EX. US-22 Time History Analysis for Sinusoidal Loading
A space frame structure is subjected to a sinusoidal (dynamic) loading. The commands necessary to describe the sine function are demonstrated in this example. Time History analysis is performed on this model.
This problem is installed with the program by default to C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\Sample Models\US\US-22 Time History Analysis for Sinusoidal Loading.STD when you install the program.
STAAD SPACE
*EXAMPLE FOR HARMONIC LOADING GENERATOR
Every STAAD input file has to begin with the word STAAD.
The word SPACE signifies that the structure is a space frame and the geometry is defined through X, Y, and Z axes. The comment line which begins with an asterisk is an optional title to identify this project.
UNIT KIP FEET
The units for the data that follows are specified above.
JOINT COORDINATES
1 0 0 0 ; 2 15 0 0 ; 3 15 0 15 ; 4 0 0 15
5 0 20 0 ; 6 7.5 20 0 ; 7 15 20 0 ; 8 15 20 7.5
9 15 20 15 ; 10 7.5 20 15 ; 11 0 20 15
12 0 20 7.5
The joint number followed by the X, Y and Z coordinates are specified above.
MEMBER INCIDENCES
1 1 5 ; 2 2 7 ; 3 3 9 ; 4 4 11 ; 5 5 6 ; 6 6 7
7 7 8 ; 8 8 9 ; 9 9 10 ; 10 10 11 ; 11 11 12 ; 12 12 5
13 6 13 ; 14 13 10 ; 15 8 13 ; 16 13 12
The members are defined by the joints to which they are connected.
UNIT INCH
MEMBER PROPERTIES
1 TO 12 PRIS YD 12 ZD 12
Members 1 to 12 are defined as PRISmatic sections with width and depth values of 12 inches. The UNIT command is specified to change the units for input from FEET to INCHes.
SUPPORTS
1 TO 4 PINNED
Joints 1 to 4 are declared to be pinned-supported.
DEFINE MATERIAL START
ISOTROPIC CONCRETE
E 3150
POISSON 0.17
DENSITY 8.68e-005
ALPHA 5e-006
DAMP 0.05
G 1346.15
TYPE CONCRETE
STRENGTH FCU 4
END DEFINE MATERIAL
CONSTANTS
MATERIAL CONCRETE ALL
The DEFINE MATERIAL command is used to specify material properties and the CONSTANT is used to assign the material to all members.
DEFINE TIME HISTORY
TYPE 1 FORCE
* FOLLOWING LINES FOR HARMONIC LOADING GENERATOR
FUNCTION SINE
AMPLITUDE 6.2831 FREQUENCY 60 CYCLES 100
*
ARRIVAL TIMES
0.0
DAMPING 0.075
There are two stages in the command specification required for a time-history analysis. The first stage is defined above. Here, the parameters of the sinusoidal loading are provided.
Each data set is individually identified by the number that follows the TYPE command. In this file, only one data set is defined, which is apparent from the fact that only one TYPE is defined.
The word FORCE that follows the TYPE 1 command signifies that this data set is for a forcing function. (If you want to specify an earthquake motion, an ACCELERATION may be specified.)
The command FUNCTION SINE indicates that instead of providing the data set as discrete TIME-FORCE pairs, a sinusoidal function, which describes the variation of force with time, is provided.
The parameters of the sine function, such as FREQUENCY, AMPLITUDE, and number of CYCLES of application are then defined. STAAD internally generates discrete TIME-FORCE pairs of data from the sine function in steps of time defined by the default value (refer to TR.31.4 Definition of Time History Load for more information). The arrival time value indicates the relative value of time at which the force begins to act upon the structure. The modal damping ratio for all the modes is set to 0.075.
LOAD 1 STATIC LOAD CASE
MEMBER LOAD
5 6 7 8 9 10 11 12 UNI GY -1.0
The above data describe a static load case.
LOAD 2 DYNAMIC LOAD CASE
SELFWEIGHT X 1.0
SELFWEIGHT Y 1.0
SELFWEIGHT Z 1.0
JOINT LOAD
8 12 FX 4.0
8 12 FY 4.0
8 12 FZ 4.0
TIME LOAD
8 12 FX 1 1
This is the second stage of command specification for time history analysis. The two sets of data specified here are:
- the weights for generation of the mass matrix
- the application of the time varying loads on the structure.
