(1) The static loading due to earthquake motion shall be determined according to the procedures given in this Article. (2) Except as provided in Sentence (12), the minimum lateral earthquake force, V, shall be calculated using the following formula:
V = S (Ta) MvIEW/ (RdRo)
except,
(a) for walls, coupled walls and wall-frame systems, V shall not be less than,
[[FORCE_FORMULA]] S (4.0) Mv IEW/ (RdRo) (b) for moment-resisting frames, braced frames and other systems, V shall not be less than,
[[FORCE_FORMULA]] S (2.0) Mv IEW/ (RdRo) (c) for buildings located on a site other than Class F and having an SFRS with an Rd equal to or greater than 1.5, V need not be greater than the larger of,
[[FORCE_FORMULA]] (2/3) · S(0.2) · I_E · W / (R_d R_o)
and
[[FORCE_FORMULA]] S (0.5) IEW/ (RdRo)
(3) Except as provided in Sentence (4), the fundamental lateral period, Ta, in the direction under consideration in Sentence (2) shall be determined as,
(a) for moment-resisting frames that resist 100% of the required lateral forces and where the frame is not enclosed by or adjoined by more rigid elements that would tend to prevent the frame from resisting lateral forces, and where hn is in metres,
(i) 0.085 (hn)3/4 for steel moment frames,
(ii) 0.075 (hn)3/4 for concrete moment frames, or
(iii) 0.1 N for other moment frames,
(b) 0.025 hn for braced frames where hn is in metres,
(c) 0.05 (hn)3/4 for shear wall and other structures where hn is in metres, or
(d) other established methods of mechanics using a structural model that complies with the requirements of Sentence 4.1.8.3. (8), except that,
(i) for moment-resisting frames, Ta shall not be taken greater than 1.5 times that determined in Clause (a),
(ii) for braced frames, Ta shall not be taken greater than 2.0 times that determined in Clause (b),
(iii) for shear wall structures, Ta shall not be taken greater than 2.0 times that determined in Clause (c),
(iv) for other structures, Ta shall not be taken greater than that determined in Clause (c), and
(v) for the purpose of calculating the deflections, the period without the upper limit specified in Subclauses (d)(i) to (iv) may be used, except that, for walls, coupled walls and wall-frame systems, Ta shall not exceed 4.0 s, and for moment-resisting frames, braced frames, and other systems, Ta shall not exceed 2.0 s. (4) For single-storey buildings with steel deck or wood roof diaphragms, the fundamental lateral period, Ta, in the direction under consideration is permitted to be taken as,
(a) 0.05 (hn)3/4 + 0.004 L for shear walls,
(b) 0.035 hn + 0.004 L for steel moment frames and steel braced frames, or
(c) the value obtained from methods of mechanics using a structural model that complies with the requirements of Sentence 4.1.8.3. (8), except that Ta shall not be greater than 1.5 times the value determined in Clause (a) or (b), as applicable,
where L is the shortest length of the diaphragm, in m, between adjacent vertical elements of the SFRS in the direction perpendicular to the direction under consideration. (5) The weight, W, of the building shall be calculated using the formula,
[[FORCE_FORMULA]] W = Σ_{i=1}^{n} W_i
(6) The higher mode factor, Mv, and its associated base overturning moment reduction factor, J, shall conform to Tables 4.1.8.11.A. to 4.1.8.11.E. (7) The total lateral seismic force, V, shall be distributed such that a portion, Ft, shall be assumed to be concentrated at the top of the building, where Ft, is equal to 0.07 TaV but need not exceed 0.25 V and may be considered as zero, where the fundamental lateral period, Ta, does not exceed 0.7 s; the remainder, V - Ft, shall be distributed along the height of the building, including the top level, in accordance with the formula,
F_x = (V − F_t) · W_x · h_x / (Σ_{i=1}^{n} W_i h_i)
(8) The structure shall be designed to resist overturning effects caused by the earthquake forces determined in Sentence (7) and the overturning moment at level x, Mx, shall be determined using the formula,
M_x = J_x · Σ_{i=x}^{n} F_i (h_i − h_x)
where,
Jx =1.0 for hx ≥ 0.6hn, and
Jx =J + (1- J)(hx / 0.6hn) for hx,< 0.6hn
where,
J =base overturning moment reduction factor conforming to Table 4.1.8.11. (9) Torsional effects that are concurrent with the effects of the forces mentioned in Sentence (7) and are caused by the simultaneous actions of the following torsional moments shall be considered in the design of the structure according to Sentence (11):
