# TR.32.10.1.7 Response Spectrum Specification per IS: 1893 (Part 1)-2002

This command may be used to specify and apply the RESPONSE SPECTRUM loading as per IS: 1893 (Part 1)-2002 for dynamic analysis.

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.

## 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, respectively.

SPECTRUM comb-method 1893 ( TORSION (DECCENTRICITY f8) (ECCENTRICITY f9) ) *{ X f1 | Y f2 | Z f3 }
{ ACCELERATION | DISPLACEMENT } (SCALE f4) {DAMP f5 | CDAMP | MDAMP } (MISSING f6) (ZPA f7) (IGNNORE f13)
({ DOMINANT f10 | SIGN }) (SAVE) (IMR f11) (STARTCASE f12)

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 } }

The following command, if present, must be on a separate line. This performs the option al soft story check.

( CHECK SOFT STORY )

The following command, if present, must be on a separate line. This performs the story drift check.

( CHECK STORY DRIFT ) (RF f14)

Where:

Table 1. Parameters used for IS: 1893 (Part 1) 2002 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 code. 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 0.0 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 f4 1.0 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 f5 0.05
The damping ratio. Specify a value of exactly 0.0000011 to ignore damping.
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.
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.

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).
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

The soil type present. Depending upon time period, types of soil and damping, average response acceleration coefficient, Sa/g is calculated.

• 1 = for rocky or hard soil
• 2 = medium soil
• 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.
RF f14

The response reduction factor. If not specified, the program will look for the factor defined under DEFINE 1893 LOAD (refer to TR.31.2.10 IS:1893 (Part 1) 2002 & Part 4 (2005) Codes - Lateral Seismic Load). If none is provided there either, a factor of 1.0 is assumed.

The response reduction factor represents ratio of maximum seismic force on a structure during specified ground motion if it were to remain elastic to the design seismic force. Actual seismic force is reduced by a factor RF to obtain design force.)

1893 indicates the analysis as per IS:1893(Part 1)-2002 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 1) –2002.
Square Root of Summation of Squares method.
ABS
Absolute sum. This method is very conservative and represents a worst case combination.
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.
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.

ACCELERATION or DISPLACEMENT
indicates whether Acceleration or Displacement spectra will be entered. The relationship between acceleration and displacement values in response spectra data is:
$Displacement = Acceleration × ( 1 / ω ) 2$
where
 ω = 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
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).
CHECK SOFT STORY
indicates that soft story checking will be performed. If omitted from input, there will be no soft story checking. Refer to TR.28.2.1 Soft Story Checking for details.
CHECK STORY DRIFT
indicates that a story drift check is to be performed.
Tip: This is done in place of post-analysis story drift checks for IS 1893-2002.

## Methodology

The design lateral shear force at each floor in each mode is computed by STAAD.Pro in accordance with the Indian IS: 1893 (Part 1)-2002 equations 7.8.4.5c and 7.8.4.5d.

Qik = Ak⋅ϕik⋅Pk⋅Wk

and

$V i k = Σ i = i + 1 n Q i k$
Note:  All symbols and notations in the above equation are as per IS: 1893(Part 1)-2002.

1. You provide the value for Z/2⋅I/R as factors for input spectrum. You calculate the expression Z/2⋅I/R and provide these values using the terms f1, f2, and f3 and applicable, where these terms an explained in the table below.
2. The program calculates time periods for first six modes or as specified.
3. The program calculates Sa/g for each mode utilizing time period and damping for each mode.
4. The program calculates the design horizontal acceleration spectrum value Ak for each mode.
5. The program then calculates mode participation factor for each mode.
6. The peak lateral seismic force at each floor in each mode is calculated.
7. All response quantities for each mode are calculated.
8. The peak response quantities are then combined as per the specified method (SRSS, CQC, ABS, CSM or TEN) to get the final results.
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 6.4.5 of the IS 1893 2002 code.

## 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.

## Notes

1. The design base shear VB, calculated from the Response Spectrum method, is compared with the base shear Vb, calculated by empirical formula for the fundamental time period. If VB is less than Vb, all of the response quantities are multiplied by Vb /VB as per Clause 7.8.2.

For this, the following input is necessary before defining any primary load case.

DEFINE  1893  LOAD
ZONE f1 1893-spec
SELFWEIGHT
JOINT WEIGHT
joint-list   WEIGHT w
MEMBER  WEIGHT
…
UNI   v1 v2 v3
mem-list
CON v4  v5
…
CHECK SOFT STORY

1893-Spec  = {RF f2, I f3, SS f4, (ST f5), DM f6, (PX f7), (PZ f8), (DT f9)}

Refer to TR.31.2.10 IS:1893 (Part 1) 2002 & Part 4 (2005) Codes - Lateral Seismic Load for full details on this command structure.

Note: STAAD.Pro does not calculate the fundamental frequency of the structure needed for the empirical base shear Vb. calculation; so you must enter either the ST parameter or the PX and PZ parameters in the DEFINE 1893 LOAD data.
2. The following interpolation formula is adopted for interpolation between damping values as given in Table 3.

Interpolation and/or extrapolation of ground response acceleration for a particular mode has been made for determining the spectrum ordinates corresponding to the modal damping value for use in Response Spectrum analysis. The relationship that shall be used for this purpose is defined by:

 Sa = Ae-ξ + B/ξ

where
 Sa = Spectrum ordinate ξ = damping ratio

Constants A and B are determined using two known spectrum ordinates Sa1 and Sa2 corresponding to damping rations ξ1 and ξ2, respectively, for a particular time period and are as follows:

 $A = S a 1 ξ 1 − S a 2 ξ 2 ξ 1 e − ξ 1 − ξ 2 e − ξ 2$

 $B = ξ 1 ξ 2 ( S a 2 e − ξ 1 − S a 1 e − ξ 2 ) ξ 1 e − ξ 1 − ξ 2 e − ξ 2$

Where:

ξ1 < ξ < ξ2

3. The story drift in any story shall not exceed 0.004 times the story height as per Clause 7.11.1. To check this, the following command should be given after the analysis command.

