4.1.8.12 — Dynamic Analysis Procedure

(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) For the purposes of this Article and Article 4.1.8.20., the following terms shall have the meaning stated herein: (a)“seismic isolation” is an alternative seismic design concept that consists of installing an isolation system with low horizontal stiffness, thereby substantially increasing the fundamental period of the structure, (b)“isolation system” is a collection of structural elements at the level of the isolation interface that includes all individual isolator units, all structural elements that transfer force between elements of the isolation system, all connections to other structural elements, and may also include a wind-restraint system, energy-dissipation devices, and a displacement restraint system, (c)“seismically isolated structure” includes the upper portion of the structure above the isolation system, the isolation system, and the portion of the structure below the isolation system, (d)“isolator unit” is a structural element of the isolation system that permits large lateral deformations under lateral earthquake design forces and is characterized by vertical-load-carrying capability combined with increased horizontal flexibility and high vertical stiffness, energy dissipation (hysteretic or viscous), self-centering capability, and lateral restraint (sufficient elastic stiffness) under non-seismic service lateral loads, (e)“isolation interface” is the boundary between the isolated upper portion of the structure above the isolation system and the lower portion of the structure below the isolation system, and (f)“wind-restraint system” is the collection of structural elements of the isolation system that provides restraint of the seismically isolated structure for wind loads and is permitted to be either an integral part of the isolator units or a separate device. (2) Every seismically isolated structure and every portion thereof shall be analyzed and designed in accordance with, (a) the loads and requirements prescribed in this Article and Article 4.1.8.20., (b) other applicable requirements of this Subsection, and (c) appropriate engineering principles and current engineering practice. (3) For the analysis and modeling of the seismically isolated structure, the following criteria shall apply: (a) three dimensional Non-linear Dynamic Analysis of the structure shall be performed in accordance with Article 4.1.8.12, (b) unless verified from rational analysis, the inherent equivalent viscous damping — excluding the hysteretic damping provided by the isolation system or supplemental energy dissipation devices — used in the analysis shall not be taken as more than 2.5% of the critical damping at the significant modes of vibration, (c) all individual isolator units shall be modeled with sufficient detail to account for their non-linear force-deformation characteristics, including effects of the relevant loads, and with consideration of variations in material properties over the design life of the structure, and (d) except for elements of the isolation system, other components of the seismically isolated structure shall be modeled using elastic material properties in accordance with Sentence 4.1.8.3. (8). (4) The ground motion histories used in Sentence (3) shall be, (a) appropriately selected and scaled following good engineering practice, (b) compatible with, (i) a response spectrum derived from the design spectral acceleration values, S(T), defined in Sentence 4.1.8.4. (9) for ground conditions of Site Classes A, B and C, and (ii) a 5% damped response spectrum based on a site-specific evaluation for ground conditions of Site Classes D, E and F, and (c) amplitude-scaled in an appropriate manner over the period range of 0.2 T1 to 1.5 T1, where T1 is the period of the isolated structure determined using the post-yield stiffness of the isolation system in the horizontal direction under consideration, or the period specified in Sentence 4.1.8.20. (1) if the post-yield stiffness of the isolation system is not well defined.

