EX. UK-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\UK\UK-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 KNS METER
The units for the data that follows are specified above.
JOINT COORDINATES
1 0 0 0 ; 2 5 0 0 ; 3 5 0 5 ; 4 0 0 5
5 0 7 0 ; 6 2.5 7 0 ; 7 5 7 0 ; 8 5 7 2.5
9 5 7 5 ; 10 2.5 7 5 ; 11 0 7 5
12 0 7 2.5 ; 13 2.5 7 2.5
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 MMS
MEMBER PROPERTIES
1 TO 4 PRIS YD 600 ZD 600
5 TO 16 PRIS YD 450 ZD 450
Members 1 to 16 are defined as PRISmatic sections with width and depth values provided using the YD and ZD options. The UNIT command is specified to change the units for length from METER to MMS.
SUPPORTS
1 TO 4 PINNED
Joints 1 to 4 are declared to be pinned-supported.
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
The modulus of elasticity (E), density and Poisson’s ratio are specified following the command CONSTANTS. Built-in default values for concrete are used.
DEFINE TIME HISTORY
TYPE 1 FORCE
* FOLLOWING LINES FOR HARMONIC LOADING GENERATOR
FUNCTION SINE
AMPLITUDE 30 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.
UNIT METER
LOAD 1
MEMBER LOAD
5 6 7 8 9 10 11 12 UNI GY -10.0
The above data describe a static load case. A uniformly distributed load of 10 kN/m acting in the negative global Y direction is applied on some members.
LOAD 2
SELFWEIGHT X 1.0
SELFWEIGHT Y 1.0
SELFWEIGHT Z 1.0
JOINT LOAD
8 12 FX 15.0
8 12 FY 15.0
8 12 FZ 15.0
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 KNS METER
JOINT COORDINATES
1 0 0 0 ; 2 5 0 0 ; 3 5 0 5 ; 4 0 0 5
5 0 7 0 ; 6 2.5 7 0 ; 7 5 7 0 ; 8 5 7 2.5
9 5 7 5 ; 10 2.5 7 5 ; 11 0 7 5
12 0 7 2.5 ; 13 2.5 7 2.5
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
13 6 13 ; 14 13 10 ; 15 8 13 ; 16 13 12
UNIT MMS
MEMBER PROPERTIES
1 TO 4 PRIS YD 600 ZD 600
5 TO 16 PRIS YD 450 ZD 450
SUPPORTS
1 TO 4 PINNED
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
DEFINE TIME HISTORY
TYPE 1 FORCE
* FOLLOWING LINES FOR HARMONIC LOADING GENERATOR
FUNCTION SINE
AMPLITUDE 30 FREQUENCY 60 CYCLES 100
*
ARRIVAL TIMES
0.0
DAMPING 0.075
UNIT METER
LOAD 1
MEMBER LOAD
5 6 7 8 9 10 11 12 UNI GY -10.0
LOAD 2
SELFWEIGHT X 1.0
SELFWEIGHT Y 1.0
SELFWEIGHT Z 1.0
JOINT LOAD
8 12 FX 15.0
8 12 FY 15.0
8 12 FZ 15.0
