# The Ontario Building Code | Dynamic Analysis Procedure

**4.1.8.12. Dynamic Analysis Procedure**

**(1) **The Dynamic Analysis Procedure shall be in accordance with one of the following methods:

(a) Linear Dynamic Analysis by either the Modal Response Spectrum Method or the Numerical Integration Linear Time History Method using a structural model that complies with the requirements of Sentence 4.1.8.3.(8), or

(b) Nonlinear Dynamic Analysis, in which case a special study shall be performed.

**(2) **The spectral acceleration values used in the Modal Response Spectrum Method shall be the design spectral acceleration values, S(T), defined in Sentence 4.1.8.4.(7).

**(3) **The ground motion histories used in the Numerical Integration Linear Time History Method shall be compatible with a response spectrum constructed from the design spectral acceleration values, S(T), defined in Sentence 4.1.8.4.(7).

**(4) **The effects of accidental torsional moments acting concurrently with the lateral earthquake forces that cause them shall be accounted for by the following methods:

(a) the static effects of torsional moments due to (± 0.10 D_{nx})F_{x} at each level x, where F_{x}is either determined from the elastic dynamic analysis or determined from Sentence 4.1.8.11.(6) multiplied by R_{d}R_{o}/I_{E}, shall be combined with the effects determined by dynamic analysis, or

(b) if B, as defined in Sentence 4.1.8.11.(9), is less than 1.7, it is permitted to use a three-dimensional dynamic analysis with the centres of mass shifted by a distance of – 0.05 D_{nx}and + 0.05 D_{nx}.

**(5) **Except as provided in Sentence (6), the design elastic base shear, V_{ed}, is equal to the elastic base shear, V_{e}, obtained from a Linear Dynamic Analysis.

**(6) **For structures located on sites other than Class F that have an SFRS with R_{d} equal to or greater than 1.5, the elastic base shear obtained from a Linear Dynamic Analysis may be multiplied by the following factor to obtain the design elastic base shear, V_{ed}:

**(7) **The design elastic base shear, V_{ed}, shall be multiplied by the importance factor, I_{E}, as determined in Article 4.1.8.5., and shall be divided by R_{d}R_{o}, as determined in Article 4.1.8.9., to obtain the design base shear, V_{d}.

**(8) **Except as required by Sentences (9) and (12), if the base shear, V_{d}, obtained in Sentence (7) is less than 80% of the lateral earthquake design force, V, of Article 4.1.8.11., V_{d} shall be taken as 0.8 V.

**(9) **For irregular structures requiring dynamic analysis in accordance with Article 4.1.8.7., V_{d}shall be taken as the larger of the V_{d} determined in Sentence (7) and 100% of V.

**(10) **Except as required by Sentence (11), the values of elastic *storey *shears,*storey *forces, member forces, and deflections obtained from the Linear Dynamic Analysis, including the effect of accidental torsion determined in Sentence (4), shall be multiplied by V_{d}/V_{e}to determine their design values, where V_{d} is the base shear.

**(11) **For the purpose of calculating deflections, it is permitted to use a value for V based on the value for T_{a} determined in Clause 4.1.8.11.(3)(d) to obtain V_{d}in Sentences (8) and (9).

**(12) ***buildings* with more than 4 *storeys*of continuous wood construction and having a timber SFRS of shear walls with wood-based panels, braced frames or moment-resisting frames as defined in Table 4.1.8.9., having a fundamental lateral period, T_{a}, as determined in Clause 4.1.8.11.(3)(d), shall have the base shear, V_{d}, taken as the larger of the base shear obtained in Sentence (7) and 100% of the lateral earthquake design force, V, as determined in Article 4.1.8.11.