# 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 CONNECT Edition\Samples\Sample Models\US\US-16 Time History Analysis for Forcing Function and Ground Motion.STD when you install the program.

### Example Problem No. 16

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
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
2 3 FX 2.5
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.

```    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
1 2 3 UNI GX 0.5
SELFWEIGHT X 1.0
SELFWEIGHT Y 1.0
2 3 FX 2.5
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
``````

```                                                                  PAGE NO.    1
****************************************************
*                                                  *
*           Version  22.08.00.***                  *
*           Proprietary Program of                 *
*           Bentley Systems, Inc.                  *
*           Date=    OCT 19, 2021                  *
*           Time=    17:55: 0                      *
*                                                  *
*  Licensed to: Bentley Systems Inc                *
****************************************************
1. STAAD PLANE EXAMPLE FOR TIME HISTORY ANALYSIS
INPUT FILE: US-16 Time History Analysis for Forcing Function and Ground Motion.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
EXAMPLE FOR TIME HISTORY ANALYSIS                        -- PAGE NO.    2
39. 1 2 3 UNI GX 0.5
41. SELFWEIGHT X 1.0
42. SELFWEIGHT Y 1.0
44. 2 3 FX 2.5
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= OCT 19,2021   TIME= 17:55: 0 ****
EXAMPLE FOR TIME HISTORY ANALYSIS                        -- PAGE NO.    8
************************************************************