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: 7:43 * * * * Licensed to: Bentley Systems Inc * **************************************************** 1. STAAD SPACE EXAMPLE FOR HARMONIC LOADING GENERATOR INPUT FILE: UK-22 Time History Analysis for Sinusoidal Loading.STD 2. UNIT KNS METER 3. JOINT COORDINATES 4. 1 0 0 0 ; 2 5 0 0 ; 3 5 0 5 ; 4 0 0 5 5. 5 0 7 0 ; 6 2.5 7 0 ; 7 5 7 0 ; 8 5 7 2.5 6. 9 5 7 5 ; 10 2.5 7 5 ; 11 0 7 5 7. 12 0 7 2.5 ; 13 2.5 7 2.5 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. 13 6 13 ; 14 13 10 ; 15 8 13 ; 16 13 12 12. UNIT MMS 13. MEMBER PROPERTIES 14. 1 TO 4 PRIS YD 600 ZD 600 15. 5 TO 16 PRIS YD 450 ZD 450 16. SUPPORTS 17. 1 TO 4 PINNED 18. DEFINE MATERIAL START 19. ISOTROPIC CONCRETE 20. E 21.0 21. POISSON 0.17 22. DENSITY 2.36158E-008 23. ALPHA 5E-006 24. DAMP 0.05 25. G 9.25 26. TYPE CONCRETE 27. STRENGTH FCU 0.0275 28. END DEFINE MATERIAL 29. CONSTANTS 30. MATERIAL CONCRETE ALL 31. DEFINE TIME HISTORY 32. TYPE 1 FORCE 33. * FOLLOWING LINES FOR HARMONIC LOADING GENERATOR 34. FUNCTION SINE 35. AMPLITUDE 30 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 36. * 37. ARRIVAL TIMES 38. 0.0 39. DAMPING 0.075 40. UNIT METER 41. LOAD 1 42. MEMBER LOAD 43. 5 6 7 8 9 10 11 12 UNI GY -10.0 44. LOAD 2 45. SELFWEIGHT X 1.0 46. SELFWEIGHT Y 1.0 47. SELFWEIGHT Z 1.0 48. JOINT LOAD 49. 8 12 FX 15.0 50. 8 12 FY 15.0 51. 8 12 FZ 15.0 52. TIME LOAD 53. 8 12 FX 1 1 54. PERFORM ANALYSIS P R O B L E M S T A T I S T I C S ----------------------------------- NUMBER OF JOINTS 13 NUMBER OF MEMBERS 16 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 = 66 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 = 27 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 1.832 0.54584 2 1.833 0.54558 3 2.179 0.45894 4 18.014 0.05551 5 18.981 0.05268 6 23.162 0.04317 MODAL WEIGHT (MODAL MASS TIMES g) IN KNS GENERALIZED MODE X Y Z WEIGHT 1 2.924784E+02 3.675141E-24 1.333421E-21 2.902617E+02 2 1.338687E-21 3.119688E-30 2.924834E+02 2.907889E+02 3 1.457481E-25 3.230663E-26 6.769659E-21 4.344889E+02 4 1.151691E-20 3.984483E-21 1.962646E-19 3.771789E+02 5 3.567685E-14 1.271663E+02 3.475675E-20 5.768673E+01 6 8.511521E-03 2.884108E-21 4.373936E-20 6.607558E+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 99.996 0.000 0.000 2 0.00 0.00 100.00 99.996 0.000 99.998 3 0.00 0.00 0.00 99.996 0.000 99.998 4 0.00 0.00 0.00 99.996 0.000 99.998 5 0.00 43.48 0.00 99.996 43.477 99.998 6 0.00 0.00 0.00 99.999 43.477 99.998 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 55. PRINT ANALYSIS RESULTS BASE SHEAR UNITS ARE -- KNS METE MAXIMUM BASE SHEAR X= -1.639967E+00 Y= -2.384186E-07 Z= -9.313226E-10 AT TIMES 0.127778 0.034722 0.063889 ANALYSIS RESULTS EXAMPLE FOR HARMONIC LOADING GENERATOR -- PAGE NO. 6 JOINT