Subject:
NBC 2020 Modal Response Spectrum Analysis and Base Shear Considerations in RFEM 6
Comment:
The National Building Code of Canada (NBC) 2020 Article 4.1.8.7 provides a clear procedure for earthquake methods of analysis. The more advanced method, the Dynamic Analysis Procedure in Article 4.1.8.12, should be used for all structure types except those that meet the criteria set forth in 4.1.8.7. The more simplistic method, the Equivalent Static Force Procedure (ESFP) in Article 4.1.8.11, can be used for all other structures.
Description:
For structures that qualify for the Dynamic Analysis Procedure, there are two further sub methods defined in 4.1.8.12 [1], including a Linear Dynamic Analysis, with either a Modal Response Spectrum Method or the Numerical Integration Linear Time History Method, or a Nonlinear Dynamic Analysis. This article will focus on a Modal Response Spectrum Method (RSA) and the further base shear requirements defined in the NBC 2020.
NBC 2020 Base Shear Variations
Assuming an RSA is calculated according to the NBC 2020 which is beyond the scope of this article, the base shear can be determined at the bottom story of the structure in each of the orthogonal directions the lateral seismic load is applied. A series of steps in Article 4.1.8.12 [1] defines the various base shear variations needed to ultimately scale the story shears, story forces, member forces, and deflection if necessary.
Step 1: In Sentence (5) [1], the elastic base shear, V-e, should be determined from a linear dynamic analysis, which is the first step in understanding the NBC base shear requirements. V-e should not include any additional factors or scaling applied to the response spectrum.
Step 2: Determine the adjusted elastic base shear, V-ed, also known as the "adjusted lateral earthquake elastic force at the base of the structure", according to Sentence (6) [1] using V-e determined from Sentence (5) [1]. For all structures located on sites other than X-F and having a seismic force-resisting system (SFRS) with a ductility-related force modification factor, R-d, equal to or greater than 1.5, then V-e should be multiplied by the larger of the following two factors to obtain V-ed:
| S(0.2) | Design spectral response acceleration for a period of T = 0.2 sec |
| S(0.5) | Design spectral response acceleration for a period of T = 0.5 sec |
| S(Ta) | Design spectral response acceleration for the fundamental lateral period of vibration of the structure in the direction under consideration |
Step 3: The previously determined V-ed should be multiplied by the importance factor, I-e, given in Article 4.1.8.5 [1] and divided by the ductility-related force modification factor multiplied by the overstrength-related force modification factor, R-dR-o, found in Table 4.1.8.9 [1] to determine the specified lateral earthquake force, V-d.
Step 4: Determine the specified lateral earthquake force, V, given in Article 4.1.8.11 [1] according to the simplified ESFP.
NBC 2020 Base Shear Scaling Requirements
With the information above in collaboration with 4.1.8.12(8) [1], if V-d from Step 3 is less than 80% of V from Step 4, then V-d should be taken as 0.8V for all regular structures and irregular structures permitted to be designed with the ESFP.
For all irregular structures which require a dynamic analysis specified in 4.1.8.7 [1], as well as wood structures greater than 4 stories which meet the criteria set forth in 4.1.8.12(12) [1], then V-d shall be taken as the larger of V-d or 100% of V stated in 4.1.8.12(9) [1].
In addition to these minimums, the scale factor V-d/V-e should be applied to elastic story shears, story forces, member forces, and deflections, including the effects of accidental torsion to determine the design values from 4.1.8.12(10) [1].
NBC 2020 Base Shear Application in RFEM 6
With the multiple variations for base shear discussed in NBC 2020, it may be difficult to determine which base shear variant is provided when running a response spectra analysis according to the standard in the structural analysis program RFEM 6.
Utilizing the Response Spectrum Analysis Add-on, there are two spectrum types available under the Response Spectrum definition details, including the "Elastic Spectrum" and the "Design Spectrum".
The "Elastic Spectrum" will provide the structure’s elastic base shear, V-e, from 4.1.8.12(5) [1] or Step 1 above. This value does not include the consideration of I-e/R-dR-o or any other factors.
The "Design Spectrum" will provide the structure’s design base shear, V-d, from 4.1.8.12(7) [1] or Step 3 above. However, it should be noted that the additional factor specified in 4.1.8.12(6) or Step 2 above is not included in this calculation. The calculation does include I-e/R-dR-o, as these variables are listed directly under the "Design Spectrum" options, whereas they are not listed for the "Elastic Spectrum".
For either spectrum type, the user will have the ability to scale the response spectrum directly to account for scale factor requirements. For example, the "Elastic Spectrum", which is needed to analyze the structure deflections as it does not in...
