# 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.

### Example Problem No. 16

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
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
2 3 FX 4000.0
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.

Note: This example is only for illustration purposes and that it may be unlikely that a TIME LOAD and GROUND MOTION both act on the structure at the same time.

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
1 2 3 UNI GX 500.0
SELFWEIGHT X 1.0
SELFWEIGHT Y 1.0
2 3 FX 4000.0
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
``````

```                                                                  PAGE NO.    1
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*                                                  *
*           Version  22.04.00.**                   *
*           Proprietary Program of                 *
*           Bentley Systems, Inc.                  *
*           Date=    APR 21, 2020                  *
*           Time=    15:40:34                      *
*                                                  *
*  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
38. 1 2 3 UNI GX 500.0
EXAMPLE FOR TIME HISTORY ANALYSIS                        -- PAGE NO.    2
40. SELFWEIGHT X 1.0
41. SELFWEIGHT Y 1.0
43. 2 3 FX 4000.0
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= APR 21,2020   TIME= 15:40:35 ****
EXAMPLE FOR TIME HISTORY ANALYSIS                        -- PAGE NO.    8
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