RAM Structural System Help

NBC of Canada 2010

Equivalent Static Force Procedure

The Equivalent Static Force Procedure is implemented according to Section 4.1.8.11, Division B of NBC 2010. You are refereed to Sections 4.1.8.1 - 4.1.8.13 as well Commentary J of User's Guide - NBC 2010 -Structural Commentaries.

Seismic Base Shear

The minimum lateral earthquake force (seismic base shear) 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 0

The above equation is subjected to the following limits:

  • For walls, coupled walls, and wall-frame systems, V > S ( 4.0 ) M v I E W R d R 0 (Note that Mv must be calculated with T ≥ 4.0)
  • For moment-resisting frames, braced frames, and other systems, V > S ( 2.0 ) M v I E W R d R 0 (Note that Mv must be calculated with T ≥ 2.0)
  • And if Rd ≥ 1.5, then V < 2 3 S ( 2.0 ) I E W R d R 0

The Fundamental Period (Ta)

The fundamental period, Ta, is based on one of the following choices:
  • Clause (a): Use 4.1.8.11.3a :
    T a = { 0.085 ( h n ) 3 / 4 for steel moment frames 0.075 ( h n ) 3 / 4 for concrete moment frames 0.1 N for other frames
  • Clause (b): Use 4.1.8.11.3b : Tα = 0.025 hn for braced frames
  • Clause (c): Use 4.1.8.11.3c : Tα = 0.050 (hn)3/4 for shear wall and other structures
Note that hn is height of the building (in meters). In the preceding equations, Clauses (a), (b), and (c) are implemented in the program except Ta = 0.1N. You may also enter your own value for Tα directly.
The program can calculate the fundamental period from an Eigenvalue analysis, and, if required, the calculated period can also be used. In this case, the program checks the following limits:
  • Clause d - i: For moment resisting frames: T a ≤ 1.5 × that determined in Clause(a)
  • Clause d - ii: For braced frames: T a ≤ 2.0 × that determined in Clause(b)
  • Clause d - iii: For shear wall structures: T a ≤ 2.0 × that determined in Clause(c)
  • Clause d - iv: For other structures: T a ≤ that determined in Clause(c)
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 systems)
Also, it is stated in the code that these upper limits specified may not be checked for deflection and period calculations.

Spectral Response Acceleration (Sa)

It is the acceleration read from Design Spectral Acceleration Curve for the value of Ta.

Higher Mode Factor (Mv)

This factor is read from Table 4.1.8.11, based on type of lateral resisting systems, Sa(0.2), Sa(2.0) and calculated value of Ta. You are required to choose lateral resisting system for each direction. Also, you may enter Mv directly.

Importance Factor (Ie)

It is given in Table 4.1.8.5 and you must provide this value.

Seismic Weight of the Building (W)

It is calculated by the program.

Force Modification Factors (Rd and Ro)

Ductility related force modification factor, Rd, reflects the capability of a structure to dissipate energy through inelastic behavior. You must provide this value for each direction. This factor is provided in Table 4.1.8.9.

Overstrength related force modification factor, Ro, accounts for the dependable portion of reserve strength in a structure. You must provide this value for each direction. This factor is provided in Table 4.1.8.9.

Design Spectral Acceleration Curve

Based on Site Class and values of Sa(0.2) and Sa(1.0), the design spectral acceleration curve is generated as follows:
S ( T ) = { F a S a ( 0.2 ) T ≤ 0.2 s F v S a ( 0.5 )    or  F a S a ( 0.2 ) , whichever is smaller T = 0.5 s F v S a ( 1.0 ) T = 1.0 s F v S a ( 2.0 ) T = 2.0 s F v S a ( 2.0 ) 2 T ≥ 4.0 s
where Fα and Fv are determined according to Tables 4.1.8.4.B and 4.1.8.4.C, respectively. For intermediate values, linear interpolation is used.

Distribution of Lateral Earthquake Force

Calculated base shear, V, is distributed over the height of the building based on the following equation:
F x = ( V − F t ) W x h x ∑ i = 1 n W i h i
where
Ft
=
concentrated force applied at the top of the building and it accounts for effects of higher order modes. It is calculated according to the following equation (Commentary J, p.J-52):
F t = { 0 T a ≤ 0.7 s 0.07 T a V 0.7 s < T a < 3.6 s 0.25 V 3.6 s ≤ T a

Overturning Moments

The overturning moment calculation as given in 4.1.8.11j is not implemented in the program.

Torsional Sensitivity (B)

Determination of torsional sensitivity requires static analysis using 3D elastic model with static lateral loads at each floor level applied at distances ±Dnx (see 4.1.8.11.9). It is only applicable for rigid diaphragms. This is not implemented in the program.

