Every seismically isolated structure and every portion thereof
shall be designed and constructed in accordance with the requirements
of this section and the applicable requirements of this
standard.
The analysis of
seismically isolated structures, including the substructure, isolators,
and superstructure, shall consider variations in seismic isolator
material properties over the projected life of the structure,
including changes due to aging, contamination, environmental
exposure, loading rate, scragging, and temperature.
DISPLACEMENT:
Design Displacement: The design earthquake lateral displacement, excluding additional displacement due to actual and accidental torsion, required for design of the isolation system.
Total Design Displacement: The design earthquake lateral displacement, including additional displacement due to actual and accidental torsion, required for design of the isolation system or an element thereof.
Total Maximum Displacement: The maximum considered earthquake lateral displacement, including additional displacement due to actual and accidental torsion, required for verification of the stability of the isolation system or elements thereof, design of structure separations, and vertical load testing of isolator unit prototypes.
DISPLACEMENT RESTRAINT SYSTEM: A collection of structural elements that limits lateral displacement of seismically isolated structures due to the maximum considered earthquake.
EFFECTIVE DAMPING: The value of equivalent viscous damping corresponding to energy dissipated during cyclic response of the isolation system.
EFFECTIVE STIFFNESS: The value of the lateral force in the isolation system, or an element thereof, divided by the corresponding lateral displacement.
ISOLATION INTERFACE: The boundary between the upper portion of the structure, which is isolated, and the lower portion of the structure, which moves rigidly with the ground.
ISOLATION SYSTEM: The collection of structural elements that includes all individual isolator units, all structural elements that transfer force between elements of the isolation system, and all connections to other structural elements. The isolation system also includes the wind-restraint system, energy-dissipation devices, and/or the displacement restraint system if such systems and devices are used to meet the design requirements of this chapter.
ISOLATOR UNIT: A horizontally flexible and vertically stiff structural element of the isolation system that permits large lateral deformations under design seismic load. An isolator unit is permitted to be used either as part of, or in addition to, the weight-supporting system of the structure.
MAXIMUM DISPLACEMENT: The maximum considered earthquake lateral displacement, excluding additional displacement due to actual and accidental torsion.
SCRAGGING: Cyclic loading or working of rubber products, including elastomeric isolators, to effect a reduction in stiffness properties, a portion of which will be recovered over time.
WIND-RESTRAINT SYSTEM: The collection of structural elements that provides restraint of the seismically isolated structure for wind loads. The wind-restraint system is permitted to be either an integral part of isolator units or a separate device.
Design Displacement: The design earthquake lateral displacement, excluding additional displacement due to actual and accidental torsion, required for design of the isolation system.
Total Design Displacement: The design earthquake lateral displacement, including additional displacement due to actual and accidental torsion, required for design of the isolation system or an element thereof.
Total Maximum Displacement: The maximum considered earthquake lateral displacement, including additional displacement due to actual and accidental torsion, required for verification of the stability of the isolation system or elements thereof, design of structure separations, and vertical load testing of isolator unit prototypes.
DISPLACEMENT RESTRAINT SYSTEM: A collection of structural elements that limits lateral displacement of seismically isolated structures due to the maximum considered earthquake.
EFFECTIVE DAMPING: The value of equivalent viscous damping corresponding to energy dissipated during cyclic response of the isolation system.
EFFECTIVE STIFFNESS: The value of the lateral force in the isolation system, or an element thereof, divided by the corresponding lateral displacement.
ISOLATION INTERFACE: The boundary between the upper portion of the structure, which is isolated, and the lower portion of the structure, which moves rigidly with the ground.
ISOLATION SYSTEM: The collection of structural elements that includes all individual isolator units, all structural elements that transfer force between elements of the isolation system, and all connections to other structural elements. The isolation system also includes the wind-restraint system, energy-dissipation devices, and/or the displacement restraint system if such systems and devices are used to meet the design requirements of this chapter.
ISOLATOR UNIT: A horizontally flexible and vertically stiff structural element of the isolation system that permits large lateral deformations under design seismic load. An isolator unit is permitted to be used either as part of, or in addition to, the weight-supporting system of the structure.
MAXIMUM DISPLACEMENT: The maximum considered earthquake lateral displacement, excluding additional displacement due to actual and accidental torsion.
SCRAGGING: Cyclic loading or working of rubber products, including elastomeric isolators, to effect a reduction in stiffness properties, a portion of which will be recovered over time.
WIND-RESTRAINT SYSTEM: The collection of structural elements that provides restraint of the seismically isolated structure for wind loads. The wind-restraint system is permitted to be either an integral part of isolator units or a separate device.
