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TR.37.6.7 Harmonic Force Loading

This set of commands may be used to specify JOINT loads on the structure, the modal damping, and the phase relationship of loads in each of the global directions. 

Response at all of the frequencies defined in TR.37.6.2 Define Harmonic Output Frequencies will be calculated.

General Format



DAMP f2 Damping ratio for all modes when DAMP is selected.  Default value is 0.05 (5% damping if 0 or blank entered).

This command specifies the damping for a case of harmonic forces.

DAMP, MDAMP, and CDAMP select source of damping input:
  • DAMP indicates to use the f2 value for all modes
  • MDAMP indicates to use the damping entered or computed with the DEFINE DAMP command if entered, otherwise default value of 0.05 will be used
  • CDAMP indicates to use the composite damping of the structure calculated for each mode. You must specify damping for different materials under the CONSTANT specification

Joint Loads

Refer to TR.32.1 Joint Load Specification for additional information on Joint Loads

JOINT LOAD ( [ PHASE *{ X | Y | Z } f7] )


PHASE f7 Phase angle in degrees. One phase angle per global direction.

Bracketed data may be entered for each global direction on the same line.  All moments specified below will be applied with a phase angle of 0.0.  All forces specified below will be applied with the phase angle specified above, if any. Default is 0.0. 

Next are the joint forces, if any. Repeat as many lines of joint force data as needed.

joint-list *{ FX f1FY f2 | FZ f3 | MX f4 | MY f5 | MZ f6 }


FX f1, FY f3, FZ f3 specify a force in the corresponding global direction.
MX f4, MY f4, MZ f6 specify a moment in the corresponding global direction.


  1. Joint numbers may be repeated where loads are meant to be additive in the joint.

  2. UNIT command may be on lines in between joint-list lines.

  3. Forces applied at a dependent degree of freedom will be ignored.

Copy Loads

The next command, Copy Load, may optionally be placed here to use the equivalent joint loads from prior cases.  This feature enables using the more complex loading commands like selfweight, floor load, wind load, etc. that are not directly available here.

i1, f1, i2, f2 ... in, fn


i1, i2 ... in prior primary load case numbers that are in this analysis set.
f1, f2 ... fn corresponding factors

This command can be continued to additional lines by ending all but last with a hyphen. These cases must have been between the Perform Steady State Analysis command and the prior Analysis command (if any).

Next is an optional amplitude versus frequency specification to be used when the ground motion acceleration is a function of frequency. For any forcing frequency an amplitude can be determined, from the data below, which will multiply the acceleration f3 entered above.  If no amplitude data is entered for a direction then the acceleration is f3 for that direction.

AMPLITUDE ( A a B b C c )
a×ω2 + b×ω + c
forcing frequency in rad/sec.
a, b, c
Constants. a and b default to 0.0 and c defaults to 1.0.


(f1 a1  f2 a2  … fn an )
f1 a1  f2 a2  … fn an Frequency - Amplitude pairs are entered to describe the variation of acceleration with frequency. Continue this data onto as many lines as needed by ending each line except the last with a hyphen (-). These pairs must be in ascending order of frequency.  Use up to 199 pairs.  Linear interpolation is used.

Leaving the direction field blank or inserting ALL will use the same Frequency versus Amplitude for all 3 force directions.

Enter amplitudes for up to three directions.  For directions without amplitude input, including moment directions, the amplitude will be set to 1.0.

The first form of the amplitude input is converted to the second form by creating 199 equally spaced frequencies, then computing the amplitude for each frequency.