TR.31.4 Definition of Time History Load
This set of commands may be used to define parameters for time history loading on the structure. The time history data may be specified using either explicit definition, function specification, a spectrum specification, or time history data provided in an external file.
General Format
DEFINE TIME HISTORY (DT x) ( MISSING MASS )
TYPE i { ACCELERATION  FORCE  MOMENT } (SCALE f7) (SAVE)
{ t1 p1 t2 p2 … tn pn  functionspec  spectrumspec  READ filename (f8) }
Repeat TYPE and Amplitude vs Time sets until all are entered, then:
ARRIVAL TIME
a_{1} a_{2} a_{3} … a_{n}
{ DAMPING d  CDAMP  MDAMP }
Entering the MISSING MASS parameter will include the missing mass procedure in the time history analysis.
The time history data can be explicitly defined using pairs of time and values of acceleration, force, or moment, where:
 ACCELERATION indicates that the time varying load type is a ground motion.
 FORCE indicates that it is a forcing function.
 MOMENT indicates that it is a moment forcing function.
Variable or Command  Default Value  Description 

DT x    Solution time step used in the stepbystep integration of the uncoupled equations. Values smaller than 0.00001 will be reset to the default DT value of 0.0013888 seconds. 
TYPE i    Type number of time varying load (integer). Up to 136 types may be provided. This number should be sequential. 
SCALE f7  1.0  The scale factor option multiplies all forces, accelerations, and amplitudes entered, read or generated within this Type. Primarily used to convert acceleration in g’s to current units (9.80665, 386.08858, etc.). 
SAVE   
The save option results in the creation of two files (input file name with .TIM and .FRC file extensions). The .TIM file contains the history of the displacements of every node. The .FRC file contains the history of the 12 end forces of every member of the structure at every time step, and the 6 reactions at each support at every step. Syntax: TYPE 1 FORCE SAVE 
t_{1 }p_{1} t_{2 } p_{2}   
Values of time (in sec.) and corresponding force (current force unit) or acceleration (current length unit/sec^{2}) depending on whether the time varying load is a forcing function or a ground motion. If the first point is not at zero time, then the forces before the first time (but after the arrival time) will be determined by extrapolation using the first two points entered. If the first point has a nonzero force, there will be a sudden application of that force over a single integration step (DT) at that time. Zero force will be assumed for all times after the last data point. 
a_{1} a_{2} a_{3} ... a_{n}   
Values of the various possible arrival times (seconds) of the various dynamic load types. Arrival time is the time at which a load type begins to act at a joint (forcing function) or at the base of the structure (ground motion). The same load type may have different arrival times for different joints and hence all those values must be specified here. The arrival times and the times from the timeforce pairs will be added to get the times for a particular set of joints in the TIME LOAD data (see TR.32.10.2 Time Varying Load for Response History Analysis). The arrival times and the timeforce pairs for the load types are used to create the load vector needed for each time step of the analysis. Refer to TR.32.10.2 Time Varying Load for Response History Analysis for information on input specification for application of the forcing function and/or ground motion loads. Up to 999 arrival time values may be specified. 
DAMPING d  0.05 
The damping ratio.
Specify a value of exactly 0.0000011 to ignore damping.

The functionspec option can be used to specify harmonic loads. Both sine and cosine harmonic functions may be specified. The program will automatically calculate the harmonic load time history based on the following specifications.
For the function and amplitude option (:
functionspec =
{ SINE  COSINE }
AMPLITUDE f0 { FREQUENCY  RPM } f2 (PHASE f3) CYCLES f4 { SUBDIV f5  STEP f6 }
Where:
Variable or Command  Default Value  Description 

DT x    Solution time step used in the stepbystep integration of the uncoupled equations. Values smaller than 0.00001 will be reset to the default DT value of 0.0013888 seconds. 
TYPE i    Type number of time varying load (integer). Up to 136 types may be provided. This number should be sequential. 
SCALE f7  1.0  The scale factor option multiplies all forces, accelerations, and amplitudes entered, read or generated within this Type. Primarily used to convert acceleration in g’s to current units (9.80665, 386.08858, etc.). 
SAVE   
The save option results in the creation of two files (input file name with .TIM and .FRC file extensions). The .TIM file contains the history of the displacements of every node. The .FRC file contains the history of the 12 end forces of every member of the structure at every time step, and the 6 reactions at each support at every step. Syntax: TYPE 1 FORCE SAVE 
AMPLITUTDE f0    Max. Amplitude of the forcing function in current units. 
FREQ  RPM f2   
If FREQUENCY, then cyclic frequency (cycles / sec.) If RPM, then revolutions per minute. 
PHASE f3  0  Phase Angle in degrees. 
CYCLES f4    No. of cycles of loading. 
SUBDIV f5  3 
Used to subdivide a ¼ cycle into this many integer time steps. 
STEP f6  (p/12) 
Time step of loading. Default is equal to one twelfth of the period corresponding to the frequency of the harmonic loading. (It is best to use the default) 
a_{1} a_{2} a_{3} ... a_{n}   
Values of the various possible arrival times (seconds) of the various dynamic load types. Arrival time is the time at which a load type begins to act at a joint (forcing function) or at the base of the structure (ground motion). The same load type may have different arrival times for different joints and hence all those values must be specified here. The arrival times and the times from the timeforce pairs will be added to get the times for a particular set of joints in the TIME LOAD data (see TR.32.10.2 Time Varying Load for Response History Analysis). The arrival times and the timeforce pairs for the load types are used to create the load vector needed for each time step of the analysis. Refer to TR.32.10.2 Time Varying Load for Response History Analysis for information on input specification for application of the forcing function and/or ground motion loads. Up to 999 arrival time values may be specified. 
DAMPING d  0.05 
The damping ratio.
Specify a value of exactly 0.0000011 to ignore damping.

