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:

Parameter	Description
SA1 f1	Seismic Data, Sa(0.2), as per Table C-2.
SA2 f2	Seismic Data, Sa(0.5), as per Table C-2.
SA3 f3	Seismic Data, Sa(1.0), as per Table C-2.
SA4 f4	Seismic Data, Sa(2), as per Table C-2.
MVX f5	The higher mode factor along the X direction. Refer NRC Table 4.1.8.11.
MVZ f6	The higher mode factor along the Z direction. Refer NRC Table 4.1.8.11.
JX f7	The numerical reduction coefficient for base overturning moment along the X direction. Refer to NRC Table 4.1.8.11.
JZ f8	The numerical reduction coefficient for base overturning moment along the Z direction. Refer to NRC Table 4.1.8.11.
IE f9	The 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 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 X direction. Refer to NRC Table 4.1.8.9.
ROX 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 X direction. Refer to NRC Table 4.1.8.9.
RDZ f12	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.
ROZ f13	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 f14	an integer corresponding to site classes A through E(where 1 = A and 6 = F). F_a and F_v are determined based on Site Class as per NRC Table 4.1.8.4.B and Table 4.1.8.4.C.
FA f15	Optional Short-Period site coefficient at 0.2s. Value must be provided if `SCLASS` set to F (i.e., f14 = 6).
FV f16	Optional Long-Period site coefficient at 1.0s. Value must be provided if `SCLASS` set to F (i.e., f14 = 6).
CT f17	Optional 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 TR.32.12.2 Generation of Seismic Loads.

Methodology

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

V = \frac{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} = \frac{S (2.0) M_{v} I_{E} W}{R_{d} R_{o}}

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

V_{\max} = \frac{2}{3} \frac{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:

T_a 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 h_n is in meter
  1. 0.085(h_n)^3/4for steel moment frames,
  2. 0.075(h_n)^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(T_a),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(T_a) is the design spectral acceleration and is determined as follows, using linear interpolation for intermediate values of T_a:

S(T_a) = F_aS_a(0.2) for T_a ≤ 0.2s
- = F_vS_a(0.5) or F_aS_a(0.2), whichever is smaller for T_a = 0.5s
- = F_vS_a(1.0) for T_a = 1.0s
- = F_vS_a(2.0) for T_a = 2.0s
- = F_vS_a(2.0)/2 for T_a ≥ 4.0s
The above terms S_a(0.2), S_a(0.5), S_a(1.0) and S_a(2.0) are the Seismic Data and are obtained as user input from the Table C-2.

Based on the above values of S_a(T_a), F_aandF_v, 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 S_a(0.2) and S_a(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 S_a(0.2) and S_a(1.0) values as required as per the above equations.
M_v 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 (M_v) and numerical reduction coefficient for base overturning moment (J), you must get the ratios of S_a(0.2)/S_a(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.
I_E 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:

$W = \overset{n}{\sum_{i = 1}} W_{i}$

Where W_i is the portion of W that is located at or assigned to level i.
R_d 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.
R_o 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 R^d and R_o 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, F_t shall be concentrated at the top of the building, where,

F_t = 0.07T_aV

but F_t is not greater than 0.25V and F_t = 0 when T_a is not greater than 0.7s.

The remainder (V- F_t), 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} = \frac{(V - F_{t}) W_{x} h_{x}}{\overset{n}{\sum_{i = 1}} W_{i} h_{i}}

where

F_x	=	the lateral force applied to level x
F_t	=	the portion of V to be concentrated at the top of the structure
W_i, W_x	=	the portion of W that is located at or assigned to level i or x, respectively
h_i, h_x	=	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

Parent topic: TR.31.2 Definitions for Static Force Procedures for Seismic Analysis

Related concepts	Related reference	Related topics
G.16.2 Seismic Load Generator	TR.32.12.2 Generation of Seismic Loads	V. NRC 2005 Static Seismic