EX. UK-16 Time History Analysis for Forcing Function and Ground Motion
Dynamic Analysis (Time History) is performed for a 3 span beam with concentrated and distributed masses. The structure is subjected to "forcing function" and "ground motion" loading. The maxima of joint displacements, member end forces and support reactions are determined.
This problem is installed with the program by default to C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\Sample Models\UK\UK-16 Time History Analysis for Forcing Function and Ground Motion.STD when you install the program.
Where:
- L1 = 1.2 m
STAAD PLANE EXAMPLE FOR TIME HISTORY ANALYSIS
Every input file has to start with the word STAAD. The term PLANE signifies that the structure is a plane frame.
UNITS CMS KNS
Specifies the units to be used.
JOINT COORDINATES 1 0.0 0.0 0.0 2 0.0 120.0 0.0 3 0.0 240.0 0.0 4 0.0 360.0 0.0
Joint number followed by the X, Y and Z coordinates are specified above.
MEMBER INCIDENCES 1 1 2 3
Incidences of members 1 to 3 are specified above.
MEMBER PROPERTIES 1 2 3 PRIS AX 100.0 IZ 833.33
All the members have PRISMATIC property specification. Since this is a plane frame, Area of cross section (AX) and Moment of Inertia (IZ) about the Z axis are adequate for the analysis.
SUPPORTS 1 4 PINNED
Pinned supports are located at nodes 1 and 4.
DEFINE MATERIAL START ISOTROPIC CONCRETE E 2850 POISSON 0.17 DENSITY 25e-006 ALPHA 5e-006 DAMP 0.05 G 925 TYPE CONCRETE STRENGTH FCU 2.75 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.
UNIT NEWTON METER DEFINE TIME HISTORY TYPE 1 FORCE 0.0 –20.0 0.5 100.0 1.0 200.0 1.5 500.0 2.0 800.0 2.5 500.0 3.0 70.0 TYPE 2 ACCELERATION 0.0 0.1 0.5 –0.25 1.0 –0.5 1.5 –0.9 2.0 –1.3 2.5 –1.0 3.0 –0.7 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. First the characteristics of the time varying load are provided. The loading type may be a forcing function (vibrating machinery) or ground motion (earthquake). The former is input in the form of time-force pairs while the latter is in the form of time-acceleration pairs. Following this data, all possible arrival times for these loads on the structure as well as the modal damping ratio are specified. In this example, the damping ratio is the same (7.5%) for all modes.
LOAD 1 STATIC LOAD MEMBER LOAD 1 2 3 UNI GX 500.0
Load case 1 above is a static load. A uniformly distributed force of 500 Newton/m acts along the global X direction on all 3 members.
LOAD 2 TIME HISTORY LOAD SELFWEIGHT X 1.0 SELFWEIGHT Y 1.0 JOINT LOAD 2 3 FX 4000.0 TIME LOAD 2 3 FX 1 1 GROUND MOTION X 2 1
This is the second stage in the command specification for time history analysis. This involves the application of the time varying load on the structure. The masses that constitute the mass matrix of the structure are specified through the selfweight and joint load commands. The program will extract the lumped masses from these weights. Following that, both the TIME LOAD and GROUND MOTION are applied simultaneously.
The Time load command is used to apply the Type 1 force, acting in the global X direction, at arrival time number 1, at nodes 2 and 3. The Ground motion, namely, the Type 2 time history loading, is also in the global X direction at arrival time 1.
PERFORM ANALYSIS
The above command initiates the analysis process.
PRINT JOINT DISPLACEMENTS
During the analysis, the program calculates joint displacements for every time step. The absolute maximum value of the displacement for every joint is then extracted from this joint displacement history. So, the value printed using the above command is the absolute maximum value for each of the six degrees of freedom at each node.
UNIT KNS METER PRINT MEMBER FORCES PRINT SUPPORT REACTION
The member forces and support reactions too are calculated for every time step. For each degree of freedom, the maximum value of the member force and support reaction is extracted from these histories and reported in the output file using the above command.
