nonlinear analysis.greg deierlein 8-24-11
TRANSCRIPT
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 1
1
NEHRP Seismic Design Technical Briefs
Acknowledgements
2
NEHRP Consultants Joint Venture ‐ partnership of the Applied Technology Council (ATC) and Consortium of Universities for Research in Earthquake Engineering (CUREE)
The technical briefs were prepared under the Joint Venture’s existing Structural and Earthquake Engineering Research Contract with NIST
NIST Structural and Earthquake Engineering Program ‐ based on recommendations developed by ATC, and published in the ATC‐57 report, The Missing Piece: Improving Seismic Design and Construction Practices.
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 2
3
Available at....http://www.nehrp.gov/pdf/nistgcr10‐917‐5.pdf
Outline
1. Introduction ‐ Background and Motivation
2. Nonlinear Demand Parameters and Model Attributes
3. Modeling of Structural Components
4. Foundation and Soil Structure Interaction
5. Nonlinear Static Analysis
6. Nonlinear Dynamic Analysis
4
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 3
Background and Motivation
Why nonlinear analysis?
1. Assess and design seismic retrofit of existing buildings
2. Design new buildings that employ structural materials, systems or other features that do not conform to current building code requirements
3. Assess building performance for specific owner requirements (e.g., desire for enhanced‐performance)
5
Seismic Retrofit: Mitchell Earth Sciences Building at Stanford
Background and Motivation: Seismic Retrofit
• 1960’s Non‐ductile Concrete Moment Frame
• Assessed and retrofitted post‐Loma Prieta in 1993‐95
• Goal: “life safety” under M7.5 earthquake on San Andreas Fault
• Early use of nonlinear static analysis (pre‐FEMA 273)
Courtesy: Degenkolb Engineers
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 4
Background and Motivation: Illustrative ExamplesBackground and Motivation: Seismic Retrofit
• FEMA 178 (ASCE 31 Tier 1) Evaluation– Soft Story– Shear Stress Check– Nonductile Detailing
• Linear Elastic Analysis (ASCE 31 Tier 2)– SAP90 Model– Response Spectrum Analysis– Beam Deficiencies: Moment and Shear
• Proposed Strengthening: Interior and Exterior Shearwalls
Courtesy: Degenkolb Engineers
Background and Motivation: Illustrative ExamplesBackground and Motivation: Seismic Retrofit
• ATC‐33 and ATC‐40 (FEMA 356 NSP) ‐ early drafts– Pseudo 3D model, Drain 2DX
– Calculate the expected displacement
– Evaluate existing frame strength and detailing
• Design alternative retrofit with reduced wall configuration
Target Displ. 14”
Courtesy: Degenkolb Engineers
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 5
Background and Motivation: Illustrative ExamplesBackground and Motivation: Seismic Retrofit
• ATC‐33 and ATC‐40 (FEMA 356 NSP) ‐ early drafts– Pseudo 3D model, Drain 2DX
– Calculate the expected displacement
– Evaluate existing frame strength and detailing
• Design alternative retrofit with reduced wall configuration
New Target Displ. ~4”
Original Pushover
Retrofitted Pushover
Courtesy: Degenkolb Engineers
Background and Motivation: Illustrative ExamplesBackground and Motivation: Seismic Retrofit
Revised RetrofitCourtesy: Degenkolb Engineers
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 6
Background and Motivation: Illustrative ExamplesBackground and Motivation: Non‐Conforming New Tall Building
One Rincon Hill64 story residential tower
• Ductile RC Core Wall w/BRB outriggers
• Exceeds ASCE 7 limits on RC wall in SDC D
• Designed in 2005 using NL Analysis
Courtesy: Magnusson Klemencic Assoc.
Background and Motivation: Illustrative ExamplesBackground and Motivation: High Performance Building
San Francisco Public Utilities Commission Headquarters Building
• 13 story, LEED Platinum with energy efficient lighting and ventilation, water re‐use, wind and solar power generation
• Post‐tensioned RC core walls to provide self‐centering, 70 percent cement replacement
• RC flat slab, integrated with raised floor, natural lighting, and thermal ballast
• Enhanced Seismic Performance
DBE – undamaged, continued functionality (< 1% peak story drift, no residual drift)
MCE – negligible damage to structure, some damage to architectural components
Courtesy: Tipping/Mar Assoc.