B_{D} | = | numerical coefficient as set forth in Table 17.5-1 for effective damping equal to β_{D} |
B_{M} | = | numerical coefficient as set forth in Table 17.5-1 for effective damping equal to β_{M} |
b | = | shortest plan dimension of the structure, in ft (mm) measured perpendicular to d |
D_{D} |
= |
design displacement, in in. (mm), at the center of rigidity of the isolation system in the direction under consideration, as prescribed by Eq. 17.5-1 |
D'_{D} |
= |
design displacement, in in. (mm), at the center of rigidity of the isolation system in the direction under rigidity of the isolation system in the direction under consideration, as prescribed by Eq. 17.6-1 |
D_{M} | = | maximum displacement, in in. (mm), at the center of rigidity of the isolation system in the direction under consideration, as prescribed by Eq. 17.5- 3 |
D'_{M} | = | maximum displacement, in in. (mm), at the center of rigidity of the isolation system in the direction under consideration, as prescribed by Eq. 17.6- 2 |
D_{TD} | = | total design displacement, in in. (mm), of an element of the isolation system including both translational displacement at the center of rigidity and the component of torsional displacement in the direction under consideration, as prescribed by Eq. 17.5-5 |
D_{TM} | = | total maximum displacement, in in. (mm), of an element of the isolation system, including both translational displacement at the center of rigidity and the component of torsional displacement in the direction under consideration, as prescribed by Eq. 17.5-6 |
d | = | longest plan dimension of the structure, in ft (mm) |
E_{loop} | = | energy dissipated in kips-in. (kN-mm), in an isolator unit during a full cycle of reversible load over a test displacement range from Δ^{+} to Δ^{-}, as measured by the area enclosed by the loop of the force-deflection curve |
e | = | actual eccentricity, in ft (mm), measured in plan between the center of mass of the structure above the isolation interface and the center of rigidity of the isolation system, plus accidental eccentricity, in ft. (mm), taken as 5% of the maximum building dimension perpendicular to the direction of force under consideration |
F^{-} | = | minimum negative force in an isolator unit during a single cycle of prototype testing at a displacement amplitude of Δ^{-} |
F^{+} | = | maximum positive force in kips (kN) in an isolator unit during a single cycle of prototype testing at a displacement amplitude of Δ^{+} |
F_{x} | = | total force distributed over the height of the structure above the isolation interface as prescribed by Eq. 17.5-9 |
k_{Dmax} | = | maximum effective stiffness, in kips/in. (kN/mm), of the isolation system at the design displacement in the horizontal direction under consideration, as prescribed by Eq. 17.8-3 |
k_{Dmin} | = | minimum effective stiffness, in kips/in. (kN/mm), of the isolation system at the design displacement in the horizontal direction under consideration, as prescribed by Eq. 17. 8-4 |
k_{Mmax} | = | maximum effective stiffness, in kips/in. (kN/mm), of the isolation system at the maximum displacement in the horizontal direction under consideration,as prescribed by Eq. 17.8-5 |
k_{Mmin} | = | minimum effective stiffness, in kips/in. (kN/mm), of the isolation system at the maximum displacement in the horizontal direction under consideration, as prescribed by Eq. 17.8-6 |
k_{eff} | = | effective stiffness of an isolator unit, as prescribed by Eq. 17.8-1 |
L | = | effect of live load in Chapter 17 |
T_{D} | = | effective period, in s, of the seismically isolated structure at the design displacement in the direction under consideration, as prescribed by Eq.17.5- 2 |
T_{M} | = | effective period, in s, of the seismically isolated structure at the maximum displacement in the direction under consideration, as prescribed by Eq. 17.5- 4 |
V_{b} | = | total lateral seismic design force or shear on elements of the isolation system or elements below isolation system, as prescribed by Eq. 17.5-7 |
V_{s} | = | total lateral seismic design force or shear on elements above the isolation system, as prescribed by Eq. 17.5-8 |
y | = | distance, in ft (mm), between the center of rigidity of the isolation system rigidity and the element of interest measured perpendicular to the direction of seismic loading under consideration |
β_{D} | = | effective damping of the isolation system at the design displacement, as prescribed by Eq.17.8-7 |
β_{M} | = | effective damping of the isolation system at the maximum displacement, as prescribed by Eq.17.8-8 |
β_{eff} | = | effective damping of the isolation system, as prescribed by Eq. 17.8-2 |
Δ^{+} | = | maximum positive displacement of an isolator unit during each cycle of prototype testing |
Δ^{-} | = | minimum negative displacement of an isolator unit during each cycle of prototype testing |
ΣE_{D} | = | total energy dissipated, in kips-in. (kN-mm), in the isolation system during a full cycle of response at the design displacement, D_{D} |
ΣE_{M} | = | total energy dissipated, in kips-in. (kN-mm), in the isolation system during a full cycle of response at the maximum displacement, D_{M} |
= | sum, for all isolator units, of the maximum absolute value of force, in kips (kN), at a positive displacement equal to D_{D} | |
= | sum, for all isolator units, of the minimum absolute value of force, in kips (kN), at a positive displacement equal to D_{D} | |
= | sum, for all isolator units, of the maximum absolute value of force, in kips (kN), at a negative displacement equal to D_{D} | |
= | sum, for all isolator units, of the minimum absolute value of force, in kips (kN), at a negative displacement equal to D_{D} | |
= | sum, for all isolator units, of the maximum absolute value of force, in kips (kN), at a positive displacement equal to D_{M} | |
= | sum, for all isolator units, of the minimum absolute value of force, in kips (kN), at a positive displacement equal to D_{M} | |
= | sum, for all isolator units, of the maximum absolute value of force, in kips (kN), at a negative displacement equal to D_{M} | |
= | sum, for all isolator units, of the minimum absolute value of force, in kips (kN), at a negative displacement equal to D_{M} |
All portions of the structure,
including the structure above the isolation system, shall be
assigned a risk category in accordance with Table 1.5-1. The
importance factor, I_{e}, shall be taken as 1.0 for a seismically
isolated structure, regardless of its risk category assignment.
The MCE_{R} spectral response acceleration parameters
S_{MS} and S_{M1} shall be determined in accordance with Section 11.4.3.
Each structure shall be designated as
having a structural irregularity based on the structural configuration
above the isolation system.
In addition to the requirements
for vertical and lateral loads induced by wind and earthquake,
the isolation system shall provide for other environmental
conditions, including aging effects, creep, fatigue, operating temperature,
and exposure to moisture or damaging substances.
Isolated structures shall resist design
wind loads at all levels above the isolation interface. At the isolation
interface, a wind-restraint system shall be provided to limit
lateral displacement in the isolation system to a value equal to
that required between floors of the structure above the isolation
interface in accordance with Section 17.5.6.
Fire resistance for the isolation
system shall meet that required for the columns, walls, or other
such gravity-bearing elements in the same region of the
structure.
The isolation system shall
be configured to produce a restoring force such that the
lateral force at the total design displacement is at least 0.025W
greater than the lateral force at 50% of the total design
displacement.
The isolation system shall
not be configured to include a displacement restraint that limits
lateral displacement due to the maximum considered earthquake
to less than the total maximum displacement unless the seismically
isolated structure is designed in accordance with the following
criteria where more stringent than the requirements of
Section 17.2:
- Maximum considered earthquake response is calculated in accordance with the dynamic analysis requirements of Section 17.6, explicitly considering the nonlinear characteristics of the isolation system and the structure above the isolation system.
