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EX. UK-22 Time History Analysis for Sinusoidal Loading

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 
    *EXAMPLE FOR HARMONIC LOADING GENERATOR

Every STAAD input file has to begin with the word STAAD.

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
    * FOLLOWING LINES FOR HARMONIC LOADING GENERATOR
    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 Definition of Time History Load 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
    LOAD 1
    MEMBER LOAD
    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
    JOINT LOAD
    8 12 FX 15.0
    8 12 FY 15.0
    8 12 FZ 15.0
    TIME LOAD
    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
* FOLLOWING LINES FOR HARMONIC LOADING GENERATOR
FUNCTION SINE
AMPLITUDE 30 FREQUENCY 60 CYCLES 100
*
ARRIVAL TIMES
0.0
DAMPING 0.075
UNIT METER
LOAD 1
MEMBER LOAD
5 6 7 8 9 10 11 12 UNI GY -10.0
LOAD 2
SELFWEIGHT X 1.0
SELFWEIGHT Y 1.0
SELFWEIGHT Z 1.0
JOINT LOAD
8 12 FX 15.0
8 12 FY 15.0
8 12 FZ 15.0
TIME LOAD
8 12 FX 1 1
PERFORM ANALYSIS
PRINT ANALYSIS RESULTS
FINI

STAAD Output File

                                                                  PAGE NO.    1
             ****************************************************        
             *                                                  *        
             *           STAAD.Pro CONNECT Edition              *        
             *           Version  22.04.00.**                   *        
             *           Proprietary Program of                 *        
             *           Bentley Systems, Inc.                  *        
             *           Date=    APR 21, 2020                  *        
             *           Time=    15:40:51                      *        
             *                                                  *        
             *  Licensed to: Bentley Systems Inc                *        
             ****************************************************        
     1. STAAD SPACE EXAMPLE FOR HARMONIC LOADING GENERATOR
INPUT FILE: UK-22 Time History Analysis for Sinusoidal Loading.STD
     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
    33. * FOLLOWING LINES FOR HARMONIC LOADING GENERATOR
    34. FUNCTION SINE
    35. AMPLITUDE 30 FREQUENCY 60 CYCLES 100
      EXAMPLE FOR HARMONIC LOADING GENERATOR                   -- PAGE NO.    2
   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
    41. LOAD 1
    42. MEMBER LOAD
    43. 5 6 7 8 9 10 11 12 UNI GY -10.0
    44. LOAD 2
    45. SELFWEIGHT X 1.0
    46. SELFWEIGHT Y 1.0
    47. SELFWEIGHT Z 1.0
    48. JOINT LOAD
    49. 8 12 FX 15.0
    50. 8 12 FY 15.0
    51. 8 12 FZ 15.0
    52. TIME LOAD
    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.
      EXAMPLE FOR HARMONIC LOADING GENERATOR                   -- PAGE NO.    3
 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 ***
      EXAMPLE FOR HARMONIC LOADING GENERATOR                   -- PAGE NO.    4
               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
      EXAMPLE FOR HARMONIC LOADING GENERATOR                   -- PAGE NO.    5
    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                    
      EXAMPLE FOR HARMONIC LOADING GENERATOR                   -- PAGE NO.    6
   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
      EXAMPLE FOR HARMONIC LOADING GENERATOR                   -- PAGE NO.    7
   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
      EXAMPLE FOR HARMONIC LOADING GENERATOR                   -- PAGE NO.    8
   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
      EXAMPLE FOR HARMONIC LOADING GENERATOR                   -- PAGE NO.    9
   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
      EXAMPLE FOR HARMONIC LOADING GENERATOR                   -- PAGE NO.   10
             *********** END OF THE STAAD.Pro RUN ***********         
               **** DATE= APR 21,2020   TIME= 15:40:52 ****
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