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 7
Historical Highlights: Seismic Assessment
• FEMA 154 Rapid Visual Screening (1988, 2002)
• ASCE 31 Seismic Evaluation of Buildings (2004)
– FEMA 178 Handbook for Seismic Assessment of Buildings (1989)
– FEMA 310 Handbook for the Seismic Evaluation of Buildings – A Prestandard (1998)
• ATC 40 (1996), Seismic Evaluation and Retrofit of Concrete Buildings
• HAZUS (mid‐90’s …) – Regional Loss Estimation (earthquake plus other hazards) Earthquake Loss for United States
• ASCE 41 Seismic Rehabilitation of Existing Buildings (2007)
– FEMA 273 (ATC 33, 1997) – NEHRP Guidelines for the Seismic Rehabilitation
– FEMA 356 (2000) – Prestandard and Commentary for the Seismic Rehabilitation
– FEMA 440 (2006) – Improvement of Nonlinear Static Seismic Analysis Procedures
• Guidelines for Tall Buildings (2008) ‐ PEER TBI, LATBSDC, CTBUH
• ATC 58 Performance Based Seismic Design (2011 – 75% Draft)
• FEMA P695 (ATC 63) Collapse Safety and Project 07 (2010)
Background and Motivation: Guidelines and Standards
Structurally
StableLife Safe
Beer!Food!
Rare events(10%/50yrs)
Very rare events(2%/50yrs)
Operational
Frequent events(50%/50yrs)
Lateral Deformation
Base Shear
DemandJoe’s
Beer!Food!
Occasional events(20%/50yrs)
Ref: R.O. Hamburger
Assessment by Static Pushover Analysis(FEMA 273/356 and ASCE 41)
Background and Motivation: Guidelines and Standards
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 8
Background and MotivationBackground and Motivation: Guidelines and Standards
Deformation Controlled Force Controlled
Generalized Component Response Curves
Background and Motivation: Guidelines and Standards
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 9
17
ASCE 41‐06* Seismic Rehabilitation of Existing Buildings
• General performance assessment framework (IO, LS, CP)
• Structural component modelling parameters and
acceptance criteria
• Nonlinear static (pushover) analysis procedure
*including 2007 supplement
Background and Motivation: Guidelines and Standards
FEMA 440 (2005) – Improved Static NL Analysis Procedures
• Evaluation of ATC‐40 and FEMA 356 procedures
• Quantifying effects of degradation (in‐cycle degradation) and new stability limit
• Improved “Coefficient Method” (C1, C2 and C3) for calculating target displacement
• Improved “Capacity‐Spectrum” (equivalent linearization) method for calculating target displacement
• Soil‐structure interaction effects
• MDOF effects
18
ASCE 7‐10 Minimum Design Loads for Buildings
• Chapter 16 – Seismic Response History Procedures
• Provisions for linear (elastic) and nonlinear (inelastic)
• Key Points
‐ analyses and checks for DBE levels
‐ selection and scaling of records
‐ general provisions for relating calculated quantities to
design acceptance criteria
NEHRP 2009 Recommended Seismic Provisions
• Modifications and commentary to Chapter 16 of ASCE 7
• Resource papers:
‐ use of Nonlinear Static Analysis in ASCE 7
‐ more complete provisions for Nonlinear Response
History Analysis in ASCE 7
NOTE – A task committee of BSSC is currently drafting revised provisions, which are more extensive and consistent with other efforts (e.g., tall building guidelines)
Background and Motivation: Guidelines and Standards
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 10
19
PEER Tall Building Initiative:
• 2010 guidelines
• supporting studies & documents
http://peer.berkeley.edu/tbi/
LA Tall Buildings Structural Design Council:
• 2011 guidelines
• annual conference
• special provisions for RC structures
Guideline Documents
• Performance Objectives
• Design Process and Documentation
• Seismic Input and Modeling Criteria
• Preliminary Design
• Service Level Evaluation
• MCE Level Evaluation
• Documentation and Peer Review
Background and Motivation: Guidelines and Standards
20
PEER/ATC 72‐1: Modeling and Acceptance
Criteria for Seismic Design and Analysis
• General Nonlinear Modeling
‐ overview of issues‐ deterioration, P‐delta, damping‐ uncertainties in models and limit states
• Moment Frame Components
‐ steel beams, columns, panel zones‐ concrete beam, columns, joints
• Shear Walls and Slab‐Column Frames
