4.1.9.1. Analysis (1) The specified loading due to earthquake motion shall be determined by the analysis given in this Subsection. (2) In this Subsection  Ar

=

response amplification to account for type of attachment of mechanical/electrical equipment, as defined in Sentence 4.1.9.1.(19),


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 4.1.9.1.(19),


Cp

=

seismic coefficient for mechanical/electrical equipment, as defined in Sentence 4.1.9.1.(19),


D

=

the dimension of the building in a direction parallel to the applied forces,


Dnx

=

plan dimension of the building at level x perpendicular to the direction of seismic loading being considered,


Ds

=

dimension of wall or braced frame which constitutes the main lateral-load-resisting system in a direction parallel to the applied forces,


ex

=

distance measured perpendicular to the direction of seismic loading between centre of mass and centre of rigidity at the level being considered,


F

=

foundation factor as given in Sentence 4.1.9.1.(11),


Ft

=

Portion of V to be concentrated at the top of the structure as defined in Sentence 4.1.9.1.(13),


Fx

=

lateral force applied to level x,


hi,hn,hx

=

the height above the base (i = 0) to level i, n, or x, respectively, where the base of the structure is that level at which the horizontal earthquake motions are considered to be imparted to the structure,


hs

=

interstorey height (hi – hi–1),


I

=

seismic importance factor of the structure, as described in Sentence 4.1.9.1.(10),


J

=

numerical reduction coefficient for base overturning moment as defined in Sentence 4.1.9.1.(23),


Jx

=

numerical reduction coefficient for moment at level “x” as defined in Sentence 4.1.9.1.(24),


Level i

=

any level in the building, i = 1 for first level above the base,


Level n

=

that level which is uppermost in the main portion of the structure,


Level x

=

that level which is under design consideration,


N

=

total number of storeys above exterior grade to level n, (N is usually numerically equal to n)


R

=

force modification factor that reflects the capacity of a structure to dissipate energy through inelastic behaviour, as given in Sentence 4.1.9.1.(8),


S

=

seismic response factor, for unit value of zonal velocity ratio, as defined in Sentence 4.1.9.1.(6),


Sp

=

horizontal force factor for part or portion of a building and its anchorage, as given in Table 4.1.9.1.D. and Sentences 4.1.9.1.(17) and (19),


T

=

fundamental period of vibration of the building or structure in seconds in the direction under consideration,


Tx

=

floor torque at level x as defined in Sentence 4.1.9.1.(28),


U

=

factor representing level of protection based on experience, as specified in Sentence 4.1.9.1.(4),


v

=

zonal velocity ratio = the specified zonal horizontal ground velocity expressed as a ratio to 1 m/s,


V

=

minimum lateral seismic force at the base of the structure, to be used with a load factor aE = 1.0,


Ve

=

equivalent lateral force at the base of the structure representing elastic response, as specified in Sentence 4.1.9.1.(5),


Vp

=

lateral force on a part of the structure,


W

=

dead load plus 25% of the design snow load specified in Subsection 4.1.7. plus 60% of the storage load for areas used for storage and the full contents of any tanks,


Wi, Wx

=

that portion of W which is located at or is assigned to level i or x, respectively,


Wp

=

the weight of a part or portion of a structure, e.g. cladding, partitions and appendages,


Za

=

acceleration-related seismic zone,


Zv

=

Velocity-related seismic zone. (3) Earthquake forces shall be assumed to act in any horizontal direction, except that independent design about each of the principal axes shall be considered to provide adequate resistance in the structure for earthquake forces applied in any direction. (4) The minimum lateral seismic force, V, shall be calculated in accordance with the following formula:  where U = 0.6. (5) The equivalent lateral seismic force representing elastic response, Ve, shall be calculated in accordance with the following formula:  where v is the zonal velocity ratio determined in conformance with Subsection 2.5.1., except when Zv = 0 and Za > 0 the value of Zv shall be taken as 1 and v as 0.05 in all requirements of Subsection 4.1.9. Table 4.1.9.1.A. Seismic Response Factors Forming Part of Sentence 4.1.9.1.(6)  T

Za/Zv

S


 

> 1.0

4.2


 

