Seismic Analysis (NBCC 2020)

How it calculates

This calculator determines the design base shear of a building using the Equivalent Static Force Procedure of the National Building Code of Canada 2020 (Article 4.1.8), then distributes that base shear over the height of the structure. The workflow moves from site seismic hazard, through the design spectral acceleration and system parameters, to the base shear and its storey-by-storey distribution.

Site parameters

The site seismic hazard is defined by the design spectral response accelerations Sa at the six periods 0.2, 0.5, 1.0, 2.0, 5.0, and 10.0 seconds (Cl. 4.1.8.4), together with the peak ground acceleration and peak ground velocity. The site is classified by site class or by the average shear wave velocity over the top 30 m, Vs30, per Table 4.1.8.4.-A. These values set the amplified spectral accelerations used to build the design spectrum.

Design spectral acceleration

The design spectral acceleration S(T) is interpolated from the six-period spectrum for the building's fundamental period. The site condition factors are applied to the spectral values, and the calculator builds the full design spectrum so that S(T) at the relevant period is available for the base shear equation.

Key building properties and period

The importance category sets the importance factor IE from Table 4.1.2.1. The fundamental lateral period Ta is either taken from the code empirical expression for the selected system type or entered as a custom period, subject to the maximum period cap of Cl. 4.1.8.11. Separate periods can be handled where the building responds differently in each direction.

Seismic design parameters

The seismic force-resisting system (SFRS) sets the ductility-related force modification factor Rd and the overstrength-related factor Ro from Table 4.1.8.9. These can be selected from the system list or entered as custom values. The product Rd·Ro reduces the elastic force demand to the design level and is central to the base shear calculation.

Design base shear

The design base shear is V = S(Ta)·Mv·IE·W / (Rd·Ro), where W is the seismic weight and Mv the higher-mode factor. The result is checked against the NBCC 2020 limits of Cl. 4.1.8.11: the base shear need not be taken greater than two-thirds of the value computed at 0.2 s for systems with Rd of at least 1.5, and must not be less than the code minimum. The governing value is reported.

Structural irregularity screening

Before the base shear is accepted, the calculator screens the building against the structural irregularities of Table 4.1.8.6, including a soft-storey check for any storey whose lateral stiffness is less than that of the storey above. Where an irregularity or a gravity-induced lateral demand condition (Qy relative to QG) is present, the calculator flags where a dynamic or elastic analysis is required rather than the static procedure alone.

Seismic force distribution

Once the base shear is established, it is distributed over the height of the building storey by storey per Cl. 4.1.8.11, including the concentrated force Ft applied at the top for taller or longer-period structures. When the configuration triggers it, the run is repeated as an elastic analysis so the distributed forces can be compared against the static result.