TR.32.10.1.3 Response SpectrumSpecification per NRC 2010
RESPONSE SPECTRUM
loading as per the 2010 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 2010 ( TORSION (DECCENTRICITY f20) (ECCENTRICITY f21) ) *{ X f1 | Y f2| Z f3} { ACCELERARTION | DISCPLACEMENT } ( SCALE f4)
{ DAMP f5| CDAMP | MDAMP } ( {LINEAR | LOGARITHMIC } ) (MISSSING 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 }
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).
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
This example input file demonstrates a seismic load using the equivalent force method and a seismic response spectrum analysis per NRC 2010.
STAAD SPACE EXAMPLE PROBLEM FOR NRC LOAD
START JOB INFORMATION
ENGINEER DATE 15-Jan-16
END JOB INFORMATION
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 3.5 0 0; 3 7 0 0; 4 13.5 0 0; 5 0 0 3.5; 6 3.5 0 3.5;
7 7 0 3.5; 8 13.5 0 3.5; 9 0 0 7; 10 3.5 0 7; 11 7 0 7; 12 13.5 0 7;
13 0 0 12.5; 14 3.5 0 12.5; 15 7 0 12.5; 16 13.5 0 12.5; 17 0 3.5 0;
18 3.5 3.5 0; 19 7 3.5 0; 20 13.5 3.5 0; 21 0 3.5 3.5; 22 3.5 3.5 3.5;
23 7 3.5 3.5; 24 13.5 3.5 3.5; 25 0 3.5 7; 26 3.5 3.5 7; 27 7 3.5 7;
28 13.5 3.5 7; 29 0 3.5 12.5; 30 3.5 3.5 12.5; 31 7 3.5 12.5;
32 13.5 3.5 12.5; 33 0 7 0; 34 3.5 7 0; 35 7 7 0; 36 13.5 7 0;
37 0 7 3.5; 38 3.5 7 3.5; 39 7 7 3.5; 40 13.5 7 3.5; 41 0 7 7;
42 3.5 7 7; 43 7 7 7; 44 13.5 7 7; 45 0 7 12.5; 46 3.5 7 12.5;
47 7 7 12.5; 48 13.5 7 12.5; 49 0 10.5 0; 50 3.5 10.5 0; 51 7 10.5 0;
52 13.5 10.5 0; 53 0 10.5 3.5; 54 3.5 10.5 3.5; 55 7 10.5 3.5;
56 13.5 10.5 3.5; 57 0 10.5 7; 58 3.5 10.5 7; 59 7 10.5 7;
60 13.5 10.5 7; 61 0 10.5 10.5; 62 3.5 10.5 10.5; 63 7 10.5 10.5;
64 13.5 10.5 10.5;
MEMBER INCIDENCES
101 17 18; 102 18 19; 103 19 20; 104 21 22; 105 22 23; 106 23 24;
107 25 26; 108 26 27; 109 27 28; 110 29 30; 111 30 31; 112 31 32;
113 33 34; 114 34 35; 115 35 36; 116 37 38; 117 38 39; 118 39 40;
119 41 42; 120 42 43; 121 43 44; 122 45 46; 123 46 47; 124 47 48;
125 49 50; 126 50 51; 127 51 52; 128 53 54; 129 54 55; 130 55 56;
131 57 58; 132 58 59; 133 59 60; 134 61 62; 135 62 63; 136 63 64;
201 17 21; 202 18 22; 203 19 23; 204 20 24; 205 21 25; 206 22 26;
207 23 27; 208 24 28; 209 25 29; 210 26 30; 211 27 31; 212 28 32;
213 33 37; 214 34 38; 215 35 39; 216 36 40; 217 37 41; 218 38 42;
219 39 43; 220 40 44; 221 41 45; 222 42 46; 223 43 47; 224 44 48;
225 49 53; 226 50 54; 227 51 55; 228 52 56; 229 53 57; 230 54 58;
231 55 59; 232 56 60; 233 57 61; 234 58 62; 235 59 63; 236 60 64;
301 1 17; 302 2 18; 303 3 19; 304 4 20; 305 5 21; 306 6 22; 307 7 23;
308 8 24; 309 9 25; 310 10 26; 311 11 27; 312 12 28; 313 13 29;
