# TR.32.10.1.1 Response Spectrum Specification - Custom

This command may be used to specify and apply a custom (i.e., "generic" method) RESPONSE SPECTRUM loading for dynamic analysis.

This command should appear as part of a loading specification. If it is the first occurrence, it should be accompanied by the load data to be used for frequency and mode shape calculations. Additional occurrences need no additional information. The maximum number of response spectrum load cases allowed in one run is 50.

Results of frequency and mode shape calculations may vary significantly depending upon the mass modeling. All masses that are capable of moving should be modeled as loads, applied in all possible directions of movement. For dynamic mass modeling, refer to TR.32 Loading Specifications and G.17.3 Dynamic Analysis. An illustration of mass modeling is available, with explanatory comments, in Example Problem No.11.

## General Format

SPECTRUM comb-method *{ X f1 | Y f2 | Z f3 } { ACCELERATION | DISPLACEMENT } (SCALE f4)
{DAMP f5 | CDAMP | MDAMP } ( { LINEAR | LOGARITHMIC } ) (MISSING f6) (ZPA f7) (FF1 f8) (FF2 f9) ( { DOMINANT f10 | SIGN } ) (SAVE) (IMR f11) (STARTCASE f12)
Note: The data from SPECTRUM through SCALE above must be on the first line of the command, the remaining data can be on the first or subsequent lines with all but last ending with a hyphen (limit of four lines per spectrum).

Starting on the next line, enter Spectra in one of these two input forms (i.e., explicit values or an external file):

{ p1 v1; p2 v2; p3 v3; … | FILE filename }

Where:

Table 1. Parameters used for generic model response spectrum
Parameter Default Value Description
X f1, Y f2, Z f3 0.0 Factors for the input spectrum to be applied in X, Y, & Z directions. Any one or all directions can be input. Directions not provided will default to zero.
SCALE f4 1.0 Linear scale factor by which the spectra data will be multiplied. Usually used to factor g’s to length/sec2 units. This input is the appropriate value of acceleration due to gravity in the current unit system (thus, 9.81 m/s2 or 32.2 ft/s2).
DAMP f5 0.05
The damping ratio. Specify a value of exactly 0.0000011 to ignore damping.
MISSING f6 0 Optional parameter to use the "Missing Mass" method to include the static effect of the masses not represented in the modes. The spectral acceleration length/sec2 for this missing mass mode is the f6 value entered in length per second squared units (this value is not multiplied by SCALE). If f6 is zero, then the spectral acceleration at the ZPA f7 frequency is used. If f7 is zero or not entered, then the spectral acceleration at 33Hz is used. The results of this calculation are SRSSed with the modal combination results.

For SRSS, CQC, and TEN the results of this calculation are SRSSed with the modal combination results. For ABS, missing mass is ignored. For ASCE, the missing mass result is algebraically added with the rigid parts of the extracted modes. For ASCE, the MIS option is assumed to be on. If any of f6, f7, f8, or f9 are not entered, the defaults will be used. Missing mass does not include the effect of masses lumped at the supports unless the support is a stiff spring or an Enforced support.

Note: If the MISSING parameter is entered on any spectrum case it will be used for all spectrum cases.
ZPA f7 33 [Hz] The zero period acceleration value for use with MISSING option only. Defaults to 33 Hz if not entered. The value is printed but not used if MISSING f6 is entered.
FF1 f8 2 [Hz] The f1 parameter defined in the ASCE 4-98 standard in Hz units. For ASCE option only.
FF2 f9 33 [Hz] The f2 parameter defined in the ASCE 4-98 standard in Hz units. For ASCE option only.
DOMINANT f10 1 (1st Mode) The dominant mode method. All results will have the same sign as mode number f10 alone would have if it were excited then the scaled results were used as a static displacements result. Defaults to mode 1 if no value entered. If a 0 value entered, then the mode with the greatest % participation in the excitation direction will be used (only one direction factor may be nonzero).
Note: Do not enter the SIGN parameter with this option. Ignored for the ABS method of combining spectral responses from each mode.
IMR f11 1 The number of individual modal responses (scaled modes) to be copied into load cases. Defaults to one. If greater than the actual number of modes extracted (NM), then it will be reset to NM. Modes one through f11 will be used. Missing Mass modes are not output.
STARTCASE f12 Highest Load Case No. + 1 The primary load case number of mode 1 in the IMR parameter. Defaults to the highest load case number used so far plus one. If f12 is not higher than all prior load case numbers, then the default will be used. For modes 2 through NM, the load case number is the prior case number plus one.

comb-method = { SRSS | ABS | CQC | ASCE | TEN | CSM | GRP } are methods of combining the responses from each mode into a total response.

