Use of PBEE to Assess and Improve Building Code Provisions

Transcription

1 Use of PBEE to Assess and Improve Building Code Provisions Greg Deierlein Stanford University with contributions by Curt Haselton & Abbie Liel Stanford University

2 Long Term: PBEE Standards and Practice O P E N O P E N O P E N Base Shear Damage Threshold Collapse Onset Deformation PBEE today PEER & ATC 58 vision IO LS CP 25% 5% 1% FEMA 356 Performance Levels $, % replacement Casualty rate Downtime, days

3 Nearer Term: Code Improvements & Evolution Benchmarking Building Performance Implied by Design Codes for New Buildings - Basis for improving/refining current provisions - More informed decision making for designing beyond the code using enhanced performance systems - ATC 63: Quantification of Building System Performance and Response Parameters (for new systems and materials) Improvement of 1 st -generation PBEE Approaches (e.g., FEMA 273/356) - Integration of new data and acceptance criteria using Nonlinear Time History (NLTH) Analysis - Definition, calibration and validation of codified models for nonlinear simulation - Improved procedures and criteria for selection and scaling of ground motions for NLTH analysis

4 PBEE COLLAPSE (SAFETY) Assessment Decision Variable Damage Measure Engineering Demand Parameter Intensity Measure DV: COLLAPSE DM: Loss of Vertical Carrying Capacity (LVCC) EDPs: Deformations & Forces EDP: Interstory Drift Ratio IM: Sa(T 1 ) + Ground Motions

5 Illustration 4 Story SMF Building Office occupancy Los Angeles Basin Design Code: 23 IBC / 22 ACI / ASCE7-2 Perimeter Frame System 8 inch PT slab Maximum considered EQ demands: S s = 1.5g; S 1 =.9g S a(2% in 5 yr) =.82g Design V/W of.94g Maximum inelastic design drift of 1.9% (2% limit) Typical Perimeter Frame Members Beams: 32 to 4 deep Columns: 24 x28 to 3 x4 Governing Design Parameters - Beams: minimum strength - Column size: joint strength - Column strength: SCWB - Drift: just meets limit

6 Simulation Model Gravity Frame(s) Joints with both bond-slip springs and shear springs Lateral Frame Column bondslip springs Gravity Frame(s) Lateral Frame Lumped plasticity beam-columns

7 Realistic component simulation 1.5 OR OTHER COMPUTER CODES Normalized Moment (M/M y ) Non-Deteriorated Backbone Experimental Results Mode l P re dic tion Chord Rotation (radians) N ) (k F orce r S hea Column Top Horizontal Deflection (mm) 7

8 Incremental Dynamic Analysis Collapse Capacity Stats.: Median = 2.2g σ LN =.36 s )[ g ] = 1. (T ṁ S a ġ Median col = 2.2g σ LN, col =.36g 1 2% in 5 year =.5.82g IDR col = 7-12%.82g is 2% in 5 year motion Maximum Interstory Drift Ratio

9 Sidesway Collapse Modes 4% of collapses 27% of collapses 17% of collapses 12% of collapses 5% of collapses 2% of collapses 9

10 Uncertainty Plastic Rotation Capacity Normalized Moment (M/My) Mean (µ) Plastic Rotation Capacity Normalized Moment (M/My) Mean minus standard Reduced deviation (lognormal) for both plastic (µ σ) rotation capacity and Plastic Rot. Cap. post-capping stiffness Total Chord Rotation (radians) Total Chord Rotation (radians) s )[ g ] = 2. (T p m o S a c s )[ g ] = 2. (T p m o S a c Maximum Interstory Drift Ratio Maximum Interstory Drift Ratio 1

11 Collapse Capacity with Modeling Uncert. p se a o l C o f y b i lit a P rob e tiv m ul a C u m Empirical CDF Lognormal CDF (RTR Var.) Lognormal CDF (RTR + Modeling Var.) Sa (T=1.s) [g] g.m..1 5% Median = 2.2g σ LN, Total =.36 σ LN, Total =.64 w/mod..82g 2% in 5 yrs Margin 2.7x P[collapse Sa =.82g] = 5% 11

12 Mean Annual Frequency of Collapse 1 MAF of Excedance (Poisson rate) p se a o l C o f y b i lit a P rob e tiv m ul a C u m Collapse CDF Empirical CDF.1 Lognormal CDF (RTR Var.) Lognormal CDF (RTR + Modeling Var.) Sa (T=1.s) [g] g.m. 2/5 Hazard Curve Sa at First Mode Period (g) Collapse Performance Margin: S a,collapse = 2.7 MCE Probability of collapse under design MCE = 5% MAF col = 1. x 1-4 (about ¼ of the MCE 2% in 5 year ground motion) 12