Torsional Effects

Torsional effects are accounted for according to the following equation (it applies for both X- and Y-directions):

Tx = Fx(ex ± 0.10Dnx)

where
ex
=
natural eccentricity due to center of rigidity and mass being at different positions
0.10 Dnx
=
The portion ± 0.05 Dnx of ± 0.10 Dnx represents accidental torsion, and the remainder takes into account natural torsion, including dynamic amplification.
Dnx
=
plan dimension of the building at a level x perpendicular to the direction of seismic loading being considered

Note that in a 3D model, the effects of ex are already included in the 3D analysis (if mass center and rigidity center are at different locations, this is already reflected in analysis results). So, there is no need to include it explicitly. Hence, the only eccentricity considered is ± 0.10 Dnx. Conveniently, this is exactly the same set of load applications required for the determination of the torsional sensitivity parameter, B. The eccentricity of ± 0.10 Dnx is implemented in the program.

Stability Factor (θx)

The stability factor as given in Commentary J, pg. J-26 is not implemented in the program.

Orthogonal Loading (4.1.8.8)

100%/30% orthogonal loading is implemented in the program as referenced in 4.1.8.8.

Direction of Loading

Four load cases are generated as follows:

Generated Load Cases for NBC of Canada 2010 Seismic

Two additional options are provided:
  • Consider Orthogonal effects (100/30)
  • Generate Additional Load Cases for Analysis with Tension-Only Members
If either of these options is selected, additional load cases are generated accordingly.

Response Spectra Analysis

Modal Response Spectrum Analysis according to 4.1.8.12 of Division B of NBC of Canada 2010 is implemented. Other methods (Numerical Integration Linear Time History Method and Nonlinear Dynamic Analysis) are not covered.

Design Spectral Acceleration

Based on Site properties, the design spectral acceleration curve is generated as follows:
S ( T ) = { F a S a ( 0.2 ) T ≤ 0.2 s F v S a ( 0.5 )    or  F a S a ( 0.2 ) , whichever is smaller T = 0.5 s F v S a ( 1.0 ) T = 1.0 s F v S a ( 2.0 ) T = 2.0 s F v S a ( 2.0 ) 2 T ≥ 4.0 s

where Fa and Fv are determined according to Tables 4.1.8.4.B and 4.1.8.4.C, respectively. For intermediate values, linear interpolation is used.

Accidental Torsional Eccentricity

Section 4.1.8.12.4 provides two alternative approaches for accidental torsional eccentricity:
  • 4.1.8.12-4a: In this approach, which can be used for any value of B (torsional sensitivity) but is intended primarily for torsionally sensitive structures, the effects of static torsional moments, ( ± 0.10 Dnx ) Fx, at each level "x" are calculated and then combined with the effects determined from a dynamic analysis that includes the actual eccentricities (i.e., eccentricities due to mass center and center of rigidity of floors. In a 3D analysis, this is already covered).
  • 4.1.8.12-4b: The second approach is only for permissible for structures that are not torsionally sensitive (B < 1.7). This approach allows the effects of accidental eccentricity to be included by shifting the center of mass by ± 0.05 Dnx.
Only the method given in 4.1.8.12-4b is implemented in the program. A maximum of 4 load cases is generated due to these eccentricities.

Dynamic Base Shear

The elastic base shear, Ve, is obtained from analysis (Linear Dynamic Analysis, also referred to as Modal Response Spectrum Analysis or Response Spectra Analysis).

The design elastic base shear is
V e d = { V e if R d < 1.5 α V e if R d ≥ 1.5
where
α
=
2 S ( 0.2 ) 3 S ( T a ) ≤ 1.0
Then, Ved is further modified to obtain the design base shear:
V d = I e R d R 0 V e d

The above equation is not implemented. Thus, reported base shear is the base shear obtained from Response Spectra Analysis (i.e., Ve), and it is the engineer's responsibility to make this adjustment.

The design base shear, Vd is subjected to the following limits:
  • Vd = 0.8V if Vd < 0.80 V, where V is the lateral earthquake design base shear that can be obtained from Equivalent Static Force Procedure (4.8.1.12-8).
  • Vd > V, then Vd can be used as the design base shear.
  • Vd = max( Vd, V) for irregular structures. In other words, reducing Vd is not permitted for irregular structures (4.1.8.12-9).

Again, this set of adjustment is not enforced in the program. It is the engineer's responsibility to include this adjustment.

Story Shears, Member Forces, and Deflections

Section 4.1.8.12.8 states that story shears, story forces, member forces, and deflections obtained from Linear Dynamic Analysis shall be multiplied by V d V e . This can be carried out in the program by setting X Scale Factor and Y Scale Factor in the load case dialog. Thus, the engineer is required to run the Response Spectra Analysis twice, once with 1.0 for these scale factors to obtain Ve and then once again with setting the scale factors to V d V e (the engineer needs to calculate Vd). Finally, at the end of this process, analysis results (displacements, story shears, and member forces) reflect this adjustment.

Parent topic: Story Forces: Seismic/Dynamic