Chapter 10 The ASCE 7-10 Design Provisions for Seismically...

Supplemental Damping and Seismic Isolation Chapter 10 – Seismic Isolation Systems

CIE 626 - Structural Control Chapter 10 – The ASCE 7-10 Design Provisions for

Seismically Isolated Buildings



Chapter 10 The ASCE 7-10 Design Provisions for


1




CONTENT 1. Introduction 2. Design Methods 3. Design Based on Static Analysis 4. Design Based on Dynamic Analysis 5. Adequacy Assessment of Bearings 6. Design Review and Testing 7. Design Example 8. Project Example

2




Major References • ASCE 7-10 Standard

– Chapter 17

3




1. Introduction • Early versions of seismic provisions for seismically

isolated structures: – Emphasized simple, statically equivalent method of design – Displacements concentrated at isolation level – Superstructure assumed to moves as a rigid body – Design based on single mode of vibration – Design forces for superstructure computed from isolator

forces at design displacement • Recent versions of seismic provisions:

– Increased situations for dynamic analysis – Incentives to encourage dynamic analysis

4




2. Design Methods • For all seismic isolation designs, necessary to first perform static analysis • Static Analysis establishes minimum level for design displacements and

forces • Static analysis (or equivalent lateral force procedure) can be used as only

design method if all following conditions are met: – Design spectral acceleration at a period of 1 second is less than or equal to 0.6 g. – Structure is located on soil type A, B, C, or D. – Structure above isolation interface not more than four stories or 20 m in height. – Isolated period of structure at design displacement less than or equal to 3

seconds. – Isolated period of structure at design displacement greater than three times the

elastic fixed-based period of the structure (i.e. ε < 1/9 ) – Structure is regular. – The isolation system does not limit MCE displacement to less than the total

maximum displacement.

5




• For all seismic isolation designs, necessary to first perform static analysis • Static Analysis establishes minimum level for design displacements and

forces • Static analysis (or equivalent lateral force procedure) can be used as only

design method if all following conditions are met: – Effective stiffness of the isolation system at design displacement greater than 1/3

of effective stiffness at 20% of design displacement.

2. Design Methods

6




• For all seismic isolation designs, necessary to first perform static analysis. • Static Analysis establishes minimum level for design displacements and

forces. • Static analysis (or equivalent lateral force procedure) can be used as only

design method if all following conditions are met: – The isolation system 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 percent of the total design displacement.

2. Design Methods

7




– All other cases, dynamic analysis is required. – Response spectrum analysis can be used in following cases:

• Structure located on soil type A, B, C, or D. • Effective stiffness of the isolation system at design displacement greater

than 1/3 of effective stiffness at 20% of design displacement. • The isolation system 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 percent of the total design displacement.

• The isolation system does not limit MCE displacement to less than the total maximum displacement.

– For all other cases, time-history dynamic analysis required.

2. Design Methods

8




3. Design Based on Static Analysis

9





10





11





12





13




• After preliminary design completed, prototype isolators constructed and tested.

• Values of kDmin and kDmax obtained from test results. • Results of prototype tests also used to refine

preliminary design, and when dynamic analysis used, needed to establish bounds on design quantities.

• Because effective stiffness and the effective damping dependent on displacement, the process of computing TD and BD is iterative.


14




• Preliminary Design Flowchart Assume a design displacement, DD

Determine the minimum lateral siffness of isolators , kDmin, at displacement DD.

Calculate effective isolated period, TD, at displacement DD:

Calculate equivalent viscous damping, ζ, and the reduction factor BD.

Calculate an updated design displacement, DD∗ :

?DD ≈ DD*

YesNo Preliminary design completedDD = DD *

*


15




16




ASCE 7-10 standard specifications


17





18





19





20





21




• RI factor for base isolated structure much lower than R factor for equivalent fixed base structure.

• In fixed-base design, several factors lead to values of R: – Period shift: as structure yields, period lengthens and force demand reduces. – Damping increase because of yielding of structural elements.

• For isolated structure, only overstrength and redundancy are applicable. – Period shift in superstructure counters effectiveness of isolation system.

• Decreases the separation between fixed base period and the isolated period. • Could attract larger forces and more participation from higher modes.

– Damping in isolated structure less than in fixed base structure.


22




• Vertical distribution of inertia forces:


23




• Incentives to use dynamic analysis:

4. Design Based on Dynamic Analysis

24




• Reduction in displacements to account for superstructure flexibility:


25




• Selection of Design Ground Motions: – Pairs of horizontal components from at least three recorded seismic events

necessary for time-history analysis. – Events must be representative of site, soil, and source characteristics and have

durations consistent with DBE or MCE. – Time- histories site within 15 km from major active fault requires near-fault

characteristics. – Ground motions scaling:

• For each ground motion pair, SRSS of 5% damped spectrum computed • Motions scaled so that average SRSS spectrum not below target spectrum for the MCE in the

period range 0.5TD to 1.25TD. – Calculation of design values:

• If three time-histories used: – Design based on maximum response quantities from three time-history analyses.

• If seven time-histories used: – Design based on mean response quantities from seven time-history analyses.


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5. Adequacy Assessment of Bearings • Adequacy Assessment of Bearings

– See Chapter 9

http://mceer.buffalo.edu/publications/catalog/reports/LRFD-Based-Analysis-and-Design-Procedures-for-Bridge-Bearings-and-Seismic-Isolators-MCEER-11-0004.html

27




Peer Review Composition:

Must be conducted by an independent team of professionals familiar with seismic isolation technology (seer ASCE 7-10, Section 17.7).

Responsibilities: 1. Review of design criteria specific to the site including:

Development of site specific design response spectra. Development of site specific design ground motion time-histories. All other design criteria developed specifically for the project.

2. Review of preliminary design including: Determination of total design displacement, DTD. Determination of maximum total design displacement, DTM. Determination of design forces.

3. Review and observation of prototype testing. 4. Review of the final design of the entire structure, the SFRS and the isolation system. 5. Review of the quality control criteria and procedures of the testing program.

6. Design Review and Testing

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Testing Requirements To verify the deformation and damping characteristics of the isolation system. Testing of two full-scale prototype specimens of each type of isolators used in

the project including wind locking mechanisms. Prototype specimens not be used in construction. Cyclic testing on each specimen under a vertical load equal to the average of the

service dead load plus half of the service live load. If the properties of the isolator depends on the rate of loading, dynamic tests

must be conducted at a frequency equal to the inverse of the effective isolation period at the design displacement, 1/TD.


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Testing Protocol: 1. Twenty load-controlled reversed cycles corresponding to the

design wind load. 2. Three displacement-controlled reversed cycles for each of the

following displacement increments: 0.25DD, 0.5DD, 1.0DD, et 1.0DM.

3. Three displacement-controlled reversed cycles corresponding to the maximum total design displacement, 1.0DTM.

4. 30SD1/SDSBD ≥ 10 cycles displacement-controlled reversed cycles corresponding to the total design displacement, , 1.0DTD.


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SRMD (Seismic Response Modification Device) Testing Facility , UC-San Diego

Concrete frame

Reaction Wall

Removable steel cross-beam and tie-down rods

Bearing specimen

Moveable platen

Horizontal actuators

Stabilizing hydrostatic slide bearing-actuators on platen’s outrigger arms

Hydrostatic slide bearing-actuators beneath platen

Concrete frame

Reaction Wall

Removable steel cross-beam and tie-down rods

Bearing specimen

Moveable platen


Stabilizing hydrostatic slide bearing-actuators on platen’s outrigger arms

Hydrostatic slide bearing-actuators beneath platen


31




SRMD (Seismic Response Modification Device) Testing Facility , UC-San Diego Spécifications

Vertical Longitudinal Transverse Force 53,400 kN

(12,000 kips) 8,900 kN

(2,000 kips) 4,450 kN

(1,000 kips) Displacement ± 0.127 m

(5 in.) ± 1.22 m (48 in.)

± 0.61 m (24 in.)

Velocity ± 254 mm/s (10 in./s)

± 1778 mm/s (70 in./sec)

± 762 mm/s (30 in./sec)

Clearance Up to 1.52 m (5 ft)

~ 4 m (13 ft)

Relative rotation

± 2° ± 2° ± 2°


32




High Bay Physics and SRMD Test Facility

LC Building

Low Bay PortionHigh Bay Portion Control Room

Pipe Trench

AccumulatorBuilding



33




Slide BearingActuator Steel Bearing Plate

10.4 m(34 ft)

Corner Fixture

18.3 m (60 ft)

Platen

HorizontalActuator

Plan View of Test System

Outrigger Arm



34




Prestressing System

Lab Floor

Slide BearingActuators

4.1 m(13.5 ft)

3.5 m(11.5 ft)

0.6 m(2 ft) 18.3 m (60 ft)

1.8 m(6 ft)

ReactionWall

Tie-Down Systemand Steel Cross Frame

Corner Fixture

PipingSystem

Longitudinal Section View of Test System



35




0.9 m (3 ft)

Cross Section View

Platen assembly

36




Schematic of Self-Reacting Frames / Foundation

Post-tensioned concrete beam across bottom of concrete frame.