‐ planar and flanged walls‐ coupling beams‐ slab‐column components and connections
• Podium Diaphragms and Collectors
‐ podium and backstay effects‐ collectors and diaphragm segments‐ modeling considerations and
recommendations
Background and Motivation: Guidelines and Standards
242 pages
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 11
21
CAPACITY DESIGN PRINCIPLES
Clearly Defined Yielding Mechanisms
‐ Deformation‐controlled components
‐ Force‐controlled components
Advantages
• Protection from sudden failure in elements that
cannot be proportioned or detailed to provide
ductile response
• Limit the locations where expensive ductile
detailing is required
• Reliable energy dissipation by enforcing
deformation modes where inelastic deformations
are distributed to ductile components
• Greater certainty in how the building will perform
under strong earthquakes and greater confidence
in how the performance can be calculated
Background and Motivation: Capacity Design Principles
Desirable nonlinear mechanism in coupled RC wall (ATC 72‐1)
22
Force‐Controlled Components for Capacity Design: The PEER TBI and LATBSDC
Tall Building Guidelines specify the following components as ones that should be
designed as force‐controlled to remain essentially elastic:
Background and Motivation: Capacity Design Principles
• Axial forces in columns
• Compressive strains due to flexure, axial or combined actions in shear walls or piers:‐ that do not have adequate confinement‐ where axial compression demand is above the balanced point
• Shear in reinforced concrete beams (other than diagonally reinforced coupling beams), columns, shear walls and diaphragms
• Punching shear in slabs and mat foundations without shear reinforcing
• Force transfer from diaphragms and collectors
• Connections that are not designed explicitly for the strength of the connected components
Note – many of these recommendations follow comparable requirements in ASCE 7, AISC and ACI, though some are more restrictive.
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 12
Outline
1. Introduction ‐ Background and Motivation
2. Nonlinear Demand Parameters and Model Attributes
3. Modeling of Structural Components
4. Foundation and Soil Structure Interaction
5. Nonlinear Static Analysis
6. Nonlinear Dynamic Analysis
23
24
Demand Parameters & Acceptance Criteria: Demand < “Capacity”
Overall Measures
• Total Drift ‐ Peak (and Residual)• Story Drift – Peak (and Residual)• Peak Floor Accelerations
Deformation‐Controlled Components
• Hinge Rotation (beams, columns, wall flexure)
• Deformation (axial, shear, sliding)
• Ductility (/y or /y)• Strain (gage lengths?)
• Generalized Strain (curvature, axial)
• Velocity (e.g., for dampers)
Force‐Controlled Components
• Force and/or Moment
• Stress (gage length or averaging area?)
Demand Parameters and Model Attributes
Deformation Measures:‐ Peak (maximum)‐ Residual ?‐ Cumulative ?
Total vs. Inelastic (plastic)
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 13
Demand Parameters and Model Attributes: Model Types
25
Drift
Col
umn
She
arPhenomenological Fundamental
Accuracy – Feasibility - Practicality
Demand Parameters and Model Attributes: Wall Models
26
Phenomenological Fundamental
Illustrative Wall Models
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 14
Demand Parameters and Model Attributes: Model Properties
27
Material and other model parameters should be specified to reflect the median*
(or expected) properties, loads and behavior ‐‐‐
Expected Material Properties
• structural steel: Fy,exp = RyFy (see AISC Seismic Provisions)
• reinforcing steel: Fy,exp = 1.17Fy (LATBSDC Tall Building Guidelines)
• concrete: f’c,exp = 1.3 f’c (LATBSDC Tall Building Guidelines)
Median (or Expected) Model Parameters
• effective “elastic” stiffness of concrete, masonry, soil (amplitude dependent)
• inelastic response
‐ yield and peak strengths‐ strain hardening‐ onset of degradation and softening‐ unloading stiffness and pinching‐ inelastic deformation
• damping (“un‐modeled energy dissipation”)
•Owing to limited data and as a practical measure, the median properties are often approximated using mean or expected values.