The CQC and ASCE4-98 methods require damping. ABS, SRSS, CRM, GRP, and TEN methods do not use damping unless spectra-period curves are made a function of damping (see File option below). CQC, ASCE, CRM, GRP, and TEN include the effect of response magnification due to closely spaced modal frequencies. ASCE includes more algebraic summation of higher modes. ASCE and CQC are more sophisticated and realistic methods and are recommended.

Square Root of Summation of Squares method.
ABS
Absolute sum. This method is very conservative and represents a worst case combination.
CQC
Resultants are calculated as:
$F=∑n∑mfnρnmfm$
where
 ρnm = $8ζ2(1+r)r2/3(1−r2)2+4ζ2r(1+r)2$ r = ωn/ωm ≤ 1.0
Note: The cross-modal coefficient array is symmetric and all terms are positive.
ASCE
NRC Regulatory Guide Rev. 2 (2006) Gupta method for modal combinations and Rigid/Periodic parts of modes are used. The ASCE4-98 definitions are used where there is no conflict. ASCE4-98 Eq. 3.2-21 (modified Rosenblueth) is used for close mode interaction of the damped periodic portion of the modes.
TEN
Ten Percent Method of combining closely spaced modes. NRC Reg. Guide 1.92 (Rev. 1.2.2, 1976).
CSM
Closely Spaced Method as per IS:1893 (Part 1)-2002 procedures.
GRP
Closely Spaced Modes Grouping Method. NRC Reg. Guide 1.92 (Rev. 1.2.1, 1976).
Note: If SRSS is selected, the program will internally check whether there are any closely spaced modes or not. If it finds any such modes, it will switch over to the CSM method. In the CSM method, the program will check whether all modes are closely spaced or not. If all modes are closely spaced, it will switch over to the CQC method.
ACCELERATION or DISPLACEMENT
indicates whether Acceleration or Displacement spectra will be entered. The relationship between acceleration and displacement values in response spectra data is:
$Displacement = Acceleration × ( 1 / ω ) 2$
where
 ω = 2π/Period (period given in seconds; ω in cycles per second)
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
LINEAR or LOGARITHMIC
Select Linear or Logarithmic interpolation of the input Spectra versus Period curves for determining the spectra value for a mode given its period. Linear is the default. Since Spectra versus Period curves are often linear only on Log-Log scales, the logarithmic interpolation is recommended in such cases; especially if only a few points are entered in the spectra curve.

When FILE filename is entered, the interpolation along the damping axis will be linear.

Note: The last interpolation parameter entered on the last of all of the spectrum cases will be used for all spectrum cases.
SAVE
This option results in the creation of a acceleration data file (with the model file name and an .acc file extension) containing the joint accelerations in g’s and radians/sec2. These files are plain text and may be opened and viewed with any text editor (e.g., Notepad).
SIGN
This option results in the creation of signed values for all results. The sum of squares of positive values from the modes are compared to sum of squares of negative values from the modes. If the negative values are larger, the result is given a negative sign. This command is ignored for ABS option.
CAUTION: Do not enter DOMINANT parameter with this option.
Spectra data is input in one of these two input forms:
1. p1, v1; p2, v2; …. ; pn, vn. Data is part of input, immediately following the SPECTRUM command. Period – Value pairs (separated by semi colons) are entered to describe the Spectrum curve. Period is in seconds and the corresponding Value is either acceleration (current length unit/sec2) or displacement (current length unit) depending on the ACC or DIS chosen. Continue the curve data onto as many lines as needed (up to 500 spectrum pairs). Spectrum pairs must be in ascending order of period. Note, if data is in g acceleration units, then set SCALE to a conversion factor to the current length unit (9.81, 386.4, etc.). Also note, do not end these lines with a hyphen (-). Each SPECTRUM command must be followed by Spectra data if this input form is used.
2. FILE filename data is in a separate file, using the format described in File Format for Spectra Data.

When the File filename command has been provided, then you must have the spectra curve data on a file named filename prior to starting the analysis. The format of the FILE spectra data allows spectra as a function of damping as well as period.

Note: If the FILE filename command is entered, it must be with the first spectrum case and will be used for all spectrum cases.

No File filename command needs to be entered with the remaining spectrum cases. The filename may not be more than 72 characters in length.