Steel cross-beam and post-tensioned steel tie-rods.

Horizontal forces (red) are reacted by the horizontal self-reacting concrete frame and the steel

cross-beam above.

Vertical forces (blue) are reacted by the

vertical self-reacting concrete and steel

frame.


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Quantity 4Capacity (tension) 4,500 kN (1,000 kips)Capacity (compr.) 7,000 kN (1,600 kips)Stroke 2.5 m (100 in)Rod diameter 0.3 m (12 in)Bore 0.5 m (20 in)Max velocity 1.8 m/s (70 in/s)Swivels ± 10°

Servovalves 19.3 m3/min (5,000 gpm)Pressure 35 MPa (5,000 psi)Weight (each) 13 ton (28 kips)

38




Vertical actuators Quantity 4Capacity (tension) NACapacity (compr.) 18,000 kN (4,000 kips)Stroke 0.25 m (10 in)Rod diameter NABore 0.81 m (32 in)Max velocity 0.4 m/s (15 in/s)Swivels ± 2°

Servovalves 11 m3/min (3,000 gpm)Pressure 35 MPa (5,000 psi)Weight (each) 4.4 ton (9.7 kips)

39




Outrigger stabilizing actuators

Quantity 4Capacity (tension) NACapacity (compr.) 534 kN (120 kips)Stroke 0.5 m (20 in)Rod diameter NABore 0.19 m (7.5 in)Max velocity 0.5 m/s (18 in/s)Swivels ± 2°

Servovalves 0.7 m3/min (180 gpm)Pressure 21 MPa (3,000 psi)Weight (each) 0.4 ton (1 kips)

40




Control Room

Hydraulic Pump

Pipe Trench

10 Accumulator Racks (10 Bottles per Rack)

Surge Tank

Accumulator Building and Control Room

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42




DIS LR Bearing, Vertical Load = 558 kips, Displacement = 22 in, velocity = 60 in/s



43




DIS LR Bearing, 400% strain



44






7. Design Example

Design of a 4-story seismically isolated building and verification of the equivalent

static force method of ASCE 7-10.

45




Four-story regular steel building part of a hospital. No in-plane or elevation irregularity. Ie = 1.5

Plan dimensions : 73.2 m x 45.75 m Total height: 19.52 m (4.88 m per story) Seismic weight above the isolation plane: 107 MN. SFRS composed of peripheral special concentrically

braced steel frames (per ASCE 7-10) R = 6

Eccentricity of 600 mm in each principal direction between the center of mass (CM) of the building above the isolation plane and the shear center (SC) of the isolation system

Design seismic parameters (per ASCE 7-10): Soil type D

SDS = 0.83 and SD1 =0.58 (DE) SMS = 1.25 and SM1 =0.87 (MCE)

Building Description

Isolation plane

4 @

4.8

8 m

e = 600 mm

CM (building)

73.2 m

45.7

5 m

SC (isolation)

e = 600 mm

46




Two types of isolation bearings with the force-displacement envelopes shown from prototype testing. 20 bearings of Type 1 34 bearings of Type 2

Linear viscous dampers in parallel with the isolation system: Provide a supplemental damping

ratio of 9.4% of critical.

Seismic Isolation System

50 mm

50 mm

0.92 kN/mm

0.77 kN/mm

2.51 kN/mm

2.09 kN/mm

1.31 kN/mm

1.10 kN/mm

2.84 kN/mm

2.37 kN/mm

Type 1

Type 2

47




1. Determine the total design displacement, DTD , and the total maximum displacement, DTM , of the bearings using the equivalent static force procedure.

2. Determine the minimum design force under and over the isolation plane. It is assumed that wind loads are not critical.

3. Verify that the equivalent static force procedure is applicable for this building.

Design Requirements

48




Design displacement at the center of rigidity of the bearings:

Equivalent viscous damping ratio and damping

reduction factor:

1. Determination of DTD and DTM for the bearings

SD1 =0.58

+ 0.094

49




Effective isolated period at the design displacement:

W = 107 MN

2Typemin1 Typeminmin 3420 DDD kkk +=

50




Seismically Isolated Buildings 51

Assume a design displacement, DD

Determine the minimum lateral siffness of isolators , kDmin, at displacement DD.

Calculate effective isolated period, TD, at displacement DD:

Calculate equivalent viscous damping, ζ, and the reduction factor BD.

Calculate an updated design displacement, DD∗ :

?DD ≈ DD*

YesNo Preliminary design completedDD = DD *

*





4-Story Isolated Building Example




DD = 311.6 mm; kDmax =76.39 kN/mm, TD = 2.59 s

DTD = 389.8 mm

53


e = 600 mm CM (isolation)

73.2 m

45.7

5 m

CM (building)

e = 600 mm




Maximum displacement at the center of rigidity of the bearings:

Equivalent viscous damping ratio and damping

reduction factor:

SM1 =0.87

+ 0.094

54





Effective isolated period at maximum displacement:

W = 107 MN

2Typemin1 Typeminmin 3420 MMM kkk +=

55





Assume a maximum displacement, DM

Determine minimum effective stiffness of the bearings, kMmin, at a displacement DM.

Calculate the effective isolated period, TM, at a displacement DM:

Calculate the equivalent viscous damping ratio, ζ, and the damping reduction factor BD.

Calculate an updated maximum displacement, DM∗ :

? DM ≈ DM*

Yes No Preliminary design completed DM = DM *

*

56




4-Story Isolated Building Example




DM = 485.3 mm; kMmax =71.68 kN/mm, TM = 2.68 s

DTM = 607.2 mm

58


e = 600 mm CM (isolation)

73.2 m

45.75 m CM (building)

e = 600 mm




Minimum design force under the isolation plane:

Minimum design force over the isolation plane:

( )( ) MN23.80mm311.6kN/mm76.39 ==bV

( ) 2226.2683

831 =→≤===≤ II RRR

( )( ) MN11.902

mm311.6kN/mm76.39==sV

59

2. Determination of minimum design force under and over the isolation plane




Vs cannot be less than: I. The design force on the structure with the same seismic

weight W on a rigid base according to the equivalent lateral force procedure of ASCE 7-10 but with an effective period TD.

II. The lateral force required to activate the isolation

system multiplied by 1.5. III. The design wind load according to ASCE 7-10. This verification is not made here.

( )

( )

DSs s

e

D1

e

SV C W with : CR I

ST R I

= =

≤( ) ( ) ( ) OKMN90.11MN99.5MN1075.1659.2

58.011 =<=== s

eD

D VWIRT

SV

( ) ( ) ( )( )( )OKMN90.11MN01.11

mm50kN/mm84.234kN/mm51.2205.134205.1

2

max,2max,1max,2

=<=

+=+=

s

yee

VVDkkV

60

2. Determination of minimum design force under and over the isolation plane




Design spectral acceleration at a period of 1 second is less than or equal to 0.6 g. SD1 =0.58

Structure is located on soil type A, B, C, or D. Soil type D

Structure above isolation interface not more than four stories or 20 m in height. Total height of the building = 19.52 m

Isolated period of structure at design displacement less than or equal to 3 seconds. TD = 2.59 s

61

3. Verification of applicability of equivalent static force procedure




Isolated period of structure at design displacement greater than three times the elastic fixed-based period of the structure. Use the empirical formula of ASCE 7-10 for the fundamental period of

concentrically braced frame: Ta = 0.0488 hn0.75 where hn is the total height

of the building in meters.

The structure is regular: by assumption The isolation system does not limit MCE displacement to less than the

total maximum displacement. To insure during the design of the bearings.

( )( ) s59.2s35.1s45.03= 3

s45.0m52.190488.0 0.0488 = 75.0750

=<===

Da

.na

TThT

62





( )

( ) ( )

( )( ) ( )

kN/mm85.031kN/mm56.1

mm6.311kN31.487

kN31.487mm50mm6.311kN/mm32.1mm50kN/mm84.2

kN/mm85.0mm32.623kN26.158

31

kN26.158mm50mm32.62kN/mm32.1mm50kN/mm84.2:2 Type Bearings

mm32.62mm6.3112.02.0

20

=>==

=−+=

==

=−+=

==

DD

D

D

D

DD

D

D

D.

