# TR.32.10.1.13 Response Spectrum Specification per IBC 2018

This command may be used to specify and apply the RESPONSE SPECTRUM loading as per the 2018 edition of the ICC specification International Building Code (IBC) and ASCE 7-16, 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 comb-method IBC 2018 (TORSION) (DECCENTRICITY f20) (ECCENTRICITY f21) *{ X f1 | Y f2 | Z f3 } ACCELERATION
{DAMP f5 | CDAMP | MDAMP } ( {LIN | LOG} ) (MIS f6) (ZPA f7) ({ DOMINANT f10 | SIGN }) (SAVE) (IMR f11) (STARTCASE f12)
Note: The data from SPECTRUM through ACC 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).

The command is completed with the following data which must be started on a new line:

{ZIP f8 | LAT f9 LONG f13 | SS f14 S1 f15 } SITE CLASS (f16) (FA f17 FV f18) TL f19

Where:

Table 1. Parameters used for IBC 2015 response spectrum
Parameter Default Value Description
DECCENTRICITY f20 1.0 Factor to be multiplied with static eccentricity (i.e., eccentricity between center of mass and center of rigidity).
ECCENTRICITY f21 0.05 Factor for accidental eccentricity. Positive values indicate clockwise torsion and negative values indicate 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.
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.
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.
ZIP f11   The zip code of the site location to determine the latitude and longitude and consequently the Ss and S1 factors.  (IBC 2018, ASCE 7-16 Chapter 22)
LAT f12   The latitude of the site used with the longitude to determine the Ss and S1 factors.  (IBC 2018, ASCE 7-16 Chapter 22)
LONG f13

The longitude of the site used with the latitude to determine the Ss and S1 factors.  (IBC 2018, ASCE 7-16 Chapter 22)

SS f14   Mapped MCE for 0.2s spectral response acceleration.  (IBC 2018, ASCE 7-16 Section 11.4.1)

This is obtained using the USGS web service.

S1 f15   Mapped spectral acceleration for a 1-second period. (IBC 2018, ASCE 7-2016 Section 11.4.1)

This is obtained using the USGS web service.

CLASS f16   Enter A through F for the Site Class as defined in the IBC code. (IBC 2018 ASCE 7-2016 Section 20.3)
FA f17   Optional Short-Period site coefficient at 0.2s. Value must be provided if SCLASS set to F (i.e., 6). (IBC 2018, ASCE 7-2016 Section 11.4.3)
FV f18   Optional Long-Period site coefficient at 1.0s. Value must be provided if SCLASS set to F (i.e., 6). (IBC 2018, ASCE 7-2016 Section 11.4.3)
TL f19   Long-Period transition period in seconds.  (IBC 2018, ASCE 7-16 Chapter 22)

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

The CQC and ASCE4-98 methods require damping. ABS, SRSS, CRM, GRP, and TEN methods do not use damping unless spectra-period curves are made a function of damping (see File option below). CQC, ASCE, CRM, GRP, and TEN include the effect of response magnification due to closely spaced modal frequencies. ASCE includes more algebraic summation of higher modes. ASCE and CQC are more sophisticated and realistic methods and are recommended.

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).
Note: If SRSS is selected, the program will internally check whether there are any closely spaced modes or not. If it finds any such modes, it will switch over to the CSM method. In the CSM method, the program will check whether all modes are closely spaced or not. If all modes are closely spaced, it will switch over to the CQC method.

IBC 2018 indicates that the spectrum should be calculated as defined in the IBC 2018 specification.

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.

ACCELERATOIN
indicates that the Acceleration spectra will be entered.
Note: IBC / ASCE 7 does 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.
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).

## Methodology

The methodology for calculating the response spectra is defined in ASCE 7-2016, section 11.4.  The following is a quick summary:

1. Input Ss and S1 (this could have been searched from database or entered explicitly)
2. Calculate

Sms= Fa × Ss

and

Sm1 = Fv × S1

Where:

Fa and Fv are determined from the specified site classes A – E and using tables 11.4-1 and 11.4-2.  For site class F, the values must be supplied.  These are required to be provided by the user. You may also specify values for Fa and Fv in lieu of table values.

3. Calculate

Sds = (2/3) Sms

and

Sd1 = (2/3) Sm1

The spectrum is generated as per section 11.4.5.

Notes:
• Exceptions 1 in Clause 11.4.8 of ASCE 7-16 is implemented. In exception 1, for Site class E and Ss > 1.0, Fa value is taking the same for site class C. In this case, there is slight reduction in the seismic force generated.
• The exception of Clause 2 in 11.4.8 of ASCE 7-16 is not implemented in STAAD.Pro for response spectra.
• The vertical ground motion for seismic design as described in clause 11.9 is not implemented as the program cannot determine the vertical time period, Tv.
• ASCE 7-2016 Clause 12.9.1.4 stipulates that if the combined response for modal base shear, V, is less than that of the calculated base shear from the equivalent lateral force procedure, Vt, then the response spectra values should be scaled up by V/Vt. STAAD.Pro does not automatically check this nor increase the response quantities in this situation. You can check this by simply analyzing the static seismic load case and comparing the base shear values. The X, Y, or Z factors for the response spectrum can be then increased accordingly if required.

## Inherent and Accidental Torsion

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.

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

## Steps

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

1. Lateral story force at each floor is calculated.
2. At each floor design eccentricity is calculated.

Thus, design eccentricity edi = f20×esi + f12×bi where f20 = 1.0 and f21 = (±) 0.05

Where:

• esi = static eccentricity between center of mass and center of rigidity at floor i.
• bi = floor plan dimension orthogonal to 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.
7. Steps 1 through 6 are performed for all modes considered and missing mass correction (if any). Finally, the peak response quantities from the different modal responses are combined as per the specified combination method (e.g., SRSS, CQC, TEN, etc.)

## 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.

Refer to Cl. 12.9.2.2.2 for the requirements of accidental torsion per the ASCE 7-16 code.

## Example

LOAD R1 LOADTYPE Mass  TITLE REF LOAD CASE 1
ZIP 92887 SITE CLASS E FA 0.900 FV 2.400 TL 8.000