The weights (from which the masses for the mass matrix are obtained) are specified in the form of selfweight and joint loads.
Following that, the sinusoidal force is applied using the TIME LOAD command. The forcing function described by the TYPE 1 load is applied on joints 8 and 12 and it starts to act starting at a time defined by the 1st arrival time number.
PERFORM ANALYSIS
PRINT ANALYSIS RESULTS
FINI
The above commands are self explanatory. The FINISH command terminates the STAAD run.
Input File
STAAD SPACE EXAMPLE FOR HARMONIC LOADING GENERATOR
UNIT KIP FEET
JOINT COORDINATES
1 0 0 0 ; 2 15 0 0 ; 3 15 0 15 ; 4 0 0 15
5 0 20 0 ; 6 7.5 20 0 ; 7 15 20 0 ; 8 15 20 7.5
9 15 20 15 ; 10 7.5 20 15 ; 11 0 20 15
12 0 20 7.5
MEMBER INCIDENCES
1 1 5 ; 2 2 7 ; 3 3 9 ; 4 4 11 ; 5 5 6 ; 6 6 7
7 7 8 ; 8 8 9 ; 9 9 10 ; 10 10 11 ; 11 11 12 ; 12 12 5
UNIT INCH
MEMBER PROPERTIES
1 TO 12 PRIS YD 12 ZD 12
SUPPORTS
1 TO 4 PINNED
DEFINE MATERIAL START
ISOTROPIC CONCRETE
E 3150
POISSON 0.17
DENSITY 8.68e-005
ALPHA 5e-006
DAMP 0.05
G 1346.15
TYPE CONCRETE
STRENGTH FCU 4
END DEFINE MATERIAL
CONSTANTS
MATERIAL CONCRETE ALL
DEFINE TIME HISTORY
TYPE 1 FORCE
* FOLLOWING LINES FOR HARMONIC LOADING GENERATOR
FUNCTION SINE
AMPLITUDE 6.2831 FREQUENCY 60 CYCLES 100
*
ARRIVAL TIMES
0.0
DAMPING 0.075
LOAD 1 STATIC LOAD CASE
MEMBER LOAD
5 6 7 8 9 10 11 12 UNI GY -1.0
LOAD 2 DYNAMIC LOAD CASE
SELFWEIGHT X 1.0
SELFWEIGHT Y 1.0
SELFWEIGHT Z 1.0
JOINT LOAD
8 12 FX 4.0
8 12 FY 4.0
8 12 FZ 4.0
TIME LOAD
8 12 FX 1 1
PERFORM ANALYSIS
PRINT ANALYSIS RESULTS
FINI
STAAD Output File
PAGE NO. 1 **************************************************** * * * STAAD.Pro CONNECT Edition * * Version 22.12.00.*** * * Proprietary Program of * * Bentley Systems, Inc. * * Date= OCT 27, 2022 * * Time= 15: 9:36 * * * * Licensed to: Bentley Systems Inc * **************************************************** 1. STAAD SPACE EXAMPLE FOR HARMONIC LOADING GENERATOR INPUT FILE: US-22 Time History Analysis for Sinusoidal Loading.STD 2. UNIT KIP FEET 3. JOINT COORDINATES 4. 1 0 0 0 ; 2 15 0 0 ; 3 15 0 15 ; 4 0 0 15 5. 5 0 20 0 ; 6 7.5 20 0 ; 7 15 20 0 ; 8 15 20 7.5 6. 9 15 20 15 ; 10 7.5 20 15 ; 11 0 20 15 7. 12 0 20 7.5 8. MEMBER INCIDENCES 9. 1 1 5 ; 2 2 7 ; 3 3 9 ; 4 4 11 ; 5 5 6 ; 6 6 7 10. 7 7 8 ; 8 8 9 ; 9 9 10 ; 10 10 11 ; 11 11 12 ; 12 12 5 11. UNIT INCH 12. MEMBER PROPERTIES 13. 1 TO 12 PRIS YD 12 ZD 12 14. SUPPORTS 15. 