(a) torsional moments introduced by eccentricity between the centres of mass and resistance and their dynamic amplification, and
(b) torsional moments due to accidental eccentricities. (10) Torsional sensitivity shall be determined by calculating the ratio Bx for each level x according to the following equation for each orthogonal direction determined independently:
[[FORCE_FORMULA]] Bx = δmax / δave
where,
B =maximum of all values of Bx in both orthogonal directions, except that the Bx for one-storey penthouses with a weight less than 10% of the level below need not be considered,
δmax =maximum storey displacement at the extreme points of the structure, at level x in the direction of the earthquake induced by the equivalent static forces acting at distances ± 0.10 Dnx from the centres of mass at each floor, and
δave =average of the displacements at the extreme points of the structure at level x produced by the above-mentioned forces. (11) Torsional effects shall be accounted for as follows:
(a) for a building with B ≤1.7 or where IEFaSa(0.2) is less than 0.35, by applying torsional moments about a vertical axis at each level throughout the building, derived for each of the following load cases considered separately,
(i) Tx = Fx(ex + 0.10 Dnx), and
(ii) Tx = Fx(ex – 0.10 Dnx)
where Fx is the lateral force at each level determined according to Sentence (6) and where each element of the building is designed for the most severe effect of the above load cases, or
(b) for a building with B >1.7, in cases where IEFaSa(0.2) is equal to or greater than 0.35, by a Dynamic Analysis Procedure as specified in Article 4.1.8.12. (12) Where the fundamental lateral period, Ta, is determined in accordance with Clause (3)(d) and the building is constructed with more than 4 storeys of continuous wood construction and has a timber SFRS consisting of shear walls with wood-based panels, braced frames or moment-resisting frames as defined in Table 4.1.8.9., the lateral earthquake force, V, as determined in accordance with Sentence (2) shall be multiplied by 1.2 but need not exceed the value determined by using Clause (2)(c).
(1) Except as provided in Articles 4.1.8.19. and 4.1.8.21., 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) Non-linear 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 Dnx)Fx at each level x, where Fx is either determined from the elastic dynamic analysis or determined from Sentence 4.1.8.11. (7) multiplied by RdRo/IE, shall be combined with the effects determined by dynamic analysis, or
(b) if B, as defined in Sentence 4.1.8.11. (10), 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 Dnx and + 0.05 Dnx. (5) Except as provided in Sentence (6), the design elastic base shear, Ved, is equal to the elastic base shear, Ve, obtained from a Linear Dynamic Analysis. (6) For structures located on sites other than Class F that have an SFRS with Rd equal to or greater than 1.5, the elastic base shear obtained from a Linear Dynamic Analysis may be multiplied by the larger of the following factors to obtain the design elastic base shear, Ved:
[[FORCE_FORMULA]] 2S(0.2)/3S(Ta) ≤ 1.0
and
[[FORCE_FORMULA]] S(0.5) / S(Ta) ≤ 1.0
(7) The design elastic base shear, Ved, shall be multiplied by the importance factor, IE, as determined in Article 4.1.8.5., and shall be divided by RdRo, as determined in Article 4.1.8.9., to obtain the design base shear, Vd. (8) Except as required by Sentence (9) or (12), if the base shear, Vd, obtained in Sentence (7) is less than 80% of the lateral earthquake design force, V, of Article 4.1.8.11., Vd shall be taken as 0.8 V. (9) For irregular structures requiring dynamic analysis in accordance with Article 4.1.8.7., Vd shall be taken as the larger of the Vd 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 Vd/Ve to determine their design values, where Vd 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 Ta determined in Clause 4.1.8.11. (3)(d) to obtain Vd in Sentences (8) and (9). (12) For buildings constructed with more than 4 storeys of continuous wood construction, having a timber SFRS consisting of shear walls with wood-based panels, braced frames or moment-resisting frames as defined in Table 4.1.8.9., and whose fundamental lateral period, Ta, is determined in accordance with Clause 4.1.8.11. (3)(d), the design base shear, Vd, shall be taken as the larger value of Vd determined in accordance with Sentence (7) and 100% of V.