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 IEFsSa(0.2,X450) and IEFsSa(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) IE 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) Fs is the site coefficient based on the average N60 or su , as defined in Article 4.1.8.2., for the top 30 m of soil below the footings, pile caps or mat foundations and has a value of (i) 1.0 for rock sites or when N60 > 5060 or su > 100 kPa, (ii) 1.6 when 15 ≤ N60 ≤ 50 or 50 kPa ≤ su ≤ 100 kPa, and (iii) 2.8 for all other cases, and (c) Sa (T, X450 ) is the 5%-damped spectral acceleration value at period T for site designation X 450, as defined in Article 4.1.8.2., determined in accordance with Subsection 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) IE 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, Vs, at the base of the structure in the direction under consideration shall be calculated as follows: Vs = Fs Sa (Ts , X450 )IE W⁄R s where, Sa (T, X450 ) = value of Sa (T, X450 ) determined by linear interpolation between the values of Sa(0.2,X450 ), Sa(0.5,X450) and Sa(1.0,X450), = Sa(0.2,X450) for Ts ≤ 0.2 s, and = Sa(1.0,X450) for Ts ≥ 1.0 s, W = sum of Wi over the height of the building, where Wi is defined in Article 4.1.8.2., and Rs = 1.5, except Rs = 1.0 for structures where the storey strength is less than that in the storey above and for an unreinforced masonry SFRS, where Ts = fundamental lateral period of vibration of the building, as defined in Article 4.1.8.2., = 0.085(hn)¾ for steel moment frames, = 0.075(hn)¾ for concrete moment frames, = 0.1N for other moment frames, = 0.025hn for braced frames, and = 0.05(hn)¾ for shear walls and other structures, where hn = height, in m, above the base to level n, as defined in Article 4.1.8.2., and N = total number of storeys above exterior grade to level n, as defined in Article 4.1.8.2., except that, in cases where Rs = 1.5, Vs need not be greater than FsSa(0.5,X450)IEW/Rs. (8) The total lateral earthquake design force, Vs, shall be distributed over the height of the building in accordance with the following formula: n Fx = Vs Wx hx / (∑ wi hi ) i=1 where, Fx = force applied through the centre of mass at level x, Wx,Wi = portion of W that is located at or is assigned to level x or i respectively, and hx, hi = height, in m, above the base to level x or i respectively, as defined in Article 4.1.8.2. (9) Accidental torsional effects applied concurrently with Fx shall be considered by applying torsional moments about the vertical axis at each level for each of the following cases considered separately: (a) +0.1DnxFx, and (b) –0.1DnxFx. (10) Deflections obtained from a linear analysis shall include the effects of torsion and be multiplied by Rs/IE to get realistic values of expected deflections. (11) The deflections referred to in Sentence (10) shall be used to calculate the largest interstorey deflection, which shall not exceed (a) 0.01hs for post-disaster buildings, (b) 0.02hs for High Importance Category buildings, and (c) 0.025hs for all other buildings, where hs is the interstorey height as defined in Article 4.1.8.2. (12) When earthquake forces are calculated using Rs = 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, Vsp, 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: Vsp = 0.9Sa (0.2, X450 )Fs IE Wp where Wp = weight of a portion of a structure as defined in Article 4.1.8.2. (14) The value of Vsp 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.