EX. US-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 2023\Samples\Sample Models\US\US-16 Time History Analysis for Forcing Function and Ground Motion.STD when you install the program.
Where:
- L1 = 3.5 ft
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 FEET KIP
Specifies the units to be used.
JOINT COORDINATES 1 0.0 0.0 0.0 2 0.0 3.5 0.0 3 0.0 7.0 0.0 4 0.0 10.5 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.
UNIT INCH MEMBER PROPERTIES 1 2 3 PRIS AX 3.0 IZ 240.0
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 14000 POISSON 0.17 DENSITY 8.7e-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 0.0 -0.0001 0.5 0.0449 1.0 0.2244 1.5 0.2244 2.0 0.6731 2.5 -0.6731 TYPE 2 ACCELERATION 0.0 0.001 0.5 -7.721 1.0 -38.61 1.5 -38.61 2.0 -115.82 2.5 115.82 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.
UNIT FEET LOAD 1 STATIC LOAD MEMBER LOAD 1 2 3 UNI GX 0.5
Load case 1 above is a static load. A uniformly distributed force of 0.5 kip/ft 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 2.5 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.
UNIT INCH 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 FEET 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 FEET KIP
JOINT COORDINATES
1 0.0 0.0 0.0
2 0.0 3.5 0.0
3 0.0 7.0 0.0
4 0.0 10.5 0.0
MEMBER INCIDENCES
1 1 2 3
UNIT INCH
MEMBER PROPERTIES
1 2 3 PRIS AX 3.0 IZ 240.0
SUPPORTS
1 4 PINNED
DEFINE MATERIAL START
ISOTROPIC CONCRETE
E 14000
POISSON 0.17
DENSITY 8.7e-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
0.0 -0.0001 0.5 0.0449 1.0 0.2244 1.5 0.2244 2.0 0.6731 2.5 -0.6731
TYPE 2 ACCELERATION
0.0 0.001 0.5 -7.721 1.0 -38.61 1.5 -38.61 2.0 -115.82 2.5 115.82
ARRIVAL TIMES
0.0
DAMPING 0.075
UNIT FEET
LOAD 1 STATIC LOAD
MEMBER LOAD
1 2 3 UNI GX 0.5
LOAD 2 TIME HISTORY LOAD
SELFWEIGHT X 1.0
SELFWEIGHT Y 1.0
JOINT LOAD
2 3 FX 2.5
TIME LOAD
2 3 FX 1 1
GROUND MOTION X 2 1
PERFORM ANALYSIS
UNIT INCH
PRINT JOINT DISPLACEMENTS
UNIT FEET
PRINT MEMBER FORCES
PRINT SUPPORT REACTION
FINISH
STAAD Output File
PAGE NO. 1 **************************************************** * * * STAAD.Pro 2023 * * Version 23.00.02.*** * * Proprietary Program of * * Bentley Systems, Inc. * * Date= DEC 14, 2023 * * Time= 9:37:17 * * * * Licensed to: Bentley Systems Inc * **************************************************** 1. STAAD PLANE EXAMPLE FOR TIME HISTORY ANALYSIS INPUT FILE: D:\Documentation\STAAD.Pro\_Automated_Py\output\2023-12-14\SPro_Output_Input_Files\Sample .. .STD 2. UNITS FEET KIP 3. JOINT COORDINATES 4. 1 0.0 0.0 0.0 5. 2 0.0 3.5 0.0 6. 3 0.0 7.0 0.0 7. 4 0.0 10.5 0.0 8. MEMBER INCIDENCES 9. 1 1 2 3 10. UNIT INCH 11. MEMBER PROPERTIES 12. 1 2 3 PRIS AX 3.0 IZ 240.0 13. SUPPORTS 14. 1 4 PINNED 15. DEFINE MATERIAL START 16. ISOTROPIC CONCRETE 17. E 14000 18. POISSON 0.17 19. DENSITY 8.7E-005 20. ALPHA 5E-006 21. DAMP 0.05 22. G 1346.15 23. TYPE CONCRETE 24. STRENGTH FCU 4 25. END DEFINE MATERIAL 26. CONSTANTS 27. MATERIAL CONCRETE ALL 28. DEFINE TIME HISTORY 29. TYPE 1 FORCE 30. 0.0 -0.0001 0.5 0.0449 1.0 0.2244 1.5 0.2244 2.0 0.6731 2.5 -0.6731 31. TYPE 2 ACCELERATION 32. 