seismic-isolation

name	seismic-isolation
description	Seismic isolation design — lead rubber bearings (LRB), friction pendulum systems (FPS), high-damping rubber bearings (HDRB), isolation period T_iso, effective stiffness K_eff, equivalent viscous damping β_eff, displacement demand D, ASCE 7 Chapter 17, IBC 2021, MCE/DBE hazard levels, vertical load capacity, non-seismic loads, testing (ASCE 7-16 Section 17.8), and applications (bridges AASHTO, buildings, industrial equipment).
metadata	{"priority":7,"promptSignals":{"phrases":["seismic isolation","base isolation","lead rubber bearing","friction pendulum","isolation system","seismic isolator"],"minScore":3}}

Seismic Isolation Design — Complete Skill

Isolation Concept

Principle of Base Isolation

Goal: Lengthen structure fundamental period from T_fixed (0.5–2 s building; 0.3–1 s bridge) to T_iso (2–4 s) → moves away from peak spectral acceleration

Period shift reduces spectral acceleration: Fixed base: S_a at T = 1.0 s might be 0.8g Isolated: S_a at T_iso = 3.0 s might be 0.15g → 5× reduction in accelerations to superstructure

Constraints: Isolation introduces large displacement (5–60 cm); must be accommodated at isolation plane (moat clearance) Wind and minor seismic: must not cause excessive movement (wind restraint or minimum stiffness) Vertical stiffness must be high (building weight; rocking prevention)

Isolation System Types

Lead Rubber Bearings (LRB)

Construction: Alternating layers of natural rubber and steel shim plates; vulcanized to steel end plates Central lead plug: provides energy dissipation (yield stress of lead: σ_y,Pb = 10 MPa)

Force-displacement behavior (bilinear): Characteristic strength Q_d = σ_y,Pb × A_Pb [N; A_Pb = cross-section area of lead plug] Post-yield stiffness K_d = G × A_rubber / T_r [G = shear modulus rubber; T_r = total rubber height] Initial stiffness K_u = (6.5 to 10) × K_d [pre-yield; effectively rigid under small loads] Yield force F_y = Q_d + K_d × F_y/K_u → iterative; F_y ≈ Q_d × K_u/(K_u - K_d)

Effective stiffness at displacement D: K_eff = K_d + Q_d / D [secant stiffness at design displacement D]

Effective damping: β_eff = 2Q_d × (D - D_y) / (π × K_eff × D²) Typical: β_eff = 15–30% at design displacement

Lead plug size and layout: Q_d typically = 3–5% of supported weight W for buildings (3%W for short periods; 5%W for longer) D_Pb = 2 × √(A_Pb / π) [diameter of lead plug] Ratio: D_Pb/D_bearing = 1/4 to 1/3 typical

Rubber properties: G = 0.5–1.5 MPa (low-damping NR); G = 0.8–1.2 MPa for standard LRB rubber Compressive modulus E_c = 6G(1 + 2κS²); S = shape factor = D/(4t_layer) for circular σ_vertical_allow ≤ 7–10 MPa (rubber bearing compressive limit; check seismic overturning)

Friction Pendulum System (FPS)

Concept: Slider on concave spherical surface of radius R; restoring force from geometry (pendulum action)

Isolation period: T_iso = 2π × √(R_eff / g) [independent of mass — all isolators have same T_iso for given R] R_eff = R - h_slider [effective radius; h_slider = height of slider] For T_iso = 3.0 s: R_eff = (T/2π)² × g = (3/2π)² × 9.81 = 2.24 m

Restoring force: F_restore = W × D / R_eff [W = supported weight; linear in D] Friction force: F_friction = μ × W [μ = friction coefficient; 3–6% for steel/PTFE]

Effective stiffness: K_eff = W/R_eff + μ × W/D [at displacement D]

Effective damping: β_eff = 2μ / (π × (D/R_eff + μ)) [typically 10–25%]

Advantage: period independent of mass; excellent for variable vertical loads; no rubber creep Double and triple FPS: multi-stage sliding with different R and μ; optimized for near-field and far-field

High-Damping Rubber Bearings (HDRB)

No lead plug: high damping achieved through filler compounds in rubber G = 0.5–1.5 MPa (varies with amplitude — scragging effect) Equivalent viscous damping β = 10–20% (amplitude-dependent; post-scragged value) Scragging: first several cycles of large amplitude reduce stiffness; values stabilize

Use: bridges; lower cost than LRB; less energy dissipation per cycle than LRB with same D

Design Displacement (ASCE 7 Chapter 17)

Design and Maximum Displacement

Design Basis Earthquake (DBE) — Level 1: S_DS, S_D1 from ASCE 7 Chapter 11 (2/3 × MCE values) Design displacement D_D (TL > T_iso): D_D = g × S_D1 × T_iso / (4π² × B_D) [meters; B_D = damping factor; T_iso in seconds] [For TL < T_iso: D_D = g×S_D1×T_iso²/(4π²×B_D×TL); TL = long-period transition period]