- The ultimate capacity of the isolation system and structural elements below the isolation system shall exceed the strength and displacement demands of the maximum considered earthquake.
- The structure above the isolation system is checked for stability and ductility demand of the maximum considered earthquake.
- The displacement restraint does not become effective at a displacement less than 0.75 times the total design displacement unless analysis demonstrates that earlier engagement does not result in unsatisfactory performance.
Each element of the isolation
system shall be designed to be stable under the design vertical
load where subjected to a horizontal displacement equal to the
total maximum displacement. The design vertical load shall be
computed using load combination 5 of Section 2.3.2 for the
maximum vertical load and load combination 7 of Section
12.4.2.3 for the minimum vertical load where S_{DS} in these equations
is replaced by S_{MS}. The vertical loads that result from
application of horizontal seismic forces, Q_{E}, shall be based on
peak response due to the maximum considered earthquake.
The factor of safety against global
structural overturning at the isolation interface shall not be less
than 1.0 for required load combinations. All gravity and seismic
loading conditions shall be investigated. Seismic forces for overturning
calculations shall be based on the maximum considered
earthquake, and W shall be used for the vertical restoring force.
Local uplift of individual elements shall not be allowed unless the resulting deflections do not cause overstress or instability of the isolator units or other structure elements.
Local uplift of individual elements shall not be allowed unless the resulting deflections do not cause overstress or instability of the isolator units or other structure elements.
- Access for inspection and replacement of all components of the isolation system shall be provided.
- A registered design professional shall complete a final series of inspections or observations of structure separation areas and components that cross the isolation interface prior to the issuance of the certificate of occupancy for the seismically isolated structure. Such inspections and observations shall indicate that the conditions allow free and unhindered displacement of the structure to maximum design levels and that all components that cross the isolation interface as installed are able to accommodate the stipulated displacements.
- Seismically isolated structures shall have a monitoring, inspection, and maintenance program for the isolation system established by the registered design professional responsible for the design of the isolation system.
- Remodeling, repair, or retrofitting at the isolation system interface, including that of components that cross the isolation interface, shall be performed under the direction of a registered design professional.
A quality control testing program
for isolator units shall be established by the registered design
professional responsible for the structural design.
A horizontal diaphragm
or other structural elements shall provide continuity
above the isolation interface and shall have adequate strength
and ductility to transmit forces (due to nonuniform ground
motion) from one part of the structure to another.
Minimum separations between
the isolated structure and surrounding retaining walls or other
fixed obstructions shall not be less than the total maximum
displacement.
Nonbuilding structures
shall be designed and constructed in accordance with the requirements
of Chapter 15 using design displacements and forces
calculated in accordance with Sections 17.5 or 17.6.
Parts or portions of an isolated structure, permanent nonstructural
components and the attachments to them, and the
attachments for permanent equipment supported by a structure
shall be designed to resist seismic forces and displacements as
prescribed by this section and the applicable requirements of
Chapter 13.
Elements
of seismically isolated structures and nonstructural components,
or portions thereof, that are at or above the isolation
interface shall be designed to resist a total lateral seismic force
equal to the maximum dynamic response of the element or component
under consideration.
EXCEPTION: Elements of seismically isolated structures and nonstructural components or portions designed to resist seismic forces and displacements as prescribed in Chapter 12 or 13 as appropriate.
EXCEPTION: Elements of seismically isolated structures and nonstructural components or portions designed to resist seismic forces and displacements as prescribed in Chapter 12 or 13 as appropriate.
Elements
of seismically isolated structures and nonstructural components,
or portions thereof, that cross the isolation interface
shall be designed to withstand the total maximum
displacement.
Elements
of seismically isolated structures and nonstructural components,
or portions thereof, that are below the isolation interface
shall be designed and constructed in accordance with the requirements
of Section 12.1 and Chapter 13.
The site-specific ground motion procedures
set forth in Chapter 21 are permitted to be used to determine
ground motions for any structure. For structures on Site
Class F sites, site response analysis shall be performed in accordance
with Section 21.1. For seismically isolated structures on
sites with S_{1} greater than or equal to 0.6, a ground motion hazard
analysis shall be performed in accordance with Section 21.2. Structures that do not require or use site-specific ground motion
procedures shall be analyzed using the design spectrum for the
design earthquake developed in accordance with Section 11.4.5.
A spectrum shall be constructed for the MCE_{R} ground motion. The spectrum for MCE_{R} ground motions shall not be taken as less than 1.5 times the spectrum for the design earthquake ground motions.
A spectrum shall be constructed for the MCE_{R} ground motion. The spectrum for MCE_{R} ground motions shall not be taken as less than 1.5 times the spectrum for the design earthquake ground motions.
Where response-history
procedures are used, ground motions shall consist of pairs of
appropriate horizontal ground motion acceleration components
developed per Section 16.1.3.2 except that 0.2T and 1.5T shall
be replaced by 0.5T_{D} and 1.25T_{M}, respectively, where T_{D} and T_{M} are defined in Section 17.5.3.
Seismically isolated structures except those defined in
Section 17.4.1 shall be designed using the dynamic procedures
of Section 17.6.
The equivalent
lateral force procedure of Section 17.5 is permitted to be used
for design of a seismically isolated structure provided that
- The structure is located at a site with S_{1} less than 0.60g.
- The structure is located on a Site Class A, B, C, or D.
- The structure above the isolation interface is less than or equal to four stories or 65 ft (19.8 m) in structural height, h_{n}.
- The effective period of the isolated structure at the maximum displacement, T_{M}, is less than or equal to 3.0 s.
- The effective period of the isolated structure at the design displacement, T_{D}, is greater than three times the elastic, fixed-base period of the structure above the isolation system as determined by Eq. 12.8-7 or 12.8-8.
- The structure above the isolation system is of regular configuration.
- The isolation system meets all of the following criteria:
- The effective stiffness of the isolation system at the design displacement is greater than one-third of the effective stiffness at 20% of the design displacement.
