simplified base isolation design...
TRANSCRIPT
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