
1 1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
3 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
4 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
2 1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
3 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
4 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
3 1 -0.0042 -0.0283 0.0000 0.0000 0.0000 -0.0017
2 2.4239 0.0091 0.0000 0.0000 0.0000 0.0063
3 1.8148 -0.0144 0.0000 0.0000 0.0000 0.0035
4 -1.8210 -0.0280 0.0000 0.0000 0.0000 -0.0060
4 1 0.0042 -0.0283 0.0000 0.0000 0.0000 0.0017
2 2.4239 0.0091 0.0000 0.0000 0.0000 0.0063
3 1.8210 -0.0144 0.0000 0.0000 0.0000 0.0060
4 -1.8148 -0.0280 0.0000 0.0000 0.0000 -0.0035
5 1 0.0163 -0.0390 0.0000 0.0000 0.0000 -0.0017
2 4.1560 0.0104 0.0000 0.0000 0.0000 0.0046
3 3.1292 -0.0214 0.0000 0.0000 0.0000 0.0022
4 -3.1048 -0.0371 0.0000 0.0000 0.0000 -0.0047
6 1 -0.0163 -0.0390 0.0000 0.0000 0.0000 0.0017
2 4.1560 0.0104 0.0000 0.0000 0.0000 0.0046
3 3.1048 -0.0214 0.0000 0.0000 0.0000 0.0047
4 -3.1292 -0.0371 0.0000 0.0000 0.0000 -0.0022
SUPPORT REACTIONS -UNIT KNS METE STRUCTURE TYPE = PLANE
-----------------
JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z
1 1 23.48 185.52 0.00 0.00 0.00 -21.57
2 133.09 59.00 0.00 0.00 0.00 250.11
3 117.43 183.39 0.00 0.00 0.00 171.40
4 -82.21 94.89 0.00 0.00 0.00 -203.76
2 1 -23.48 185.52 0.00 0.00 0.00 21.57
2 133.09 59.00 0.00 0.00 0.00 250.11
3 82.21 183.39 0.00 0.00 0.00 203.76
4 -117.43 94.89 0.00 0.00 0.00 -171.40
MEMBER END FORCES STRUCTURE TYPE = PLANE
-----------------
ALL UNITS ARE -- KNS METE
MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z
1 1 1 185.52 -23.48 0.00 0.00 0.00 -21.57
3 -183.37 23.48 0.00 0.00 0.00 -48.85
2 1 59.00 133.09 0.00 0.00 0.00 250.11
3 59.00 133.09 0.00 0.00 0.00 149.17
3 1 183.39 82.21 0.00 0.00 0.00 171.40
3 -93.28 117.43 0.00 0.00 0.00 75.24
4 1 94.89 -117.43 0.00 0.00 0.00 -203.76
3 -181.78 -82.21 0.00 0.00 0.00 -148.52
2 1 2 185.52 23.48 0.00 0.00 0.00 21.57
4 -183.37 -23.48 0.00 0.00 0.00 48.85
2 2 59.00 133.09 0.00 0.00 0.00 250.11
4 59.00 133.09 0.00 0.00 0.00 149.17
3 2 183.39 117.43 0.00 0.00 0.00 203.76
4 -93.28 82.21 0.00 0.00 0.00 148.52
4 2 94.89 -82.21 0.00 0.00 0.00 -171.40
4 -181.78 -117.43 0.00 0.00 0.00 -75.24
3 1 3 70.53 -43.63 0.00 0.00 0.00 -65.87
5 -68.38 43.63 0.00 0.00 0.00 -65.03
2 3 9.07 8.95 0.00 0.00 0.00 3.88
5 9.07 8.95 0.00 0.00 0.00 27.13
3 3 59.70 -26.01 0.00 0.00 0.00 -46.49
5 -44.49 39.44 0.00 0.00 0.00 -28.42
4 3 46.10 -39.44 0.00 0.00 0.00 -52.32
5 -58.09 26.01 0.00 0.00 0.00 -69.12
4 1 4 70.53 43.63 0.00 0.00 0.00 65.87
6 -68.38 -43.63 0.00 0.00 0.00 65.03
2 4 9.07 8.95 0.00 0.00 0.00 3.88
6 9.07 8.95 0.00 0.00 0.00 27.13
3 4 59.70 39.44 0.00 0.00 0.00 52.32
6 -44.49 -26.01 0.00 0.00 0.00 69.12
4 4 46.10 26.01 0.00 0.00 0.00 46.49
6 -58.09 -39.44 0.00 0.00 0.00 28.42
5 1 3 -20.16 112.84 0.00 0.00 0.00 114.73
4 20.16 112.84 0.00 0.00 0.00 -114.73
2 3 0.00 49.47 0.00 0.00 0.00 148.41
4 0.00 49.47 0.00 0.00 0.00 148.41
3 3 -15.12 121.73 0.00 0.00 0.00 197.35
4 15.12 121.73 0.00 0.00 0.00 25.26
4 3 -15.12 47.53 0.00 0.00 0.00 -25.26
4 15.12 47.53 0.00 0.00 0.00 -197.35
6 1 5 43.63 68.38 0.00 0.00 0.00 65.03
6 -43.63 68.38 0.00 0.00 0.00 -65.03
2 5 0.00 9.04 0.00 0.00 0.00 27.13
6 0.00 9.04 0.00 0.00 0.00 27.13
3 5 32.73 58.07 0.00 0.00 0.00 69.12
6 -32.73 58.07 0.00 0.00 0.00 -28.42
4 5 32.73 44.50 0.00 0.00 0.00 28.42
6 -32.73 44.50 0.00 0.00 0.00 -69.12
************** END OF LATEST ANALYSIS RESULT **************
53. LOAD LIST 1 3 4
54. PARAMETER
55. CODE BRITISH
56. SELECT ALL
STAAD.Pro MEMBER SELECTION - (BSI )
**************************
ALL UNITS ARE - KNS METE (UNLESS OTHERWISE NOTED)
MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/
FX MY MZ LOCATION
=======================================================================
1 ST UC254X254X73 PASS ANNEX I.1 0.767 4
181.78 C 0.00 203.76 -
2 ST UC254X254X73 PASS ANNEX I.1 0.767 3
183.39 C 0.00 203.76 -
3 ST UC203X203X46 PASS BS-4.3.6 0.551 4
46.10 C 0.00 69.12 0.00
4 ST UC203X203X46 PASS BS-4.3.6 0.551 3
59.70 C 0.00 69.12 0.00
5 ST UB457X191X82 PASS BS-4.3.6 0.898 3
15.12 T 0.00 197.35 0.00
6 ST UB356X171X45 PASS ANNEX I.1 0.979 4
32.73 C 0.00 69.12 -
************** END OF TABULATED RESULT OF DESIGN **************
57. FINISH
****************************************************************************
**WARNING** SOME MEMBER SIZES HAVE CHANGED SINCE LAST ANALYSIS.
IN THE POST PROCESSOR, MEMBER QUERIES WILL USE THE LAST
ANALYSIS FORCES WITH THE UPDATED MEMBER SIZES.
TO CORRECT THIS INCONSISTENCY, PLEASE DO ONE MORE ANALYSIS.
FROM THE UPPER MENU, PRESS RESULTS, UPDATE PROPERTIES, THEN
FILE SAVE; THEN ANALYZE AGAIN WITHOUT THE GROUP OR SELECT
COMMANDS.
****************************************************************************
*********** END OF THE STAAD.Pro RUN ***********
**** DATE= TIME= ****
************************************************************
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