- The isolation system is capable of producing a restoring force as specified in Section 17.2.4.4.
- The isolation system does not limit maximum considered earthquake displacement to less than the total maximum displacement.
The dynamic procedures of
Section 17.6 are permitted to be used as specified in this section.
Response-spectrum
analysis shall not be used for design of a seismically isolated
structure unless
- The structure is located on a Site Class A, B, C, or D.
- The isolation system meets the criteria of Item 7 of Section 17.4.1.
The response-history
procedure is permitted for design of any seismically isolated
structure and shall be used for design of all seismically isolated
structures not meeting the criteria of Section 17.4.2.1.
Where the equivalent lateral force procedure
is used to design seismically isolated structures, the requirements
of this section shall apply.
Minimum lateral earthquake design displacements and forces on
seismically isolated structures shall be based on the deformation
characteristics of the isolation system. The deformation characteristics
of the isolation system shall explicitly include the effects
of the wind-restraint system if such a system is used to meet the
design requirements of this standard. The deformation characteristics
of the isolation system shall be based on properly substantiated
tests performed in accordance with Section 17.8.
The isolation system shall be
designed and constructed to withstand minimum lateral earthquake
displacements, D_{D}, that act in the direction of each of the
main horizontal axes of the structure using Eq. 17.5-1:
(17.5-1)
where
g | = | acceleration due to gravity. The units for g are in./s^{2} (mm/s^{2}) if the units of the design displacement, D_{D}, are in. (mm) |
S_{D}_{1} | = | design 5% damped spectral acceleration parameter at 1-s period in units of g-s, as determined in Section 11.4.4 |
T_{D} | = | effective period of the seismically isolated structure in seconds, at the design displacement in the direction under consideration, as prescribed by Eq. 17.5-2 |
B_{D} | = | numerical coefficient related to the effective damping of the isolation system at the design displacement, β_{D}, as set forth in Table 17.5-1 |
The effective
period of the isolated structure at design displacement,
T_{D}, shall be determined using the deformational characteristics of
the isolation system and Eq. 17.5-2:
(17 .5-2)
where
W | = | effective seismic weight of the structure above the isolation interface as defined in Section 12.7.2 |
k_{D}_{min} | = | minimum effective stiffness in kips/in. (kN/rnm) of the isolation system at the design displacement in the horizontal direction under consideration, as prescribed by Eq. 17.8-4 |
g | = | acceleration due to gravity |
The maximum displacement
of the isolation system, D_{M}, in the most critical direction
of horizontal response shall be calculated using Eq. 17.5-3:
Table 17.5-1 Damping Coefficient, B_{D} or B_{M}
^{a}The damping coefficient shall be based on the effective damping of the
isolation system determined in accordance with the requirements of Section
17.8.5.2.
^{b}The damping coefficient shall be based on linear interpolation for effective damping values other than those given.
(17.5-3)
where
g | = | acceleration of gravity |
S_{M}_{1} | = | maximum considered earthquake 5% damped spectral acceleration parameter at 1-s period, in units of g-s, as determined in Section 11.4.3 |
T_{M} | = | effective period, in seconds, of the seismically isolated structure at the maximum displacement in the direction under consideration, as prescribed by Eq. 17.5-4 |
B_{M} | = | numerical coefficient related to the effective damping of the isolation system at the maximum displacement, β_{M}, as set forth in Table 17.5-1 |
Table 17.5-1 Damping Coefficient, B_{D} or B_{M}
Effective Damping, β_{D} or β_{M} (percentage of critical)^{a,b} | B_{D} or B_{M} Factor |
---|---|
≤2 5 10 20 30 40 ≥50 |
0.8 1.0 1.2 1.5 1.7 1.9 2.0 |
^{b}The damping coefficient shall be based on linear interpolation for effective damping values other than those given.
The
effective period of the isolated structure at maximum displacement,
T_{M}, shall be determined using the deformational characteristics
of the isolation system and Eq. 17.5-4:
(17.5-4)
where
W | = | effective seismic weight of the structure above the isolation interface as defined in Section 12.7.2 (kip or kN) |
k_{M}_{min} | = | minimum effective stiffness, in kips/in. (kN/mm), of the isolation system at the maximum displacement in the horizontal direction under consideration, as prescribed by Eq. 17.8-6 |
g | = | the acceleration of gravity |
The total design displacement,
D_{TD}, and the total maximum displacement, D_{TM}, of elements of
the isolation system shall include additional displacement due to
actual and accidental torsion calculated from the spatial distribution
of the lateral stiffness of the isolation system and the most
disadvantageous location of eccentric mass.
The total design displacement, D_{TD}, and the total maximum displacement, D_{TM}, of elements of an isolation system with uniform spatial distribution of lateral stiffness shall not be taken as less than that prescribed by Eqs. 17.5-5 and 17.5-6:
EXCEPTION: The total design displacement, D_{TD}, and the total maximum displacement, D_{TM}, are permitted to be taken as less than the value prescribed by Eqs. 17.5-5 and 17.5-6, respectively, but not less than 1.1 times D_{D} and D_{M}, respectively, provided the isolation system is shown by calculation to be configured to resist torsion accordingly.
The total design displacement, D_{TD}, and the total maximum displacement, D_{TM}, of elements of an isolation system with uniform spatial distribution of lateral stiffness shall not be taken as less than that prescribed by Eqs. 17.5-5 and 17.5-6:
(17.5-5)
(17.5-6)
where
D_{D} | = | design displacement at the center of rigidity of the isolation system in the direction under consideration as prescribed by Eq. 17.5-1 |
D_{M} | = | maximum displacement at the center of rigidity of the isolation system in the direction under consideration as prescribed by Eq. 17.5-3 |
y | = | the distance between the centers of rigidity of the isolation system and the element of interest measured perpendicular to the direction of seismic loading under consideration |
e | = | the actual eccentricity measured in plan between the center of mass of the structure above the isolation interface and the center of rigidity of the isolation system, plus accidental eccentricity, in ft (mm), taken as 5% of the longest plan dimension of the structure perpendicular to the direction of force under consideration |
b | = | the shortest plan dimension of the structure measured perpendicular to d |
d | = | the longest plan dimension of the structure |
EXCEPTION: The total design displacement, D_{TD}, and the total maximum displacement, D_{TM}, are permitted to be taken as less than the value prescribed by Eqs. 17.5-5 and 17.5-6, respectively, but not less than 1.1 times D_{D} and D_{M}, respectively, provided the isolation system is shown by calculation to be configured to resist torsion accordingly.