D

kk

F

k

F

D

50 mm

0.92 kN/mm

0.77 kN/mm

2.51 kN/mm

2.09 kN/mm

Type 1

50 mm

1.31 kN/mm

1.10 kN/mm

2.84 kN/mm

2.37 kN/mm

Type 2

( )

( ) ( )

( )( ) ( )

kN/mm73.031kN/mm18.1

mm6.311kN17.366


kN/mm73.0mm32.623kN83.136

31


mm32.62mm6.3112.020

20

=>==

=−+=

==

=−+=

==

DD

D

D

D

DD

D

D

D.

D

kk

F

k

F

D.

63


Effective stiffness of the isolation system at design displacement greater than 1/3 of effective stiffness at 20% of design displacement.

Same conclusion if minimum stiffness values are used.




The isolation system 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 percent of the total design displacement.

Same conclusion if minimum stiffness values are used.

50 mm

0.92 kN/mm

0.77 kN/mm

2.51 kN/mm

2.09 kN/mm

Type 1

50 mm

1.31 kN/mm

1.10 kN/mm

2.84 kN/mm

2.37 kN/mm

Type 2

( )

( ) ( )( ) ( )

( ) ( )( ) ( ) kN14.587mm50mm8.389kN/mm31.1mm50kN/mm84.2




mm9.194mm8.3895.05.0

50

50

=−+=

=−+=

=−+=

=−+=

==

TD

TD

TD

TD

D

D.

D

D.

TD

F

F

F

F

DDTD0.5DTD

Force

Déplacement

TDDF

TDDF

5.0

WFFTDTD DD

025.05.0

+≥

( ) ( )( ) ( )

( ) MN14.19MN1070.025MN46.16025.0MN73.28

MN46.16kN82.33134kN81.25820

MN73.28kN14.58734kN12.43820:System Isolation Complete

50

50

=+=+≥=

=+=

=+=

WFF

F

F

TDTD

TD

TD

D.D

D.

D

64







8. Project Example Design of a Base Isolated Building per

ASCE 7-10 Standard

Contributor: Jorge Mario Cueto Baiz

65




General Description of the Building • Use

– Residential • Plan Dimensions

– 20 m x 20 m • Floor Area

– 340 m2

(Residential) – 430 m2

(Basement)

66




General Description of the Building • # of Floors

– 10 + 2 Basements

• Story Height – 2.40m

67




General Description of the Building • Structural System

– This building has two different structural systems.

– Residential Floors (Upper System) • Reinforced Concrete (RC) Bearing Walls with flat RC slab. • Walls Thickness: 0.12m • Slabs Thickness: 0.10m

– Basement Floors (Lower System)

• RC Structural Walls with ribbed slab • Walls Thickness: 0.40m

68




General Description of the Building • Comments on the Structural System (Why two?)

– Big cities have one common problem: lack of space. – Bearing Walls is a cheap and fast way to construct residential

buildings. – Walls systems are not good to provide space for parking lots,

therefore, frame systems must be used for basements. – This means that the systems must be combined, however:

• The design must meet a significant number of requirements imposed by codes.

• The behavior of the overall building is driven by the interface between both systems.

• That interface is subjected to a high demands from the upper level which might leads to a non-ductile behavior. That is undesirable.

69




General Description of the Building • Base Isolation as a Solution

– Instead of combining the systems, let’s divide them using an adequate interface called: The Isolation Level.

– Two reasons why this building is expected to be a good candidate: • Look at the overall dimensions of the upper system: 20 x 20 x 25 m, is almost a cube! • The upper system has several walls. This means that its behavior will be close to a rigid

body. Keep in mind that not all the walls have to be structural.

– However, there are issues to be aware of: • Accommodate the displacement in the interface. Stairs, elevators, ducts, access ramps, etc.

This is the most critical one but is a reminder that the success of these kind of projects relies on the interaction of all the professional involved: architect, electrical, structural, geotechnical, etc.

• The elements that will support the isolators could end up being so massive that the parking space is significantly reduced.

70




Load Analysis • Dead Load (DL)

– Self Weight • A preliminary model could be built in order to have a sense of

the self-weight of the structural elements.

• SW Upper Level: 28470kN

• SW Lower Level: 7900 kN

71




Load Analysis • Dead Load (DL)

– External • This load will depend on several aspects such as:

– Use of the building (Luxurious condos and rental apartments will have different type of finishing).

– Materials to be use in the nonstructural walls. – Non structural components different than the walls (ceilings, ducts, etc.). – The finishing and the nonstructural components are different in the

residential floors, in the basements levels and in the roofs.

• For this particular case, the external dead loads are: Upper Level: 2.0 kN/m2 x (340 m2 x 10 + 430 m2 x 1 ) = 7660 kN Lower Level: 1.2 kN/m2 x (430 m2 x 1 ) = 516 kN

72




Load Analysis • Live Load (LL)

– Using the ASCE 7-10; Table 4-1.

• For this case in particular the live loads are: Upper Level: 7030 kN Lower Level: 830 kN

73




Load Analysis • Summary

DL (SW + Ext) LL(kN) (kN)

36130 7030

8416 830ISOLATION LEVEL

SEISMIC WEIGHT TO ISOLATE

74




Location and Seismic Hazard Information • Specific Location

– The project is assumed to be located in: Palos Verdes, California, 90274(USA).

75




Location and Seismic Hazard Information • Risk Category and Importance Factor. ASCE 7-

10

–For seismically isolated buildings, Table 1.5-2 DOES NOT APPLY, instead:

RESIDENTIAL

I ASCE 7-10, Table 1.5-11 ASCE 7-10, 17.2.1

USERISK CATEGORY

Importance Factor

76




Location and Seismic Hazard Information • Seismic Hazard Information

– Site Class: the geotechnical report for this project specifies the soil parameters and classifies it as a soft rock. According to ASCE 7-10, Table 20.3-1 the Site class is:

77





– Spectral Response Acceleration Parameters: The USGS US Seismic Design Map Web Application is used to obtain the basic parameters to build up both spectra, DE and MCE. The input data is:

78





– Spectral Response Acceleration Parameters: The output provided by the USGS US Seismic Design Map Web Application is:

79





– Site Coefficients: With the basic parameters from USGS application output, ASCE 7-10, Table 11.4-1 and -2 are used to compute Fa and Fv.

80





– MCE and Design Spectral Acceleration Parameters: As per ASCE 7-10, 11.4.3 and 11.4.4:

SMS=FaSs = 1.0x1.498 =1.498

SM1=FvS1 = 1.3x0.574 = 0.746

SDS=2/3SMS = 0.67x1.498 = 0.999

SD1=2/3SM1 = 0.67x0.746 = 0.497 81





– MCE and Design Response Spectra: Following the steps in ASCE 7-10, 11.4.5, the spectral information and graphs is as follows:

SITE CLASS C SMS (g) 1.498 To (s) 0.100SS (g) 1.498 SM1 (g) 0.746 Ts (s) 0.498S1 (g) 0.574 SDS (g) 0.999 TL (s) 8.00

FA 1.00 SD1 (g) 0.497FV 1.30

ASCE 7-10, Fig. 22-12

82





– Seismic Design Category (SDC) As per ASCE 7-10, 11.6.

Risk Cat. IS1 < 0.75 YES

SDC - SDS D SDC Due to SDS, Table 11.6-1SDC - SD1 D SDC Due to SD1, Table 11.6-2

SDC D

83




Fixed-Base Seismic Analysis • Modeling

– SAP2000 is used to model the structure.

84




Fixed-Base Seismic Analysis • Periods and Mode Shapes

– MODE 1 • T1 = 0.81s • Main Direction: Rotational

85





– MODE 2 • T2 = 0.58s • Main Direction: Y

86





– MODE 3 • T3 = 0.52s • Main Direction: X

87




Fixed-Base Seismic Analysis – Period Determination. ASCE 7-10; 12.8.2

• T < Cu x Ta , where Ta is from eq 12.8-7 and Cu is from Table 12.8-1.

