# TR.31.2.3 Canadian Seismic Code (NRC) – 2005 Volume 1

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- 2005 Volume 1 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

STAAD.Pro utilizes the following format to generate the lateral seismic loads.

DEFINE NRC 2005 (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 JX f7 JZ f8 IE f9 RDX f10 ROX f11 RDZ f12 ROZ f13 SCLASS f14 ( FA f15 ) ( FV f16 ) ( CT f17 ) ( PX f18 ) ( PZ f19) }

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 f5The higher mode factor along the X direction. Refer NRC Table 4.1.8.11.
MVZ f6The higher mode factor along the Z direction. Refer NRC Table 4.1.8.11.
JX f7The numerical reduction coefficient for base overturning moment along the X direction. Refer to NRC Table 4.1.8.11.
JZ f8The numerical reduction coefficient for base overturning moment along the Z direction. Refer to NRC Table 4.1.8.11.
IE f9The earthquake importance factor of the structure. This input is based on Importance Category and ULS / SLS. Refer to NRC Table 4.1.8.11.
RDX f10The 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.
ROX f11The 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.
RDZ f12The 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.
ROZ f13The 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 f14an 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 NRC Table 4.1.8.4.B and Table 4.1.8.4.C.
FA f15Optional Short-Period site coefficient at 0.2s. Value must be provided if SCLASS set to F (i.e., f14 = 6).
FV f16Optional Long-Period site coefficient at 1.0s. Value must be provided if SCLASS set to F (i.e., f14 = 6).
CT f17Optional CT value used in calculating the period of the structure based on the empirical method.
Note: The CT parameter entered is used directly in the calculation of the fundamental period, Ta. Therefore, care should be taken to convert the CT value to imperial units as the program internally uses the height of the building in feet for this calculation.
PX f18 Optional period of the 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 period of the 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.

If the ACCIDENTAL option is specified, the program calculates the accidental torsion per the NRC 2005 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 ACC option along with accidental eccentricity factor (default 0.1 as per NRC 2005) 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 GUID-6D9B5C48-9FFF-4548-BFB4-ACAE1E973743.

## Methodology

The minimum lateral seismic force or base shear (V) is automatically calculated by STAAD.Pro using the appropriate equation (s).

$V = S ( T a ) M v I E W R d R o$
as per section 4.1.8.11(2) of NBC of Canada 2005, Volume 1

Except that V shall not be less than:

$V min ⁡ = S ( 2.0 ) M v I E W R d R o$

and for an Rd= 1.5, V need not be greater than:

$V max ⁡ = 2 3 S ( 0.2 ) I E W R d R o$
(i.e., the upper limit of V)

Description of the terms of the equation to calculate V:
• Ta is the fundamental lateral period in the direction under consideration and is determined as:

1. For moment-resisting frames that resist 100% of the required lateral forces and where the frame is not enclosed by or adjoined by more rigid elements that would tend to prevent the frame from resisting lateral forces, and is calculated by the empirical formulae as described below provided hn is in meter

1. 0.085(hn)3/4for steel moment frames,
2. 0.075(hn)3/4for concrete moment frames, or
2. The period is also calculated in accordance with the Rayleigh method but could be overridden by user specified time period (PX, PZ).

If design spectral acceleration, S(Ta),calculated considering structural time period calculated based on method (b) is greater than 0.8 time the same calculated considering structural time period calculated based on method (a), the former is used for further calculation. Otherwise, the later time period is used.

3. Other established methods of mechanics using a structural model that complies with the requirements of Sentence 4.1.8.3.(8), except that

1. for moment resisting frames, Ta shall not be greater than 1.5 times that determined in Clause (a).
2. for braced frames, Ta shall not be greater than 2.0 times that determined in Clause (b).
3. for shear wall structures, Ta shall not be greater than 2.0 times that determined in Clause (c), and
4. for the purpose of calculating the deflections, the period without the upper limit specified is referred from Appendix A.
• S(Ta) is the design spectral acceleration and is determined as follows, using linear interpolation for intermediate values of Ta:

S(Ta) = FaSa(0.2) for Ta ≤ 0.2s

• = FvSa(0.5) or FaSa(0.2), whichever is smaller for Ta = 0.5s
• = FvSa(1.0) for Ta = 1.0s
• = FvSa(2.0) for Ta = 2.0s
• = FvSa(2.0)/2 for Ta ≥ 4.0s

The above terms Sa(0.2), Sa(0.5), Sa(1.0) and Sa(2.0) are the Seismic Data and are obtained as user input from the Table C-2.

Based on the above values of Sa(Ta), Fa andFv, 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.

• Mv is the factor to account for higher mode effect on base shear and the associated base overturning moment reduction factor is J which are obtained as user input from the Table 4.1.8.11. To get this higher mode factor (Mv) and numerical reduction coefficient for base overturning moment (J), you must get the ratios of Sa(0.2)/Sa(2.0) as also the "Type of Lateral Resisting System."

For values of Mv between fundamental lateral periods, Ta of 1.0 and 2.0 s, the product S(Ta). Mv shall be obtained by linear interpolation.

Values of J between fundamental lateral periods, Ta of 0.5 and 2.0 s shall be obtained by linear interpolation.

• IE is the earthquake importance factor of the structure and is determined from the Table 4.1.8.5. This is a user input depending on Importance Category and ULS / SLS
• W is the weight of the building and shall be calculated internally using the following formula:

$W = ∑ i = 1 n W i$

Where Wi is the portion of W that is located at or assigned to level i.

• Rd is 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.

• Ro is 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.

These Rd and Ro values are the user inputs depending on the type of SFRS

As per 4.1.8.11(6), the total lateral seismic force, V, shall be distributed such that a portion, Ft shall be concentrated at the top of the building, where,

• Ft = 0.07TaV

but Ft is not greater than 0.25V and Ft = 0 when Ta is not greater than 0.7s.

The remainder (V- Ft), shall be distributed along the height of the building, including the top level, in accordance with the following formula [as per section 4.1.8.11(6)]:
$F x = ( V − F t ) W x h x ∑ i = 1 n W i h i$
where
 Fx = the lateral force applied to level x Ft = the portion of V to be concentrated at the top of the structure Wi, Wx = the portion of W that is located at or assigned to level i or x, respectively hi, hx = the height above the base (i=0) to level i or x, respectively i = is any level in the building (e.g., i = 1 for the first level above the base) n = is the uppermost level in the main portion of the structure

## Example

DEFINE NRC 2005 ACC LOAD
SA1 .33 SA2 .25 SA3 .16 SA4 .091 MVX 1.2 MVZ 1.5 JX .7 JZ .5 IE 1.3 -
RDX 4.0 ROX 1.5 RDZ 3.0 ROZ 1.3 SCLASS 4
SELFWEIGHT
JOINT WEIGHT
17 TO 48 WEIGHT 7
49 TO 64 WEIGHT 3.5
LOAD 1 EARTHQUAKE ALONG X
NRC LOAD X 1.0
PERFORM ANALYSIS PRINT LOAD DATA
CHANGE