simplified base isolation design...

Simplified Base Isolation Design ProcedureGordon Wray, P.E.

SEAONC Protective Systems Subcommittee Objectives

> Current Unique Code Requirements• More sophisticated engineering analysis• Geotechnical – need site specific study• Peer review is required by the code and needs

to be done concurrently with the design.

> Why Simplify the Process?• Base isolated structure is a structural system

that is closest to SDOF• Only structure in US codes that often requires

non-linear time history analysis

> SEAONC PSSC believes that the design and analysis process must be simplified for more widespread use of the technology

Breaking Down the Process

> Input Parameters • Vy: Nominal (Target) system yield

strength as a fraction of total building weight

• T2: Nominal (Target) second slope system period

Displacement

Force

Vy

Displacement

Force

gKWT

22 2π=

K2

Vy = 0.9*Dp2

K2 = GrAr/h

Vy = Friction Coefficient

R

K2 = W/R

Lead Rubber Bearing

Friction Pendulum Bearing

High Damping Rubber – Vy based on rubber properties

> Consider Property Variation Upper Bound Properties Increase Base Shear

• Accounts for aging, contamination, first cycle effects, specification tolerance

• 1.33 for LRB, FPS• 1.50 for HDR

Lower Bound Properties Increase Maximum Displacement• Accounts for specification tolerance• 0.85 for all systems

> Displacement due to Accidental Torsion DTM includes 1.2 amplification factor on DM

Breaking Down the Process

DMDTM

Sample ResultT2 = 3 seconds

0

0.05

0.1

0.15

0.2

0.25

0.3

0 5 10 15 20 25

Displacement (in)

Bas

e Sh

ear (

g)

Upper

Bou

nd

(x1.

33)

Lower Bound

(x0.85)

Nomin

al

Vmax

DM DTM

Breaking Down the Process

Determine SM1

Choose T2 & DTM Choose T2 & Vy

orUse Table to determine

minimum Vy

Use Table to determine DTM

Use Chart to Determine Vmax

Determine Design Shear, Vs

Distribute Forces Vertically

Check Isolator Tension/Uplift

Design Structure

Isolator System Layout

Design Process

Design Response Spectra

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

0.0 1.0 2.0 3.0 4.0

Period (sec)

Spec

tral A

ccel

erat

ion

(g)

SM1 = 0.80g

Determine SM1

Choose T2 & DTM Choose T2 & Vy

orUse Table to determine

minimum Vy

Use Table to determine DTM

Use Chart to Determine Vmax

Determine Design Shear, Vs

Distribute Forces Vertically

Check Isolator Tension/Uplift

Design Structure

Isolator System Layout

Design Process

Determine VyT2 SM1 Max Vy

12 18 24 30 36 420.4 0.027 0.0650.5 0.048 0.023 0.08

3.0 0.6 0.078 0.037 0.021 0.080.7 0.117 0.056 0.031 0.080.8 0.166 0.079 0.045 0.028 0.080.9 0.108 0.061 0.038 0.08

DTM

T2 SM1 Max Vy12 18 24 30 36 42

0.4 0.030 0.0350.5 0.054 0.029 0.06

4.0 0.6 0.087 0.046 0.028 0.0750.7 0.130 0.069 0.041 0.027 0.080.8 0.098 0.059 0.038 0.080.9 0.134 0.080 0.052 0.036 0.08

DTM

T2 SM1 Max Vy12 18 24 30 36 42

0.4 -0.5 0.062 0.034 0.021 0.035

5.0 0.6 0.098 0.054 0.033 0.022 0.060.7 0.079 0.049 0.032 0.070.8 0.110 0.068 0.045 0.032 0.080.9 0.091 0.061 0.043 0.031 0.08

DTM

If Sm1 >= 0.7 then minimum Vy >= 0.04, otherwise minimum Vy >= 0.03

Gray area not permitted, values included for interpolation only

Notes applicable on all tables

Determine SM1

Choose T2 & DTM Choose T2 & Vy

orUse Table to determine

minimum Vy

Use Table to determine DTM

Use Chart to Determine Vmax

Determine Design Shear, Vs

Distribute Forces Vertically

Check Isolator Tension/Uplift

Design Structure

Isolator System Layout

Design Process

Determine Vmax

Unreduced Isolation System Base Shear, Vm versus S1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

S1 (g)

Vm (V

/Wt)

T2 = 2 secT2 = 2.5 secT2 = 3 secT2 = 4 secT2 = 5 secT2 = 6 sec

Vm = 0.6 x Sm1 - 0.035

Vm = 0.45 x Sm1 - 0.020

Vm = Sm1 / 3 + 0.002

Vm = Sm1 / T2

Determine SM1

Choose T2 & DTM Choose T2 & Vy

orUse Table to determine

minimum Vy

Use Table to determine DTM

Use Chart to Determine Vmax

Determine Design Shear, Vs

Distribute Forces Vertically

Check Isolator Tension/Uplift

Design Structure

Isolator System Layout

Design Process

> Select Structural System Determine Ri (typically 2)

• Concrete Shear Wall, Ri = 2.0• Ordinary Braced Frame, Ri = 1.6

> Calculate Design Base Shear Vs = Vmax/Ri

• Vs = 0.17g in example (0.27/1.6)• Vs = 0.21g for fixed base OCBF, type B soil

> Check Minimum Base Shear Requirements Vs > 1.5* Vy Vs > Wind Load Vs > Base Shear for a fixed base structure with Period TD

Design Base Shear

Simplified Modeling Procedure

Horizontally Rigid Isolator Elements (pins)

