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) (TORSION) (DECCENTRICITY f8) (ECCENTRICITY f9) *{ X f1 | Y f2| Z f3 } ALPHA-

{DAMP f4 | CDAMP | MDAMP }  ( { LINEAR | LOGARITHMIC } ) (MISSING f5) ( ZPA f6 ) ({ DOMINANT f10| SIGN }) (SAVE)  (IMR f11) (STARTCASE f12) -

{ ( 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
DECCENTRICITY f8	0	(Optional input) It is a factor which when multiplied with static eccentricity (i.e., eccentricity between center of mass and center of rigidity) gives dynamic eccentricity. Since the applied load is acting at the center of mass, the effect of inherent torsion arising due to static eccentricity is included in the analysis. Note: The torsion arising due to dynamic eccentricity (i.e,. static eccentricity multiplied by dynamic amplification factor) between center of mass and center of rigidity is applied along with accidental torsion. The dynamic eccentricity is automatically calculated by the program while you can specify the amount of accidental eccentricity (if not specified, the default of 5% of lateral dimension of the floor in the direction of the earthquake will be considered).
ECCENTRICITY f9	0.05	A factor which indicates the extent of accidental eccentricity. For all buildings this factor is to be provided as 0.05. However, for highly irregular buildings this factor may be increased to 0.10. This factor is to be externally provided to calculate design eccentricity. Since accidental eccentricity can be on either side, you must consider lateral force acting at a floor level to be accompanied by a clockwise or a counterclockwise accidental torsion moment. If the value is positive, it indicates clockwise torsion whereas a negative value indicates counterclockwise torsion.
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).
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.
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.

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).

FREQUENT | FORTIFIED | RARE

The earthquake type.

Inherent and Accidental Torsion

Note: STAAD.Pro does not support the coupled torsion methodology as per GB50011-2010. This implementation enables the general "inherent and accidental torsion" for GB50011 response spectrum analysis. Note that this implementation does not comply with Cl. 5.2.3 of GB50011-2010.

In response spectrum analysis all the response quantities (i.e., joint displacements, member forces, support reactions, plate stresses, etc.) are calculated for each mode of vibration considered in the analysis. These response quantities from each mode are combined using a modal combination method (either CQC or SRSS) to produce a single positive result for the given direction of acceleration. This computed result represents a maximum magnitude of the response quantity that is likely to occur during seismic loading. The actual response is expected to vary from a range of negative to the positive value of this maximum computed quantity.

No information is available from response spectrum analysis as to when this maximum value occurs during the seismic loading and what will be the value of other response quantities at that time. For example, consider two joints J2 and J3 whose maximum joint displacement in the global X direction come out to be X1 and X2 respectively. This implies that during seismic loading joint J1 will have X-direction displacement that is expected to vary from -X1 to +X1 and that for joint J2 from -X2 to +X2. However, this does not necessarily mean that the point of time at which the X displacement of joint J1 is X1, the X displacement of joint J2 will also be X2.

For the reason stated above, the torsional moment at each floor arising due to dynamic eccentricity along with accidental eccentricity (if any) is calculated for each mode. Lateral story shear from this torsion is calculated forming global load vectors for each mode. Static analysis is carried out with this global load vector to produce global joint displacement vectors for each mode due to torsion. These joint displacements from torsion for each mode are algebraically added to the global joint displacement vectors from response spectrum analysis for each mode. The final joint displacements from the response spectrum along with torsion for all modes are combined using a specified modal combination method to get the final maximum possible joint displacements.