– Ta = Ct x hnX

– Tmax = Cu x Ta

– T from model THEREFORE:

hn (m) 25Ct 0.049x 0.75

Ta (s) 0.55

SD1 0.497Cu 1.40 Table 12.8-1

Tmax (s) 0.77

Mode T UpFixed (s) Direction1 0.810 Rotational2 0.580 Y3 0.516 X

Tx (S) 0.52Ty (S) 0.58

Definite Fundamental Periods

88




Fixed-Base Seismic Analysis – Irregularities. ASCE 7-10; Table 12.3-1 & Table 12.3-2 – 1aH and 1bH Torsional and Extreme Torsional

10 0.0648 0.0452 0.0085 0.0086 0.0100 OK NA NA 1.009 0.0563 0.0393 0.0085 0.0086 0.0101 OK NA NA 1.008 0.0478 0.0335 0.0085 0.0086 0.0100 OK NA NA 1.007 0.0393 0.0276 0.0082 0.0084 0.0097 OK NA NA 1.006 0.0311 0.0219 0.0078 0.0079 0.0092 OK NA NA 1.005 0.0233 0.0165 0.0071 0.0073 0.0085 OK NA NA 1.004 0.0162 0.0115 0.0062 0.0063 0.0074 OK NA NA 1.003 0.0100 0.0072 0.0050 0.0051 0.0060 OK NA NA 1.002 0.0050 0.0036 0.0035 0.0036 0.0042 OK NA NA 1.001 0.0015 0.0011 0.0015 0.0016 0.0019 OK NA NA 1.00

TSLAB 0.0000 0.0000 0.0000 0.0000 0.0000 Apply Ax 0 0 #¡DIV/0!

10 0.0695 0.064203 0.0092 0.0105 0.0123 OK NA NA 1.009 0.0602 0.055869 0.0092 0.0106 0.0123 OK NA NA 1.008 0.0510 0.047493 0.0091 0.0105 0.0122 OK NA NA 1.007 0.0418 0.039162 0.0089 0.0102 0.0119 OK NA NA 1.006 0.0330 0.031031 0.0084 0.0097 0.0113 OK NA NA 1.005 0.0246 0.023296 0.0076 0.0088 0.0103 OK NA NA 1.004 0.0170 0.016194 0.0066 0.0077 0.0090 OK NA NA 1.003 0.0104 0.009991 0.0053 0.0062 0.0072 OK NA NA 1.002 0.0051 0.004987 0.0036 0.0043 0.0050 OK NA NA 1.001 0.0015 0.001502 0.0015 0.0018 0.0021 OK NA NA 1.00

TSLAB 0.0000 0 0.0000 0.0000 0.0000 Apply Ax 0 0 #¡DIV/0!

Level δ X1 (m) δ X2 (m) ∆1 (m) ∆ MAX T (m) ∆ MAX E (m) OBSERV δ MAX (m) δ PROM (m) A X

Level δ Y1 (m) δ Y2 (m) ∆1 (m) ∆ MAX T (m) ∆ MAX E (m) OBSERV δ MAX (m) δ PROM (m) A X

δX1

δX2

δY1 δY

2

89




Fixed-Base Seismic Analysis – Irregularities. ASCE 7-10; Table 12.3-1 & Table 12.3-2 – Diaphragm Irregularities

– CLASSIFICATION OF THE STRUCTURE:

3H. Diaphragm Discontinuity Irregularity

Open Area 9.1 m2.Diaph Area 337 m2.

Open Area < 0.50xDiaph Area - OK!

4H to 5H: NOT APPLICABLE

1V to 5V: NOT APPLICABLE

2H. Reentrant Corner Irregularity NOT APPLICABLE

REGULAR90




Seismic Analysis of Base Isolated Building • Codes and References

– For the design example, reference will be made to the following documents:

1. ASCE Standard (ASCE/SEI 7-10), Minimum Design Loads for Buildings and Other Structures, American Society of Civil Engineers, Reston, Virginia.

2. C. Christopoulos and A. Filiatrault, Principles of Passive Supplemental Damping and Seismic Isolation, IUSS Press, Pavia, Italy, 2006.

3. Constantinou, M.C, Kalpakidis, I., Filiatrault, A., Ecker R.A., LRFD-Based Analysis and Design Procedures for Bridge Bearings and Seismic Isolators, MCEER Report 11-0004, September 26, 2011.

4. Constantinou, M.C, Whittaker, A.S., Kalpakidis, Y., Fenz, D.M and Warn G.P., Performance of Seismic Isolation Hardware under Service and Seismic Loading, MCEER Report 07-0012, August 27, 2007.

91




Seismic Analysis of Base Isolated Building • Preliminary Design of Isolators

– Why preliminary? • The design of isolators is highly sensitive to geometry and material. • The capacity of the isolator depends on the displacement they are subjected to. This means that the

displacement has to be known (or assumed) to find out the properties. • The preliminary design then, is used to start with some initial values of the isolators and then iterate up to the

point where the displacement assumed is equal to the displacement from the spectra. Also, project requirements must be satisfied, i.e. minimum overlap factor, limits on the shape factor and maximum displacement. Then, with the values of load and maximum displacements, adequacy assessment of the stability and strength of isolators must be performed.

– Type of isolator. • The selection of the type of isolator hardware (TFP, Lead-Rubber, among others) depends on many reasons.

For this project, the isolator to be used is Lead-Rubber. – Recommended Procedure for Preliminary Design .

• There is an 8-steps procedure recommended to perform the Preliminary Design.

92




Seismic Analysis of Base Isolated Building

• Preliminary Design of Isolators – Step 1 – Geometric Properties

• Ref. 3 recommends the following as a starting point:

Do ≈ 3Di to 6Di Tr ≥ Di

Where: –Do: Diameter of rubber –Di: Diameter of the lead plug. –Tr: Total thickness of rubber.

93





– Step 2 – Material Properties • The properties of the material depends on fabricator, however, the

rubber and lead can be typically found with the following values:

Where: –Geff: Effective Shear Modulus of Rubber. –K: Compression modulus (or Bulk Modulus). –GLEAD: Shear Modulus of Lead. −τpy: Shear Lead Strength. –Lower and Upper Bound Values are according to recommendations of Ref. 3 and fabricator.

Average Lower Bound Upper BoundValues Values Values

Geff (MPa) 0.7 0.595 0.805K (MPa) 2000 2000 2000

GLEAD (MPa) 150 127.5 172.5

τpy (MPa) 10 8.5 11.5

MATERIAL PROPERTIES

94





– Step 3 – Hysteresis Information for One Isolator • The hysteresis loop can be characterized with the following

parameters:

Where: –Qd: Characteristic Strength (kN). –AL: Lead Plug Area (mm2). –Arubber: Bonded Rubber Area (mm2). –Kd: Post-elastic Stiffness (kN/mm). –Y = 25 mm as recommended in Ref. 2.

95





– Step 4 – Weight to Isolate and Number of Isolators

• The number of isolators is selected depending upon the requirements for the project. For this example, the

isolators are located on top of the walls of the lower system.

NUMBER OF ISOLATORS : 28

96





• Preliminary Design of Isolators – Step 5 – Properties of the System of Isolators

• With the number of isolators, the characteristics parameters for the hysteresis loop of all the isolators can be computed:

• Where N Is the number of isolators.

97





• Preliminary Design of Isolators – Step 6 – Assumption of Displacement Xb and

Computation of Dynamic Properties:

98





– Step 7 – Computation of Design Displacement (Sd) and Verification of Xb

• With the damping of the system and the information of the response acceleration spectra given, the design displacement can be computed.

• To do so, a damping modification factor B must be computed, according to Ref. 3:

• With the period Teff and the displacement reduced response spectra, Sd can be read and iteration on Xb must be performed until Xb=Sd.

99





– Step 8 – Preliminary Checking • Some limits are checked in order to have preliminary results on

parameters that might changes assumptions done at the beginning. These are:

– Project Requirement Checking:

» Maximum Displacement. For this project, the maximum displacement allowed due to issues with the ducts is 250mm.

Xb ≤ 250mm

– Overlapping Area Factor (Ar /A ) and Shape Factor (S) Checking: » This initial checking estimates buckling and shear strain issues.

100





– Summary Flow Chart for Preliminary Design

101





• Results from Preliminary Analysis – Once the iterative process is done for both, lower bound

(LB) and Upper Bound (UB) properties, two targets are sought:

1. Dynamic Properties of the System:

DE MCE DE MCEβEFF 0.208 0.161 0.223 0.18

Teff (s) 1.72 1.88 1.41 1.57Sd (mm) 137 230 110 189

LOWER BOUND UPPER BOUND

102




Seismic Analysis of Base Isolated Building • Results from Preliminary Analysis

2. Material Properties for Modeling: 2.1 Lateral Properties

Keff is the only one that changes because is the only one dependent on the displacement.

2.2 Vertical Stiffness

All these values are for the system, therefore, have to be divided by 28.

