4.1.8. Earthquake Load and Effects (TBC)

4.1.8. Earthquake Load and Effects
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 4.1.8.22.
  2. Where IEFsSa(0.2) and IEFsSa(2.0) 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
    1. IE is the earthquake importance factor and has a value of 0.8, 1.0, 1.3 and 1.5 for buildings of Low, Normal, High and Post-Disaster importance respectively,
    2. Fs is the site coefficient based on the average 60 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
      1. 1.0 for rock sites or when N60 > 50 or su > 100 kPa,
      2. 1.6 when 15 ≤ N60 ≤ 50 or 50 kPa ≤ su ≤ 100 kPa, and
      3. 2.8 for all other cases, and
    3. Sa(T) is the 5% damped spectral response acceleration value for period T, determined in accordance with Subsection 1.1.3.
  3. The structure shall have a clearly defined
    1. Seismic Force Resisting System (SFRS) to resist the earthquake loads and their effects, and
    2. load path (or paths) that will transfer the inertial forces generated by the earthquake to the foundations and supporting ground.
  4. An unreinforced masonry SFRS shall not be permitted where
    1. IE is greater than 1.0, or
    2. the height above grade is greater than or equal to 30 m.
  5. The height above grade of 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 15m.
  6. Earthquake forces shall be assumed to act horizontally and independently about any two orthogonal axes.
  7. The minimum lateral earthquake design force, Vs, at the base of the structure in the direction under consideration shall be calculated as follows:

    where

    Sa(Ts) =valueofSa at Ts determined by linear interpolation between the value of Sa at 0.2 s, 0.5 s, and 1.0 s, and
    = Sa(0.2) for Ts ≤ 0.2 s,
    Wt = 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,
    = 0.1 N for other moment frames,
    = 0.025hn for braced frames, and
    = 0.05(hn)¾ for shear walls and other structures,
    where
    hn = height above the base, in m, as defined in Article 4.1.8.2., except that Vs shall not be less than FsSa(1.0)IEWt/Rs and, in cases where Rs =1.5, Vs need not be greater than FsSa(0.5)IEWt/Rs.
  8. The total lateral earthquake design force, Vs, shall be distributed over the height of the building in accordance with the following formula:

    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 of level x and level i as per 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:
    1. +0.1DnxFx, and
    2. -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
    1. 0.01hs for post-disaster buildings,
    2. 0.02hs for High Importance Category buildings, and
    3. 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%:
    1. diaphragms and their chords, connections, struts and collectors,
    2. tie downs in wood or drywall shear walls,
    3. connections and anchor bolts in steel- and wood-braced frames,
    4. connections in precast concrete, and
    5. 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:

    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.
4.1.8.2. Notation
  1. In this Subsection
    Ar = response amplification factor to account for type of attachment of mechanical/electrical equipment, as defined in Sentence 4.1.8.18.(1),
    Ax = amplification factor at level x to account for variation of response of mechanical/electrical equipment with elevation within the building, as defined in Sentence 4.1.8.18.(1),
    Bx = ratio at level x used to determine torsional sensitivity, as defined in Sentence 4.1.8.11.(10),
    B = maximum value of Bx, as defined in Sentence 4.1.8.11.(10),
    Cp = seismic coefficient for mechanical/electrical equipment, as defined in Sentence 4.1.8.18.(1),
    Dnx = plan dimension of the building at level x perpendicular to the direction of seismic loading being considered,
    ex = distance measured perpendicular to the direction of earthquake loading between centre of mass and centre of rigidity at the level being considered (see Note A-4.1.8.2.(1)),
    Fa = site coefficient for application in Subsection 4.1.8., as defined in Sentence 4.1.8.4.(7),
    F(PGA) = site coefficient for PGA, as defined in Sentence 4.1.8.4.(5),
    F(PGV) = site coefficient for PGV, as defined in Sentence 4.1.8.4.(5),
    Fs = site coefficient as defined in Sentence 4.1.8.1.(2) for application in Article 4.1.8.1.,
    F(T) = site coefficient for spectral acceleration, as defined in Sentence 4.1.8.4.(5),
    Ft = portion of V to be concentrated at the top of the structure, as defined in Sentence 4.1.8.11.(7),
    Fv = site coefficient for application in Subsection 4.1.8., as defined in Sentence 4.1.8.4.(7),
    Fx = lateral force applied to level x, as defined in Sentence 4.1.8.11.(7),
    hi, hn, hx = the height above the base (i = 0) to level i, n, or x respectively, where the base of the structure is the level at which horizontal earthquake motions are considered to be imparted to the structure,
    hs = interstorey height (hi - hi-1),
    IE = earthquake importance factor of the structure, as described in Sentence 4.1.8.5.(1),
    J = numerical reduction coefficient for base overturning moment, as defined in Sentence 4.1.8.11.(6),
    Jx = numerical reduction coefficient for overturning moment at level x, as defined in Sentence 4.1.8.11.(8),
    Level i = any level in the building, i = 1 for first level above the base,
    Level n = level that is uppermost in the main portion of the structure,
    Level x = level that is under design consideration,
    Mv = factor to account for higher mode effect on base shear, as defined in Sentence 4.1.8.11.(6),
    Mx = overturning moment at level x, as defined in Sentence 4.1.8.11.(8),
    N = total number of storeys above exterior grade to level n,
    N60     = Average Standard Penetration Resistance for the top 30 m, corrected to a rod energy efficiency of 60% of the theoretical maximum,
    PGA = Peak Ground Acceleration expressed as a ratio to gravitational acceleration, as defined in Sentence 4.1.8.4.(1),
    PGAref = reference PGA for determining F(T), F(PGA) and F(PGV), as defined in Sentence 4.1.8.4.(4),
    PGV = Peak Ground Velocity, in m/s, as defined in Sentence 4.1.8.4.(1),
    PI = plasticity index for clays,
    Rd = ductility-related force modification factor reflecting the capability of a structure to dissipate energy through reversed cyclic inelastic behaviour, as given in Article 4.1.8.9.,
    Ro = overstrength-related force modification factor accounting for the dependable portion of reserve strength in a structure designed according to these provisions, as defined in Article 4.1.8.9.,
    Rs = combined overstrength and ductility-related modification factor, as defined in Sentence 4.1.8.1.(7), for application in Article 4.1.8.1.,
    Sp = horizontal force factor for part or portion of a building and its anchorage, as given in Sentence 4.1.8.18.(1),
    S(T) = design spectral response acceleration, expressed as a ratio to gravitational acceleration, for a period of T, as defined in Sentence 4.1.8.4.(9),
    Sa(T) = 5% damped spectral response acceleration, expressed as a ratio to gravitational acceleration, for a period of T, as defined in Sentence 4.1.8.4.(1),
    SFRS = Seismic Force Resisting System(s) is that part of the structural system that has been considered in the design to provide the required resistance to the earthquake forces and effects defined in Subsection 4.1.8.,
    su = average undrained shear strength in the top 30 m of soil,
    T = periodin seconds,
    Ta = fundamental lateral period of vibration of the building or structure, in s, in the direction under consideration, as defined in Sentence 4.1.8.11.(3),
    Ts = fundamental lateral period of vibration of the building or structure, in s, in the direction under consideration, as defined in Sentence 4.1.8.1.(7),
    Tx = floor torque at level x, as defined in Sentence 4.1.8.11.(11),
    TDD = Total Design Displacement of any point in a seismically isolated structure, within or above the isolation system, obtained by calculating the mean + (IE × the standard deviation) of the peak horizontal displacements from all sets of ground motion histories analyzed, but not less than √IE × themean, where the peak horizontal displacement is based on the vector sum of the two orthogonal horizontal displacements considered for each time step,
    V = lateral earthquake design force at the base of the structure, as determined by Article 4.1.8.11.,
    Vd = lateral earthquake design force at the base of the structure, as determined by Article 4.1.8.12.,
    Ve = lateral earthquake elastic force at the base of the structure, as determined by Article 4.1.8.12.,
    Ved = lateral earthquake design elastic force at the base of the structure, as determined by Article 4.1.8.12.,
    Vp = lateral force on a part of the structure, as determined by Article 4.1.8.18.,
    Vs = lateral earthquake design force at the base of the structure, as determined by Sentence 4.1.8.1.(7), for application in Article 4.1.8.1.,
    Vs30     = average shear wave velocity in the top 30m of soil or rock,
    W = dead load, as defined in Article 4.1.4.1., except that the minimum partition load as defined in Sentence 4.1.4.1.(3) need not exceed 0.5 kPa, plus 25% of the design snow load specified in Subsection 4.1.6., plus 60% of the storage load for areas used for storage, except that storage garages need not be considered storage areas, and the full contents of any tanks (see Note A-4.1.8.2.(1)),
    Wi, Wx = portion of W that is located at or is assigned to level i or x respectively,
    Wp = weight of a part or portion of a structure, e.g., cladding, partitions and appendages,
    Wt = sum of Wi over the height of the building, for application in Sentence 4.1.8.1.(7),
    δave = average displacement of the structure at level x, as defined in Sentence 4.1.8.11.(10), and
    δmax = maximum displacement of the structure at level x, as defined in Sentence 4.1.8.11.(10).
4.1.8.3. General Requirements
  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. (See Note A-4.1.8.3.(4).)
  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 precast walls or panels, shall be
    1. 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
    2. made part of the SFRS and satisfy the requirements of this Subsection. (See Note A-4.1.8.3.(6).)
  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
    1. in calculating the period of the structure for determining forces if the added stiffness decreases the fundamental lateral period by more than 15%,
    2. 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 (see Note A-4.1.8.3.(7)(b) and (c)), and
    3. in designing the SFRS if inclusion of the elements not part of the SFRS in the analysis has an adverse effect on the SFRS (see Note A-4.1.8.3.(7)(b) and (c)).
  8. Structural modeling 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
    1. the effect of cracked sections in reinforced concrete and reinforced masonry elements,
    2. the effect of the finite size of members and joints,
    3. sway effects arising from the interaction of gravity loads with the displaced configuration of the structure, and
    4. other effects that influence the lateral stiffness of the building.
      (See Note A-4.1.8.3.(8).)
4.1.8.4. Site Properties
  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 1.1.3. and are based on a 2% probability of exceedance in 50 years.