The isolation system, the foundation, and all
structural elements below the isolation system shall be designed
and constructed to withstand a minimum lateral seismic force,
V_{b}, using all of the appropriate requirements for a nonisolated
structure and as prescribed by Eq. 17.5-7:
V_{b} shall not be taken as less than the maximum force in the isolation system at any displacement up to and including the design displacement.
(17.5-7)
where
k_{D}_{max} | = | maximum effective stiffness, in kips/in. (kN/mm), of the isolation system at the design displacement in the horizontal direction under consideration as prescribed by Eq. 17.8-3 |
D_{D} | = | design displacement, in in. (mm), at the center of rigidity of the isolation system in the direction under consideration, as prescribed by Eq. 17.5-1 |
V_{b} shall not be taken as less than the maximum force in the isolation system at any displacement up to and including the design displacement.
The
structure above the isolation system shall be designed and constructed
to withstand a minimum shear force, V_{s}, using all of the
appropriate requirements for a nonisolated structure and as prescribed
by Eq. 17.5-8:
The R_{I} factor shall be based on the type of seismic force-resisting system used for the structure above the isolation system and shall be three-eighths of the value of R given in Table 12.2-1, Table 15.4-1, or Table 15.4-2, as appropriate, with a maximum value not greater than 2.0 and a minimum value not less than 1.0.
(17.5-8)
where
k_{D}_{max} | = | maximum effective stiffness, in kips/in. (kN/mm), of the isolation system at the design displacement in the horizontal direction under consideration |
D_{D} | = | design displacement, in in. (mm), at the center of rigidity of the isolation system in the direction under consideration, as prescribed by Eq. 17.5-1 |
R_{I} | = | numerical coefficient related to the type of seismic forceresisting system above the isolation system |
The R_{I} factor shall be based on the type of seismic force-resisting system used for the structure above the isolation system and shall be three-eighths of the value of R given in Table 12.2-1, Table 15.4-1, or Table 15.4-2, as appropriate, with a maximum value not greater than 2.0 and a minimum value not less than 1.0.
The value of V_{s} shall not be taken as less
than the following:
- The lateral seismic force required by Section 12.8 for a fixed-base structure of the same effective seismic weight, W, and a period equal to the isolated period, T_{D}.
- The base shear corresponding to the factored design wind load.
- The lateral seismic force required to fully activate the isolation system (e.g., the yield level of a softening system, the ultimate capacity of a sacrificial wind-restraint system, or the break-away friction level of a sliding system) multiplied by 1.5.
The shear force V_{s} shall
be distributed over the height of the structure above the isolation
interface using Eq. 17.5-9:
At each level designated as x, the force, F_{x}, shall be applied over the area of the structure in accordance with the mass distribution at the level.
(17.5-9)
where
F_{x} | = | portion of V_{s} that is assigned to level x |
V_{x} | = | total lateral seismic design force or shear on elements above the isolation system as prescribed by Eq. 17.5-8 |
w_{x} | = | portion of W that is located at or assigned to level i, n, or x, respectively |
h_{x} | = | height above the base of level i, n, or x, respectively |
At each level designated as x, the force, F_{x}, shall be applied over the area of the structure in accordance with the mass distribution at the level.
The maximum story drift of the structure
above the isolation system shall not exceed 0.015h_{s}_{x}. The drift
shall be calculated by Eq. 12.8-15 with C_{d} for the isolated structure
equal to R_{I}, as defined in Section 17.5.4.2.
Where dynamic analysis is used to design seismically
isolated structures, the requirements of this section shall
apply.
The mathematical models of the isolated
structure including the isolation system, the seismic force-resisting
system, and other structural elements shall conform to
Section 12.7.3 and to the requirements of Sections 17.6.2.1 and
17.6.2.2.
The isolation system shall be
modeled using deformational characteristics developed and verified
by test in accordance with the requirements of Section
17.5.2. The isolation system shall be modeled with sufficient
detail to
- Account for the spatial distribution of isolator units;
- Calculate translation, in both horizontal directions, and torsion of the structure above the isolation interface considering the most disadvantageous location of eccentric mass;
- Assess overturning/uplift forces on individual isolator units; and
- Account for the effects of vertical load, bilateral load, and/ or the rate of loading if the force-deflection properties of the isolation system depend on one or more of these attributes.
The maximum displacement of
each floor and design forces and displacements in elements of
the seismic force-resisting system are permitted to be calculated
using a linear elastic model of the isolated structure provided
that both of the following conditions are met:
- Stiffness properties assumed for the nonlinear components of the isolation system are based on the maximum effective stiffness of the isolation system; and
- All elements of the seismic force-resisting system of the structure above the isolation system remain elastic for the design earthquake.
Response-spectrum and response-history
procedures shall be performed in accordance with Section 12.9
and Chapter 16 and the requirements of this section.
The design earthquake ground
motions shall be used to calculate the total design displacement
of the isolation system and the lateral forces and displacements
in the isolated structure. The maximum considered earthquake
shall be used to calculate the total maximum displacement of the
isolation system.
Response-spectrum
analysis shall be performed using a modal damping value for the
fundamental mode in the direction of interest not greater than
the effective damping of the isolation system or 30% of critical,
whichever is less. Modal damping values for higher modes shall
be selected consistent with those that would be appropriate for
response-spectrum analysis of the structure above the isolation
system assuming a fixed base.
Response-spectrum analysis used to determine the total design displacement and the total maximum displacement shall include simultaneous excitation of the model by 100% of the ground motion in the critical direction and 30% of the ground motion in the perpendicular, horizontal direction. The maximum displacement of the isolation system shall be calculated as the vectorial sum of the two orthogonal displacements.