DE MCE DE MCEK1 SYSTEM (kN/mm) 120 120 163 163

Fy SYSTEM (kN) 3006 3006 4067 4067

Qd SYSTEM (kN) 2692 2692 3642 3642Kd SYSTEM (kN/mm) 29.4 29.4 39.8 39.8

KEFF (kN/mm) 49.1 41.1 72.9 59.1


For Non linear Analysis Cases

For Linear Analysis Cases

LB UBKvγ (kN/m) 1962261 2654824

KvV (kN/m) 3392920 3392920

KVERTICAL (kN/m) 1243244 1489416

103




Seismic Analysis of Base Isolated Building • Selection of analysis Procedure. ASCE 7-10, 17.4

– Seven criteria must be evaluated to know which procedure is applicable. This selection is only for Equivalent Lateral Force (ELF) or Modal Response Spectrum Analysis (MRSA). Time-History Analysis (THA) is always permitted

LOWER BOUND

1. S1 (g) 0.574 OK!

2. SITE CLASS C OK! (ELF and MRSA)

3. Height Above Isol (m) 24 ELF IS NA!!3. # of Floors 10 ELF IS NA!!

4. TM (s) 1.88 Tm < 3.0 s; OK!

Tx FIXED-BASE (s) 0.52

Ty FIXED-BASE (s) 0.58

3 x TMAX FIXED-BASE (s) 1.74

5. TD (s) 1.72 Td < 3Tfix; ELF IS NA!!

6. REGULAR? REGULAR OK!

7a Effective Stiffness Keff at Xb (kN/mm) 49.1

Keff at 0.2Xb (kN/mm) 128 OK! (ELF and MRSA)7b Restoring Force Xb (mm) 137

F at Xb (kN) 6303

0.5Xb (mm) 69

F at 0.5Xb (kN) 4286 OK! (ELF and MRSA)

104





• Selection of analysis Procedure. ASCE 7-10, 17.4 UPPER BOUND

1. S1 (g) 0.574 OK!

2. SITE CLASS C OK! (ELF and MRSA)

3. Height Above Isol (m) 24 ELF IS NA!!3. # of Floors 10 ELF IS NA!!

4. TM (s) 1.57 Tm < 3.0 s; OK!

Tx FIXED-BASE (s) 0.52

Ty FIXED-BASE (s) 0.58

3 x TMAX FIXED-BASE (s) 1.74

5. TD (s) 1.41 Td < 3Tfix ELF IS NA!!

6. REGULAR? REGULAR OK!

7a Effective Stiffness Keff at Xb (kN/mm) 72.9

Keff at 0.2Xb (kN/mm) 205 OK! (ELF and MRSA)7b Restoring Force Xb (mm) 110

F at Xb (kN) 7452

0.5Xb (mm) 55

F at 0.5Xb (kN) 5262 OK! (ELF and MRSA)

USE: MRSA 105




Seismic Analysis of Base Isolated Building • Modal Response Spectrum Analysis

– Objectives: • # of modes to use. • Determine isolated and non-isolated modes and periods. • Verify mass participation > 90%. • Build up the “Reduced Spectra”. • Must be done for Lower and Upper Bound and DE and MCE. • Check seismic design requirement as per ASCE 7-10.

– Number of Modes to Use: • It is recommended to use:

– (Number of DOF x 3) + (Number of Isolators x 3 ). – 14* x 3 + 28 x 3 = 126 modes.

» * 14 = 10 residential floors + 2 machinery and elevators roofs + 2 basements.

106




Seismic Analysis of Base Isolated Building • Modal Response Spectrum Analysis

– Isolated and Non-Isolated Modes. • This is done in order to identify the periods of vibration that

will be reduced by the new damping introduced by the isolator. • In this example, the first three modes were clearly isolated. • ISOLATED MODES:

• NON-ISOLATED FIRST THREE MODES:

Mode 1 Mode 2 Mode 3

Mode 4 Mode 5 Mode 6

107




Seismic Analysis of Base Isolated Building • Modal Response Spectrum Analysis. (LB – DE)

– Isolated Periods and Mass Verification.

TABLE: Modal Participating Mass RatiosOutputCase StepType StepNum Period UX UY UZ SumUX SumUY SumUZ

Text Text Unitless Sec Unitless Unitless Unitless Unitless Unitless UnitlessMODAL Mode 1 1.805304 0.00176 0.83951 2.41E-09 0.00176 0.83951 2.41E-09MODAL Mode 2 1.792631 0.84255 0.00193 3.059E-07 0.84431 0.84144 3.083E-07MODAL Mode 3 1.519694 0.00133 0.00277 2.126E-08 0.84565 0.8442 3.295E-07MODAL Mode 4 0.543093 2.252E-07 0.00172 3.795E-07 0.84565 0.84592 7.09E-07MODAL Mode 5 0.413024 7.226E-06 0.00338 4.397E-07 0.84565 0.8493 1.149E-06MODAL Mode 6 0.40044 0.0035 6.197E-06 0.00003517 0.84915 0.84931 0.00003632

MODAL Mode 66 0.01282 2.887E-06 0.00047 0.00135 0.98762 0.99247 0.90003MODAL Mode 67 0.012592 0.0000222 0.00094 0.00147 0.98764 0.99341 0.9015MODAL Mode 68 0.011889 0.00003171 0.00035 0.00088 0.98767 0.99376 0.90237MODAL Mode 69 0.011391 2.767E-06 0.0011 0.00022 0.98767 0.99486 0.90259MODAL Mode 70 0.011 0.00008376 4.638E-06 0.0005 0.98776 0.99487 0.9031

108




Seismic Analysis of Base Isolated Building • Modal Response Spectrum Analysis. (LB – MCE)



Text Text Unitless Sec Unitless Unitless Unitless Unitless Unitless UnitlessMODAL Mode 1 1.959463 0.00094 0.84343 1.128E-09 0.00094 0.84343 1.128E-09MODAL Mode 2 1.948408 0.84453 0.00101 2.169E-07 0.84547 0.84445 2.18E-07MODAL Mode 3 1.630073 0.00117 0.00114 1.617E-08 0.84663 0.84559 2.342E-07MODAL Mode 4 0.554051 1.826E-07 0.00124 3.975E-07 0.84663 0.84683 6.317E-07MODAL Mode 5 0.415845 0.00000469 0.00239 4.267E-07 0.84664 0.84922 1.058E-06MODAL Mode 6 0.403004 0.00246 4.096E-06 0.00003569 0.8491 0.84922 0.00003675

MODAL Mode 67 0.012607 0.00002566 0.00096 0.00158 0.98762 0.99405 0.90155MODAL Mode 68 0.011882 0.00002191 0.00036 0.00085 0.98764 0.99442 0.9024MODAL Mode 69 0.011397 5.029E-07 0.00126 0.00023 0.98764 0.99568 0.90263MODAL Mode 70 0.010996 0.00008992 4.101E-07 0.00048 0.98773 0.99568 0.90312MODAL Mode 71 0.009875 0.0002 0.00051 0.00002329 0.98793 0.99619 0.90314

109




Seismic Analysis of Base Isolated Building • Modal Response Spectrum Analysis. (UB – DE)



Text Text Unitless Sec Unitless Unitless Unitless Unitless Unitless UnitlessMODAL Mode 1 1.520651 0.00372 0.82 9.972E-09 0.00372 0.82 9.972E-09MODAL Mode 2 1.502621 0.83607 0.0044 6.376E-07 0.83979 0.8244 6.475E-07MODAL Mode 3 1.321077 0.00206 0.01467 3.431E-08 0.84184 0.83908 6.819E-07MODAL Mode 4 0.51306 2.35E-07 0.00342 3.261E-07 0.84185 0.8425 1.008E-06MODAL Mode 5 0.404853 0.00001963 0.00703 4.831E-07 0.84186 0.84953 1.491E-06MODAL Mode 6 0.39304 0.00746 0.00001599 0.00003358 0.84933 0.84955 0.00003507

MODAL Mode 67 0.012489 0.00001133 0.00072 0.00058 0.98769 0.99104 0.90138MODAL Mode 68 0.011918 0.00004821 0.00029 0.00097 0.98774 0.99133 0.90236MODAL Mode 69 0.011396 0.00001479 0.00055 0.00016 0.98775 0.99187 0.90252MODAL Mode 70 0.01101 0.00007117 0.00004731 0.00055 0.98783 0.99192 0.90307MODAL Mode 71 0.009766 0.00035 0.00073 0.0000236 0.98818 0.99265 0.9031

110




Seismic Analysis of Base Isolated Building • Modal Response Spectrum Analysis. (UB – MCE)