    Table 4.1.8.4.-A
    Site Classification for Seismic Site Response
    Forming Part of Sentences 4.1.8.4.(1) to (3)

    Notes to Table 4.1.8.4.-A:
    (1) Site Classes A and B, hard rock and rock, are not to be used if there is more than 3 m of softer materials between the rock and the underside of footing or mat foundations. The appropriate Site Class for such cases is determined on the basis of the average properties of the total thickness of the softer materials (see Note A-4.1.8.4.(3) and Table 4.1.8.4.-A).
    (2) Where Vs30 has been measured in-situ, the F(T) values for Site Class A derived from Tables 4.1.8.4.-B to 4.1.8.4.-G are permitted to be multiplied by the factor 0.04 + (1500/Vs30 )½.
    (3) Other soils include:
    (a) liquefiable soils, quick and highly sensitive clays, collapsible weakly cemented soils, and other soils susceptible to failure or collapse under seismic loading,
    (b) peat and/or highly organic clays greater than 3 m in thickness,
    (c) highly plastic clays (PI > 75) more than 8 m thick, and
    (d) soft to medium stiff clays more than 30 m thick.

  2. Site classifications for ground shall conform to Table 4.1.8.4.-A and shall be determined using Vs30 , or where Vs30 is not known, using Sentence (3).
  3. If average shear wave velocity, Vs30, is not known, Site Class shall be determined from energy-corrected Average Standard Penetration Resistance, N60, or fromsoil average undrained shear strength, su, as noted in Table 4.1.8.4.-A, N60 and su being calculated based on rational analysis. (See Note A-4.1.8.4.(3) and Table 4.1.8.4.-A.)
  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 v

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