PRINT STOREY DRIFT

A warning message will be printed if story drift exceeds this limitation.

4. If any soft story (as per definition in Table 5 of IS:1893-2002) is detected, a warning message will be printed in the output.

## Torsion

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. 7.9.2 of the IS 1893 code. The dynamic eccentricity is automatically calculated by the program (in both cases of TOR and TOR OPP options), while the amount of accidental eccentricity can be specified through the ECC option (if not specified, default of 5% of lateral dimension of the floor in the direction of the earthquake will be considered).

Non-symmetric or torsionally unbalanced buildings are prone to earthquake damage due to coupled lateral and torsional movements (i.e., the translational vibration of the building couples with its torsional vibrations within elastic range). The level of coupling between lateral and torsional vibrations of the building can be larger, thus leading to significantly higher lateral-torsional coupling than that predicted by elastic analysis.

• Cl. 7.8.4.5 of IS 1893 (Part 1) : 2002 is valid for buildings with regular or nominally irregular plan configurations. For buildings which are irregular in plan, it is better to consider torsion from dynamic eccentricity into analysis; even if torsionally coupled vibration is considered during response spectrum analysis.
• Cl. 7.9.2 Note 2 of Amendment No. 1 January 2005 states that, in the case that a 3D dynamic analysis is carried out, the dynamic amplification factor 1.5—as given by Cl. 7.9.2—can be replaced by 1.0. This implies that the code also recommends to use Cl. 7.9.2 for all types of buildings by including torsion from both dynamic and accidental eccentricity in the response spectrum analysis.

## Torsion Methodology

As per IS1893-2002 code, provision shall be made in all buildings for increase in shear forces on the lateral force resisting elements resulting from the horizontal torsional moment arising due to eccentricity between the center of mass and the center of rigidity.

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 by CQC, SRSS, ABS, TEN PERCENT, etc) 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 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. As for example, consider two joints J2 and J3 whose maximum joint displacement in 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, 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 response spectrum along with torsion for all modes are combined using specified modal combination method to get final maximum possible joint displacements. Refer to the steps explained below.

## Steps

For each mode following steps are performed to include Torsion provision.

1. Lateral story force at each floor is calculated. Refer Cl. 7.8.4.5c of IS 1893 (Part 1) : 2002. (Qik at floor i for mode k)
2. At each floor design eccentricity is calculated. Refer Cl. 7.9.2 and Cl. 7.9.2 Note 2 of Amendment No. 1 January 2005 of IS 1893 (Part 1) : 2002.

Thus, design eccentricity edi = f15×esi + f12×bi where f15 = 1.0 and f12 = (±) 0.05

Where:

• esi = dynamic eccentricity arising due to center of mass and center of rigidity at floor i (static eccentricity multiplied by dynamic amplification factor 1.0 for response spectrum analysis),
• bi = floor plan dimension in the direction of earthquake loading.
3. Torsional moment is calculated at each floor. (Mik = Qik × edi at floor i for mode k)
4. The lateral nodal forces corresponding to torsional moment are calculated at each floor. These forces represent the additional story shear due to torsion.
5. Static analysis of the structure is performed with these nodal forces.
6. The analysis results (i.e., member force, joint displacement, support reaction, etc) from torsion are algebraically added to the corresponding modal response quantities from response spectrum analysis.

## Modal Combination

Steps 1 to 6 are performed for all modes considered and missing mass correction (if any). Finally the peak response quantities from different modal response are combined as per CQC or SRSS or TEN PERCENT or CSM method.

## Notes

After the analysis is complete following files are generated.
1. Story shear for each mode for each load case is given in the file <filename>_RESP1893.txt.
2. Rotational stiffness of each floor is given in the file <filename>_ROT1893.txt.
3. Center of mass, center of rigidity, design eccentricity at each floor level and additional shear due to torsion at each floor level for each mode for each load case is given in the file <filename>_TOR1893.txt.

## Dynamic Eccentricity

The static eccentricity is generally defined as the distance between the center of mass (CM) and the center of rigidity (CR) at respective floors levels. Accidental eccentricity generally accounts for factors such as:
• the rotational component of ground motion about the vertical axis,
• the difference between computed and actual values of the mass, stiffness, or strength, and
• uneven live mass distribution.
The provision for design eccentricity edi at ith floor of a building is given by the following equation:

 edi = DEC×esi + ECC×bi

where
 esi = static eccentricity at ith floor bi = plan dimension of the ith floor normal to the direction of ground motion ECC and DEC = Factors to determine the design eccentricity. These are input parameters.
IS 1893-2002 clause 7.8.2 defines two equations:

 edi = 1.5×esi + 0.05×bi

 edi = 1.0×esi - 0.05×bi

By including the optional command TORSION, the first equation is used by default. To account for the second equation, you may simply specify DEC -0.05 (at which point the default for ECC is then 1.0).

## Example

Refer to V. IS 1893 2002 Response Spectrum for a detailed explanation of this example.

LOAD 1 LOADTYPE None  TITLE RS_X
SPECTRUM SRSS 1893 X 0.036 ACC DAMP 0.05
SOIL TYPE 1