FINISH
Input File
STAAD PLANE EXAMPLE FOR TIME HISTORY ANALYSIS
UNITS CMS KNS
JOINT COORDINATES
1 0.0 0.0 0.0
2 0.0 120.0 0.0
3 0.0 240.0 0.0
4 0.0 360.0 0.0
MEMBER INCIDENCES
1 1 2 3
MEMBER PROPERTIES
1 2 3 PRIS AX 100.0 IZ 833.33
SUPPORTS
1 4 PINNED
DEFINE MATERIAL START
ISOTROPIC CONCRETE
E 2850
POISSON 0.17
DENSITY 25e-006
ALPHA 5e-006
DAMP 0.05
G 925
TYPE CONCRETE
STRENGTH FCU 2.75
END DEFINE MATERIAL
CONSTANTS
MATERIAL CONCRETE ALL
UNIT NEWTON METER
DEFINE TIME HISTORY
TYPE 1 FORCE
0.0 -20.0 0.5 100.0 1.0 200.0 1.5 500.0 2.0 800.0 2.5 500.0 3.0 70.0
TYPE 2 ACCELERATION
0.0 0.1 0.5 -0.25 1.0 -0.5 1.5 -0.9 2.0 -1.3 2.5 -1.0 3.0 -0.7
ARRIVAL TIMES
0.0
DAMPING 0.075
LOAD 1 STATIC LOAD
MEMBER LOAD
1 2 3 UNI GX 500.0
LOAD 2 TIME HISTORY LOAD
SELFWEIGHT X 1.0
SELFWEIGHT Y 1.0
JOINT LOAD
2 3 FX 4000.0
TIME LOAD
2 3 FX 1 1
GROUND MOTION X 2 1
PERFORM ANALYSIS
PRINT JOINT DISPLACEMENTS
UNIT KNS METER
PRINT MEMBER FORCES
PRINT SUPPORT REACTION
FINISH
STAAD Output File
PAGE NO. 1 **************************************************** * * * STAAD.Pro CONNECT Edition * * Version 22.08.00.*** * * Proprietary Program of * * Bentley Systems, Inc. * * Date= OCT 19, 2021 * * Time= 17:53:41 * * * * Licensed to: Bentley Systems Inc * **************************************************** 1. STAAD PLANE EXAMPLE FOR TIME HISTORY ANALYSIS INPUT FILE: UK-16 Time History Analysis for Forcing Function and Ground Motion.STD 2. UNITS CMS KNS 3. JOINT COORDINATES 4. 1 0.0 0.0 0.0 5. 2 0.0 120.0 0.0 6. 3 0.0 240.0 0.0 7. 4 0.0 360.0 0.0 8. MEMBER INCIDENCES 9. 1 1 2 3 10. MEMBER PROPERTIES 11. 1 2 3 PRIS AX 100.0 IZ 833.33 12. SUPPORTS 13. 1 4 PINNED 14. DEFINE MATERIAL START 15. ISOTROPIC CONCRETE 16. E 2850 17. POISSON 0.17 18. DENSITY 25E-006 19. ALPHA 5E-006 20. DAMP 0.05 21. G 925 22. TYPE CONCRETE 23. STRENGTH FCU 2.75 24. END DEFINE MATERIAL 25. CONSTANTS 26. MATERIAL CONCRETE ALL 27. UNIT NEWTON METER 28. DEFINE TIME HISTORY 29. TYPE 1 FORCE 30. 0.0 -20.0 0.5 100.0 1.0 200.0 1.5 500.0 2.0 800.0 2.5 500.0 3.0 70.0 31. TYPE 2 ACCELERATION 32. 0.0 0.1 0.5 -0.25 1.0 -0.5 1.5 -0.9 2.0 -1.3 2.5 -1.0 3.0 -0.7 33. ARRIVAL TIMES 34. 0.0 35. DAMPING 0.075 36. LOAD 1 STATIC LOAD 37. MEMBER LOAD 38. 1 2 3 UNI GX 500.0 EXAMPLE FOR TIME HISTORY ANALYSIS -- PAGE NO. 2 39. LOAD 2 TIME HISTORY LOAD 40. SELFWEIGHT X 1.0 41. SELFWEIGHT Y 1.0 42. JOINT LOAD 43. 2 3 FX 4000.0 44. TIME LOAD 45. 2 3 FX 1 1 46. GROUND MOTION X 2 1 47. PERFORM ANALYSIS P R O B L E M S T A T I S T I C S ----------------------------------- NUMBER OF JOINTS 4 NUMBER OF MEMBERS 3 NUMBER OF PLATES 0 NUMBER OF SOLIDS 0 NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 2 Using 64-bit analysis engine. SOLVER USED IS THE IN-CORE ADVANCED MATH SOLVER TOTAL PRIMARY LOAD CASES = 2, TOTAL DEGREES OF FREEDOM = 8 TOTAL LOAD COMBINATION CASES = 0 SO FAR. ***NOTE: MASSES DEFINED UNDER LOAD# 2 WILL FORM THE FINAL MASS MATRIX FOR DYNAMIC ANALYSIS. MORE MODES WERE REQUESTED THAN THERE ARE FREE MASSES. NUMBER OF MODES REQUESTED = 6 NUMBER OF EXISTING MASSES IN THE MODEL = 4 NUMBER OF MODES THAT WILL BE USED = 4 *** EIGENSOLUTION : ADVANCED METHOD *** EXAMPLE FOR TIME HISTORY ANALYSIS -- PAGE NO. 3 CALCULATED FREQUENCIES FOR LOAD CASE 2 MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC) 