Distribution of Lateral Forces in BaseIsolated Buildings

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Distribution of Lateral Forces in Base-Isolated
Buildings

• Presenting Author Keri L. Ryan
• Additional Author Kelby York
• ASCE Structures Congress
• May 19, 2007

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Motivation The static design method for isolated
buildings needs a reliable approximation of
seismic force distribution.

• Wider use of static design methods would improve
  economy of isolation systems.
• Code force distribution is approximate.
• No comprehensive study has been conducted.
  Observations by
• Theodossiou and Constantinou (1991)
• Winters and Constantinou (1993)

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Existing Approximations to Static Lateral Force
Distribution

• Uniform Distribution
• Represents uniform first mode shape
• Assumes linear isolators
• Used by early isolation codes
• Inverted Triangle Distribution
• Representative of linear first mode shape
• Indirectly accounts for nonlinear isolators
• Used by current IBC/ASCE 7

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Existing Approximations to Static Lateral Force
Distribution (cont)

• Inverted Triangle Distribution with Additional
  Base Force
• Considered by SEAONC PSC
• Compromise that accounts for nonlinear effects
  and base inertia

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RESEARCH OBJECTIVES

• Develop improved estimates of the seismic lateral
  force distribution in base-isolated buildings.
• Based on parametric response history analysis of
  frames
• Account for isolation system nonlinearity
• Suitable for code application
• Evaluate existing approximate distributions.

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Modeling Assumptions Superstructure

• 3, 6 and 9-story single bay generic frames.
• Axially rigid, elastic beam-column elements
• Story stiffnesses calibrated to give linear first
  mode shape
• Identical mass at each level of superstructure
  (except base)
• Superstructure Rayleigh damping (5 in 1st and
  4th mode frequencies of system).

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Modeling Assumptions Isolators

• Bilinear force-deformation of isolators
• Strength Q and postyield stiffness kb selected to
  match desired equivalent stiffness and damping
• Displacement ubo is median spectral displacement
  for SAC LA 10 in 50 year motions

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Details of parametric study

• Parameters varied included
• Effective period of isolation system Td (1.5
  4 sec)
• Effective damping in isolation system ? (0
  30)
• Isolation to superstructure frequency ratio ?d/?s
• Range depends on building height and suitable
  period shift
• Superstructure to total weight ratio Ws/W
• Base mass varied from 1 to 2 times superstructure
  story mass
• Many simulations, determine median story shears
  and static forces as function of parameters

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A regression model was developed to estimate
superstructure to base shear ratio.

• Assumed regression model
• Satisfies limits
• Vs ? Vb as mass at base ? 0
• Vs ? 0 as mass in structure ? 0
• Vs/Vb ? Ws/W as damping ? 0 (identical to uniform
  distribution)
• Coefficient a 2.2 with R2 0.85 determined by
  nonlinear least squares regression of data

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No correction for nonlinearity/damping leads to
overprediction of the force applied at the base.
(Vs/Vb)/(Ws/W)
Weight ratio Ws/W
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Small correction for damping improves correlation
between approximate and observed base force.
(Vs/Vb)/(Ws/W)1-a?
Weight ratio Ws/W
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Several regression models were considered to
estimate superstructure force distribution,
modeled after various codes.

• k-distribution
• kft distribution

where
where
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k distribution and kft distribution are
compared to numerically observed median force
distribution
?5
?15
?25
Ts0.4s
Story Level
Ts0.8s
Normalized Story Force Fi/Vs
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Existing approximations and proposed method are
compared to numerically observed median force
distribution.
3-story ?5, Ts0.15s
6-story ?10, Ts0.3s
Story Level
9-story ?15, Ts0.45s
Story Force Fi/Vb
Story Shear Vi/Vb
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Existing approximations and proposed method are
compared to numerically observed median force
distribution.
3-story ?20, Ts0.4s
6-story ?25, Ts0.8s
Story Level
9-story ?30, Ts1.2s
Story Force Fi/Vb
Story Shear Vi/Vb
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Conclusions

• Equations developed here are simple and amenable
  to code implementation (further verification
  needed)
• Current IBC distribution is generally
  conservative, except for highly damped isolation
  systems or relatively flexible superstructures
• PSC proposed distribution is generally accurate
  for lightly damped structures, but tends to
  underestimate the shear force in lower levels.