1.0

3.0


≤ 0.25

< 1.0

2.1


> 0.25 but < 

> 1.0

4.2 – 8.4(T – 0.25)


0.50

1.0

3.0 – 3.6(T – 0.25)


 

< 1.0

2.1


≥ 0.50

All values

1.5/(T)1/2


Column 1

2

3 (6) The seismic response factor, S, shall conform to Table 4.1.9.1.A. (7) The fundamental period, T, in Sentence (6) shall be determined by (a) the formula 0.1 N for any moment-resisting frame, or by the formulae 0.085(hn)3/4 for a steel moment-resisting frame or 0.075(hn)3/4 for a concrete moment-resisting frame, where the moment-resisting system is a frame which resists 100% of the required lateral forces and 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, (b) the formula 0.09 hn/(Ds)1/2 for other structures, where hn and Ds are in metres, and Ds = length of wall or braced frame which constitutes the main lateral-force-resisting system in the direction parallel to the applied forces; if the main lateral-force-resisting system does not have a well-defined length, then D shall be used in lieu of Ds, or (c) other established methods of mechanics; the value of Ve used for design shall be not less than 0.80 of the value computed using the period calculated in Clause (a) or (b). (8) Except as provided for in Sentences 4.1.9.3.(1), (2) and (3), values of the force modification factor, R, shall conform to Table 4.1.9.1.B. (9) For the purpose of applying Table 4.1.9.1.B. (a) a ductile moment-resisting frame shall mean a frame that is designed to resist the specified seismic forces and that, in addition, has adequate ductility or energy-absorptive capacity, (b) for combinations of different types of lateral-load-resisting systems acting in the same direction, R shall be taken as the lowest value of R corresponding to these systems except as given in Clause (c), (c) if one of the lateral-force-resisting systems of the structure is designed to take 100% of the lateral force, R can be selected as appropriate for the system; the components of the structure not considered to be part of the lateral-force-resisting system must be capable of resisting their gravity loads under seismically induced deformations calculated in accordance with Sentence 4.1.9.2.(2), (d) if it can be demonstrated through research or experience that the seismic performance of a structural system is at least equivalent to one of Cases 1-8, 10-14, 16-18 or 20-21 in Table 4.1.9.1.B., then such a structural system will qualify for a value of R corresponding to the equivalent case in that Table. Table 4.1.9.1.B. Force Modification Factors Forming Part of Sentence 4.1.9.1.(8)  Case

Type of Lateral Load Resisting System

R


 

Steel Structures Designed and Detailed According to CAN/CSA-S16.1-M

 


1

ductile moment-resisting frame

4.0


2

ductile eccentrically braced frame

4.0


3

ductile steel plate shear wall

4.0


4

ductile braced frame

4.0


5

moment-resisting frame with nominal ductility

3.0


6

nominally ductile steel plate shear wall 

3.0


7

braced frame with nominal ductility

2.0


8

ordinary steel plate shear wall 

2.0


9

other lateral-force-resisting systems not defined in Cases 1 to 8

1.5


 

Reinforced Concrete Structures Designed and Detailed According to CAN/CSA-A23.3-M

 


10

ductile moment-resisting frame

4.0


11

ductile coupled wall 

4.0


12

other ductile wall systems

3.5


13

moment-resisting frame with nominal ductility

2.0


14

wall with nominal ductility

2.0


15

other lateral-force-resisting systems not defined in Cases 10 to 14

1.5


 

Timber Structures Designed and Detailed According to CSA-O86.1

 


16

nailed shear panel with plywood, waferboard or OSB

3.0


17

concentrically braced heavy timber frame with ductile connections

2.0


18

moment-resisting wood frame with ductile connections

2.0


19

other systems not included in Cases 16 to 18

1.5


 

Masonry Structures Designed and Detailed According to CSA-S304.1

 


20

reinforced masonry wall with nominal ductility

2.0


21

reinforced masonry

1.5


22

unreinforced masonry

1.0


23

Other Lateral-force-resisting Systems not Defined in Cases 1 to 22

1.0


Column 1

2

3 (10) The seismic importance factor, I, shall equal 1.5 for post-disaster buildings, 1.3 for schools and 1.0 for all other buildings. (11) The foundation factor, F, shall conform to Table 4.1.9.1.C., except that the product F.S need not exceed 3.0 where Za does not exceed Zv and need not exceed 4.2 where Za is greater than Zv. Table 4.1.9.1.C. Foundation Factors Forming Part of Sentence 4.1.9.1.(11)  Categories