(1) For the purposes of this Article and Article 4.1.8.22., the following terms shall have the meaning stated herein: (a)“supplemental energy dissipation device” is a dedicated structural element of the supplemental energy dissipation system that dissipates energy due to relative motion of each of its ends or by alternative means, and includes all pins, bolts, gusset plates, brace extensions and other components required to connect it to the other elements of the structure; a device may be classified as either displacement-dependent or velocity-dependent, or a combination thereof, and may be configured to act in either a linear or non-linear manner, and (b)“supplemental energy dissipation system” is a collection of energy dissipation devices installed in a structure that supplement the energy dissipation of the SFRS. (2) Every structure with a supplemental energy dissipation system and every portion thereof shall be designed and constructed in accordance with, (a) the loads and requirements prescribed in this Article and Article 4.1.8.22., (b) other applicable requirements of this Subsection, and (c) appropriate engineering principles and current engineering practice. (3) Where supplemental energy dissipation devices are used across the isolation interface of a seismically isolated structure, displacements, velocities, and accelerations shall be determined in accordance with Article 4.1.8.20. (4) For the analysis and modeling of structures with supplemental energy dissipation devices, the following criteria shall apply: (a) a three-dimensional Non-linear Dynamic Analysis of the structure shall be performed in accordance with Article 4.1.8.12., (b) for SFRS with Rd > 1.0, the non-linear hysteretic behaviour of the SFRS shall be explicitly — with sufficient detail — accounted for in the modeling and analysis of the structure, (c) unless verified from rational analysis, the inherent equivalent viscous damping — excluding the damping provided by the supplemental energy dissipation devices — used in the analysis shall not be taken as more than 2.5% of the critical damping at the significant modes of vibration, (d) all supplemental energy dissipation devices shall be modeled with sufficient detail to account for their non-linear force deformation characteristics, including effects of the relevant loads, and with consideration of variations in their properties over the design life of the structure, and (e) except for the SFRS and elements of the supplemental energy dissipation system, other components of the structure shall be modeled using elastic material properties in accordance with Sentence 4.1.8.3. (8). (5) The ground motion histories used in Sentence (4) shall be, (a) appropriately selected and scaled following good engineering practice, (b) compatible with a 5% damped response spectrum derived from the design spectral acceleration values, S(T), defined in Sentence 4.1.8.4. (9), and (c) amplitude-scaled in an appropriate manner over the period range of 0.2 T1 to 1.5 T1, where T1 is the fundamental lateral period of the structure with the supplemental energy dissipation system.

(1) The building shall be designed to meet the requirements of this Subsection and of the design standards referenced in Section 4.3. (2) Structures shall be designed with a clearly defined load path, or paths, that will transfer the inertial forces generated in an earthquake to the supporting ground. (3) The structure shall have a clearly defined Seismic Force Resisting System(s) (SFRS), as defined in Article 4.1.8.2. (4) The SFRS shall be designed to resist 100% of the earthquake loads and their effects. (5) All structural framing elements not considered to be part of the SFRS must be investigated and shown to behave elastically or to have sufficient non-linear capacity to support their gravity loads while undergoing earthquake-induced deformations calculated from the deflections determined in Article 4.1.8.13. (6) Stiff elements that are not considered part of the SFRS, such as concrete, masonry, brick or pre-cast walls or panels, shall be, (a) separated from all structural elements of the building such that no interaction takes place as the building undergoes deflections due to earthquake effects as calculated in this Subsection, or (b) made part of the SFRS and satisfy the requirements of this Subsection. (7) Stiffness imparted to the structure from elements not part of the SFRS, other than those described in Sentence (6), shall not be used to resist earthquake deflections but shall be accounted for, (a) in calculating the period of the structure for determining forces if the added stiffness decreases the fundamental lateral period by more than 15%, (b) in determining the irregularity of the structure, except the additional stiffness shall not be used to make an irregular SFRS regular or to reduce the effects of torsion, and (c) in designing the SFRS if inclusion of the elements not part of the SFRS in the analysis has an adverse effect on the SFRS. (8) Structural modelling shall be representative of the magnitude and spatial distribution of the mass of the building and of the stiffness of all elements of the SFRS, including stiff elements that are not separated in accordance with Sentence 4.1.8.3. (6), and shall account for, (a) the effect of cracked sections in reinforced concrete and reinforced masonry elements, (b) the effect of the finite size of members and joints, (c) sway effects arising from the interaction of gravity loads with the displaced configuration of the structure, and (d) other effects that influence the lateral stiffness of the building.