The spectrumspec option can be used to specify a synthetic ground motion acceleration time history based statistically on a user supplied acceleration spectrum.
The program will automatically calculate the acceleration time history based on the following specifications. Enter f12, f13, and f14 to indicate the rise, steady, & decay times, respectively.
For the spectrum option:
spectrumspec =
SPECTRUM (TMAX f9) (DTI f10) (DAMP f11) (T1 f12) (T2 f13) (T3 f14) (SEED f15)
OPTIONS NF f16 NITR f17 ( THPRINT f18 ) ( SPRINT f19 ) ( FREQ )
Starting on the next line, enter Spectra in the following input form:
P1, V1; P2, V2; … ; Pn, Vn
Where:
Variable or Command  Default Value  Description 

DT x    Solution time step used in the stepbystep integration of the uncoupled equations. Values smaller than 0.00001 will be reset to the default DT value of 0.0013888 seconds. 
TYPE i    Type number of time varying load (integer). Up to 136 types may be provided. This number should be sequential. 
SCALE f7  1.0  The scale factor option multiplies all forces, accelerations, and amplitudes entered, read or generated within this Type. Primarily used to convert acceleration in g’s to current units (9.80665, 386.08858, etc.). 
SAVE   
The save option results in the creation of two files (input file name with .TIM and .FRC file extensions). The .TIM file contains the history of the displacements of every node. The .FRC file contains the history of the 12 end forces of every member of the structure at every time step, and the 6 reactions at each support at every step. Syntax: TYPE 1 FORCE SAVE 
TMAX f9  20 seconds  The Max. time (in seconds) in the generated time history. This value must be greater than f14 (T3). 
DTI f10  0.2  Delta time step (in seconds) in the generated time history. 
DAMP f11  0.05  Damping ratio (5% is entered as 0.05) associated with the input spectrum. 
T1 f12  4 seconds  Ending time of the acceleration rise time. This value must be greater than zero. 
T2 f13  9 seconds  Ending time of the steady acceleration. This value must be greater than zero and greater than f12 (T1). 
T3 f14  14 seconds  Ending time of the acceleration decay. This value must be greater than f13 (T2). 
SEED f15  Optional random Seed. Enter a positive integer (in the range of 1 to 2,147,483,647) to be used as a unique random number generation "seed." A unique time history will be produced for each seed value. Change this value when you want to produce a "different (from the time history generated with the prior seed value)" but statistically equivalent time history. Omit this entry to get the default value (normal option).  
NF f16  The input shock spectrum will be redigitized at NF equally spaced frequencies by interpolation. Default is the greater of 35 or the number of points in the input spectrum.  
NITR f17  10  The number of iterations which will be used to perfect the computed time history. 
THPRINT f18  1 
Print the time history that is generated. Omit the THPRINT parameter to avoid printing.

SPRINT f19  1  Print the spectrum generated from the time history that is generated. Omit the SPRINT parameter to avoid printing 
FREQ  If entered, then frequencyspectra pairs are entered rather than periodspectra pairs.  
P1, V1 P2, V2 … Pn, Vn 
Data is part of input, immediately following SPECTRUM command. Period (or frequency if FREQ option entered above) Value pairs (separated by semi colons) are entered to describe the Spectrum curve. Enter the period in seconds (or frequency in Hz.) and the corresponding Value is in acceleration (current length unit/sec^{2}) units. Continue the curve data onto as many lines as needed (up to 999 spectrum pairs). Spectrum pairs must be in ascending or descending order of period (or frequency). 

a_{1} a_{2} a_{3} ... a_{n}   
Values of the various possible arrival times (seconds) of the various dynamic load types. Arrival time is the time at which a load type begins to act at a joint (forcing function) or at the base of the structure (ground motion). The same load type may have different arrival times for different joints and hence all those values must be specified here. The arrival times and the times from the timeforce pairs will be added to get the times for a particular set of joints in the TIME LOAD data (see TR.32.10.2 Time Varying Load for Response History Analysis). The arrival times and the timeforce pairs for the load types are used to create the load vector needed for each time step of the analysis. Refer to TR.32.10.2 Time Varying Load for Response History Analysis for information on input specification for application of the forcing function and/or ground motion loads. Up to 999 arrival time values may be specified. 
DAMPING d  0.05 
The damping ratio.
Specify a value of exactly 0.0000011 to ignore damping.

