TR.32.10.1.15 Response Spectrum Specification per SP 14.13330.2011

This command may be used to specify and apply the RESPONSE SPECTRUM loading as per SP 14.13330.2011 for dynamic analysis.

General Format

SPECTRUM { SRSS | CQC } SP11 (ECCENTRICITY) A f₁ *{ {X f₂ | Y f₃ | Z f₄} ACCELERATION (SCALE f₅) 
(DAMP f₆ ) (LOG) (MIS f₇) (ZPA f₈) ({ DOMINANT f₉ | SIGN }) SOIL { 1 | 2 | 3}

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 SP 14.13330.2011 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.
X f2 Y f3 Z f5	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 f5		A linear scaling factor by which the spectrum data will be multiplied according to the provisions of SP 14.13330.2011.
DAMP f6	0.05	The damping ratio. Specify a value of exactly 0.0000011 to ignore damping. If `CDAMP` is specified, then composite damping is used as determined by the values for material damping (and spring damping, if specified). Refer to TR.26.2 Specifying Constants for Members and Elements If `MDAMP` is specified, then modal damping is calculated using the method defined in a `DEFINE DAMPING INFORMATION` command, which must be included in the input file. Refer to TR.26.4 Modal Damping Information
MISSING f7		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 f7 value entered in length per second squared units (this value is not multiplied by `SCALE`). If f7 is zero, then the spectral acceleration at the `ZPA` f8 frequency is used. If f8 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 of f7 or f8 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 f8	33.0 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 f7` is entered.
DOMINANT f9	1	The dominant mode method. All results will have the same sign as mode number f9 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.

SRSS

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

CQC

Complete Quadratic Combination method (Default). This method is recommended for closely spaced modes instead of SRSS.

Resultants are calculated as:

F = \sqrt{\sum_{n} \sum_{m} f_{n} ρ_{n m} f_{m}}

where

ρ_nm	=	$\frac{8 ζ^{2} (1 + r) r^{2 / 3}}{{(1 - r^{2})}^{2} + 4 ζ^{2} r {(1 + r)}^{2}}$
r	=	ω_n/ω_m ≤ 1.0

Note: The cross-modal coefficient array is symmetric and all terms are positive.

The specifier SP11 is mandatory to denote that the applied loading is as per the guidelines of SP 14.13330.2011.

ECCENTRICITY

automatic introduction of artificial mass eccentricity according to SP 14.13330.2011.

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.

Non-weathered rock and rocklike geological formation or permafrost subsoil.
Weathered rock or deep deposits of medium dense sand, gravel or medium stiff clays.
Loose cohesion less soil deposits or deposits with soft to medium stiff cohesive soil.

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 more information on dynamic mass modeling, refer to sections TR.32 Loading Specifications and G.17.3 Dynamic Analysis

Example

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 1
*NEXT LOAD WILL BE RESPONSE SPECTRUM LOAD
*WITH MASSES PROVIDED IN TERMS OF LOAD.
LOAD 1 SEISMIC LOADING
JOINT LOAD
3 4 FX 310.586
3 4 FY 310.586
5 6 FX 310.586
5 6 FY 310.586
SPECTRUM CQC SP11 ECC A 1.0 X 1.0 ACC MIS SOIL 2
PERFORM ANALYSIS
PRINT MODE SHAPES
PRINT STORY DRIFT
PRINT ANALYSIS RESULTS
FINISH