Text Text Unitless Sec Unitless Unitless Unitless Unitless Unitless UnitlessMODAL Mode 1 1.664335 0.00268 0.83306 4.79E-09 0.00268 0.83306 4.79E-09MODAL Mode 2 1.649563 0.83996 0.00301 4.32E-07 0.84263 0.83607 4.37E-07MODAL Mode 3 1.420457 0.00159 0.00618 2.72E-08 0.84422 0.84225 4.64E-07MODAL Mode 4 0.530193 2.54E-07 0.00238 3.57E-07 0.84422 0.84463 8.21E-07MODAL Mode 5 0.409602 0.00001137 0.00477 4.57E-07 0.84423 0.8494 1.278E-06MODAL Mode 6 0.397337 0.00499 0.00000955 0.00003452 0.84923 0.84941 0.0000358

MODAL Mode 66 0.01281 3.85E-07 0.00053 0.0006 0.98764 0.9916 0.90025MODAL Mode 67 0.012563 0.0000182 0.00088 0.0012 0.98766 0.99248 0.90145MODAL Mode 68 0.011899 0.00004062 0.00033 0.00091 0.9877 0.99282 0.90236MODAL Mode 69 0.011388 6.987E-06 0.00088 0.0002 0.98771 0.99369 0.90256MODAL Mode 70 0.011004 0.00007795 0.00001739 0.00053 0.98779 0.99371 0.90308

111




Seismic Analysis of Base Isolated Building • Modal Response Spectrum Analysis.

– Comments on the Isolated Periods and Mass Verification. • The following table shows the periods computed previously in the

Preliminary Analysis and the extracted from the Modeling process.

• Isolated translational modes (T1 and T2) vs Teff… Why the difference?

– Influence of the translational natural modes of the building. Suggesting that the “Rigid Body” is, as expected, not that rigid. – Influence of the base of the isolators which is not fixed but is an structural system with its own stiffness.

• Isolated rotational mode (T3) vs T1 and T2 … Why the difference? – Strong Influence of the rotational natural mode of the building. Somehow expected because in the fixed-base structure, the

fundamental mode is rotational and is 40% bigger than translational fixed-base.

DE MCE DE MCEPreliminary Analysis Teff (s) 1.72 1.88 1.41 1.57

T1 (s) 1.81 1.96 1.52 1.66

T2 (s) 1.79 1.95 1.50 1.65

T3 (s) 1.52 1.63 1.32 1.42

Modelling


112




Seismic Analysis of Base Isolated Building • Effective Damping and Reduced Spectra

– Once the analysis is done, the reduced spectra can be build by applying the reduction due to the damping for the isolated modes and keeping in 5% the damping for the rest of the spectrum.

– LB - DE

1 1.812 1.793 1.52

ISOLATED MODES

DAMPING and REDUCTION FACTOR

β system 0.208B 1.53

β < 30%, ASCE 7-10; 17.6.3.3

113





– LB - MCE

1 1.962 1.953 1.63

ISOLATED MODES



β < 30%, ASCE 7-10; 17.6.3.3

114





• Effective Damping and Reduced Spectra – UB - DE

1 1.522 1.503 1.32

ISOLATED MODES



β < 30%, ASCE 7-10; 17.6.3.3

115





– UB – MCE

• Note: These spectra are already affected by the damping provided by the isolator system. Therefore, the function damping ratio and the modal damping specified in the program shall be zero!

1 1.662 1.653 1.42

ISOLATED MODES



β < 30%, ASCE 7-10; 17.6.3.3

116





• Seismic Design Requirements – For the dynamic analysis, the ASCE 7- Chapter 17,

specifies four criteria to be met: 1. Minimum Lateral Force – ASCE 7-10, 17.6.4.1 & 17.6.4.2 2. Minimum Displacement for the Isolation System – ASCE 7-

10, 17.6.4.1 3. Scaling Design Values of Combined Response – ASCE 7-10,

17.6.4.3 4. Checking Minimum Design Shear Stories – ASCE 7-10,

17.6.3.3

117




Seismic Analysis of Base Isolated Building • Seismic Design Requirements

– Minimum Lateral Force. • Design Displacement (DD) and MCE Displacement (DM) must

be computed according to 17.5.3.1 and 17.5.3.3 • Iterative process must be conducted and is shown

simultaneously for DD and DM

DD O (mm) 139 DM O (mm) 252

K D MIN (kN/mm) 49 K M MIN (kN/mm) 40

Effective Period, eq) 17.5-2TD (s) 1.73 TM (s) 1.90

Displacement - Initial ValueDisplacement - Initial Value Displacement - Initial Value

Effective Stiffness Effective Stiffness

Computation of DD and DM

Effective Period, eq) 17.5-4

Effective Stiffness

118





– Minimum Lateral Force. • Design Displacement (DD) and MCE Displacement (DM) must

be computed according to 17.5.3.1 and 17.5.3.3

Effective DampingβDamper 0.000 βDamper 0.000

β Isol 0.207 β Isol 0.153

β system 0.207 β system 0.153

Damping Coefficient*BD. = (βsystem/0.05)^0.3 1.53 BM. = (βsystem/0.05)^0.3 1.40

BD. = 4/(1-ln βsystem) 1.55 BM. = 4/(1-ln βsystem) 1.39*Two formulas are presented for comparison purposes only *Two formulas are presented for comparison purposes only

Damping Coefficient*

Effective Damping

(ASCE 7-10; Table 17.5-1)βD or βM (%) BD or BM.

< = 2 0.85 1

10 1.220 1.530 1.740 1.9

> = 50 2

119





• Seismic Design Requirements – Minimum Lateral Force.

• Design Displacement (DD) and MCE Displacement (DM) must be computed according to 17.5.3.1 and 17.5.3.3

SD1 (g) 0.497 SM1 (g) 0.746

DD (mm) eq) 17.5-1 139 DM (mm) eq) 17.5-3 252

DD O (mm) 139 Ok DM O (mm) 252 Ok

Checking Assumption of DD.

Ground Motion InfoGround Motion Info Ground Motion Info

Checking Assumption of DD.

120






• Minimum Seismic Force for Isolation System and Below (Vb) and Minimum Seismic Force for Elements Above (Vs) must be computed according to 17.5.4.1 and 17.5.4.2

• Computation of Vb

Base Shear (VB) for Isolator and Structure Below - 17.5.4.1

DD (mm) 139

KD MAX (kN/mm) 66

VB eq. 17.5-7 (kN) 9195

VB MIN (kN) Eq. 17.5-7

121






• Computation of Vs

Base Shear (VS) for Structure Above Isolator - 17.6.4.2

SMRF Table 12.2-1: A.2

Description: Spetial RC Shear Wall

R 5Ωo 2.5

Cdi 1.9 ASCE 7-10; 17.6.4.4

SDC D

Max. Height (m) 48.0 Ok; h = 24.0m < 48.0mRi = 3/8 R 1.88 OK; 1.0 < Ri < 2.0

VS MIN (kN) 4904

VS MIN Eq. 17.5-8

122





– Minimum Lateral Force. • Computation of Vs

SDS (g) 0.999

SD1 (g) 0.497

TL (s) 8.0

Ie (Table 1.5-2) 1

CS eq) 12.8-2 0.20

TD (s) 1.73

CS UP LIMIT eq) 12.8-3 or- 4 0.058CS MIN eq) 12.8-5 0.044

CS MIN S1 > 0.6g eq) 12.8-6 0.00

CS DEFINITE 0.058

VS MIN 1 (Cs) (kN) 2082

VS MIN 2 (Wind) (kN) 0VS MIN 3 (Fully Active) (kN) 0

VS MIN (kN) 2082

VS eq. 17.5-8 (kN) 4904

VS MIN 17.5.4.3

123





– Minimum Lateral Force. • For the Isolation System and the structure below, the minimum

base shear can be reduced by 10% with respect to the static analysis base shear.

• The latter is also applied to the elements above the isolation system but the reduction is of 20% if the structure is regular and 10% if is irregular.