1 TO 4 PINNED 16. DEFINE MATERIAL START 17. ISOTROPIC CONCRETE 18. E 3150 19. POISSON 0.17 20. DENSITY 8.68E-005 21. ALPHA 5E-006 22. DAMP 0.05 23. G 1346.15 24. TYPE CONCRETE 25. STRENGTH FCU 4 26. END DEFINE MATERIAL 27. CONSTANTS 28. MATERIAL CONCRETE ALL 29. DEFINE TIME HISTORY 30. TYPE 1 FORCE 31. * FOLLOWING LINES FOR HARMONIC LOADING GENERATOR 32. FUNCTION SINE 33. AMPLITUDE 6.2831 FREQUENCY 60 CYCLES 100 EXAMPLE FOR HARMONIC LOADING GENERATOR -- PAGE NO. 2 FOR SEQUENTIAL HARMONIC FORCING CURVE NUMBER= 1 NUMBER OF POINTS IN DIGITIZED HARMONIC FUNCTION= 1201 NUMBER OF POINTS PER QUARTER CYCLE OF HARMONIC FUNCTION= 3 FORCE STEP DELTA TIME PER POINT 1.38889E-03 ENDING TIME FOR THIS DIGITIZED HARMONIC FUNCTION 1.66667E+00 34. * 35. ARRIVAL TIMES 36. 0.0 37. DAMPING 0.075 38. LOAD 1 STATIC LOAD CASE 39. MEMBER LOAD 40. 5 6 7 8 9 10 11 12 UNI GY -1.0 41. LOAD 2 DYNAMIC LOAD CASE 42. SELFWEIGHT X 1.0 43. SELFWEIGHT Y 1.0 44. SELFWEIGHT Z 1.0 45. JOINT LOAD 46. 8 12 FX 4.0 47. 8 12 FY 4.0 48. 8 12 FZ 4.0 49. TIME LOAD 50. 8 12 FX 1 1 51. PERFORM ANALYSIS P R O B L E M S T A T I S T I C S ----------------------------------- NUMBER OF JOINTS 12 NUMBER OF MEMBERS 12 NUMBER OF PLATES 0 NUMBER OF SOLIDS 0 NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 4 Using 64-bit analysis engine. SOLVER USED IS THE IN-CORE ADVANCED MATH SOLVER TOTAL PRIMARY LOAD CASES = 2, TOTAL DEGREES OF FREEDOM = 60 TOTAL LOAD COMBINATION CASES = 0 SO FAR. ***NOTE: MASSES DEFINED UNDER LOAD# 2 WILL FORM THE FINAL MASS MATRIX FOR DYNAMIC ANALYSIS. EXAMPLE FOR HARMONIC LOADING GENERATOR -- PAGE NO. 3 EIGEN METHOD : SUBSPACE ------------------------- NUMBER OF MODES REQUESTED = 6 NUMBER OF EXISTING MASSES IN THE MODEL = 24 NUMBER OF MODES THAT WILL BE USED = 6 *** EIGENSOLUTION : ADVANCED METHOD *** EXAMPLE FOR HARMONIC LOADING GENERATOR -- PAGE NO. 4 CALCULATED FREQUENCIES FOR LOAD CASE 2 MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC) 1 1.202 0.83191 2 1.204 0.83057 3 1.451 0.68908 4 7.559 0.13229 5 11.073 0.09031 6 11.670 0.08569 MODAL WEIGHT (MODAL MASS TIMES g) IN KIP GENERALIZED MODE X Y Z WEIGHT 1 2.299868E+01 5.213994E-29 2.154110E-25 2.280506E+01 2 2.148403E-25 9.984362E-31 2.299902E+01 2.293083E+01 3 2.180358E-21 1.626557E-31 2.281548E-21 3.300665E+01 4 1.122613E-24 1.446952E-29 2.732241E-24 2.026121E+01 5 4.006222E-23 5.345261E-06 4.306780E-20 1.127253E+01 6 1.341889E-20 1.076830E+01 1.183963E-23 1.025517E+01 MASS PARTICIPATION FACTORS MASS PARTICIPATION FACTORS IN PERCENT -------------------------------------- MODE X Y Z SUMM-X SUMM-Y SUMM-Z 1 100.00 0.00 0.00 99.998 0.000 0.000 2 0.00 0.00 100.00 99.998 0.000 100.000 3 0.00 0.00 0.00 99.998 0.000 100.000 4 0.00 0.00 0.00 99.998 0.000 100.000 5 0.00 0.00 0.00 99.998 0.000 100.000 6 0.00 46.82 0.00 