TR.32.10.1.2 Response Spectrum Specification per NRC2005
RESPONSE SPECTRUM
loading as per the 2005 edition of the
National Research Council specification
National Building Code of Canada (NBC) , 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 NRC 2005 ( TORSION (DECCENTRICITY f20) (ECCENTRICITY f21) ) *{ X f1 | Y f2| Z f3} { ACC | DIS } ( SCALE f4)
{ DAMP f5| CDAMP | MDAMP } ( { LINEAR | LOGARITHMIC } ) (MISSING f6) (ZPA f7) ({ DOMINANT f10| SIGN }) (SAVE) (IMR f11) (STARTCASE f12)
SPECTRUM
through
SCALE
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 spectrum data which must be started on a new line:
{ p1 v1; p2 v2; p3 v3; … pn vn | FILE filename }
Where:
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. |
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
If f6is zero, then the spectral acceleration at the
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.
|
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.
- 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: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
Inherent and Accidental 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
orDISPLACEMENT
-
indicates whether Acceleration or Displacement spectra will be entered. The relationship between acceleration and displacement values in response spectra data is:
-
DAMP
,MDAMP
, andCDAMP
- 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 theDEFINE 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 theCONSTANT
specification
-
-
LINEAR
orLOGARITHMIC
-
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 enterDOMINANT
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).
-
p1, v1; p2, v2; …. ; pn, vn.
Data is part of input, immediately following theSPECTRUM
command. Period – Value pairs (separated by semi colons) are entered to describe the Spectrum curve. Period is in seconds and the corresponding Value is either acceleration (current length unit/sec2) or displacement (current length unit) depending on the ACC or DIS chosen. Continue the curve data onto as many lines as needed (up to 500 spectrum pairs). Spectrum pairs must be in ascending order of period. Note, if data is in g acceleration units, then set SCALE to a conversion factor to the current length unit (9.81, 386.4, etc.). Also note, do not end these lines with a hyphen (-). Each SPECTRUM command must be followed by Spectra data if this input form is used. -
FILE filename data is in a separate file, using the format described in File Format for Spectra Data.
When the
File filename
command has been provided, then you must have the spectra curve data on a file named filename prior to starting the analysis. The format of the FILE spectra data allows spectra as a function of damping as well as period.Note: If theFILE filename
command is entered, it must be with the first spectrum case and will be used for all spectrum cases.No
File filename
command needs to be entered with the remaining spectrum cases. The filename may not be more than 72 characters in length.
TR.32.10.1.1 Response Spectrum Specification - Custom for additional details on IMR load case generation.
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.
Steps
For each mode following steps are performed to include Torsion provision.
- Lateral story force at each floor is calculated.
-
At each floor design eccentricity is calculated.
Thus, design eccentricity edi = f20×esi + f12×bi where f20 = 1.0 and f21 = (±) 0.05
-
Torsional moment is calculated at each floor.
Mik = Qik × edi at floor i for mode k
- The lateral nodal forces corresponding to torsional moment are calculated at each floor. These forces represent the additional story shear due to torsion.
- Static analysis of the structure is performed with these nodal forces.
- 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.
- 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 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.
Example
LOAD 1 LOADTYPE None TITLE RS_X
SPECTRUM SRSS NRC 2005 X 0.5 ACC DAMP 0.05 LIN
0 9.80665; 0.06 18.6326; 0.12 24.5166; 0.18 24.5166; 0.24 24.5166; 0.3 24.5166;
0.36 24.5166; 0.42 23.3492; 0.48 20.4305; 0.54 18.1605; 0.6 16.3444;
0.66 14.8586; 0.72 13.6203; 0.78 12.5726; 0.84 11.6746; 0.9 10.8963;
0.96 10.2153; 1.02 9.61436; 1.08 9.08023; 1.14 8.60233; 1.2 8.17221;
1.26 7.78306; 1.32 7.42928; 1.38 7.10627; 1.44 6.81018; 1.5 6.53777;
1.56 6.28632; 1.62 6.05349; 1.68 5.83729; 1.74 5.63601; 1.8 5.44814;
1.86 5.2724; 1.92 5.10763; 1.98 4.95286; 2.04 4.80718; 2.1 4.66984;
2.16 4.54012; 2.22 4.41741; 2.28 4.30116; 2.34 4.19088; 2.4 4.08611;
2.46 3.98645; 2.52 3.89153; 2.58 3.80103; 2.64 3.71464; 2.7 3.63209;
2.76 3.55314; 2.82 3.47754; 2.88 3.40509; 2.94 3.3356; 3 3.26889; 3.06 3.20479;
3.12 3.14316; 3.18 3.08385; 3.24 3.02675; 3.3 2.97171; 3.36 2.91865;
3.42 2.86744; 3.48 2.818; 3.54 2.77024; 3.6 2.72407; 3.66 2.67941; 3.72 2.6362;
3.78 2.59435; 3.84 2.55382; 3.9 2.51453; 3.96 2.47643; 4.02 2.45166;
4.08 2.45166; 4.14 2.45166; 4.2 2.45166; 4.26 2.45166; 4.32 2.45166;
4.38 2.45166; 4.44 2.45166; 4.5 2.45166; 4.56 2.45166; 4.62 2.45166;
4.68 2.45166; 4.74 2.45166; 4.8 2.45166; 4.86 2.45166; 4.92 2.45166;
4.98 2.45166; 5.04 2.45166; 5.1 2.45166; 5.16 2.45166; 5.22 2.45166;
5.28 2.45166; 5.34 2.45166; 5.4 2.45166; 5.46 2.45166; 5.52 2.45166;
5.58 2.45166; 5.64 2.45166; 5.7 2.45166; 5.76 2.45166; 5.82 2.45166;
5.88 2.45166; 5.94 2.45166;