The design shear at any story shall not be less than the story shear resulting from application of the story forces calculated using Eq. 17.5-9 and a value of V_{s} equal to the base shear obtained from the response-spectrum analysis in the direction of interest.
Response-spectrum analysis used to determine the total design displacement and the total maximum displacement shall include simultaneous excitation of the model by 100% of the ground motion in the critical direction and 30% of the ground motion in the perpendicular, horizontal direction. The maximum displacement of the isolation system shall be calculated as the vectorial sum of the two orthogonal displacements.
The design shear at any story shall not be less than the story shear resulting from application of the story forces calculated using Eq. 17.5-9 and a value of V_{s} equal to the base shear obtained from the response-spectrum analysis in the direction of interest.
Where a response-history
procedure is performed, a suite of not fewer than three
pairs of appropriate ground motions shall be used in the analysis;
the ground motion pairs shall be selected and scaled in accordance
with Section 17.3.2.
Each pair of ground motion components shall be applied simultaneously to the model considering the most disadvantageous location of eccentric mass. The maximum displacement of the isolation system shall be calculated from the vectorial sum of the two orthogonal displacements at each time step.
The parameters of interest shall be calculated for each ground motion used for the response-history analysis. If seven or more pairs of ground motions are used for the response-history analysis, the average value of the response parameter of interest is permitted to be used for design. If fewer than seven pairs of ground motions are used for analysis, the maximum value of the response parameter of interest shall be used for design.
Each pair of ground motion components shall be applied simultaneously to the model considering the most disadvantageous location of eccentric mass. The maximum displacement of the isolation system shall be calculated from the vectorial sum of the two orthogonal displacements at each time step.
The parameters of interest shall be calculated for each ground motion used for the response-history analysis. If seven or more pairs of ground motions are used for the response-history analysis, the average value of the response parameter of interest is permitted to be used for design. If fewer than seven pairs of ground motions are used for analysis, the maximum value of the response parameter of interest shall be used for design.
The isolation system, foundation, and all
structural elements below the isolation system shall be designed
using all of the appropriate requirements for a nonisolated structure
and the forces obtained from the dynamic analysis without
reduction, but the design lateral force shall not be taken as less
than 90% of V_{b} determined in accordance as prescribed by Eq.
17.5-7.
The total design displacement of the isolation system shall not be taken as less than 90% of D_{TD} as specified by Section 17.5.3.5. The total maximum displacement of the isolation system shall not be taken as less than 80% of D_{TM} as prescribed by Section 17.5.3.5.
The limits on displacements specified by this section shall be evaluated using values of D_{TD} and D_{TM} determined in accordance with Section 17.5.3.5 except that D'_{D} is permitted to be used in lieu of D_{D}, and D'_{M} is permitted to be used in lieu of D_{M} as prescribed in Eqs. 17.6-1 and 17.6-2:
The total design displacement of the isolation system shall not be taken as less than 90% of D_{TD} as specified by Section 17.5.3.5. The total maximum displacement of the isolation system shall not be taken as less than 80% of D_{TM} as prescribed by Section 17.5.3.5.
The limits on displacements specified by this section shall be evaluated using values of D_{TD} and D_{TM} determined in accordance with Section 17.5.3.5 except that D'_{D} is permitted to be used in lieu of D_{D}, and D'_{M} is permitted to be used in lieu of D_{M} as prescribed in Eqs. 17.6-1 and 17.6-2:
(17.6-1)
(17.6-2)
where
D_{D} | = | design displacement, in in. (mm), at the center of rigidity of the isolation system in the direction under consideration, as prescribed by Eq. 17.5-1 |
D_{M} | = | maximum displacement in in. (mm), at the center of rigidity of the isolation system in the direction under consideration, as prescribed by Eq. 17.5-3 |
T | = | elastic, fixed-base period of the structure above the isolation system as determined by Section 12.8.2 |
T_{D} | = | effective period of seismically isolated structure in s, at the design displacement in the direction under consideration, as prescribed by Eq. 17.5-2 |
T_{M} | = | effective period, in s, of the seismically isolated structure, at the maximum displacement in the direction under consideration, as prescribed by Eq. 17.5-4 |
Subject to the procedure-specific limits of this section, structural
elements above the isolation system shall be designed using the
appropriate requirements for a nonisolated structure and the
forces obtained from the dynamic analysis reduced by a factor
of R_{I}, as determined in accordance with Section 17.5.4.2. The
design lateral shear force on the structure above the isolation
system, if regular in configuration, shall not be taken as less
than 80% of V_{s}, or less than the limits specified by Section
17.5.4.3.
EXCEPTION: The lateral shear force on the structure above the isolation system, if regular in configuration, is permitted to be taken as less than 80%, but shall not be less than 60% of V_{s}, where the response-history procedure is used for analysis of the seismically isolated structure.
The design lateral shear force on the structure above the isolation system, if irregular in configuration, shall not be taken as less than V_{s} or less than the limits specified by Section 17.5.4.3.
EXCEPTION: The design lateral shear force on the structure above the isolation system, if irregular in configuration, is permitted to be taken as less than 100%, but shall not be less than 80% of V_{s}, where the response-history procedure is used for analysis of the seismically isolated structure.
EXCEPTION: The lateral shear force on the structure above the isolation system, if regular in configuration, is permitted to be taken as less than 80%, but shall not be less than 60% of V_{s}, where the response-history procedure is used for analysis of the seismically isolated structure.
The design lateral shear force on the structure above the isolation system, if irregular in configuration, shall not be taken as less than V_{s} or less than the limits specified by Section 17.5.4.3.
EXCEPTION: The design lateral shear force on the structure above the isolation system, if irregular in configuration, is permitted to be taken as less than 100%, but shall not be less than 80% of V_{s}, where the response-history procedure is used for analysis of the seismically isolated structure.