99.998 46.821 100.000 EXAMPLE FOR HARMONIC LOADING GENERATOR -- PAGE NO. 5 A C T U A L MODAL D A M P I N G USED IN ANALYSIS MODE DAMPING 1 0.07500000 2 0.07500000 3 0.07500000 4 0.07500000 5 0.07500000 6 0.07500000 TIME STEP USED IN TIME HISTORY ANALYSIS = 0.00139 SECONDS NUMBER OF MODES WHOSE CONTRIBUTION IS CONSIDERED = 6 TIME DURATION OF TIME HISTORY ANALYSIS = 1.667 SECONDS NUMBER OF TIME STEPS IN THE SOLUTION PROCESS = 1200 52. PRINT ANALYSIS RESULTS BASE SHEAR UNITS ARE -- KIP INCH MAXIMUM BASE SHEAR X= -2.228746E-01 Y= 1.490116E-08 Z= 2.273737E-13 AT TIMES 0.194444 1.519444 0.072222 ANALYSIS RESULTS EXAMPLE FOR HARMONIC LOADING GENERATOR -- PAGE NO. 6 JOINT DISPLACEMENT (INCH RADIANS) STRUCTURE TYPE = SPACE ------------------ JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN 1 1 0.00000 0.00000 0.00000 -0.01045 0.00000 0.01045 2 0.00000 0.00000 0.00000 0.00000 0.00000 -0.00037 2 1 0.00000 0.00000 0.00000 -0.01045 0.00000 -0.01045 2 0.00000 0.00000 0.00000 -0.00000 0.00000 -0.00037 3 1 0.00000 0.00000 0.00000 0.01045 0.00000 -0.01045 2 0.00000 0.00000 0.00000 0.00000 -0.00000 -0.00037 4 1 0.00000 0.00000 0.00000 0.01045 0.00000 0.01045 2 0.00000 0.00000 0.00000 -0.00000 -0.00000 -0.00037 5 1 0.00118 -0.09524 0.00118 0.02103 0.00000 -0.02103 2 0.06536 0.00008 0.00000 -0.00000 0.00000 -0.00008 6 1 0.00000 -1.56841 0.00118 0.02103 0.00000 0.00000 2 0.06537 0.00000 0.00000 0.00000 -0.00000 0.00004 7 1 -0.00118 -0.09524 0.00118 0.02103 0.00000 0.02103 2 0.06536 -0.00008 -0.00000 0.00000 0.00000 -0.00008 8 1 -0.00118 -1.56841 0.00000 0.00000 0.00000 0.02103 2 0.06587 -0.00008 0.00000 0.00000 0.00000 -0.00008 9 1 -0.00118 -0.09524 -0.00118 -0.02103 0.00000 0.02103 2 0.06536 -0.00008 0.00000 -0.00000 -0.00000 -0.00008 10 1 0.00000 -1.56841 -0.00118 -0.02103 0.00000 0.00000 2 0.06537 0.00000 0.00000 0.00000 0.00000 0.00004 11 1 0.00118 -0.09524 -0.00118 -0.02103 0.00000 -0.02103 2 0.06536 0.00008 -0.00000 0.00000 -0.00000 -0.00008 12 1 0.00118 -1.56841 0.00000 0.00000 0.00000 -0.02103 2 0.06587 0.00008 0.00000 0.00000 0.00000 -0.00008 EXAMPLE FOR HARMONIC LOADING GENERATOR -- PAGE NO. 7 SUPPORT REACTIONS -UNIT KIP INCH STRUCTURE TYPE = SPACE ----------------- JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z 1 1 5.95 180.00 5.95 0.00 0.00 0.00 2 -0.06 -0.15 -0.00 0.00 0.00 0.00 2 1 -5.95 180.00 5.95 0.00 0.00 0.00 2 -0.06 0.15 0.00 0.00 0.00 0.00 3 1 -5.95 180.00 -5.95 0.00 0.00 0.00 2 -0.06 0.15 -0.00 0.00 0.00 0.00 4 1 5.95 180.00 -5.95 0.00 0.00 0.00 2 -0.06 -0.15 0.00 0.00 0.00 0.00 EXAMPLE FOR HARMONIC LOADING GENERATOR -- PAGE NO. 8 