13 Nonstructural Damage and Losses (Caltech) Expected Annual Loss: about 1% of building value Conditional Loss (1/5): about 2% of building value Judy Mitrani-Reiser 13

14 Nearer Term: Code Improvements & Evolution Benchmarking Building Performance Implied by Design Codes for New Buildings - Basis for improving/refining current provisions - More informed decision making for designing beyond the code using enhanced performance systems - ATC 63: Quantification of Building System Performance and Response Parameters (for new systems and materials) Improvement of 1 st -generation PBEE Approaches (e.g., FEMA 273/356) - Integration of new data and acceptance criteria using Nonlinear Time History (NLTH) Analysis - Definition, calibration and validation of codified models for nonlinear simulation - Improved procedures and criteria for selection and scaling of ground motions for NLTH analysis

15 Shortcomings of FEMA 273/356 5 Experimenta l Re s ults ) N k( e cr o F r a e h S Element backbone predicted by FEMA 356 (Table 6-8) Column Top Horizontal Deflection (mm) Over-reliance on - static pushover method - highly idealized (and conservative) backbone curves - discrete deterministic component acceptance criteria 15

16 Enhanced FEMA 356 Realistic Inelastic Model Nonlinear Time History Analysis 2 ground motions (1 pairs) with their geometric mean scaled to hazard at Sa(T1) Statistical evaluation of deformation demands to input ground motions Probabilistic assessment of component acceptance criteria to test data Probability[Θ p >Θ p,limit-state ] = X 16

17 RC Beam-Column Simulation Model Calibration Μ Θ Cap,pl OVERVIEW OF CALIBRATION EFFORT Basic Hysteretic Model My Ke αke 5 parameter backbone curve 2 (x4) hysteretic parameters Previous RC Behavioral Studies Θ y Θ -Fardis et al. (Θcap, Θu) Experimental Results Model Pre diction -Eberhard et al. (EDP criteria for spalling and bar buckling) N ) (k F orce r S hea Current effort: Systematic calibration to 226 flexurally dominated columns Column Top Horizontal Deflection (mm) Goal: Validated model to be vetted through consensus process 17

18 Consensus on Parametric Models 1.5 M, Column Base Moment Θ, Chord Rotation Θ M Input: material, config. & geometry, details, Response Parameters: - strength and deformation anchor points - cyclic hysteretic response Damage Parameters (EDP DM) Characteristic Mean & COVs 18

19 Probabilistic EDP Statistics (e.g. drift, Θ p ) At 2% in 5 year (MCE) Sa: ] g c )[ = 1se (T ṁ S a ġ y it D ens y b i lit a P rob Peak Story Drift Ratio (story three) Mean IDR =.28 Fitted Lognormal PDF Inters tory Drift Ratio, Story Three PDF (probability density function) Drift: IDR max =.16 to.5 Mean IDR max =.28 COV = 37% Beams: Θ p,max =.12 to.45 Mean Θ p,max =.25 COV = 43% (vs. FEMA 356 Θ cp <.25) Columns: Θ p,max = to.3 Mean Θ p,max =.1 COV = 11% (vs. FEMA 356 Θ cp <.2) 19

20 Probabilistic Limit State Assessment Θ pl,max Column Plastic Rotation Demand Column Plastic Rotation Capacity Μ Θ pl,cap Θ Cap,pl y it D ens y b i lit a P rob Θ pl,cap My Θ y Ke αke Θ Demand (Θ pl,max ) µ σ ln Capacity (Θ pl,cap ) µ σ ln Peak Column Plastic Rotation Demand Beams Col s P ln, z [ D C] = 1 Φ σ ln, z where: µ µ ln, z = µ ln, D µ ln, C σ = σ + σ 2 ln, z 2 ln, D 2 ln, C Φ (standard normal table) Component Limit State Checks: Beams P[D>C] = 6 % Columns P[D>C] = 6 % (just a coincidence that they turn out the same) 2

21 IMPACT Future PBEE Codes (e.g., ATC 58) Framework Transparent, Scientific, Modular, Extendable Standardize Component Models & Criteria Structural Component Simulation & Damage Models Nonstructural Damage (Fragility) Models Systematize Decision Support Articulation of Decision Variables (Metrics) Design Support EDP to DV relationships Consistent Approaches across: Hazards, Materials, Disciplines 21