TR.32.10.1.6 Response Spectrum Specification per GB 50011 2010

This command may be used to specify and apply the RESPONSE SPECTRUM loading as per the 2016 edition of the Chinese specification Code for seismic design of building, for dynamic analysis. The graph of frequency – acceleration pairs are calculated based on the input requirements of the command and as defined in the code.

General Format

SPECTRUM { CQC | SRSS } GB50011 (2010) *{ X f1 | Y f2| Z f3 } ALPHA-

{DAMP f4 | CDAMP | MDAMP }  ( { LINEAR | LOGARITHMIC } ) (MISSING f5) ( ZPA f6 ) ({ DOMINANT f10| SIGN }) -

{ ( INTENSITY f9 ) ( FREQUENT | FORTIFIED | RARE ) ( GROUP f11 ) ( SCLASS f12 ) }

Note: The data from SPECTRUM through ALPHA must be on the first line of the command. The data shown on the second line above can be continued on the first line or one or more new lines with all but last ending with a hyphen (limit of four lines per spectrum).

Where:

Table 1. Parameters used for GB 50011-2010 response spectrum
Parameter	Default Value	Description
X f1, Y f2, Z f3	-	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 if the global axis is not specified. If the direction is specified, then the default factor for X and Z is 1.0 where as the default factor for Y is 0.65. At least one direction must be specified. Any directions that is not specified will default to zero.
DAMP f4	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 f5		Optional parameter to use "Missing Mass" method. The static effect of the masses not represented in the modes is included. The spectral acceleration for this missing mass mode is the f6value entered in length/sec². If the "missing mass" option is used, then this value must be provided. Note: If the `MISSING` parameter is entered on any spectrum case it will be used for all spectrum cases.
ZPA f6	33 (Hz)	The zero-period acceleration value used with the MISSING option only.
DOMINANT f7	1 (1st Mode)	Dominant mode method. All results will have the same sign as mode number f7 alone would have if it were excited then the results were used as a static displacements result. Defaults to mode 1 if no value is entered. If a value of 0 is entered, then the mode with the greatest % participation in the excitation direction will be used (only 1 direction factor may be nonzero).
INTENSITY f9	7	Fortification seismic intensity. Permitted values are: 6, 7, 7A, 8, 8A, or 9
GROUP f10	2	Design seismic group.
SCLASS f11	2	Site class.

{ SRSS | CQC } are methods of combining the responses from each mode into a total response. The CQC methods requires damping. SRSS method do not use damping unless spectra-period curves are made a function of damping. CQC includes the effect of response magnification due to closely spaced modal frequencies. CQC is a more sophisticated and realistic method and is recommended.

SRSS

Square Root of Summation of Squares method.

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.

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 | LOGARITHMIC

Specifies the type of interpolation of the input seismic coefficient versus time period curves for determining the seismic coefficient value for a mode given its period. Linear is the default if not specified.

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.

Warning: Do not enter DOMINANT parameter with this option.

FREQUENT | FORTIFIED | RARE

The earthquake type.