Type and Depth of Rock and Soil Measured from the Foundation or Pile Cap Level

F


1

Rock, dense and very dense coarse-grained soils, very stiff and hard fine-grained soils; compact coarse-grained soils and firm and stiff fine-grained soils from 0 to 15 m deep

1.0


2

Compact coarse-grained soils, firm and stiff fine-grained soils with a depth greater than 15 m; very loose and loose coarse-grained soils and very soft and soft fine-grained soils from 0 to 15 m deep

1.3


3

Very loose and loose coarse-grained soils, with depth greater than 15 m

1.5


4

Very soft and soft fine-grained soils with depth greater than 15 m

2.0


Column 1

2

3 (12) The weight, W, of the building shall be calculated in accordance with the following formula: (13) The total lateral seismic force, V, shall be distributed as follows: (a) a portion, Ft, shall be assumed to be concentrated at the top of the building and equal to 0.07 TV, except that Ft, need not exceed 0.25 V and may be considered as zero where T 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  (b) by dynamic analysis, with the seismic effects scaled such that the base shear from the dynamic analysis equals V as given in Sentence 4.1.9.1.(4). (14) The total shear in any horizontal plane shall be distributed to the various elements of the lateral-force-resisting system in proportion to their rigidities according to rational analysis, with due regard to the capacities and stiffnesses of the nonstructural elements and to the effects of torsion as required by Sentence 4.1.9.1.(28). (15) Except as provided for in Sentence (16), parts of buildings as described in Tables 4.1.9.1.D. and 4.1.9.1.E. and their anchorage shall be designed to accommodate the deflections defined in Article 4.1.9.2., and for a lateral force, Vp, equal to v.I.Sp.Wp, distributed according to the distribution of mass of the element under consideration, where v is determined in conformance with Subsection 2.5.1., and I is the same importance factor as used for the building. (16) For non post-disaster buildings in zones where Za and Zv are equal to or less than 1.0 and F is equal to or less than 1.3, the requirements of Sentence (15) shall not apply to Table 4.1.9.1.E. or to cases 7, 8, and 9 of Table 4.1.9.1.D. (17) Except as provided for in Sentence (21), the values of Sp in Sentences (15) and (16) for architectural components shall conform to Table 4.1.9.1.D. (18) All fasteners and anchors in a ductile connection, such as bolts, inserts, welds, or dowels, shall be capable of developing 3 times the yield load of the body of the connection. (19) The values of Sp in Sentences (15) and (16) for mechanical/electrical components shall be equal to: Sp = Cp•Ar•Ax where  Cp

=

seismic coefficient for components of mechanical and electrical equipment as given Table 4.1.9.1.E.,


Ar

=

1.0 for components that are both rigid and rigidly connected and for non-brittle pipes and ducts,


 

=

1.5 for components located on the ground that are flexible or flexibly connected except for non-brittle pipes and ducts,


 

=

3.0 for all other cases,


Ax

=

1.0 + (hx/hn). Table 4.1.9.1.D. Values of Sp for Architectural Parts or Portions of Buildings Forming Part of Sentence 4.1.9.1.(15)  Category

Architectural Part or Portion of Building

Direction    of Force

Value of Sp


1

All exterior and interior walls except those of Categories 2 and 3

Normal to   flat surface

1.5


2

Cantilever parapet and other cantilever walls except retaining walls

Normal to    flat surface

6.5


3

Exterior and interior ornamentations and appendages

Any direction

6.5


4

Connections/attachments for Categories 1, 2 and 3

 

 


 

The body of ductile connections/ attachments

Any direction

2.5


 

All fasteners and anchors in the ductile connection, such as bolts, inserts, welds or dowels

Any direction

(1)


 

Non-ductile connections/ attachments

Any direction

15.0


5

Floors and roofs acting as diaphragms(2) 

Any direction

0.7


6

Towers, chimneys, smokestacks and penthouses when connected to or forming part of a building(2) 

Any direction

4.5


7

Horizontally cantilevered floors, balconies, beams, etc. 