Determine SM1

Choose T2 & DTM Choose T2 & Vy

orUse Table to determine

minimum Vy

Use Table to determine DTM

Use Chart to Determine Vmax

Determine Design Shear, Vs

Distribute Forces Vertically

Check Isolator Tension/Uplift

Design Structure

Isolator System Layout

Design Process

Vertical Distribution

Low Strength, Vy < 0.04W

High Displacement

High Strength, Vy > 0.06W

Low Displacement

>Current code distribution approximates dynamic response of high strength system

>Low Strength, High Displacement results in better performance

Overturning Moments ComparisonMoment Frame, T2 = 3 seconds

0

10

20

30

40

50

60

70

0 2 4 6 8 10

Overturning Moment (k-ft/W)

Hei

ght (

ft)

Vy = 0.03 Dynamic

Overturning Moments ComparisonMoment Frame, T2 = 3 seconds

0

10

20

30

40

50

60

70

0 2 4 6 8 10

Overturning Moment (k-ft/W)

Hei

ght (

ft)

Vy = 0.03 Dynamic

Vy = 0.03 Code

Overturning Moments ComparisonMoment Frame, T2 = 3 seconds

0

10

20

30

40

50

60

70

0 2 4 6 8 10

Overturning Moment (k-ft/W)

Hei

ght (

ft)

Vy = 0.08 Dynamic

Vy = 0.03 Dynamic

Overturning Moments ComparisonMoment Frame, T2 = 3 seconds

0

10

20

30

40

50

60

70

0 2 4 6 8 10

Overturning Moment (k-ft/W)

Hei

ght (

ft)

Vy = 0.08 Dynamic

Vy = 0.08 Code

Determine SM1

Choose T2 & DTM Choose T2 & Vy

orUse Table to determine

minimum Vy

Use Table to determine DTM

Use Chart to Determine Vmax

Determine Design Shear, Vs

Distribute Forces Vertically

Check Isolator Tension/Uplift

Design Structure

Isolator System Layout

Design Process

Check Isolator Tension/Uplift0.8D 0.8D 0.8D 0.8D

Fm3

Fm2

Fm1

Tension

>Check with Manufacturer for Isolator Tension Capacity – Sliding isolators cannot resist uplift

100 psi

Check Isolator Tension/Uplift0.8D 0.8D 0.8D

Fm3

Fm2

Fm1

>Check strength/stability after progressively removing isolator elements.

0.8D

Determine SM1

Choose T2 & DTM Choose T2 & Vy

orUse Table to determine

minimum Vy

Use Table to determine DTM

Use Chart to Determine Vmax

Determine Design Shear, Vs

Distribute Forces Vertically

Check Isolator Tension/Uplift

Design Structure

Isolator System Layout

Design Process

Design Structure1.2D+L 1.2D+L 1.2D+L

Fm3

Fm2

Fm1

1.2D+L

P

P

∆ = DTM

P∆/2

P∆/2

>Design framing above isolators for Vs

Determine SM1

Choose T2 & DTM Choose T2 & Vy

orUse Table to determine

minimum Vy

Use Table to determine DTM

Use Chart to Determine Vmax

Determine Design Shear, Vs

Distribute Forces Vertically

Check Isolator Tension/Uplift

Design Structure

Isolator System Layout

Design Process

Isolator System Layout

> Use Spreadsheet to Layout Isolators Arrange Sizes, Types, Lead Core Locations

• Friction Isolator> Vy: Friction Coefficient a function of bearing

stress> T2: Function of Weight/Radius

• Lead Rubber Isolator> Vy: Function of Lead Core> T2: Function of Rubber Area and Height

• Confirm Properties with Manufacturer for varying axial loads

• Sum properties and confirm system meets Vyand T2 requirements

Isolator System Layout

> Locate Center of Stiffness/Center of Mass Design for Least Amount of Accidental Torsion

• DTM/DM assumption uses 1.2 factor as limit for torsionally regular buildings

• Arrange isolators to align center of stiffness (K2) and center of strength (Vy) to center of mass.

• Committee working on recommendations for maximum allowed eccentricity from center of mass.

Isolator System Layout

-20

0

20

40

60

80

100

120

140

160

180

-20 0 20 40 60 80 100 120 140

X Location (ft)

Y Lo

catio

n (ft

)

Isolator Type A Isolator Type B Center of MassCenter of K2 Center of Vy

Summary

> Isolator System Properties• Site dictates SM1 or Cv

• Engineer chooses T2, DTM

• Easily determine Vmax, Vy

• Useful preliminary design tool

> Alternative Modeling• Choose structural system• Build static model with horizontally rigid

isolators• Apply static loads, including P∆ load case• Layout isolators and confirm properties

with manufacturer

> Work in Progress• Modification to vertical distribution• Confirmation of allowed center of K2,

center of Vy eccentricity

Questions…

K2 Qd K2 Qd K2 Qd

Contamination - - 1.0 1.1 - -

Aging 1.1 1 1 1.1 1.2 1.2

Scragging 1 1.2 1 1.1 1.2 1.2

Upper Bound Factor from Nominal Properties 1.10 1.20 1.00 1.33 1.44 1.44

System Property Modification Factor

Maximum Upper Bound Factor from Nominal Properties

Adjusted Upper Bound Factor

System Upper Bound Specification Tolerance

System Lower Bound Specification Tolerance

Final Upper Bound Factor From Nominal Properties

Final Lower Bound Factor From Nominal Properties

1.10 1.10

0.85 0.85 0.85

0.850.850.85

1.25 1.34 1.42

1.10

1.44

0.66 0.66 0.66

Property Modification Factor Table

1.13 1.22 1.29

LRB FPS HDR

1.20 1.33