The time history data can also be defined in an external file, where:
Variable or Command  Default Value  Description 

DT x    Solution time step used in the stepbystep integration of the uncoupled equations. Values smaller than 0.00001 will be reset to the default DT value of 0.0013888 seconds. 
TYPE i    Type number of time varying load (integer). Up to 136 types may be provided. This number should be sequential. 
SCALE f7  1.0  The scale factor option multiplies all forces, accelerations, and amplitudes entered, read or generated within this Type. Primarily used to convert acceleration in g’s to current units (9.80665, 386.08858, etc.). 
SAVE   
The save option results in the creation of two files (input file name with .TIM and .FRC file extensions). The .TIM file contains the history of the displacements of every node. The .FRC file contains the history of the 12 end forces of every member of the structure at every time step, and the 6 reactions at each support at every step. Syntax: TYPE 1 FORCE SAVE 
READ filename  Filename for an external file containing time varying load history data.  
f8  The optional delta time spacing used for the external file data  
a_{1} a_{2} a_{3} ... a_{n}   
Values of the various possible arrival times (seconds) of the various dynamic load types. Arrival time is the time at which a load type begins to act at a joint (forcing function) or at the base of the structure (ground motion). The same load type may have different arrival times for different joints and hence all those values must be specified here. The arrival times and the times from the timeforce pairs will be added to get the times for a particular set of joints in the TIME LOAD data (see TR.32.10.2 Time Varying Load for Response History Analysis). The arrival times and the timeforce pairs for the load types are used to create the load vector needed for each time step of the analysis. Refer to TR.32.10.2 Time Varying Load for Response History Analysis for information on input specification for application of the forcing function and/or ground motion loads. Up to 999 arrival time values may be specified. 
DAMPING d  0.05 
The damping ratio.
Specify a value of exactly 0.0000011 to ignore damping.

Examples
Using Force and Acceleration options:
UNIT … DEFINE TIME HISTORY TYPE 1 FORCE 0.0 1.0 1.0 1.2 2.0 1.8 3.0 2.2 4.0 2.6 5.0 2.8 TYPE 2 ACCELERATION SCALE 9.80665 0.0 1.0 1.0 1.2 2.0 1.8 3.0 2.2 4.0 2.6 5.0 2.8 ARRIVAL TIME 0.0 1.0 1.8 2.2 3.5 4.4 DAMPING 0.075
Using the Spectrum option:
UNIT … DEFINE TIME HISTORY TYPE 1 ACCELERATION SCALE 9.80665 SPECTRUM TMAX 19 DTI 0.01 DAMP 0.03 OPTIONS NF 40 0.03 1.00 ; 0.05 1.35 0.1 1.95 ; 0.2 2.80 0.5 2.80 ; 1.0 1.60 ARRIVAL TIME 0.0 1.0 1.8 2.2 3.5 4.4 DAMPING 0.075
Using the Harmonic Loading Generator:
UNIT … DEFINE TIME HISTORY TYPE 1 FORCE *Following lines for Harmonic Loading Generator FUNCTION SINE AMPLITUDE 6.2831 FREQUENCY 60 CYCLES 100 STEP 0.02 ARRIVAL TIME 0.0 DAMPING 0.075
To define more than one sinusoidal load, the input specification is as follows:
DEFINE TIME HISTORY TYPE 1 FORCE FUNCTION SINE AMPLITUDE 1.925 RPM 10794.0 CYCLES 1000 TYPE 2 FORCE FUNCTION SINE AMPLITUDE 1.511 RPM 9794.0 CYCLES 1000 TYPE 3 FORCE FUNCTION SINE AMPLITUDE 1.488 RPM 1785.0 CYCLES 1000 ARRIVAL TIME 0.0 0.0013897 0.0084034 DAMPING 0.04
The data in the external file must be provided as one or more timeforce pairs per line as shown in the following example.
Data in Input file
UNIT … DEFINE TIME HISTORY TYPE 1 FORCE READ THFILE ARRIVAL TIME 0.0 DAMPING 0.075
Data in the External file THFILE:
0.0 1.0 1.0 1.2 2.0 1.8 3.0 2.2 4.0 2.6
Notes
 By default the response (displacements, forces etc.) will contain the contribution of only those modes whose frequency is less than or equal to 108 cps. Use the CUT OFF FREQUENCY command to change this limit. Contributions of modes with frequency greater than the Cut Off Frequency are not considered.
 Results are the individual maximums over the time period. Thus, derived quantities such as section forces and stresses, plate surface stresses and principal stresses should not be used.
 Results from harmonic input are the maximum over the time period including the startup transient period. These results are not the steadystate results.
 By default, the results do not include the time period after the time loads end. Use the CUT OFF TIME command to lengthen (or shorten) the time period. If an intense shortterm loading is used, the loading should be continued until after the expected peak response is reached.
 The READ filename command is to be provided only if the history of the time varying load is to be read from an external file. filename is the file name and may be up to 72 characters long. If the data on the file consists only of amplitudes, then enter f8 as the delta time spacing.