# TR.32.10.1.13 Response Spectrum Specification per SNiP II-7-81

This command may be used to specify and apply the RESPONSE SPECTRUM loading as per SNiP II-7-81 for dynamic analysis.

## General Format

SPECTRUM comb-method SNIP A f1 *{ {X f2 | KWX f3 KX1 f4} | { Y f5 | KWY f6 KY1 f7 } | { Z f8 | KWZ f9 KZ1 f10 } ACCELERATION (SCALE f11)
{DAMP f12 | CDAMP | MDAMP } ( { LINEAR | LOGARITHMIC } ) (MISSING f13) (ZPA f14) ({ DOMINANT f15 | SIGN }) SOIL { 1 | 2 | 3} (SAVE)

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).

Where:

Table 1. Parameters for SNiP II-7-81 response spectrum
Parameter Default Value Description
A f1   Zoning factor, A, which is based on maximum acceleration factor for the seismic zone. This factor must be modified for SOIL types other than 2. The exact zone factor value used for a specific location requires engineering judgment. The following table serves as a guide for accelerations and corresponding zone factors which would be used.
X f2

Y f5

Z f8

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. Alternatively, you may input individual parameters such as KWX, KX1 the product of which would be used as the factor along that direction.
SCALE f11   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 f12 0.05
The damping ratio. Specify a value of exactly 0.0000011 to ignore damping.
MISSING f13   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 f13 value entered in length per second squared units (this value is not multiplied by SCALE). If f13 is zero, then the spectral acceleration at the ZPA f14 frequency is used. If f14 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 and CQC, the results of this calculation are SRSSed with the modal combination results. If either f13 or f14 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 f14   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 f13 is entered.
DOMINANT f15   The dominant mode method. All results will have the same sign as mode number f15 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.

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

The CQC method requires damping. The SRSS method does not use damping unless spectra-period curves are made a function of damping (see File option below). CQC includes the effect of response magnification due to closely spaced modal frequencies. CQC is a more sophisticated and realistic methods and is recommended.

Square root of summation of squares method as prescribed by the SNiP II-7-81 code.
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.

The specifier SNIP is mandatory to denote that the applied loading is as per the guidelines of SNiP II-7-81.

ACCELERATOIN
indicates that the Acceleration spectra will be entered.
Note: SNiP II-7-81 / SP 14.13330.2011 do not have provisions for displacement response spectra.
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.
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.
SOIL
Defines the subsoil conditions on which the response spectrum will be generated.
Note: The Zoning Factor, A (f1), must be adjusted for soil types other than type 2.
1. Non-weathered rock and rocklike geological formation or permafrost subsoil.
2. Weathered rock or deep deposits of medium dense sand, gravel or medium stiff clays.
3. Loose cohesion less soil deposits or deposits with soft to medium stiff cohesive soil.
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).

## Description

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, see sections TR.32 Loading Specifications and G.17.3 Dynamic Analysis. An illustration of mass modeling is available, with explanatory comments, in the sample file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\Rus\Seismic_Russ.STD.

## Example 1

The definition of a SNiP response spectrum in the X direction on a structure built on weather rock and where the Zoning Factor is 0.7071. As this is the first load case with a response spectrum, then the masses are modeled as loads.

LOAD 2 LOADTYPE Seismic TITLE SPECTRUM IN X-DIRECTION
*Masses
SELFWEIGHT X 1.0
SELFWEIGHT Y 1.0
SELFWEIGHT Z 1.0
10 FX 17.5
10 FY 17.5
10 FZ 17.5
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
*SNiP Spectrum definition
SPECTRUM SRSS SNIP A 0.7071 X 1.0 ACC DAMP 0.05 SCALE 1.0 LIN MIS 0 ZPA 40 SOIL 2
…

Note: The maximum response spectrum load cases allowed in one run is 50.

For full details on Response Spectrum refer to section TR.32.10.1 Response Spectrum Analysis.

## Example 2

STAAD PLANE RESPONSE SPECTRUM ANALYSIS
START JOB INFORMATION
JOB NAME Plane Russian example
ENGINEER DATE 12-Feb-08
END JOB INFORMATION
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 7.2 0 0; 3 0 4.5 0; 4 7.2 4.5 0; 5 0 9.0 0; 6 7.2 9.0 0;
MEMBER INCIDENCES
1 1 3; 2 2 4; 3 3 5; 4 4 6; 5 3 4; 6 5 6;
MEMBER PROPERTY RUSSIAN
1 TO 4 PRIS AY 10000 YD 0.6 ZD 0.6
5 TO 6 PRIS YD 0.9 ZD 0.3
SUPPORTS
1 TO 2 FIXED BUT MZ
3 TO 6 FIXED BUT FX
CONSTANTS
E 30.0e+006 ALL
POISSON 0.2 ALL
CUT OFF MODE SHAPE 2
FINISH