314 14 30; 315 15 31; 316 16 32; 317 17 33; 318 18 34; 319 19 35;
320 20 36; 321 21 37; 322 22 38; 323 23 39; 324 24 40; 325 25 41;
326 26 42; 327 27 43; 328 28 44; 329 29 45; 330 30 46; 331 31 47;
332 32 48; 333 33 49; 334 34 50; 335 35 51; 336 36 52; 337 37 53;
338 38 54; 339 39 55; 340 40 56; 341 41 57; 342 42 58; 343 43 59;
344 44 60; 345 45 61; 346 46 62; 347 47 63; 348 48 64;
START GROUP DEFINITION
MEMBER
_B1 301 TO 303 305 TO 307 309 TO 311 317 TO 319 321 TO 323 325 TO 327 -
333 TO 335 337 TO 339 341 TO 343 345 TO 347
END GROUP DEFINITION
MEMBER PROPERTY CANADIAN
101 TO 136 201 TO 236 PRIS YD 0.4 ZD 0.3
301 TO 303 305 TO 307 309 TO 311 317 TO 319 321 TO 323 325 TO 327 333 -
334 TO 335 337 TO 339 341 TO 343 345 TO 347 TABLE ST W460X52
304 308 312 TO 316 320 324 328 TO 332 336 340 344 348 TABLE ST W530X85
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 2.5e+007
POISSON 0.17
DENSITY 24
ISOTROPIC STEEL
E 2.05e+008
POISSON 0.3
DENSITY 76.8195
ALPHA 1.2e-005
DAMP 0.03
TYPE STEEL
STRENGTH FY 253200 FU 407800 RY 1.5 RT 1.2
ISOTROPIC CONCRETE
E 2.17185e+007
POISSON 0.17
DENSITY 23.5616
ALPHA 1e-005
DAMP 0.05
TYPE CONCRETE
STRENGTH FCU 27579
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 MEMB 101 TO 136 201 TO 236
MATERIAL STEEL MEMB 301 TO 348
SUPPORTS
1 TO 16 FIXED
CUT OFF MODE SHAPE 10
DEFINE REFERENCE LOADS
LOAD R1 LOADTYPE Mass
SELFWEIGHT X 1
SELFWEIGHT Y 1
SELFWEIGHT Z 1
JOINT LOAD
17 TO 48 FX 7
49 TO 64 FX 3.5
17 TO 48 FY 7
49 TO 64 FY 3.5
17 TO 48 FZ 7
49 TO 64 FZ 3.5
END DEFINE REFERENCE LOADS
FLOOR DIAPHRAGM
DIA 1 TYPE RIG HEI 3.5
DIA 2 TYPE RIG HEI 7
DIA 3 TYPE RIG HEI 10.5
*** Equivelant Lateral Force Definition ***
DEFINE NRC 2010 LOAD
SA1 0.28 SA2 0.17 SA3 0.11 SA4 0.063 I 1.3 SCL 3 MVX 1.2 MVZ 1.2 -
RDX 1.4 RDZ 3 ROX 1.5 ROZ 1.5 STX 3 STZ 4 MD 1
*****************************************************
*** X-DIRECTION
LOAD 1 FX+TX
NRC LOAD X 1 DEC 1 ACC 0.1
LOAD 2 FX-TX
NRC LOAD X 1 DEC 1 ACC -0.1
LOAD 3 -FX-TX
NRC LOAD X -1 DEC 1 ACC -0.1
LOAD 4 -FX+TX
NRC LOAD X -1 DEC 1 ACC 0.1
*** Z-DIRECTION
LOAD 5 FZ+TZ
NRC LOAD Z 1 DEC 1 ACC 0.1
LOAD 6 FZ-TZ
NRC LOAD Z 1 DEC 1 ACC -0.1
LOAD 7 -FZ-TZ
NRC LOAD Z -1 DEC 1 ACC -0.1
LOAD 8 -FZ+TZ
NRC LOAD Z -1 DEC 1 ACC 0.1
*****************************************************
**** RESPONSE SPECTRUM ****
*** X-DIRECTION
LOAD 9
SPECTRUM CQC NRC 2010 TOR X 1 ACC DAMP 0.05
0.03 1; 0.05 1.35; 0.1 1.95; 0.2 2.8; 0.5 2.8; 1 1.6;
LOAD 10
*** Z-DIRECTION
SPECTRUM CQC NRC 2010 TOR Z 1 ACC DAMP 0.05
0.03 1; 0.05 1.35; 0.1 1.95; 0.2 2.8; 0.5 2.8; 1 1.6;
PERFORM ANALYSIS PRINT LOAD DATA
PRINT SUPPORT REACTION
PRINT DIA CR
FINISH