DISPLACEMENT (CM RADIANS) STRUCTURE TYPE = SPACE ------------------ JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN 1 1 0.0000 0.0000 0.0000 -0.0001 0.0000 0.0001 2 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0001 2 1 0.0000 0.0000 0.0000 -0.0001 0.0000 -0.0001 2 0.0000 0.0000 0.0000 -0.0000 0.0000 -0.0001 3 1 0.0000 0.0000 0.0000 0.0001 0.0000 -0.0001 2 0.0000 0.0000 0.0000 0.0000 -0.0000 -0.0001 4 1 0.0000 0.0000 0.0000 0.0001 0.0000 0.0001 2 0.0000 0.0000 0.0000 -0.0000 -0.0000 -0.0001 5 1 0.0001 -0.0046 0.0001 0.0002 0.0000 -0.0002 2 0.0414 0.0001 0.0000 -0.0000 0.0000 -0.0000 6 1 0.0000 -0.0487 0.0000 0.0001 0.0000 0.0000 2 0.0414 0.0000 0.0000 0.0000 0.0000 0.0000 7 1 -0.0001 -0.0046 0.0001 0.0002 0.0000 0.0002 2 0.0414 -0.0001 -0.0000 0.0000 0.0000 -0.0000 8 1 -0.0000 -0.0487 0.0000 0.0000 0.0000 0.0001 2 0.0416 -0.0005 0.0000 0.0000 0.0000 -0.0000 9 1 -0.0001 -0.0046 -0.0001 -0.0002 0.0000 0.0002 2 0.0414 -0.0001 0.0000 -0.0000 -0.0000 -0.0000 10 1 0.0000 -0.0487 -0.0000 -0.0001 0.0000 0.0000 2 0.0414 0.0000 0.0000 0.0000 -0.0000 0.0000 11 1 0.0001 -0.0046 -0.0001 -0.0002 0.0000 -0.0002 2 0.0414 0.0001 -0.0000 0.0000 -0.0000 -0.0000 12 1 0.0000 -0.0487 0.0000 0.0000 0.0000 -0.0001 2 0.0416 0.0005 0.0000 0.0000 0.0000 -0.0000 13 1 0.0000 -0.0604 0.0000 0.0000 0.0000 0.0000 2 0.0416 -0.0000 0.0000 0.0000 0.0000 0.0000 EXAMPLE FOR HARMONIC LOADING GENERATOR -- PAGE NO. 7 SUPPORT REACTIONS -UNIT KNS METE STRUCTURE TYPE = SPACE ----------------- JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z 1 1 2.15 50.00 2.15 0.00 0.00 0.00 2 -0.41 -1.13 -0.02 0.00 0.00 0.00 2 1 -2.15 50.00 2.15 0.00 0.00 0.00 2 -0.41 1.13 0.02 0.00 0.00 0.00 3 1 -2.15 50.00 -2.15 0.00 0.00 0.00 2 -0.41 1.13 -0.02 0.00 0.00 0.00 4 1 2.15 50.00 -2.15 0.00 0.00 0.00 2 -0.41 -1.13 0.02 0.00 0.00 0.00 EXAMPLE FOR HARMONIC LOADING GENERATOR -- PAGE NO. 8 MEMBER END FORCES STRUCTURE TYPE = SPACE ----------------- ALL UNITS ARE -- KNS METE (LOCAL ) MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z 1 1 1 50.00 -2.15 2.15 0.00 0.00 0.00 5 -50.00 2.15 -2.15 0.00 -15.03 -15.03 2 1 -1.13 0.41 -0.02 0.00 0.00 0.00 5 1.13 -0.41 0.02 0.00 0.12 2.87 2 1 2 50.00 2.15 2.15 0.00 0.00 0.00 7 -50.00 -2.15 -2.15 0.00 -15.03 15.03 2 2 1.13 0.41 0.02 0.00 0.00 0.00 7 -1.13 -0.41 -0.02 0.00 -0.12 2.87 3 1 3 50.00 2.15 -2.15 0.00 -0.00 0.00 9 -50.00 -2.15 2.15 0.00 15.03 15.03 2 3 1.13 0.41 -0.02 0.00 0.00 0.00 9 -1.13 -0.41 0.02 0.00 0.12 2.87 4 1 4 50.00 -2.15 -2.15 0.00 -0.00 0.00 