4.1.8.1. Analysis

(1)

Except as permitted in Sentence (2), the deflections and specified loading due to earthquake motions shall be determined according to the requirements of Articles 4.1.8.2. to 4.1.8.23.

(2)

Where I_E F_s S_a (0.2,X₄₅₀) and I_E F_s S_a (2.0,X₄₅₀) are less than 0.16 and 0.03 respectively, the deflections and specified loading due to earthquake motions are permitted to be determined in accordance with Sentences (3) to (15), where

(a)

I_E is the earthquake importance factor and has a value of 0.8, 1.0, 1.3 and 1.5 for buildings in the Low, Normal, High and Post-disaster Importance Categories respectively,

(b)

F_s is the site coefficient based on the average

or

, as defined in Article [[b-4.1.8.2.|4.1.8.2.]], for the top 30 m of *[[a-1.4.1.2.#soil|soil]]* below the footings, *[[a-1.4.1.2.#pile|pile]]* caps or mat *[[a-1.4.1.2.#foundation|foundations]]* and has a value of

(i)

1.0 for rock sites or when

₆₀ or

,

(ii)

1.6 when

or

, and

(iii)

2.8 for all other cases, and

(c)

is the 5%-damped spectral acceleration value at period T for site designation X₄₅₀, as defined in Article [[b-4.1.8.2.|4.1.8.2.]], determined in accordance with Subsection [[b-1.#^113hplca|1.1.3.]] and corresponding to a 2% probability of exceedance in 50 years.

(3)

The structure shall have a clearly defined

(a)

seismic force resisting system (SFRS) to resist the earthquake loads and their effects, and

(b)

load path (or paths) that will transfer the inertial forces generated in an earthquake to the supporting ground.

(4)

An unreinforced masonry SFRS shall not be permitted where

(a)

I_E is greater than 1.0, or

(b)

the height above grade is greater than or equal to 30 m.

(5)

The height above grade of an SFRS designed in accordance with CSA S136, “North American Specification for the Design of Cold-Formed Steel Structural Members (using the Appendix B provisions applicable to Canada),” shall be less than 15 m.

(6)

Earthquake forces shall be assumed to act horizontally and independently about any two orthogonal axes.

(7)

The specified lateral earthquake force, V_s, at the base of the structure in the direction under consideration shall be calculated as follows:

where,

= value of

determined by linear interpolation between the values of S_a (0.2,X₄₅₀), S_a (0.5,X₄₅₀) and S_a (1.0,X₄₅₀), = S_a (0.2,X₄₅₀) for T_s ≤ 0.2 s, and = S_a (1.0,X₄₅₀) for T_s ≥ 1.0 s, W = sum of W_i over the height of the *[[a-1.4.1.2.#building|building]]*, where W_i is defined in Article [[b-4.1.8.2.|4.1.8.2.]], and R_s = 1.5, except R_s = 1.0 for structures where the *[[a-1.4.1.2.#storey|storey]]* strength is less than that in the *[[a-1.4.1.2.#storey|storey]]* above and for an unreinforced masonry SFRS, where T_s = fundamental lateral period of vibration of the *[[a-1.4.1.2.#building|building]]*, as defined in Article [[b-4.1.8.2.|4.1.8.2.]], = 0.085(h_n) ¾ for steel moment frames, = 0.075(h_n) ¾ for concrete moment frames, = 0.1N for other moment frames, = 0.025h_n for braced frames, and = 0.05(h_n) ¾ for shear walls and other structures, where h_n = height, in m, above the base to level n, as defined in Article [[b-4.1.8.2.|4.1.8.2.]], and N = total number of *[[a-1.4.1.2.#storey|storeys]]* above exterior *[[a-1.4.1.2.#grade|grade]]* to level n, as defined in Article [[b-4.1.8.2.|4.1.8.2.]], except that, in cases where R_s = 1.5, V_s need not be greater than F_s S_a (0.5,X₄₅₀)I_E W/R_s.

(8)

The total lateral earthquake design force, V_s, shall be distributed over the height of the building in accordance with the following formula:

where, F_x = force applied through the centre of mass at level x, W_x,W_i = portion of W that is located at or is assigned to level x or i respectively, and h_x, h_i = height, in m, above the base to level x or i respectively, as defined in Article [[b-4.1.8.2.|4.1.8.2.]]

(9)

Accidental torsional effects applied concurrently with F_x shall be considered by applying torsional moments about the vertical axis at each level for each of the following cases considered separately:

(a)

+0.1D_nx F_x, and

(b)

–0.1D_nx F_x.

(10)

Deflections obtained from a linear analysis shall include the effects of torsion and be multiplied by R_s /I_E to get realistic values of expected deflections.

(11)

The deflections referred to in Sentence (10) shall be used to calculate the largest inter storey deflection, which shall not exceed

(a)

0.01h_s for post-disaster buildings,

(b)

0.02h_s for High Importance Category buildings, and

(c)

0.025h_s for all other buildings, where h_s is the interstorey height as defined in Article 4.1.8.2.

(12)

When earthquake forces are calculated using R_s = 1.5, the following elements in the SFRS shall have their design forces due to earthquake effects increased by 33%:

(a)

diaphragms and their chords, connections, struts and collectors,

(b)

tie downs in wood or drywall shear walls,

(c)

connections and anchor bolts in steel- and wood-braced frames,

(d)

connections in precast concrete, and

(e)

connections in steel moment frames.

(13)

Except as provided in Sentence (14), where cantilever parapet walls, other cantilever walls, exterior ornamentation and appendages, towers, chimneys or penthouses are connected to or form part of a building, they shall be designed, along with their connections, for a lateral force, V_sp, distributed according to the distribution of mass of the element and acting in the lateral direction that results in the most critical loading for design using the following equation:

where W_p = weight of a portion of a structure as defined in Article [[b-4.1.8.2.|4.1.8.2.]]

(14)

The value of V_sp shall be doubled for unreinforced masonry elements.

(15)

Structures designed in accordance with this Article need not comply with the seismic requirements stated in the applicable design standard referenced in Section 4.3.