1 3.087 0.32397 2 11.955 0.08365 3 443.457 0.00226 4 768.090 0.00130 MODAL WEIGHT (MODAL MASS TIMES g) IN NEWT GENERALIZED MODE X Y Z WEIGHT 1 8.600000E+03 0.000000E+00 0.000000E+00 8.600000E+03 2 3.840329E-24 0.000000E+00 0.000000E+00 8.600000E+03 3 0.000000E+00 6.000000E+02 0.000000E+00 6.000000E+02 4 0.000000E+00 1.748000E-27 0.000000E+00 6.000000E+02 MASS PARTICIPATION FACTORS MASS PARTICIPATION FACTORS IN PERCENT -------------------------------------- MODE X Y Z SUMM-X SUMM-Y SUMM-Z 1 100.00 0.00 0.00 100.000 0.000 0.000 2 0.00 0.00 0.00 100.000 0.000 0.000 3 0.00 100.00 0.00 100.000 100.000 0.000 4 0.00 0.00 0.00 100.000 100.000 0.000 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 TIME STEP USED IN TIME HISTORY ANALYSIS = 0.00139 SECONDS NUMBER OF MODES WHOSE CONTRIBUTION IS CONSIDERED = 2 EXAMPLE FOR TIME HISTORY ANALYSIS -- PAGE NO. 4 WARNING-NUMBER OF MODES LIMITED TO A FREQUENCY OF 360.0 DUE TO THE DT VALUE ENTERED. TIME DURATION OF TIME HISTORY ANALYSIS = 3.000 SECONDS NUMBER OF TIME STEPS IN THE SOLUTION PROCESS = 2160 48. PRINT JOINT DISPLACEMENTS BASE SHEAR UNITS ARE -- NEWT METE MAXIMUM BASE SHEAR X= -2.777266E+03 Y= 0.000000E+00 Z= 0.000000E+00 AT TIMES 2.054167 0.000000 0.000000 JOINT DISPLACE EXAMPLE FOR TIME HISTORY ANALYSIS -- PAGE NO. 5 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 -0.0041 2 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0084 2 1 0.4002 0.0000 0.0000 0.0000 0.0000 -0.0020 2 0.8420 0.0000 0.0000 0.0000 0.0000 -0.0042 3 1 0.4002 0.0000 0.0000 0.0000 0.0000 0.0020 2 0.8420 0.0000 0.0000 0.0000 0.0000 0.0042 4 1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0041 2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0084 ************** END OF LATEST ANALYSIS RESULT ************** 49. UNIT KNS METER 50. PRINT MEMBER FORCES MEMBER FORCES EXAMPLE FOR TIME HISTORY ANALYSIS -- PAGE NO. 6 MEMBER END FORCES STRUCTURE TYPE = PLANE ----------------- ALL UNITS ARE -- KNS METE (LOCAL ) MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z 1 1 1 0.00 0.90 0.00 0.00 0.00 -0.00 2 0.00 -0.30 0.00 0.00 0.00 0.72 2 1 0.00 1.39 0.00 0.00 0.00 0.00 2 0.00 -1.39 0.00 0.00 0.00 1.67 2 1 2 0.00 0.30 0.00 0.00 0.00 -0.72 3 0.00 0.30 0.00 0.00 0.00 0.72 2 2 0.00 0.00 0.00 0.00 0.00 -1.67 3 0.00 0.00 0.00 0.00 0.00 1.67 3 1 3 0.00 -0.30 0.00 0.00 0.00 -0.72 4 0.00 0.90 0.00 0.00 0.00 0.00 2 3 0.00 -1.39 0.00 0.00 0.00 -1.67 4 0.00 1.39 0.00 0.00 0.00 0.00 ************** END OF LATEST ANALYSIS RESULT ************** 51. PRINT SUPPORT REACTION SUPPORT REACTION EXAMPLE FOR TIME HISTORY ANALYSIS -- PAGE NO. 7 SUPPORT REACTIONS -UNIT KNS METE STRUCTURE TYPE = PLANE ----------------- JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z 1 1 -0.90 0.00 0.00 0.00 0.00 0.00 2 -1.39 0.00 0.00 0.00 0.00 0.00 4 1 -0.90 0.00 0.00 0.00 0.00 0.00 2 -1.39 0.00 0.00 0.00 0.00 0.00 ************** END OF LATEST ANALYSIS RESULT ************** 52. FINISH *********** END OF THE STAAD.Pro RUN *********** **** DATE= OCT 19,2021 TIME= 17:53:42 **** EXAMPLE FOR TIME HISTORY ANALYSIS -- PAGE NO. 8 ************************************************************ * 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 * ************************************************************