Demand Parameters and Model Attributes: Response Envelopes
Monotonic versus Cyclic Envelope
28Test Data: Gatto & Uang, ASCE JSE, Oct. 2003
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 15
Hysteretic Component Response From Earthquake Time Histories
(a) 1985 Chile record (b) 1995 Kobe record
Shin, PEER, 2005
Demand Parameters and Model Attributes: Loading History Effects
Time, sec
Displacemen
t
Michael Scott, PEER, 2003; FEMA 440
Demand Parameters and Model Attributes: Types of Degradation
In‐cycle strength degradation
Cyclic strength degradation
Types of strength degradation
Strength loss in subsequent cycles (not during one cycle)
Strength loss during one cycle
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 16
Demand Parameters and Model Attributes: Backbone Curves
Backbone Curves for Alternative Model Types (PEER TBI and ATC 72‐1 for details)
31
Demand Parameters and Model Attributes: Backbone Curves
Generalized Component Response
• Response curves in ASCE 41 are essentially the same as “Option 2”
– cyclic envelope fit to cyclic test data
– ASCE 41 (FEMA 273) originally envisioned for static pushover analysis without any cyclic deformation in the analysis
• Option 2/ASCE 41: reasonable for most analysis programs that track post peak “in‐cycle” degradation but do not simulate cyclic degradation of the backbone curve
• Post‐Peak Response: dashed line connecting points C‐E in ASCE 41 response curve is more reasonable representation of post‐peak (softening) response
32
ASCE 41 (and related models)
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 17
Geometric Nonlinear (P‐) Effects• Negative stiffness effect of P‐
• Increases internal forces associated with overturning:
• Key Points
– “W” should reflect the seismic mass that is being stabilized by the lateral system (not just the tributary gravity load)
– “Linear P‐” formulations accurate for drift ratios up to about 5‐10%; for larger drifts, large rotation (e.g., “co‐rotational”) formulations should be used.
– P‐ effects are can have large effect on post‐peak degradation, even if they appear negligible for the elastic structure.
V
Kg = -W/h
h
W = Pg
WV
Mot=Vh + P
Demand Parameters and Model Attributes: P‐Effects
Geometric Nonlinear (P‐) Effects• Negative stiffness effect of P‐
• Increases internal forces associated with overturning:
• Key Points
V
Kg = -W/h
h
W = Pg
WV
Mot=Vh + P
Demand Parameters and Model Attributes: P‐Effects
Gravity Load Combination for NL Analysis (ASCE 7‐10, Tall Building Guidelines):
1.0D + Lexp, where Lexp is 25% of the specified (unreduced) live load
(note – ASCE 41‐06 applies a 1.1 multiplier to this load combination)
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 18
Demand Parameters and Model Attributes: Uncertainties
Uncertainties in Seismic Assessment: Large variability in demand predictions, with dispersion (coefficient of variation) on the order of 0.5 to 0.8.
• Ground Motion Hazard Intensity
“2% in 50 year mean annual frequency of exceedence”
• Ground Motion Characteristics
• frequency content and duration
• so‐called “record‐to‐record” uncertainty
• Structural Properties, Behavior and Models
• variability in structural properties (materials, dimensions, etc.)
• variability in nonlinear behavior of structural components and systems
• accuracy of mathematical models used in analysis
35
Demand Parameters and Model Attributes
Quality Assurance in Nonlinear Response History Analysis
– Basic Checks of Analysis Model and Ground Motions
• Elastic modes, masses, effective masses, participation factors, total gravity load
• Generate elastic (displacement) response spectra of the input ground motions
• Perform elastic response spectra and elastic dynamic analyses to compare with each other and with nonlinear analyses
– Nonlinear Static Analysis
• Check response quantities against elastic analysis and/or inelastic strength limits
• Equilibrium checks of selected components
• Perform model sensitivity analyses
– Nonlinear Dynamic Analysis
• Check response quantities against elastic analysis and/or inelastic strength limits
• Plot hysteresis responses of selected components
• Perform model sensitivity analyses
36
Above all: 1. Know the capabilities and limitations of the software2. Use capacity design to control response3. Apply judgment to assess the calculated response
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 19
Outline
1. Introduction ‐ Background and Motivation
2. Nonlinear Demand Parameters and Model Attributes
3. Modeling of Structural Components
4. Foundation and Soil Structure Interaction
5. Nonlinear Static Analysis
6. Nonlinear Dynamic Analysis
37