Where the factored lateral shear
force on structural elements, determined using either response-spectrum
or response-history procedure, is less than the minimum
values prescribed by Sections 17.6.4.1 and 17.6.4.2, all response
parameters, including member forces and moments, shall be
adjusted upward proportionally.
Maximum story drift corresponding to
the design lateral force including displacement due to vertical
deformation of the isolation system shall not exceed the following
limits:
The secondary effects of the maximum considered earthquake lateral displacement of the structure above the isolation system combined with gravity forces shall be investigated if the story drift ratio exceeds 0.010/R_{I}, .
- The maximum story drift of the structure above the isolation system calculated by response-spectrum analysis shall not exceed 0.015h_{sx}
- The maximum story drift of the structure above the isolation system calculated by response-history analysis based on the force-deflection characteristics of nonlinear elements of the seismic force-resisting system shall not exceed 0.020h_{sx}.
The secondary effects of the maximum considered earthquake lateral displacement of the structure above the isolation system combined with gravity forces shall be investigated if the story drift ratio exceeds 0.010/R_{I}, .
A design review of the isolation system and related test programs
shall be performed by an independent engineering team, including
persons licensed in the appropriate disciplines and experienced
in seismic analysis methods and the theory and application
of seismic isolation. Isolation system design review shall include,
but not be limited to, the following:
- Review of site-specific seismic criteria including the development of site-specific spectra and ground motion histories and all other design criteria developed specifically for the project.
- Review of the preliminary design including the determination of the total design displacement, the total maximum displacement, and the lateral force level.
- Overview and observation of prototype testing (Section 17.8).
- Review of the final design of the entire structural system and all supporting analyses.
- Review of the isolation system quality control testing program (Section 17.2.4.9).
The deformation characteristics and damping
values of the isolation system used in the design and analysis of
seismically isolated structures shall be based on tests of a selected
sample of the components prior to construction as described in
this section.
The isolation system components to be tested shall include the wind-restraint system if such a system is used in the design.
The tests specified in this section are for establishing and validating the design properties of the isolation system and shall not be considered as satisfying the manufacturing quality control tests of Section 17.2.4.9.
The isolation system components to be tested shall include the wind-restraint system if such a system is used in the design.
The tests specified in this section are for establishing and validating the design properties of the isolation system and shall not be considered as satisfying the manufacturing quality control tests of Section 17.2.4.9.
Prototype tests shall be performed
separately on two full-size specimens (or sets of specimens, as
appropriate) of each predominant type and size of isolator unit
of the isolation system. The test specimens shall include the
wind-restraint system and individual isolator units if such
systems are used in the design. Specimens tested shall not be
used for construction unless accepted by the registered design
professional responsible for the design of the structure and
approved by the authority having jurisdiction.
For each cycle of each test, the force-deflection
and hysteretic behavior of the test specimen shall be
recorded.
The following sequence of
tests shall be performed for the prescribed number of cycles at
a vertical load equal to the average dead load plus one-half the
effects due to live load on all isolator units of a common type
and size:
- Twenty fully reversed cycles of loading at a lateral force corresponding to the wind design force.
- Three fully reversed cycles of loading at each of the following increments of the total design displacement–0.25D_{D}, 0.5D_{D}, 1.0D_{D}, and 1.0D_{M} where D_{D} and D_{M} are as determined in Sections 17.5.3.1 and 17.5.3.3, respectively, or Section 17.6 as appropriate.
- Three fully reversed cycles of loading at the total maximum displacement, 1.0D_{TM}.
- 30S_{D}_{1}/S_{DS}B_{D}, but not less than 10, fully reversed cycles of loading at 1.0 times the total design displacement, 1.0D_{TD}.
If the force-deflection
properties of the isolator units depend on the rate of
loading, each set of tests specified in Section 17.8.2.2 shall be
performed dynamically at a frequency equal to the inverse of the
effective period, T_{D}.
If reduced-scale prototype specimens are used to quantify rate-dependent properties of isolators, the reduced-scale prototype specimens shall be of the same type and material and be manufactured with the same processes and quality as full-scale prototypes and shall be tested at a frequency that represents fullscale prototype loading rates.
The force-deflection properties of an isolator unit shall be considered to be dependent on the rate of loading if the measured property (effective stiffness or effective damping) at the design displacement when tested at any frequency in the range of 0.1 to 2.0 times the inverse of T_{D} is different from the property when tested at a frequency equal to the inverse of T_{D} by more than 15%.
If reduced-scale prototype specimens are used to quantify rate-dependent properties of isolators, the reduced-scale prototype specimens shall be of the same type and material and be manufactured with the same processes and quality as full-scale prototypes and shall be tested at a frequency that represents fullscale prototype loading rates.
The force-deflection properties of an isolator unit shall be considered to be dependent on the rate of loading if the measured property (effective stiffness or effective damping) at the design displacement when tested at any frequency in the range of 0.1 to 2.0 times the inverse of T_{D} is different from the property when tested at a frequency equal to the inverse of T_{D} by more than 15%.
If the force-deflection
properties of the isolator units are dependent on bilateral
load, the tests specified in Sections 17.8.2.2 and 17.8.2.3
shall be augmented to include bilateral load at the following
increments of the total design displacement, D_{TD}: 0.25 and 1.0,
0.5 and 1.0, 0.75 and 1.0, and 1.0 and 1.0
If reduced-scale prototype specimens are used to quantify bilateral-load-dependent properties, the reduced-scale specimens shall be of the same type and material and manufactured with the same processes and quality as full-scale prototypes.
The force-deflection properties of an isolator unit shall be considered to be dependent on bilateral load if the effective stiffness where subjected to bilateral loading is different from the effective stiffness where subjected to unilateral loading, by more than 15%.
If reduced-scale prototype specimens are used to quantify bilateral-load-dependent properties, the reduced-scale specimens shall be of the same type and material and manufactured with the same processes and quality as full-scale prototypes.
The force-deflection properties of an isolator unit shall be considered to be dependent on bilateral load if the effective stiffness where subjected to bilateral loading is different from the effective stiffness where subjected to unilateral loading, by more than 15%.