(1) The peak ground acceleration (PGA), peak ground velocity (PGV) and the 5% damped spectral response acceleration values, Sa(T), for the reference ground conditions (Site Class C in Table 4.1.8.4.A.) for periods T of 0.2 s, 0.5 s, 1.0 s, 2.0 s, 5.0 s and 10.0 s, shall be determined in accordance with Subsection 1.1.2. and are based on a 2% probability of exceedance in 50 years. (2) Site classifications for ground shall conform to Table 4.1.8.4.A. and shall be determined using V̄_S30 or, where V̄_S30 is not known, using Sentence (3). (3) If average shear wave velocity, V̄_S30, is not known, Site Class shall be determined from energy-corrected Average Standard Penetration Resistance, N̄_60, or from soil average undrained shear strength, su, as noted in Table 4.1.8.4.A., N̄_60 and su being calculated based on rational analysis. (4) For the purpose of determining the values of F(T) to be used in the calculation of design spectral acceleration, S(T), in Sentence (9), and the values of F(PGA) and F(PGV), the value of PGAref to be used with Tables 4.1.8.4.B. to 4.1.8.4.I. shall be taken as, (a) 0.8 PGA, where the ratio Sa(0.2)/PGA < 2.0, and (b) 1 PGA, in all other cases. (5) The values of the site coefficient for design spectral acceleration at period T, F(T), and of similar coefficients F(PGA) and F(PGV) shall conform to Tables 4.1.8.4.B. to 4.1.8.4.I. using linear interpolation for intermediate values of PGAref. (6) Site-specific evaluation is required to determine F(T), F(PGA) and F(PGV) for Site Class F. (7) For all applications in Subsection 4.1.8., Fa = F(0.2) and Fv = F(1.0). (8) For structures with a fundamental period of vibration equal to or less than 0.5 s that are built on liquefiable soils, Site Class and the corresponding values of F(T) may be determined as described in Tables 4.1.8.4.A., 4.1.8.4.B., and 4.1.8.4.C. by assuming that the soils are not liquefiable. (9) The design spectral acceleration values of S(T) shall be determined as follows, using linear interpolation for intermediate values of T: S(T) =F(0.2)Sa(0.2) or F(0.5)Sa(0.5), whichever is larger, for T ≤ 0.2 s =F(0.5)Sa(0.5) for T = 0.5 s =F(1.0)Sa(1.0) for T = 1.0 s =F(2.0)Sa(2.0) for T = 2.0 s =F(5.0)Sa(5.0) for T = 5.0 s =F(10.0)Sa(10.0) for T ≥ 10.0 s

(1) The earthquake importance factor, IE, shall be determined according to Table 4.1.8.5.

(1) Analysis for design earthquake actions shall be carried out in accordance with the Dynamic Analysis Procedure described in Article 4.1.8.12., except that the Equivalent Static Force Procedure described in Article 4.1.8.11. may be used for structures that meet any of the following criteria: (a) in cases where IEFaSa(0.2) is less than 0.35, (b) regular structures that are less than 60 m in height and have a fundamental lateral period, Ta, less than 2 s in each of two orthogonal directions as defined in Article 4.1.8.8., or (c) structures with structural irregularity, of Type 1, 2, 3, 4, 5, 6 or 8 as defined in Table 4.1.8.6., that are less than 20 m in height and have a fundamental lateral period, Ta, less than 0.5 s in each of two orthogonal directions as defined in Article 4.1.8.8.

(1) Except as provided in Sentence 4.1.8.20. (7), the values of Rd and Ro and the corresponding system restrictions shall conform to Table 4.1.8.9. and the requirements of this Subsection. (2) When a particular value of Rd is required by this Article, the corresponding Ro shall be used. (3) For combinations of different types of SFRS acting in the same direction in the same storey, RdRo shall be taken as the lowest value of RdRo corresponding to these systems. (4) For vertical variations of RdRo, excluding rooftop structures not exceeding two storeys in height whose weight is less than the greater of 10% of W and 30% of Wi of the level below, the value of RdRo used in the design of any storey shall be less than or equal to the lowest value of RdRo used in the given direction for the storeys above, and the requirements of Sentence 4.1.8.15. (5) must be satisfied. (5) If it can be demonstrated through testing, research and analysis that the seismic performance of a structural system is at least equivalent to one of the types of SFRS mentioned in Table 4.1.8.9., then such a structural system will qualify for values of Rd and Ro corresponding to the equivalent type in that Table.