TR.32.10.1.9 Response Spectrum Specification per IS: 1893 (Part 4)-2015

This command may be used to specify and apply the RESPONSE SPECTRUM loading as per IS: 1893 (Part 4)-2015 for dynamic analysis of industrial and stack-like structures.

The seismic load generator can be used to generate lateral loads in the X, Y, and Z directions.

Note: This facility has not been developed for cases where the Z axis is set to be the vertical direction using the SET Z UP command.

Note: For vertical motions (i.e., when forces are applied in the Y direction), the resulting forces are taken as 2/3 of the horizontal forces as per 6.4.6 of the IS 1893 2016 Part 1 code.

General Format

The data in the following format can be contained all on a single line or broken into two or three lines, so long as the second and third lines start with the ACC and DOMINANT or SIGN commands.

SPECTRUM comp-method IS1893 2015-P4 LOAD ( TORSION (DECCENTRICITY f8) (ECCENTRICITY f9) ) *{ X f1 | Y f2  | Z f3 }

{ ACCELERATION | DISPLACEMENT } (SCALE f4) {DAMP f5 | CDAMP | MDAMP } (MISSING f6) (ZPA f7) (IGNORE f13) 
({ DOMINANT f10 | SIGN }) (IMR f11) (STARTCASE f12) (RSMIN f14 )

The following command (SOIL TYPE parameter or response spectra data pairs) must be in a separate line.

{ SOIL TYPE f11 | *{ P1,V1; P2,V2; P3,V3;…PN,VN } }

Note: The spectrum type options ACCELERATION or DISPLACEMENT should only be used with custom soil types for IS 1893 2015 (Part 4).

Where:

Table 1. Parameters used for IS: 1893 (Part 4) 2015 response spectrum
Parameter	Default Value	Description
DECCENTRICITY f8	When `ECC` > 0, `DEC` defaults to 1.5 When `ECC` < 0, `DEC` defaults to 1.0	(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, as per the recommendations of Cl. 7.8.2 of the IS 1893 Part 1 specification. 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). For details See Torsion Methodology.
ECCENTRICITY f9	0.05	It is 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 f9 value is positive, it indicates clockwise torsion whereas a negative value indicates counterclockwise torsion.
X f1 \| Y f2 \| Z f3	0	Factors for the input spectrum to be applied in X, Y, & Z directions.  These must be entered as the product of [(Z/2)×(I/R)] for standard specific spectra. Any one or all directions can be input.  Directions not provided will default to zero. Based on Clause7.3 of IS 1893(Part 4): 2015.
SCALE f4	1	Linear scale factor by which design horizontal acceleration spectrum will be multiplied. This factor signifies that the structures and foundations, at which level base shear will be calculated, are placed below the ground level. Note: If site specific spectra curve is used then f4 value is to be multiplied by the scale factor by which spectra data will be multiplied. Usually to factor g’s to length/sec² units.
DAMP f5	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 f6		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 (this value is not multiplied by SCALE). If f6is zero, then the spectral acceleration at the `ZPA` f7frequency is used. If f7is zero or not entered, the spectral acceleration at 33Hz (Zero Period Acceleration, ZPA) is used. The results of this calculation are SRSSed with the modal combination results. 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.
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). The dominant mode is selected based on the actual base shear of the mode and not the greatest % participation factor. 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.
SOIL TYPE f11	2	The soil type present. Depending upon time-period, types of soil and damping, average response acceleration coefficient, Sa/g is calculated from reference to Fig.1 of this code where: 1 = Type 1 - for rocky or hard soil 2 = Type 2 - medium soil 3 = Type 3 - soft soil sites
custom P1,V1; P2,V2; P3,V3; … Pn,Vn		Data is part of input immediately following spectrum command for a "custom" response spectrum. Period - Value pairs (pairs separated by semicolons) are entered to describe the spectrum curve. Period is in seconds and the corresponding Value is acceleration (current length unit/ sec²). If data is in g acceleration units then the factor by which spectra data will be multiplied is g to the current length unit (9.81, 386.4, etc). Note: Do not enter if a SOIL TYPE f11 value is specified.
IGNORE f13	0.009	(Optional input) It indicates the mass participation (in percent) of those modes to be excluded while considering torsion provision of IS-1893. Depending upon the model it may be found that there are many local modes and torsional modes whose mass participation is practically negligible. These modes can be excluded without much change in the final analysis result. If not provided all modes will be considered. If none provided the default value of 0.009% will be considered. If IGN is entered on any one spectrum case it will be used for all spectrum cases. Note: If the value of f14 is considerable it may lead to considerable variation of analysis result from the actual one. Hence caution must be taken while using `IGNORE` command. If the `MODE SELECT` command is provided along with the `IGNORE` command, the number of modes excluded from the analysis will be those deselected by the `MODE SELECT` command and also those deselected by the `IGNORE` command.
RSMIN f14	2.0	Used to enter a factor, given in percent, to multiply by the total seismic weight of the structure to obtain a minimum base shear value. This percentage is taken from Table 2 of IS:1839(Part 4)-2015. This percentage must match a value in this table. The default value is taken for a structure category 1 and zone 2. If the minimum base shear value exceed the calculated response spectrum base shear, then all analysis results of the response spectrum load case are scaled by the ratio of the minimum base shear to the calculated response spectrum base shear. This multiplying factor will be noted in the output.

1893 2015-P4 indicates the analysis as per IS:1893(Part 4)-2015 procedures.

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

Note: CQC, SRSS, and CSM Grouping methods are recommended by IS:1893 (Part 4) –2015.

SRSS

Square Root of Summation of Squares method.

ABS

Absolute sum. This method is very conservative and represents a worst case combination.

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.

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).

TORSION

indicates that the torsional moment (in the horizontal plane) arising due to eccentricity between the center of mass and center of rigidity needs to be considered. See Torsion for additional information.

Note: If TORSION is entered on any one spectrum case it will be used for all spectrum cases.

Lateral shears at story levels are calculated in global X and Z directions. For global Y direction the effect of torsion will not be considered.

The Torsion methodology as per Clause 10.4 of IS 1893 (Part4): 2015 remains same as IS1893(Part1):2016 and is only applicable for ST=4.

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 \times {(1 / ω)}^{2}

where

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

For response spectra analysis, the damping ratio coefficients for steel and concrete that are recommended (other than the default value of 5%) for industrial structures as per Clause 9.4 (Table 5) are as follows:

Material	DBE	MCE
Steel	0.02	0.04
Reinforced concrete	0.05	0.07
Prestressed concrete	0.03	0.05

Note: For combined material structures, the damping ratio coefficient shall be determined based on well established procedures. If a composite damping ratio coefficient is not evaluated, it shall be taken as that corresponding to material having lower value of damping.

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.

Note: The last interpolation parameter entered on the last of all of the spectrum cases will be used for all spectrum cases.

Note: The LINEAR or LOGARITHMIC option can only be used for custom soil types (e.g., when response spectra data pairs are specified). Do not use these commands when the SOIL TYPE command is used.

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.

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).

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.

Refer to TR.32.10.1.1 Response Spectrum Specification - Custom for additional details on IMR load case generation.

Example

LOAD 1 LOADTYPE None  TITLE RS_X
SPECTRUM SRSS IS1893 2015-P4 LOAD X 0.0432 DAMP 0.05
SOIL TYPE 1