Isolator
units that carry vertical load shall be statically tested for
maximum and minimum downward vertical load at the total
maximum displacement. In these tests, the combined vertical
loads shall be taken as specified in Section 17.2.4.6 on any one
isolator of a common type and size. The dead load, D, and live
load, L, are specified in Section 12.4. The seismic load E is given
by Eqs. 12.4-1 and 12.4-2 where S_{DS} in these equations is
replaced by S_{MS} and the vertical loads that result from application
of horizontal seismic forces, Q_{E}, shall be based on the peak
response due to the maximum considered earthquake.
If a sacrificial
wind-restraint system is to be utilized, its ultimate capacity shall
be established by test.
Prototype tests are not required
if an isolator unit is of similar size and of the same type and
material as a prototype isolator unit that has been previously
tested using the specified sequence of tests.
The force-deflection characteristics of the isolation system shall
be based on the cyclic load tests of prototype isolator specified
in Section 17.8.2.
As required, the effective stiffness of an isolator unit, k_{eff}, shall be calculated for each cycle of loading as prescribed by Eq. 17.8-1:
(17.8-1)
where F^{+} and F^{-} are the positive and negative forces, at △^{+} and
△^{-}, respectively.
As required, the effective damping, β_{eff}, of an isolator unit shall be calculated for each cycle of loading by Eq. 17.8-2:
(17.8-2)
where the energy dissipated per cycle of loading, E_{loop}, and the
effective stiffness, k_{eff}, shall be based on peak test displacements
of △^{+} and △^{-}.
As required, the effective stiffness of an isolator unit, k_{eff}, shall be calculated for each cycle of loading as prescribed by Eq. 17.8-1:
(17.8-1)
As required, the effective damping, β_{eff}, of an isolator unit shall be calculated for each cycle of loading by Eq. 17.8-2:
(17.8-2)
The performance of the test
specimens shall be deemed adequate if the following conditions
are satisfied:
- The force-deflection plots for all tests specified in Section 17.8.2 have a positive incremental force-resisting capacity.
- For each increment of test displacement specified in item 2 of Section 17.8.2.2 and for each vertical load case specified in Section 17.8.2.2,
- For each test specimen, the difference between the effective stiffness at each of the three cycles of test and the average value of effective stiffness is no greater than 15%.
- For each cycle of test, the difference between effective stiffness of the two test specimens of a common type and size of the isolator unit and the average effective stiffness is no greater than 15%.
- For each specimen there is no greater than a 20% change in the initial effective stiffness over the cycles of test specified in item 4 of Section 17.8.2.2.
- For each specimen there is no greater than a 20% decrease in the initial effective damping over the cycles of test specified in item 4 of Section 17.8.2.2.
- All specimens of vertical-load-carrying elements of the isolation system remain stable where tested in accordance with Section 17.8.2.5.
At the
design displacement, the maximum and minimum effective stiffness
of the isolated system, k_{D}_{max} and k_{D}_{min}, shall be based on the
cyclic tests of item 2 of Section 17.8.2.2 and calculated using
Eqs. 17.8-3 and 17.8-4:
(17.8-3)
(17.8-4)
At the maximum displacement, the maximum and minimum
effective stiffness of the isolation system, k_{M}_{max} and k_{M}_{min}, shall
be based on the cyclic tests of item 3 of Section 17.8.2.2 and
calculated using Eqs. 17.8-5 and 17.8-6:
(17.8-5)
For isolator units that are found by the tests of Sections 17.8.2.2, 17.8.2.3, and 17.8.2.4 to have force-deflection characteristics that vary with vertical load, rate of loading, or bilateral load, respectively, the values of k_{D}_{max} and k_{M}_{max} shall be increased and the values of k_{D}_{min} and k_{M}_{min} shall be decreased, as necessary, to bound the effects of measured variation in effective stiffness.
(17.8-3)
(17.8-4)
(17.8-5)
(17.8-6)
The maximum effective stiffness of the isolation system, k_{D}_{max}
( or k_{M}_{max}), shall be based on forces from the cycle of prototype
testing at a test displacement equal to D_{D} (or D_{M}) that produces
the largest value of effective stiffness. Minimum effective stiffness of the isolation system, k_{D}_{min} ( or k_{M}_{min}), shall be based on
forces from the cycle of prototype testing at a test displacement
equal to D_{D} (or D_{M}) that produces the smallest value of effective
stiffness.
For isolator units that are found by the tests of Sections 17.8.2.2, 17.8.2.3, and 17.8.2.4 to have force-deflection characteristics that vary with vertical load, rate of loading, or bilateral load, respectively, the values of k_{D}_{max} and k_{M}_{max} shall be increased and the values of k_{D}_{min} and k_{M}_{min} shall be decreased, as necessary, to bound the effects of measured variation in effective stiffness.
At the design displacement, the
effective damping of the isolation system, β_{D}, shall be based on
the cyclic tests of item 2 of Section 17.8.2.2 and calculated using
Eq. 17.8-7:
At the maximum displacement, the effective damping of the isolation system, β_{M}, shall be based on the cyclic tests of item 2 of Section 17.8.2.2 and calculated using Eq. 17.8-8:
(17.8-7)
In Eq. 17.8-7, the total energy dissipated per cycle of design
displacement response, ΣE_{D}, shall be taken as the sum of the
energy dissipated per cycle in all isolator units measured at a test
displacement equal to D_{D} and shall be based on forces and
deflections from the cycle of prototype testing at test displacement
D_{D} that produces the smallest values of effective damping.
At the maximum displacement, the effective damping of the isolation system, β_{M}, shall be based on the cyclic tests of item 2 of Section 17.8.2.2 and calculated using Eq. 17.8-8:
(17.8-8)
In Eq. 17.8-8, the total energy dissipated per cycle of design
displacement response, ΣE_{M}, shall be taken as the sum of the
energy dissipated per cycle in all isolator units measured at a test
displacement equal to D_{M} and shall be based on forces and
deflections from the cycle of prototype testing at test displacement
D_{M} that produces the smallest value of effective damping.