Canadian Code Seismic Calculation Example

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January 29, 2025

Civil and Structural Design Calculations, Engineering Concepts – Civil & Structural

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The National Building Code of Canada (NBC) 2020 provides the latest guidelines for seismic design, ensuring structures can withstand seismic events. Here’s an overview of the seismic calculation procedure as per NBC 2020:

1. Determine Seismic Hazard Values

Utilize the 2020 National Building Code of Canada Seismic Hazard Tool to obtain site-specific seismic hazard values. This tool provides spectral acceleration values at different periods, which are essential for design calculations.

2. Site Classification

Classify the site based on soil properties, ranging from Class A (hard rock) to Class F (soft soil). This classification influences the seismic response of the structure.

3. Design Spectral Acceleration Values

Adjust the obtained spectral acceleration values using site coefficients corresponding to the site’s classification. This results in the design spectral acceleration values for different periods.

4. Seismic Weight Calculation

Calculate the total seismic weight of the structure, including all permanent and applicable live loads that contribute to seismic forces.

5. Base Shear Calculation

Compute the base shear force (V) using the formula:

V = S(T_a) × M_v× I × W

Where:

S(Ta) : Design spectral acceleration at the fundamental period Ta
Mv : Higher mode factor
I: Importance factor of the structure
W: Total seismic weight

6. Lateral Force Distribution

Distribute the calculated base shear along the height of the structure based on the mass and stiffness of each level.

7. Drift and Deformation Checks

Ensure that the inter-story drifts and overall deformations are within the permissible limits specified by NBC 2020.

8. Detailed Analysis

For complex structures, perform a dynamic analysis, such as the Response Spectrum or Time-History Analysis, to capture the structure’s response more accurately.

Certainly! Let’s walk through a seismic design calculation example based on the National Building Code of Canada (NBCC) 2020. This example will illustrate the steps to determine the base shear for a hypothetical building.

Example Building Details:

Location: Vancouver, British Columbia
Site Class: C (Very Dense Soil and Soft Rock)
Importance Category: Normal (Importance Factor, I=1.0 )
Building Height: 20 meters
Number of Stories: 5
Total Seismic Weight ( W ): 5,000 kN

Step-by-Step Calculation:

Obtain Seismic Hazard Values:

Use the 2020 National Building Code of Canada Seismic Hazard Tool to retrieve the spectral acceleration values for Vancouver. For this example, let’s assume the following values:

- Spectral Acceleration at 0.2s ( Sa(0.2)) : 0.75
- Spectral Acceleration at 0.5s ( Sa(0.5)) : 0.60
- Spectral Acceleration at 1.0s ( Sa(1.0)) : 0.30
- Spectral Acceleration at 2.0s ( Sa(2.0)) : 0.15

Determine Site Coefficients:

Based on Site Class C, the NBCC 2020 provides site coefficients Fa and Fv corresponding to different spectral periods. For simplicity, let’s assume:

- Fa (at 0.2s): 1.0
- Fv (at 1.0s): 1.0

Calculate Design Spectral Acceleration Values:

S_aD(0.2)=Fa×Sa(0.2)=1.0×0.75=0.75
S_aD(0.5)=Fa×Sa(0.5)=1.0×0.60=0.60
S_aD(1.0)=Fv×Sa(1.0)=1.0×0.30=0.30
S_aD(2.0)=Fv×Sa(2.0)=1.0×0.15=0.15 .

Determine Fundamental Period ( T ):

For a building with a height of 20 meters, the fundamental period can be estimated using empirical formulas provided in NBCC 2020. A common approximation is:

- T=0.05×H^0.75= 0.05 × 20^0.75≈ 0.56 seconds

Calculate Base Shear ( V ):

The base shear is determined using the formula:

- **V=S(T)×Mv×I×W

Where:

- - S(T): Design spectral acceleration at period T
  - Mv: Higher mode factor (typically taken as 1.0 for regular structures)
  - I: Importance factor
  - W: Total seismic weight

For T=0.56 seconds, interpolate S(T) between S_aD(0.5) and S_aD(1.0)

S(T)=S_aD(0.5) + [(T−0.5)/(1.0−0.5)×(S_aD(1.0)−S_aD(0.5))]

S(0.56)=0.60+[(0.56−0.5)/(1.0−0.5)×(0.30−0.60)] S(0.56)=0.60+[0.12×(−0.30)]=0.60−0.036 = 0.564

Assuming Mv=1.0 and I=1.0:

- V=0.564×1.0×1.0×5,000=2,820 KN

Distribute Lateral Forces:

The calculated base shear VVV is distributed along the height of the building based on the mass and stiffness of each story. This involves calculating the story shear and applying lateral forces accordingly.

Note: This example provides a simplified overview of the seismic design calculation process. In practice, additional factors such as torsional effects, ductility, and overstrength need to be considered.