0.0 0.001 0.5 -7.721 1.0 -38.61 1.5 -38.61 2.0 -115.82 2.5 115.82 33. ARRIVAL TIMES 34. 0.0 35. DAMPING 0.075 36. UNIT FEET 37. LOAD 1 STATIC LOAD 38. MEMBER LOAD EXAMPLE FOR TIME HISTORY ANALYSIS -- PAGE NO. 2 39. 1 2 3 UNI GX 0.5 40. LOAD 2 TIME HISTORY LOAD 41. SELFWEIGHT X 1.0 42. SELFWEIGHT Y 1.0 43. JOINT LOAD 44. 2 3 FX 2.5 45. TIME LOAD 46. 2 3 FX 1 1 47. GROUND MOTION X 2 1 48. 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 14.559 0.06869 2 56.387 0.01773 3 944.536 0.00106 4 1635.985 0.00061 MODAL WEIGHT (MODAL MASS TIMES g) IN KIP GENERALIZED MODE X Y Z WEIGHT 1 5.021924E+00 0.000000E+00 0.000000E+00 5.021924E+00 2 2.258180E-27 0.000000E+00 0.000000E+00 5.021924E+00 3 0.000000E+00 2.192400E-02 0.000000E+00 2.192400E-02 4 0.000000E+00 3.824466E-33 0.000000E+00 2.192400E-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 = 2.500 SECONDS NUMBER OF TIME STEPS IN THE SOLUTION PROCESS = 1800 49. UNIT INCH BASE SHEAR UNITS ARE -- KIP FEET MAXIMUM BASE SHEAR X= -2.864840E+00 Y= 0.000000E+00 Z= 0.000000E+00 AT TIMES 2.006944 0.000000 0.000000 50. PRINT JOINT DISPLACEMENTS JOINT DISPLACE EXAMPLE FOR TIME HISTORY ANALYSIS -- PAGE NO. 5 JOINT DISPLACEMENT (INCH RADIANS) STRUCTURE TYPE = PLANE ------------------ JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN 1 1 0.00000 0.00000 0.00000 0.00000 0.00000 -0.00103 2 0.00000 0.00000 0.00000 0.00000 0.00000 -0.00075 2 1 0.03537 0.00000 0.00000 0.00000 0.00000 -0.00050 2 0.02632 0.00000 0.00000 0.00000 0.00000 -0.00038 3 1 0.03537 0.00000 0.00000 0.00000 0.00000 0.00050 2 0.02632 0.00000 0.00000 0.00000 0.00000 0.00038 4 1 0.00000 0.00000 0.00000 0.00000 0.00000 0.00103 2 0.00000 0.00000 0.00000 0.00000 0.00000 0.00075 ************** END OF LATEST ANALYSIS RESULT ************** 51. UNIT FEET 52. PRINT MEMBER FORCES MEMBER FORCES EXAMPLE FOR TIME HISTORY ANALYSIS -- PAGE NO. 6 MEMBER END FORCES STRUCTURE TYPE = PLANE ----------------- ALL UNITS ARE -- KIP FEET (LOCAL ) MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z 1 1 1 0.00 2.62 0.00 0.00 0.00 -0.00 2 0.00 -0.88 0.00 0.00 0.00 6.12 2 1 0.00 1.43 0.00 0.00 0.00 0.00 2 0.00 -1.43 0.00 0.00 0.00 5.01 2 1 2 0.00 0.88 0.00 0.00 0.00 -6.12 3 0.00 0.88 0.00 0.00 0.00 6.12 2 2 0.00 0.00 0.00 0.00 0.00 -5.01 3 0.00 0.00 0.00 0.00 0.00 5.01 3 1 3 0.00 -0.88 0.00 0.00 0.00 -6.12 4 0.00 2.62 0.00 0.00 0.00 0.00 2 3 0.00 -1.43 0.00 0.00 0.00 -5.01 4 0.00 1.43 0.00 0.00 0.00 0.00 ************** END OF LATEST ANALYSIS RESULT ************** 53. PRINT SUPPORT REACTION SUPPORT REACTION EXAMPLE FOR TIME HISTORY ANALYSIS -- PAGE NO. 7 SUPPORT REACTIONS -UNIT KIP FEET STRUCTURE TYPE = PLANE ----------------- JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z 1 1 -2.62 0.00 0.00 0.00 0.00 0.00 2 -1.43 0.00 0.00 0.00 0.00 0.00 4 1 -2.62 0.00 0.00 0.00 0.00 0.00 2 -1.43 0.00 0.00 0.00 0.00 0.00 ************** END OF LATEST ANALYSIS RESULT ************** 54. FINISH *********** END OF THE STAAD.Pro RUN *********** **** DATE= DEC 14,2023 TIME= 9:37:18 **** 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 * ************************************************************