# TR.31.2.4 Canadian Seismic Code (NRC) - 2010

This set of commands may be used to define the parameters for generation of equivalent static lateral loads for seismic analysis per National Building Code (NRC/CNRC) of Canada- 2010 edition. Depending on this definition, equivalent lateral loads will be generated in horizontal direction(s).

The seismic load generator can be used to generate lateral loads in the X & Z directions for Y up or X & Y for Z up.  Y up or Z up is the vertical axis and the direction of gravity loads (See the SET Z UP command in TR.5 Set Command Specification).  All vertical coordinates of the floors above the base must be positive and the vertical axis must be perpendicular to the floors.

## General Format

DEFINE NRC 2010 (ACCIDENTAL) LOAD
nrc-spec
weight-data

Refer to Common Weight Data for information on how to specify structure weight for seismic loads.

Where:

nrc-spec = { SA1 f1 SA2 f2 SA3 f3 SA4 f4 MVX f5 MVZ f6 I f7 RDX f8 ROX f9 RDZ f10 ROZ f11 SCLASS f12 STX f13 STZ f14 MD f15 ( CTX f16 ) ( CTZ f17 ) ( PX f18 ) ( PZ f19 ) ( FA f20 ) ( FV f21 ) }

where:

ParameterDescription
SA1 f1Seismic Data, Sa(0.2), as per Table C-2.
SA2 f2Seismic Data, Sa(0.5), as per Table C-2.
SA3 f3Seismic Data, Sa(1.0), as per Table C-2.
SA4 f4Seismic Data, Sa(2), as per Table C-2.
MVX f5 The higher mode factor along the X and Z direction. Refer to NRC Table 4.1.8.11.
MVZ f6 The higher mode factor along the Z direction. Refer to NRC Table 4.1.8.11.
I f7Earthquake Importance Factor, Ie, of the structure as determined from table 4.1.8.5 in the code. This dependent on the Importance Category and ULS/SLS.
RDX f8 The ductility-related force modification factor reflecting the capability of a structure to dissipate energy through inelastic behavior as described in article 4.1.8.9. along the X direction. Refer to NRC Table 4.1.8.9.
RDZ f10 The ductility-related force modification factor reflecting the capability of a structure to dissipate energy through inelastic behavior as described in article 4.1.8.9. along the Z direction. Refer to NRC Table 4.1.8.9.
ROX f9 the over strength-related force modification factor accounting for the dependable portion of reserve strength in a structure designed according to the provision of the Article 4.1.8.9. along the X direction. Refer to NRC Table 4.1.8.9.
ROZ f11 the over strength-related force modification factor accounting for the dependable portion of reserve strength in a structure designed according to the provision of the Article 4.1.8.9. along the Z direction. Refer to NRC Table 4.1.8.9.
SCLASS f12 an integer corresponding to site classes A through E (where 1 = A and 6 = F). Fa and Fv are determined based on Site Class as per Table 4.1.8.4.B and Table 4.1.8.4.C.
STX f13 Type of lateral resisting system along the X direction. The parameters can take values from 1 to 5:
• 1 = Moment Resisting Frames
• 2 = Coupled Walls
• 3 = Braced Frames
• 4 = Walls, wall-frame systems
• 5 = Other systems
STZ f14 Type of lateral resisting system along the Z direction. The parameters can take values from 1 to 5:
• 1 = Moment Resisting Frames
• 2 = Coupled Walls
• 3 = Braced Frames
• 4 = Walls, wall-frame systems
• 5 = Other systems
MD f15 Command to check if the time period calculated is for the purpose of Member Strength or Deflection as per Clause 4.1.8.11.(3).(v)
• 1 = Member strength
• 2 = Deflection
CTX f16 Optional CT value along the X direction to calculate time period.
CTZ f17 Optional CT value along the Z direction to calculate time period.
PX f18 Optional Periods of structure (in sec) in the X direction to be used as fundamental period of the structure. If not entered the value is calculated from the code.
PZ f19 Optional Periods of structure (in sec) in the Z direction to be used as fundamental period of the structure. If not entered the value is calculated from the code.
FA f20 Optional Short-Period site coefficient at 0.2s.
Note: Value must be provided if SCLASS set to F (i.e., f12 = 6).
FV f21 Optional Long-Period site coefficient at 1.0s.
Note: Value must be provided if SCLASS set to F (i.e., f12 = 6).

If the ACCIDENTAL option is specified, the program calculates the accidental torsion per the NRC 2010 specifications. The value of the accidental torsion is based on the center of mass for each level. The center of mass is calculated from the SELFWEIGHT, JOINT WEIGHT, and MEMBER WEIGHT commands.

The ACCIDENTAL option along with accidental eccentricity factor (default 0.1 as per NRC 2010) needs to be provided in the NRC seismic primary load case (i.e., NRC LOAD X / Z f1 ACC f3 ). f3 can be negative.

To consider horizontal torsion in cases where a floor diaphragm is present in the model, the ACCIDENTAL option should not be specified. Instead, dynamic eccentricity along with accidental eccentricity should be provided in the NRC seismic primary load case (i.e., NRC LOAD X / Z f1 DEC f2 ACC f3 ). For equivalent seismic analysis, f2 is 1 and f3 is 0.1 as per NRC 2005 code. f1 is always positive or zero, however f2 can be negative. If f2 is 0.0, only accidental torsion will be considered for this particular load case.

Note: For additional details on the application of a seismic load definition used to generate loads, refer to TR.32.12.2 Generation of Seismic Loads.

## Methodology

The equivalent static force procedure to obtain the base shear is implemented according to section 4.1.8.11, Division B of NBCC 2010.