Vertical

4.5


8

Suspended ceilings, light fixtures and other attachments to ceilings with independent vertical support

Any direction

2.0


9

Masonry veneer connections

Normal to    flat surface

5.0


Col. 1

2

3

4 Notes to Table 4.1.9.1.D.: (1) See Sentence 4.1.9.1.(18). (2) See Sentence 4.1.9.1.(21). (20) For the purpose of applying Sentence (19) (a) components that are both rigid and rigidly connected are defined as those having a fundamental period for the component and connection less than or equal to 0.06 s, and (b) flexible components or connections are defined as those having a fundamental period greater than 0.06 s. Table 4.1.9.1.E. Values of Cp for Mechanical/Electrical Parts or Portions of Buildings Forming Part of Sentence 4.1.9.1.(15)  Category

Mechanical/Electrical Part or Portion of Building

Direction of Force

Value of Cp


1

Machinery, fixtures, equipment, ducts, tanks and pipes (including contents) except as noted elsewhere in this table(1)

Any direction

1.0


2

Machinery, fixtures, equipment, ducts, tanks and pipes (including contents) containing toxic or explosive materials, materials having a flash point below 38°C or fire fighting fluids. 

Any direction

1.5


3

Flat bottom tanks (including contents) attached directly to a floor at or below grade within a building.

Any direction

0.7


4

Flat bottom tanks (including contents) attached directly to a floor at or below grade within a building containing toxic or explosive materials having a flash point below 38°C or fire fighting fluids.

Any direction

1.0


Column 1

2

3

4 (21) Floors and roofs acting as diaphragms shall be designed for a minimum force corresponding to a value of Sp equal to 0.7 applied to loads tributary from that storey, unless a greater force Fx is assigned to the level under consideration as in Sentences (13) and (14). (22) When the mass of a tank plus contents is greater than 10% of the mass of the supporting floor, the lateral forces shall be determined by rational analysis. (23) The overturning moment, M, at the base of the structure shall be multiplied by a reduction coefficient, J, where (a) J = 1 where T is less than 0.5, (b) J = (1.1 – 0.2T) where T is not less than 0.5, but not more than 1.5, and (c) J = 0.8 where T is greater than 1.5. (24) The overturning moment Mx at any level x shall be (a) multiplied by Jx where  (b) distributed as required in Sentences (25), (26) and (27). (25) The incremental changes in the design overturning moments, in the storey under consideration, shall be distributed to the various resisting elements in the same proportion as the distribution of shears in the resisting system. (26) Where other vertical members are provided which are capable of partially resisting the overturning moments, a redistribution may be made to these members if framing members of sufficient strength and stiffness to transmit the required loads are provided. (27) Where a vertical-resisting element is discontinuous, the overturning moment carried by the lowest storey of that element shall be carried down as loads to the foundation. (28) Torsional moments about a vertical axis of the building shall be calculated as (a) for an analysis carried out in accordance with Clause 4.1.9.1.(13)(a), the torsional moments applied at each level throughout the building shall be derived for each of the following load cases considered separately (i) Tx = Fx(1.5ex + 0.1 Dnx) (ii) Tx = Fx(1.5ex – 0.1 Dnx) (iii) Tx = Fx(0.5ex + 0.1 Dnx) (iv) Tx = Fx(0.5ex – 0.1 Dnx) where Fx is the lateral floor force at each level as given by Clause 4.1.9.1.(13)(a) and the term 0.1 Dnx·Fx represents the accidental torsional moment applied at each level and where each element in the building is designed for the most severe effect of the above load cases, or (b) the effects of accidental torsional moments applied at each level throughout the building shall be derived for each of the following load cases considered separately and shall be added to the effects of a three dimensional dynamic analysis (i) Tx = + 0.1 Dnx·Fx (ii) Tx = – 0.1 Dnx·Fx and where each element in the building is designed for the most severe effect of the above load cases and Fx is the lateral floor force at each level as given by Clause 4.1.9.1.(13)(a). (29) The building design shall take full account of the possible effects of setbacks.