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.

### Example Problem No. 22

```    STAAD SPACE

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.

Note: Semicolons (;) are used as line separators to allow for input of multiple sets of data on one line.
```    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
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 時刻歴荷重の定義 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
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
8 12 FX 15.0
8 12 FY 15.0
8 12 FZ 15.0
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:

1. the weights for generation of the mass matrix
2. 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
FUNCTION SINE
AMPLITUDE 30 FREQUENCY 60 CYCLES 100
*
ARRIVAL TIMES
0.0
DAMPING 0.075
UNIT METER
5 6 7 8 9 10 11 12 UNI GY -10.0
SELFWEIGHT X 1.0
SELFWEIGHT Y 1.0
SELFWEIGHT Z 1.0
8 12 FX 15.0
8 12 FY 15.0
8 12 FZ 15.0
8 12 FX 1 1
PERFORM ANALYSIS
PRINT ANALYSIS RESULTS
FINI
``````

```                                                                  PAGE NO.    1
****************************************************
*                                                  *
*           Version  22.08.00.***                  *
*           Proprietary Program of                 *
*           Bentley Systems, Inc.                  *
*           Date=    OCT 19, 2021                  *
*           Time=    17:53:58                      *
*                                                  *
*  Licensed to: Bentley Systems Inc                *
****************************************************
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
34. FUNCTION SINE
35. AMPLITUDE 30 FREQUENCY 60 CYCLES 100
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
43. 5 6 7 8 9 10 11 12 UNI GY -10.0
45. SELFWEIGHT X 1.0
46. SELFWEIGHT Y 1.0
47. SELFWEIGHT Z 1.0
49. 8 12 FX 15.0
50. 8 12 FY 15.0
51. 8 12 FZ 15.0
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.
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 ***
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
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
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
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
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
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
*********** END OF THE STAAD.Pro RUN ***********
**** DATE= OCT 19,2021   TIME= 17:53:58 ****
************************************************************