Seismic Base Shear

The minimum lateral earthquake force is calculated according to the following equation (see 4.1.8.11.2)

$V = S ( T a ) M v I E W R d R o$
• · For walls, coupled walls and wall-frame systems, V shall not be less than

S(2.0)MvIEW/RdRo)

Mv must be calculated with T ≥ 4.0
• For moment-resisting frames, braced-frames and other systems, V shall not be less than

S(2.0)MvIEW/RdRo)

Mv must be calculated with T ≥ 2.0
• And for V > 1.5, V need not be greater than
$23S(0.2)IEW/(RdRo)$

Fundament Period, Ta

The fundamental period, Ta, is based on one of the following choices:
• Clause (a): Use 4.1.18.11.3a:
1. 0.085(hn)3/4 for steel moment frames
2. 0.075(hn)3/4 for concrete moment frames
• Clause (b):
• 0.025hn for braced frames
• Clause (c):
• 0.05(hn)3/4 for shear walls and other structures
where
 hn = the height of the building in meters
In the preceding equations, clauses (a), (b) and (c) are implemented except Ta = 0.1N. The period is also calculated in accordance with the Rayleigh method
You may also specify the time period using parameters PX an PX. In this case the program checks the following limits:
• Clause d-i: For moment resisting frames: Ta ≤ 1.5×that determined in clause (a)
• Clause d-ii: For braced frames: Ta ≤ 2.0×that determined in clause (b)
• Clause d-iii: For shear wall structures: Ta ≤ 2.0×that determined in clause (c)
• Clause d-iv: For other structures: Ta that determined in clause (c)
However, if the load case is created for drift provisions, (i.e., calculating drift/deflections), the above limits are not checked but instead the following limits are enforced (see Clause d-v):
• Ta≤2.0 if it is a moment-resisting frame, braced frame, or other system
• Ta≤4.0 for all others (i.e., walls, coupled walls, and wall frame system)
Also, it is stated in code that these upper limits specified may not be checked for deflection and period calculations.

Design Spectral Response Acceleration, S(T)

The design spectral acceleration, S(T), is determined as follows, using linear interpolation for intermediate values of T:
$S(T) =FaSa(0.2)forT≤0.2sFvSa(0.5)orFaSa(0.2)whichever is smallerforT=0.5sFvSa(1.0)forT=1.0sFvSa(2.0)forT=2.0s12FvSa(2.0)forT≥4.0s$

The above data Sa(0.2), Sa(0.5), Sa(1.0) and Sa(2) are the seismic data and are provided in the parameters SA1, SA2, SA3, and SA4, respectively, from the table C-2.

Based on the above values of Sa(Ta), Fa and Fv, the acceleration- and velocity- based site coefficients are determined from the Tables 4.1.8.4.B and 4.1.8.4.C, using linear interpolation for intermediate values of Sa(0.2) and Sa(1.0). It is to be mentioned that, these are the user inputs based on the site classes from A to E and the desired Sa(0.2) and Sa(1.0) values as required as per the above equations.

Higher Mode Factor, Mv

Mv is the factor to account for higher mode effect on base shear which is obtained from the Table 4.1.8.11 based on Lateral Resisting System, Sa(0.2), and Sa(2.0). To get this higher mode factor (Mv), you must evaluate the ratios of Sa(0.2)/Sa(2.0) as also the "Type of Lateral Resisting System." You may alternatively directly specify Mv using the MVX and MVZ parameters.

Force Modification Factors, Rd and Ro

The ductility related force modification factor, Rd, reflects the capability of a structure to dissipate energy through inelastic behavior. The over-strength-related force modification factor,Ro , accounts for the dependable portion of reserve strength in a structure designed according to the provision of Article 4.1.8.9. These values are specified using the RDX, ROX, RDZ, and ROZ parameters and depend on the type of SFRS.

Seismic Weight of the Building, W

Calculated by the program as:
$W=∑i=1nWi$
where
 Wi = the portion of W that is located at or assigned to level i

Distribution of Lateral Earthquake Force

The calculated base shear, V, is distributed over the height of the building by the following equation:
$Fx=(V−Ft)Wxhx∑i=1nWihi$
where
 Ft = Concentrated force applied on the top of the building and it accounts for effects of higher order modes. As per Clause 4.1.8.11(6) Ft is equal to 0.07TaV, but Ft is not greater than 0.25V and Ft = 0 when Ta is not greater than 0.7s Wi, Wx = the portion of W that is located at or assigned to level i or x respectively hi, hx = height above the base(i=0) to level i or x respectively i = any level of the building, i=1 for the first floor above the base and i=n for the uppermost level in the main portion of the structure

Torsional Effect

Torsional effects are accounted for according to the Clause 4.1.8.11(10):

 Tx = Fx(ex + 0.10 Dnx)

 Tx = Fx(ex - 0.10 Dnx)

where
 ex = natural eccentricity due to center of rigidity and center of mass being at different positions Dnx = plan dimension normal to the direction of ground motion
Note: The overturning moment calculation as given in 4.1.8.11 is not evaluated by the program.

## 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
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
SELFWEIGHT X 1
SELFWEIGHT Y 1
SELFWEIGHT Z 1
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
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 ***
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
NRC LOAD X 1 DEC 1 ACC 0.1
NRC LOAD X 1 DEC 1 ACC -0.1
NRC LOAD X -1 DEC 1 ACC -0.1
NRC LOAD X -1 DEC 1 ACC 0.1
*** Z-DIRECTION
NRC LOAD Z 1 DEC 1 ACC 0.1
NRC LOAD Z 1 DEC 1 ACC -0.1
NRC LOAD Z -1 DEC 1 ACC -0.1
NRC LOAD Z -1 DEC 1 ACC 0.1
*****************************************************
**** RESPONSE SPECTRUM ****
*** X-DIRECTION
FINISH