11 -50.00 2.15 2.15 0.00 15.03 -15.03 2 4 -1.13 0.41 0.02 0.00 0.00 0.00 11 1.13 -0.41 -0.02 0.00 -0.12 2.87 5 1 5 2.09 25.00 0.06 1.34 -0.07 16.37 6 -2.09 -0.00 -0.06 -1.34 -0.07 14.88 2 5 -0.10 -1.03 -0.05 -0.03 0.08 -2.49 6 0.10 1.03 0.05 0.03 0.06 -0.08 6 1 6 2.09 0.00 -0.06 -1.34 0.07 -14.88 7 -2.09 25.00 0.06 1.34 0.07 -16.37 2 6 0.10 -1.03 -0.05 -0.03 0.06 -0.08 7 -0.10 1.03 0.05 0.03 0.08 -2.49 7 1 7 2.09 25.00 0.06 1.34 -0.07 16.37 8 -2.09 0.00 -0.06 -1.34 -0.07 14.88 2 7 -0.04 0.14 0.08 -0.38 -0.08 0.14 8 0.04 -0.14 -0.08 0.38 -0.12 0.21 8 1 8 2.09 0.00 -0.06 -1.34 0.07 -14.88 9 -2.09 25.00 0.06 1.34 0.07 -16.37 2 8 -0.04 -0.14 -0.08 0.38 0.12 -0.21 9 0.04 0.14 0.08 -0.38 0.08 -0.14 9 1 9 2.09 25.00 0.06 1.34 -0.07 16.37 10 -2.09 0.00 -0.06 -1.34 -0.07 14.88 EXAMPLE FOR HARMONIC LOADING GENERATOR -- PAGE NO. 9 MEMBER END FORCES STRUCTURE TYPE = SPACE ----------------- ALL UNITS ARE -- KNS METE (LOCAL ) MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z 2 9 0.10 1.03 0.05 0.03 -0.08 2.49 10 -0.10 -1.03 -0.05 -0.03 -0.06 0.08 10 1 10 2.09 -0.00 -0.06 -1.34 0.07 -14.88 11 -2.09 25.00 0.06 1.34 0.07 -16.37 2 10 -0.10 1.03 0.05 0.03 -0.06 0.08 11 0.10 -1.03 -0.05 -0.03 -0.08 2.49 11 1 11 2.09 25.00 0.06 1.34 -0.07 16.37 12 -2.09 0.00 -0.06 -1.34 -0.07 14.88 2 11 0.04 -0.14 -0.08 0.38 0.08 -0.14 12 -0.04 0.14 0.08 -0.38 0.12 -0.21 12 1 12 2.09 0.00 -0.06 -1.34 0.07 -14.88 5 -2.09 25.00 0.06 1.34 0.07 -16.37 2 12 0.04 0.14 0.08 -0.38 -0.12 0.21 5 -0.04 -0.14 -0.08 0.38 -0.08 0.14 13 1 6 0.12 -0.00 0.00 0.00 -0.00 -2.67 13 -0.12 0.00 -0.00 -0.00 -0.00 2.67 2 6 0.00 0.00 0.10 0.17 -0.11 0.00 13 -0.00 -0.00 -0.10 -0.17 -0.13 0.00 14 1 13 0.12 0.00 -0.00 -0.00 0.00 -2.67 10 -0.12 -0.00 0.00 0.00 0.00 2.67 2 13 0.00 -0.00 -0.10 -0.17 0.13 -0.00 10 -0.00 0.00 0.10 0.17 0.11 -0.00 15 1 8 0.12 -0.00 -0.00 0.00 -0.00 -2.67 13 -0.12 0.00 0.00 -0.00 0.00 2.67 2 8 -0.03 0.24 0.00 -0.00 -0.00 0.76 13 0.03 -0.24 -0.00 0.00 -0.00 -0.17 16 1 13 0.12 0.00 -0.00 -0.00 0.00 -2.67 12 -0.12 -0.00 0.00 0.00 0.00 2.67 2 13 0.03 0.24 0.00 -0.00 -0.00 -0.17 12 -0.03 -0.24 -0.00 0.00 -0.00 0.76 ************** END OF LATEST ANALYSIS RESULT ************** 56. FINI EXAMPLE FOR HARMONIC LOADING GENERATOR -- PAGE NO. 10 *********** END OF THE STAAD.Pro RUN *********** **** DATE= OCT 27,2022 TIME= 15: 7:44 **** ************************************************************ * 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 * ************************************************************