VB eq. 17.5-7 (kN) 9195

VB MIN (kN) 8276

Structure Above: REGULARVS eq. 17.5-8 (kN) 4904

Reduction Factor 0.80VS MIN (kN) 3923

Isolation and Structure Below

Structure Above

124





– Minimum Displacements. • For the dynamic analysis, the total displacements can be affected by the ratio of the period of

the fixed-base structure (TFIXED) over the design period of isolated building (TD) as specified in eqs. 17.6-1 and -2. Also reduction factor of 0.8 for DE displacement and 0.9 for MCE is applicable.

b (m) 18.68 b (m) 18.68d (m) 19.16 d (m) 19.16

emax (m) 0.958 emax (m) 0.958

ymax (m) 9.58 ymax (m) 9.58

TD ISOL (s) 1.73 TM ISOL (s) 1.90

TFIXED (s) 0.52 TFIXED (s) 0.52

DD (mm) 139 DM (mm) 252

D'D (mm) 133 D'M (mm) 244

DTD (mm) 154 DTM (mm) 281Reduction Factor 0.90 Reduction Factor 0.80

D TD MIN (mm) 139 D TM MIN (mm) 225

Min. Design Displacement Min. MCE Displacement

125





• Seismic Design Requirements – Scaling Design Values of Combined Response

• A scale factor (SF) is computed in order for the base shear to use in the MRSA be at least the 80% (for regular structures) of the base shear (VS) from eq. 17.5-8. i.e., the minimum base shear (VS MIN)

LB – DE LB - MCE

UB – DE UB - MCE

VSPEC-D (kN) VS MIN (kN) SFX DIRECTION 3466 3923 1.13Y DIRECTION 3429 3923 1.14




126





• Seismic Design Requirements – Modification Factor (MF) due to story shear distribution

• The design shear force in each story must not be smaller than the story shear using the ELF distribution and using as a base shear (Vs) the base shear that comes from the MRSA.

LB-DE

127





– Modification Factor (MF) due to story shear distribution LB –MCE

UB –DE

128





– Modification Factor (MF) due to story shear distribution

UB –MCE

– Comments on Modal Spectral Analysis:

•No advantage except for the 20% reduction in the static design base shear. •Nonlinear time-history analysis should be considered as an alternative.

129




Seismic Analysis of Base Isolated Building • Load Combinations

– Due to the different types of structural system that are present in the project, multiple combinations are arranged for different purposes:

SDS 1.00ρ 1.30Ri 1.88Cdi 1.88Ωo 2.5Ie 1.00

Service LoadsFactored LoadsDispl, Forces and TensionDesign Upper SystemDesign TSLAB ElementsDesign Lower System

COMBINATIONS

Factored Loads

General Parameters

GROUPS

ASCE 12.4.2.3 - Combinations 5 and 6 using ρ & Ri = 1.0 ASCE 12.4.2.3 - Combinations 5 and 6 using Ωo ASCE 12.4.2.3 - Combinations 5 and 6 using ρ ASCE 12.4.2.3 - Combinations 5 and 6 with ± 0.2SDS with ρ =1.0 and using Cdi for displacements

Dead plus Live

130




Seismic Analysis of Base Isolated Building • Load Combinations

– Due to the different types of structural system that are present in the project, multiple combinations are arranged for different purposes:

D L Design SPECX Design SPECY What For:D 1.0 0.0 0.0 0.0 ServiceD+L 1.0 1.0 0.0 0.0 Service1.4D 1.4 0.0 0.0 0.0 Ultimate Gravity Design Upper, Tslab and Lower1.2D+ 1.6L 1.2 1.6 0.0 0.0 Ultimate Gravity Design Upper, Tslab and LowerCOMB1 1.40 1.0 1.88 0.56 Displ. and Max. Compression Force in IsolatorsCOMB2 1.40 1.0 0.56 1.88 Displ. and Max. Compression Force in IsolatorsCOMB3 0.70 0.0 1.88 0.56 Displ. and Max. Tension Force in IsolatorsCOMB4 0.70 0.0 0.56 1.88 Displ. and Max. Tension Force in IsolatorsCOMB5 1.40 1.0 1.30 0.4 Design Upper SystemCOMB6 1.40 1.0 0.39 1.3 Design Upper SystemCOMB7 0.70 0.0 1.30 0.4 Design Upper SystemCOMB8 0.70 0.0 0.39 1.3 Design Upper SystemCOMB9 1.40 1.0 2.50 0.8 Design TSLAB ElementsCOMB10 1.40 1.0 0.75 2.5 Design TSLAB ElementsCOMB11 0.70 0.0 2.50 0.8 Design TSLAB ElementsCOMB12 0.70 0.0 0.75 2.5 Design TSLAB ElementsCOMB13 1.40 1.0 2.44 0.7 Design Lower SystemCOMB14 1.40 1.0 0.73 2.4 Design Lower SystemCOMB15 0.70 0.0 2.44 0.7 Design Lower SystemCOMB16 0.70 0.0 0.7 2.4 Design Lower System

COMBINATIONS

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Load Combinations Combinations for the calculations of the displacements and

compression/tension forces on the isolators.

QEX and QEY are the effects of the design seismic forces in the X and Y directions, respectively.

132





Load Combinations Combinations for the calculations of the structural

elements above the isolators.

QEX and QEY are the effects of the design seismic forces

in the X and Y directions, respectively.

133





Load Combinations Combinations for the calculations of the elements of

the transition slab.

QEX and QEY are the effects of the design seismic forces

in the X and Y directions, respectively.

134





Load Combinations Combinations for the calculations of the structural

elements below the isolators.

QEX ou QEY est l'effet des forces sismiques de calcula

dans les directions X et Y, respectivement.

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Displacements and Tension Forces in Isolators • Isolation Level Displacements

– Following are presented the min. and max. values of total displacement throughout the 28 isolators. The total displacement is computed as the SRSS of the X and Y displacements for each isolator, for each type of analysis (LB, UB – DE, MCE) and for the appropriate combinations.

As expected, the displacements for UB are smaller than the ones from LB analysis given that the latter ones

have the lowest isolator stiffness.

LB-DE COMB 1 COMB 2δ TMIN (m) 0.186 0.200δ TMAX (m) 0.204 0.208

LB-MCE COMB 1 COMB 2δ TMIN (m) 0.230 0.237δ TMAX (m) 0.252 0.241

UB-DE COMB 1 COMB 2δ TMIN (m) 0.114 0.110δ TMAX (m) 0.126 0.126

UB-MCE COMB 1 COMB 2δ TMIN (m) 0.188 0.187δ TMAX (m) 0.207 0.203

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Displacements and Tension Forces in Isolators • Isolation Level Torsional Irregularity Factor

– The same concept applied for the non-isolated buildings, is applied it here in order to detect whether excessive rotation is occurring at the isolation level.

Torsional Irregularity if

Extreme Torsional Irregularity if

∆ MAX T =

∆ MAX E =

COMPUTATION OF ISOLATION LEVEL TORSIONAL IRREGULARITIES

δX1

δX2

δY1 δY

2

137





LOWER BOUND - DE

COMB1 0.174 0.188 0.1879 0.2170 0.2532 OK NA NA 1.00

COMB2 0.196 0.189 0.1955 0.2309 0.2694 OK NA NA 1.00

OBSERV δ MAX (m) δ PROM (m) A X

OBSERV δ MAX (m) δ PROM (m) A X

COMB δ Y1 (m) δ Y2 (m) ∆1 (m) ∆ MAX T (m) ∆ MAX E (m)

COMB δ X1 (m) δ X2 (m) ∆1 (m) ∆ MAX T (m) ∆ MAX E (m)

LOWER BOUND - MCE

COMB1 0.218 0.235 0.2350 0.2718 0.3171 OK NA NA 1.00

COMB2 0.226 0.196 0.2262 0.2533 0.2955 OK NA NA 1.00

COMB δ X1 (m) δ X2 (m) ∆1 (m) ∆ MAX T (m) ∆ MAX E (m) OBSERV δ MAX (m) δ PROM (m) A X

COMB δ Y1 (m) δ Y2 (m) ∆1 (m) ∆ MAX T (m) ∆ MAX E (m) OBSERV δ MAX (m) δ PROM (m) A X

138





UPPER BOUND - DE

COMB1 0.107 0.116 0.1165 0.1341 0.1564 OK NA NA 1.00

COMB2 0.115 0.101 0.1146 0.1296 0.1512 OK NA NA 1.00

COMB δ X1 (m) δ X2 (m) ∆1 (m) ∆ MAX T (m) ∆ MAX E (m) OBSERV δ MAX (m) δ PROM (m) A X


UPPER BOUND - MCE

COMB1 0.177 0.193 0.1925 0.2216 0.2585 OK NA NA 1.00

COMB2 0.188 0.175 0.1876 0.2175 0.2537 OK NA NA 1.00

COMB δ X1 (m) δ X2 (m) ∆1 (m) ∆ MAX T (m) ∆ MAX E (m) A X


OBSERV δ MAX (m) δ PROM (m)

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Displacements and Tension Forces in Isolators • Tension forces in isolators

– The type of isolators used in this project are bolted isolators. Therefore, tension forces could be developed. Ref. 4 provides a recommendation in which the maximum tension force must be limited to the cavitation force which is equal to PCAV = 3GeffA.