MEMBER END FORCES STRUCTURE TYPE = SPACE ----------------- ALL UNITS ARE -- KIP INCH (LOCAL ) MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z 1 1 1 180.00 -5.95 5.95 0.00 0.00 -0.00 5 -180.00 5.95 -5.95 0.00 -1428.10 -1428.10 2 1 -0.15 0.06 -0.00 0.00 0.00 0.00 5 0.15 -0.06 0.00 0.00 0.00 13.37 2 1 2 180.00 5.95 5.95 0.00 0.00 0.00 7 -180.00 -5.95 -5.95 0.00 -1428.10 1428.10 2 2 0.15 0.06 0.00 0.00 0.00 0.00 7 -0.15 -0.06 -0.00 0.00 -0.00 13.37 3 1 3 180.00 5.95 -5.95 0.00 -0.00 0.00 9 -180.00 -5.95 5.95 0.00 1428.10 1428.10 2 3 0.15 0.06 -0.00 0.00 0.00 0.00 9 -0.15 -0.06 0.00 0.00 0.00 13.37 4 1 4 180.00 -5.95 -5.95 0.00 0.00 0.00 11 -180.00 5.95 5.95 0.00 1428.10 -1428.10 2 4 -0.15 0.06 0.00 0.00 0.00 0.00 11 0.15 -0.06 -0.00 0.00 -0.00 13.37 5 1 5 5.95 90.00 -0.00 -0.00 0.00 1428.10 6 -5.95 -0.00 0.00 0.00 -0.00 2621.90 2 5 -0.01 -0.15 -0.01 -0.00 0.84 -13.37 6 0.01 0.15 0.01 0.00 0.00 -0.00 6 1 6 5.95 -0.00 -0.00 0.00 0.00 -2621.90 7 -5.95 90.00 0.00 -0.00 0.00 -1428.10 2 6 0.01 -0.15 -0.01 -0.00 0.00 0.00 7 -0.01 0.15 0.01 0.00 0.84 -13.37 7 1 7 5.95 90.00 0.00 -0.00 -0.00 1428.10 8 -5.95 -0.00 -0.00 0.00 0.00 2621.90 2 7 -0.01 0.00 0.02 0.00 -0.84 0.00 8 0.01 -0.00 -0.02 -0.00 -1.41 0.00 8 1 8 5.95 0.00 0.00 0.00 -0.00 -2621.90 9 -5.95 90.00 -0.00 -0.00 -0.00 -1428.10 2 8 -0.01 -0.00 -0.02 0.00 1.41 -0.00 9 0.01 0.00 0.02 -0.00 0.84 -0.00 9 1 9 5.95 90.00 -0.00 -0.00 0.00 1428.10 10 -5.95 -0.00 0.00 0.00 0.00 2621.90 EXAMPLE FOR HARMONIC LOADING GENERATOR -- PAGE NO. 9 MEMBER END FORCES STRUCTURE TYPE = SPACE ----------------- ALL UNITS ARE -- KIP INCH (LOCAL ) MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z 2 9 0.01 0.15 0.01 0.00 -0.84 13.37 10 -0.01 -0.15 -0.01 -0.00 0.00 -0.00 10 1 10 5.95 0.00 -0.00 0.00 0.00 -2621.90 11 -5.95 90.00 0.00 -0.00 0.00 -1428.10 2 10 -0.01 0.15 0.01 0.00 0.00 0.00 11 0.01 -0.15 -0.01 -0.00 -0.84 13.37 11 1 11 5.95 90.00 0.00 -0.00 -0.00 1428.10 12 -5.95 0.00 -0.00 0.00 0.00 2621.90 2 11 0.01 -0.00 -0.02 0.00 0.84 -0.00 12 -0.01 0.00 0.02 -0.00 1.41 -0.00 12 1 12 5.95 0.00 0.00 0.00 -0.00 -2621.90 5 -5.95 90.00 -0.00 -0.00 -0.00 -1428.10 2 12 0.01 0.00 0.02 0.00 -1.41 0.00 5 -0.01 -0.00 -0.02 -0.00 -0.84 0.00 ************** END OF LATEST ANALYSIS RESULT ************** 53. FINI *********** END OF THE STAAD.Pro RUN *********** **** DATE= OCT 27,2022 TIME= 15: 9:37 **** EXAMPLE FOR HARMONIC LOADING GENERATOR -- PAGE NO. 10 ************************************************************ * 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 * ************************************************************