Maximum Considered Earthquake (MCE) — Level 2 (1.5× DBE): D_M = g × S_M1 × T_iso / (4π² × B_M)

Damping modification factor B: β_eff = 5%: B = 1.0; 10%: B = 1.2; 20%: B = 1.5; 30%: B = 1.7; 40%: B = 2.0 (ASCE 7 Table 17.5-1)

Total maximum displacement (including torsion): D_TM = D_M × [1 + y × 12e/(b² + d²)] [y = distance from CM; e = eccentricity; b,d = plan dimensions]

Example: T_iso = 2.5 s; S_D1 = 0.6g; S_M1 = 0.9g; β_eff = 20% → B_D = B_M = 1.5; TL = 12 s (long period region) D_D = 9.81 × 0.6 × 2.5 / (4π² × 1.5) = 14.72 / 59.2 = 0.249 m = 249 mm D_M = 9.81 × 0.9 × 2.5 / (4π²× 1.5) = 374 mm

Isolation Period Calculation

Required stiffness K_eff from displacement requirement: T_iso = 2π × √(W / (g × K_eff_total)) → K_eff_total = W × (2π/T_iso)² / g

For N isolators of effective stiffness K_eff_each: K_eff_total = N × K_eff_each → K_eff_each = K_eff_total / N

Isolation period iteration:

1. Assume D → compute K_eff from bilinear model → compute β_eff → get B factor → compute D from spectral demand
2. Iterate until D converges (typically 2–3 iterations)

Structural Response Above Isolation

Base shear to superstructure: V_b = K_eff × D_D [at design level; ASCE 7 uses D_D with B_D]

Superstructure base shear coefficient: V_s = V_b / W [for regular structures; ASCE 7 Eq. 17.5-9: V_s = K_eff × D_D / W] Minimum: V_s ≥ V fixed-base × I_E × S_DS / (B_D × R/Ω₀) [ASCE 7 lower limit]

Floor accelerations: Reduced by isolation (key benefit for equipment, contents, nonstructural elements) Typical: spectral acceleration at isolation level ≈ K_eff × D / W ≈ S_a(T_iso) / B

Vertical Load Capacity

LRB vertical capacity: σ_c = P / A ≤ allowable (7–10 MPa static; higher dynamic if rubber tested) Rollout (stability): P_cr = (π²/4) × G × A × D_rubber/T_r [Euler buckling analog] P_cr must exceed applied P × SF (SF = 2.0 typical under combined seismic + vertical)

Uplift check: Overturning moment from seismic → uplift on tension isolators LRB: can resist limited tension (bonded construction) — verify with manufacturer; typical limit 1–2 MPa FPS: cannot resist tension; check no uplift occurs

Testing Requirements (ASCE 7-16 Section 17.8)

Prototype testing (each type/size):

• 3 cycles at 0.25D, 0.5D, 1.0D, 1.0D + eccentric, D_TM
• Vertical loads: 1.0D + 0.5L ± overturning
• Measure K_eff and β_eff at each displacement
• Requirements: K_eff within ±15% of nominal; β_eff ≥ 80% nominal

Production testing (each bearing):

• 1 cycle at 1.0D_D; vertical = 1.0D + 0.5L
• K_eff within ±15%; acceptance rate: 100%

Standards and References

Standard	Scope
ASCE 7-22 Chapter 17	Seismically isolated structures — buildings
IBC 2021	International Building Code (references ASCE 7)
AASHTO Guide Spec. 1999	Seismic isolation of bridges
FEMA 461	Testing protocols for nonstructural components
Naeim & Kelly "Design of Seismically Isolated Structures"	Reference textbook
ISO 22762	Elastomeric seismic isolation bearings

Output

Provide: site seismic hazard (S_DS; S_D1; S_M1; site class; TL [s]), isolation system type (LRB/FPS/HDRB; basis for selection), isolator layout (N bearings; column grid; tributary weight per isolator [kN]), isolation period T_iso [s] (target and actual from K_eff), design displacement D_D [mm] and D_M [mm] (with B_D; B_M; β_eff [%]), isolator properties per unit (LRB: Q_d [kN]; K_d [kN/mm]; K_eff at D_D [kN/mm] | FPS: R_eff [m]; μ; K_eff at D_D), vertical load capacity (σ_c [MPa] vs. allow; P_cr [kN] vs. applied P; uplift check), superstructure base shear V_b [kN] and V_s/W [g], moat clearance (D_TM [mm] + tolerance; gap around building perimeter), prototype and production test requirements (displacements; acceptance K_eff/β_eff limits), and applicable standard (ASCE 7 Chapter 17; AASHTO if bridge; ISO 22762).