## Examples

LOAD 2 SPECTRUM IN X-DIRECTION
SELFWEIGHT X 1.0
SELFWEIGHT Y 1.0
SELFWEIGHT Z 1.0
10 FX 17.5
10 FY 17.5
10 FZ 17.5
SPECTRUM SRSS X 1.0 ACC SCALE 32.2
0.20 0.2 ; 0.40 0.25 ; 0.60 0.35 ; 0.80 0.43 ; 1.0 0.47
1.2 0.5 ; 1.4 0.65 ; 1.6 0.67 ; 1.8 0.55 ; 2.0 0.43

An example using member loads and the CQC combination method:

LOAD 2 SEISMIC LOADING
SELFWEIGHT X 1.0
SELFWEIGHT Y 1.0
5  CON  GX  5.0  6.0
5  CON  GY  5.0  6.0
5  CON  GX  7.5  10.0
5  CON  GY  7.5  10.0
5  CON  GX  5.0  14.0
5  CON  GY  5.0  14.0
SPECTRUM CQC X 1.0 ACC DAMP 0.05 SCALE 32.2
0.03  1.00  ;  0.05  1.35
0.1  1.95  ;  0.2  2.80
0.5  2.80  ;  1.0  1.60

## Multiple Response Spectra

If there is more than one response spectrum defined in the input file, the load data (representing the dynamic weight) should accompany the first set of spectrum data only. In the subsequent load cases, only the spectra should be defined. See example below.

LOAD 1 SPECTRUM IN X-DIRECTION
SELFWEIGHT X 1.0
SELFWEIGHT Y 1.0
SELFWEIGHT Z 1.0
10 FX 17.5
10 FY 17.5
10 FZ 17.5
SPECTRUM SRSS X 1.0 ACC SCALE 32.2  IMR 2 STARTCASE 11
0.20 0.2 ; 0.40 0.25 ; 0.60 0.35 ; 0.80 0.43 ; 1.0 0.47
1.2 0.5 ; 1.4 0.65 ; 1.6 0.67 ; 1.8 0.55 ; 2.0 0.43
PERFORM ANALYSIS
CHANGE
*
SPECTRUM SRSS Y 1.0 ACC SCALE 32.2
0.20 0.1 ; 0.40 0.15 ; 0.60 0.33 ; 0.80 0.45 ; 1.00 0.48
1.20 0.51 ; 1.4 0.63 ; 1.6 0.67 ; 1.8 0.54 ; 2.0 0.42

## File Format for Spectra Data

The format of the FILE spectra data allows spectra as a function of damping as well as period. The format is:

    Dataset 1      MDAMPCV NPOINTCV                       (no of values = 2)
Dataset 2      Damping Values in ascending order      (no of values = Mdampcv)
Dataset 3a     Periods                                (no of values = Npointcv)
3b     Spectra                                (no of values = Npointcv)

For ASCE, the MIS option is assumed to be on. If any of f6, f7, f8, f9 are not entered the defaults will be used.

Repeat Data set 3 Mdampcv times (3a,3b , 3a,3b , 3a,3b , etc.) (i.e., for each damping value).

Data sets 2, 3a and 3b must have exactly Npointcv values each. Blanks or commas separate the values. The data may extend to several lines. Do not end lines with a hyphen (-). No comment lines (*) or semi-colons. Multiple values may be entered per line.

where
 MDAMPCV = Number of damping values for which there will be separate Spectra vs. Period curves. NPOINTCV = Number of points in each Spectra vs. Period curve. If NPOINTCV is negative, then the period-spectra values are entered as pairs.

## Examples of Spectra Data files

An example of spectral data for use in the X direction:

1,-10
0.05
0.20 0.2 0.40 0.25 0.60 0.35 0.80 0.43 1.0 0.47
1.2 0.5 1.4 0.65 1.6 0.67 1.8 0.55 2.0 0.43

An example of spectral data for use in the Z direction:

1 10
0.05
0.20 0.40 0.60 0.80 1.0 1.2 1.4 1.6 1.8 2.0
0.1 0.15 0.33 0.45 0.48 0.51 0.63 0.67 0.54 0.42
Note: It is important that any STAAD plain text file be encoded with ANSI/UTF-8. If you use a text editor in a non-English user interface, ensure that the correct encoding is used when saving the file.

## Individual Modal Response Case Generation

Individual modal response (IMR) cases are simply the mode shape scaled to the magnitude that the mode has in this spectrum analysis case before it is combined with other modes. If the IMR parameter is entered, then STAAD.Pro will create load cases for the first specified number of modes for this response spectrum case (i.e., if five is specified then five load cases are generated, one for each of the first five modes). Each case will be created in a form like any other primary load case.

The results from an IMR case can be viewed graphically or through the print facilities. Each mode can therefore be assessed as to its significance to the results in various portions of the structure. Perhaps one or two modes could be used to design one area/floor and others elsewhere.

You can use subsequent load cases with TR.32.11 Repeat Load Specification combinations of these scaled modes and the static live and dead loads to form results that are all with internally consistent signs (unlike the usual response spectrum solutions). The modal applied loads vector will be omega squared times mass times the scaled mode shape. Reactions will be applied loads minus stiffness matrix times the scaled mode shape.

With the Repeat Load capability, you can combine the modal applied loads vector with the static loadings and solve statically with P-Delta or tension only.

Note: When the IMR option is entered for a Spectrum case, then a TR.37 Analysis Specification & TR.38 Change Specification must be entered after each such Spectrum case.