Seismic Analysis (NBCC 2025)

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 2025 (Article 4.1.8), then distributes that shear over the height of the structure. The workflow runs from the site seismic hazard, through the design spectrum and system parameters, to the base shear, its code limits and the storey force distribution.

Site hazard and site coefficient

The seismic hazard is defined by the design spectral response accelerations Sa at 0.2, 0.5, 1.0, 2.0, 5.0 and 10.0 seconds, together with the peak ground acceleration and peak ground velocity. NBCC 2025 adds the X450 spectral accelerations at 0.2 and 2.0 seconds. The site is classified by site class or by the average shear wave velocity over the top 30 m, and the site coefficient Fs follows from the site condition. These values can flow from the project defaults or be overridden per calculation.

Importance factor and seismic category

The building importance category sets the earthquake importance factor IE. The seismic category is then assigned from the importance-weighted hazard: a building reaches SC4 where IE·Sa(0.2) exceeds 0.75 or IE·Sa(1.0) exceeds 0.3, with lower categories following the corresponding thresholds. The seismic category governs which irregularity and system restrictions apply.

Fundamental period

The fundamental lateral period Ta comes from the code empirical expression for the selected system type, or from a custom value. The empirical period is capped by a maximum period Tmax that depends on the system category, for example 1.5 × 0.085 × hn^0.75 for a steel moment frame. Single-storey buildings with a steel deck or wood roof diaphragm on a moment or braced frame use the diaphragm-specific expression that includes the diaphragm span. Separate periods can be carried for the X and Y directions.

Design spectral acceleration

The design spectral acceleration S(Ta) is interpolated from the six-period spectrum at the fundamental period, with the site coefficient applied. Below 0.2 seconds the 0.2 second value governs, and the spectrum is built across the full period range so the value at Ta is available for the base shear equation.

Higher mode factor

The higher mode factor Mv depends on the spectral ratio S(0.2)/S(5.0) and on the seismic force-resisting system category. The calculator evaluates Mv at 1.0, 2.0 and 5.0 seconds by interpolating on the spectral ratio within the code bands, then selects or interpolates the value appropriate to Ta. For short-period structures with Ta at or below 0.5 seconds, Mv is unity.

Design base shear

The calculated base shear is

V,calc = S(Ta) × Mv × IE × W / (Rd × Ro)

where W is the total effective seismic weight summed from the storey table, Rd the ductility-related force modification factor and Ro the overstrength-related factor, both set by the selected system or entered as custom values. The result is bounded by a maximum and a minimum:

V,max = max( 2/3 × Sa(0.2) × IE × W / (Rd × Ro), Sa(0.5) × IE × W / (Rd × Ro) )

V,min = S(4.0)Mv × IE × W / (Rd × Ro)

For systems with Rd of at least 1.5 the governing value is max( min(V,calc, V,max), V,min ), and the calculator reports which limit governed. Where a Type 6 weak-storey irregularity is present, the governing shear is amplified by Rd·Ro per the requirement of Sentence 4.1.8.10.(1).

Irregularity and system restrictions

The building is screened against the structural irregularities of Table 4.1.8.6. The calculator distinguishes irregularities that merely trigger a dynamic analysis from restricted irregularities that are not permitted for the given importance category and hazard level, and it checks the minimum Rd permitted for high importance and post-disaster buildings. Where the height, period or irregularity combination puts the building outside the scope of the static procedure, that limitation is flagged rather than silently accepted.

Force distribution and elastic analysis

Once the base shear is established it is distributed over the height of the building in proportion to the weight-height product Wx·hx, with a concentrated force Ft applied at the top for structures with Ta above 0.7 seconds. The storey table reports the lateral force Fx and the cumulative storey shear Vx at each level, and these forces are exported for diaphragm design.

A parallel elastic analysis is reported alongside the design result, using Rd of 1.3 and Ro of 1.0 with unit importance factor, and its own hazard spectrum at the required probability of exceedance. This gives the elastic base shear and force distribution next to the design-level values without a second run.