Simplified Base Isolation Design Procedure. Gordon Wray, P.E.

Simplified Base Isolation Design Procedure Gordon 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 V y : Nominal (Target) system yield strength as a fraction of total building weight Force V y Displacement T 2 : Nominal (Target) second slope system period Force K 2 Displacement T2 = 2π W K g 2

Lead Rubber Bearing V y = 0.9*Dp 2 K 2 = G r A r /h K 2 = W/R Friction Pendulum Bearing R V y = Friction Coefficient High Damping Rubber V y based on rubber properties

Breaking Down the Process > 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 D TM includes 1.2 amplification factor on D M D D TM M

Breaking Down the Process Sample Result T2 = 3 seconds 0.3 V max 0.25 0.2 Nominal Upper Bound (x1.33) Lower Bound (x0.85) 0.15 0.1 Base Shear (g) 0.05 0 0 5 10 15 20 25 Displacement (in) D M D TM

Design Process Determine S M1 & D TM Use Table to determine minimum V y or & V y Use Table to determine D TM Use Chart to Determine V max Determine Design Shear, V s Distribute Forces Vertically Check Isolator Tension/Uplift Design Structure Isolator System Layout

Design Response Spectra Spectral Acceleration (g) 1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 S M1 = 0.80g 0.00 0.0 1.0 2.0 3.0 4.0 Period (sec)

Determine V y T2 SM1 DTM Max Vy 12 18 24 30 36 42 0.4 0.027 0.065 If S 0.5 0.048 0.023 m1 >= 0.7 then minimum V 0.08 y >= 0.04, otherwise 3.0 0.6 0.078 0.037 0.021 minimum V y >= 0.03 0.08 0.7 0.117 0.056 0.031 0.08 0.8 0.166 0.079 0.045 0.028 0.08 0.9 0.108 0.061 0.038 0.08 T2 SM1 DTM Max Vy 12 18 24 30 36 42 0.4 0.030 0.035 Gray area not permitted, values 0.5 0.054 0.029 included for interpolation only 0.06 4.0 0.6 0.087 0.046 0.028 0.075 0.7 0.130 0.069 0.041 0.027 0.08 0.8 0.098 0.059 0.038 0.08 0.9 0.134 0.080 0.052 0.036 0.08 T2 SM1 DTM Max Vy 12 18 24 30 36 42 0.4 - Notes applicable on all tables 0.5 0.062 0.034 0.021 0.035 5.0 0.6 0.098 0.054 0.033 0.022 0.06 0.7 0.079 0.049 0.032 0.07 0.8 0.110 0.068 0.045 0.032 0.08 0.9 0.091 0.061 0.043 0.031 0.08

Determine V max Unreduced Isolation System Base Shear, Vm versus S1 0.6 0.5 Vm = 0.6 x Sm1-0.035 Vm (V/Wt) 0.4 0.3 Vm = 0.45 x Sm1-0.020 Vm = Sm1 / 3 + 0.002 0.2 0.1 T2 = 2 sec T2 = 2.5 sec T2 = 3 sec T2 = 4 sec T2 = 5 sec T2 = 6 sec Vm = Sm1 / T2 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 S1 (g)

Design Base Shear > Select Structural System Determine R i (typically 2) Concrete Shear Wall, R i = 2.0 Ordinary Braced Frame, R i = 1.6 > Calculate Design Base Shear V s = V max /R i 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 T D

Simplified Modeling Procedure Horizontally Rigid Isolator Elements (pins)

Vertical Distribution Low Strength, V y < 0.04W High Displacement High Strength, V y > 0.06W Low Displacement >Current code distribution approximates dynamic response of high strength system >Low Strength, High Displacement results in better performance

70 Overturning Moments Comparison Moment Frame, T 2 = 3 seconds Height (ft) 60 50 40 30 20 10 0 V y 0.03 Dynamic y = V y 0.08 y = 0.08 0.03 Dynamic Dynamic V y = V y 0.08 V= y 0.03 = Code 0.03 Dynamic Code 0 2 4 6 8 10 Overturning Moment (k-ft/w)

Check Isolator Tension/Uplift Fm3 0.8D 0.8D 0.8D 0.8D 100 psi Fm2 Fm1 Tension >Check with Manufacturer for Isolator Tension Capacity Sliding isolators cannot resist uplift

Check Isolator Tension/Uplift Fm3 0.8D 0.8D 0.8D 0.8D Fm2 Fm1 >Check strength/stability after progressively removing isolator elements.

Design Structure Fm3 1.2D+L 1.2D+L 1.2D+L 1.2D+L Fm2 Fm1 P P = D TM P /2 P /2 >Design framing above isolators for Vs

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 V y and T 2 requirements

Isolator System Layout > Locate Center of Stiffness/Center of Mass Design for Least Amount of Accidental Torsion D TM /D M assumption uses 1.2 factor as limit for torsionally regular buildings Arrange isolators to align center of stiffness (K 2 ) and center of strength (V y ) to center of mass. Committee working on recommendations for maximum allowed eccentricity from center of mass.

Isolator System Layout 180 160 140 120 Y Location (ft) 100 80 60 40 20 0-20 -20 0 20 40 60 80 100 120 140 X Location (ft) Isolator Type A Isolator Type B Center of Mass Center of K2 Center of Vy

Summary > Isolator System Properties Site dictates S M1 or C v Engineer chooses T 2, D TM Easily determine V max, V y 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 K 2, center of V y eccentricity

Questions

Property Modification Factor Table LRB FPS HDR 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 System Property Modification Factor 1.10 1.20 1.00 1.33 1.44 1.44 0.66 0.66 0.66 Maximum Upper Bound Factor from Nominal Properties 1.20 1.33 1.44 Adjusted Upper Bound Factor 1.13 1.22 1.29 System Upper Bound Specification Tolerance 1.10 1.10 1.10 System Lower Bound Specification Tolerance Final Upper Bound Factor From Nominal Properties 0.85 0.85 0.85 1.25 1.34 1.42 Final Lower Bound Factor From Nominal Properties 0.85 0.85 0.85