PCAV (kN)LB 485UB 656

COMB3 COMB4LB - DE 219 310 OK

LB - MCE 228 298 OKUB - DE 196 199 OK

UB - MCE 322 414 OK

COMPUTATION OF TENSION REACTIONS

TMAX (kN)OBSERV

140




Assessment of Adequacy of Isolators • General Procedure

– As the final step before designing the elements of the building, the adequacy of the lead-rubber bearings must be checked. For this, three general steps must be followed:

• Geometric and Material Properties. The properties established in the preliminary design are about to become the final design, therefore another parameters such as, rubber layers, shims layers and end plates must be included.

• Maximum Vertical Loads on Isolators. From the MRSA, the information of the forces, displacements and rotations are gathered. The displacements to be used must be bigger than the DTMIN computed previously.

• Strain, buckling and shims thickness checking. These revisions must be done for three different state of loads, i.e., Factored Vertical Load, LB-DE and LB-MCE. UB is not necessary because the max. displacements occur for LB.

141




Assessment of Adequacy of Isolators • Geometric and Material Properties

– For the vertical factored load (Static) it is recommended to use 80% of the nominal values. – Hysteresis loop info and vertical stiffness for the nominal values are presented in order to be compared with

the data from the fabricator.

Do (mm) 600 DYNAMICTr (mm) 160 Lower BoundDi (mm) 120 Geff (MPa) 0.7 0.56 0.595tr (mm) 8.00 K (MPa) 2000 2000 2000

Rubber Layers 20.0 GLEAD (MPa) 150 120 128

Shims 19.0 τpy (MPa) 10.0 8.0 8.5

t shims (mm) 4.76 (3/16")Fy shims (MPa) 420 Qd (kN) 113.10

End Plates (mm) 50 (2 x 1") Kd (kN/mm) 1.237Y (mm) 25

h ISOL (mm) 250 Fy (kN) 126.3

h ISOL+PLATES (mm) 300

S 18.00 KVγ (kN/m) 2308543

KVV (kN/m) 3392920

KVERTICAL (kN/m) 1373806

GEOMETRIC PROPERTIES

NOMINAL STATIC

MATERIAL PROPERTIES

HYSTERESIS LOOP INFO

VERTICAL STIFFNESS

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Assessment of Adequacy of Isolators

• Maximum Loads and Displacements – From the MRSA, the loads and displacements are:

Type P (kN) D (mm) θ (rad)Factored Vertical 3350 0 0.01

LB - DE 4190 208 0.01LB - MCE 4210 252 0.01

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Assessment of Adequacy of Isolators • Service Loads Checking

– Initial Data – Strain Checking – Buckling Checking – Minimum Thickness of Shims

Lat. Displ.K/G S f1 (T 5-1) γu

C-S OBSERV. γuS-S K/G S f2 (T 5-8) γu

r-S

3571 18.0 1.17 1.43 < 3.5; OK! 0.00 3571 18.0 0.32 0.900 2.33 < 6.0; OK!

COMPRESSION ROTATION OBSERV.Σ γu

C-S + γuS-S+ γu

r-S

P (kN) D (mm) θ (rad) δ. Ao Ar Ar / Ao3350 0 0.01 3.14 271434 271434 1.000

Factor Pcr (kN) P'cr (kN) Pu (kN) P'cr / Pu OBSERV.0.738 9128 9128 3350 2.72 > 2.0; OK

α. ts MIN 1 (mm) ts MIN 2 (mm) ts MIN (mm) ts (mm) OBSERV.1.65 0.38 1.9 1.90 4.76 > ts min; OK

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Assessment of Adequacy of Isolators • DE Checking

– Initial Data

– Strain Checking – Minimum Thickness of Shims



C OBSERV. γuS K/G S f2 (T 5-8) γu

r

3361 18.0 1.18 3.00 < 3.5; OK! 1.30 3361 18.0 0.32 0.900 5.20 < 6.0; OK!

COMPRESSION ROTATION OBSERV.Σ γu

C + γuS+ γu

r


< 7.0 OK!

Note: No buckling check required for DE.

145




Assessment of Adequacy of Isolators • MCE Checking

– Initial Data – Strain Checking – Buckling Checking – Minimum Thickness of Shims



C OBSERV. γuS K/G S f2 (T 5-8) γu

r

3361 18.0 1.18 3.55 NA 1.58 3361 18.0 0.32 0.900 6.02 < 9.0; OK!

OBSERV.Σ γu

C + γuS+ γu

r

COMPRESSION ROTATION

Factor Pcr (kN) P'cr (kN) Pu (kN) P'cr / Pu OBSERV.0.738 9698 4669 4210 1.11 > 1.1; OK


146




Drifts and Acceleration Results • Drifts

– ASCE 7-10, 17.6.4.4 requires that for MRSA, the maximum drift shall not be higher than 1.5% the height of the floor.

– Results of drifts from previous analysis done for the building without isolators are shown.

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Drifts and Acceleration Results • Accelerations

– There is not a clear specification on the limits for the acceleration. The limits are highly dependent on the type of non-structural component within the building.

– Results of drifts from previous analysis done for the building without isolators are shown.

148




Design Forces in Selected Walls • Selected Walls

149




Design Forces in Selected Walls • Results of Walls in X Direction

TABLE: Section Cut Forces - SectionCut OutputCase P VX MX P VX MX

Text Text KN KN KN-m KN KN KN-mMX1A DESIGNSPECX -1551 -698 -1278 -420 -183 -356MX1A 1.4D -1054 2.0 97.8 -947 222.5 450.7MX1A 1.2D + 1.6L -1147 4.5 109.4 -1041 238.3 484.2MX1A COMB5 -2098 -369 -583 -1401 2 48MX1A COMB6 -2359 -356 -580 -1400 -161 -209MX1A COMB7 -1540 -372 -637 -920 -107 -174MX1A COMB8 -1801 -359 -634 -919 -270 -431

MX3A DESIGNSPECX -3492 -506 -15963 -776 -180 -5103MX3A 1.4D -2114 -249.4 27.2 -2341 -707.3 -1361.5MX3A 1.2D + 1.6L -2243 -273.6 -0.5 -2486 -789.8 -1577.7MX3A COMB5 -4766 -591 -7414 -3741 -960 -5393MX3A COMB6 -6194 -696 -4549 -5065 -1021 -3699MX3A COMB7 -3682 -458 -7410 -2605 -592 -4650MX3A COMB8 -5110 -562 -4545 -3929 -654 -2956

ISOLATED - Upper BoundORIGINAL

150




Design Forces in Selected Walls • Results of Walls in Y Direction

TABLE: Section Cut Forces SectionCut OutputCase P VY MY P VY MY

Text Text KN KN KN-m KN KN KN-mMY1A DESIGNSPECY -2333 -1210 20881 -487 -203 7288MY1A 1.4D -2006 -1111.4 -3689.7 -2180 -767.8 -2415.6MY1A 1.2D + 1.6L -2152 -1195.9 -3985.5 -2356 -834.7 -2636.2MY1A COMB5 -4057 -1893 37 -3353 -1090 -390MY1A COMB6 -3616 -1867 5140 -2943 -1032 2661MY1A COMB7 -3013 -1312 1974 -2270 -705 826MY1A COMB8 -2571 -1286 7077 -1860 -647 3878

MY1B DESIGNSPECY -2541 -1274 27988 -746 -80 2136MY1B 1.4D -2292 1221.7 3974.5 -2691 432.8 1135.6MY1B 1.2D + 1.6L -2461 1301.8 4238.9 -2899 456.8 1194.4MY1B COMB5 -4572 419 9507 -4050 162 2727MY1B COMB6 -4066 560 16460 -3694 317 3000MY1B COMB7 -3378 -211 7453 -2719 -46 2183MY1B COMB8 -2871 -70 14407 -2363 109 2456

ISOLATED - Upper BoundORIGINAL

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Design Forces in Selected Walls • Comments on the results (For this Project)

– Three groups were shown, why? • DesignSpec: In order to see the difference from the spectrum analysis only

without vertical loads and directional effects. In this one, it can be seen that isolating the building gives a reduction of 75% (avg) of the forces.

• 1.4D and 1.2D+1.6L: This combination is shown in order to realize that the

fact of having isolators makes that the upper system is supported in “point supports” instead of the continuous walls like in the original building. This means that the vertical displacement of the slab above the isolators, plays a significant role in the moments of the walls, and shall not be discarded when designing isolated buildings.

• COMBS 5 to 8: This is the final combination to design. In general, it can be seen that the reduction in design forces due to the isolation system is about 40%.

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