Modeling of Structural Components: RC Moment Frames
38
RC Moment Frames
• Primary Components‐ beams, columns, beam‐column joints
• Preferred Model: concentrated plasticity (hinge) type
• Resources‐ ASCE 41, supplement 1 (2008)‐ ATC 72‐1 (2010)‐ PEER RC Column Database (~400 tests)
http://nisee.berkeley.edu/spd/‐ Tall Building Guidelines (LATBSDC, PEER TBI)
• Status of Models
‐ considerable data on flexure‐dominant beam‐columns with low to moderate axial load and beam‐column joints
‐ more limited data on beams, columns with high shear and/or axial load, splices
‐ uniaxial hinges – well developed hysteretic models that account for degradation
‐ P‐M hinges – basic models available but with limited hysteretic degradation capabilities
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 20
Modeling of Structural Components: Beam‐Column Hinge
39
Key Parameters:
• strength
• initial stiffness
• post‐yield stiffness
• plastic rotation (capping) capacity
• post‐capping slope
• cyclic deterioration rate
Calibration Process:
• 250+ columns (PEER database)
• flexure & flexure‐shear dominant
• calibrated to expected values
Demand Parameter Output: hinge rotation
KEY ASSUMPTION: bond slip is incorporated in the beam‐column model parameters
Semi‐Empirical ‐‐ calibrated from tests, fiber analyses, and basic mechanics:
• Secant Stiffness (EIeff)
• Yield Strength (My)
• Hardening Stiffness
Empirical ‐ calibrated from tests:
• Capping (peak) point
• Post‐peak unloading (strain softening) stiffness
• Hysteretic stiffness/strength degradation
cap
40
Modeling of Structural Components: Beam‐Column Hinge
Dispersion ~0.1 to 0.3 Dispersion ~0.6 to 0.8
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 21
Modeling of Structural Components: Beam‐Column Hinge
41
0.6 f’c Ag0.6 f’c Ag
0.15 f’c Ag0.15 f’c Ag
Post Peak Response: Key Parameter: P/Pbalance
Tests by Moehle and Sezen (UC Berkeley)
Modeling of Structural Components: RC initial stiffness EI/EIg
42
P/Po 0.1 0.3 0.6
0.4Py (EI/EIg) 0.30 0.60 0.80
Py (EI/EIg) 0.20 0.35 0.60
Haselton, et al. (2007); ATC 72‐1 (2010)
ASCE 41 – 2008 Supplement (Elwood et al., 2007)
(ln) = 0.35
P/Po 0.1 0.3 0.5
Py (EI/EIg) 0.30 0.50 0.70
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 22
Modeling of Structural Components: RC plastic rotation
43
cap
Median:
Dispersion:
Haselton, et al. (2008)
Modeling of Structural Components: RC plastic and ultimate rotation
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 23
Modeling of Structural Components: RC plastic rotation, compared w/ ASCE 41
a
ATC 72‐1 (2010)Haselton (2008)
ASCE 41‐S (2008)
Modeling of Structural Components: Steel Moment Frames
46
Steel Moment Frames
• Primary Components‐ beams, columns, joint panel zone
• Preferred Model: concentrated plasticity (hinge) type
• Resources‐ ASCE 41, supplement 1 (2008)‐ ATC 72‐1 (2010)‐ FEMA 355D, “State of Art Report on Connection
Performance” (2000)
• Status of Models
‐ considerable data on beams and beam‐column joints
‐ more limited data on columns, particularly ones where torsional‐flexural buckling is possible
‐ uniaxial hinges – well developed hysteretic models that account for degradation
‐ P‐M hinges – basic models available but with limited hysteretic degradation capabilities
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 24
Modeling of Structural Components: RC Shear Walls
47
RC Shear Walls
• Primary Components‐ slender walls, squat walls, coupling beams
• Preferred Model: fiber wall panels, or in limited cases, lumped plasticity beam‐column idealizations
• Resources‐ ASCE 41, supplement 1 (2008)‐ ATC 72‐1 (2010)‐ Powell, G., “Detailed Example of a Tall Shear Wall
Building using PERFORM 3D”, CSI, Berkeley, CA.
• Status of Models
‐ reasonable confidence for modeling coupling beams and slender shear walls with low axial stress
‐ less well‐developed models for squat shear walls or slender walls that are sensitive to compressive or shear failures
‐ determination of strains are sensitive fiber‐element discretization and assumed gage length
Modeling of Structural Components: RC Shear Walls
48
T‐shaped wall specimen
Rectangular wall specimen
Model Sensitivity in RC Shear Walls
• calculated strains are sensitive to fiber‐element discretization and gage length
Note – recommended to discretize hinge length by one element.
• influence of large inelastic cyclic (tensile‐compressive) loading on the compressive response of wall boundary members
Note ‐ compressive strain at 2% drift is on the order of 0.015.
Tests and analyses by Wallace (ATC 72‐1)
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 25
Modeling of Structural Components: Masonry Infill Walls
49
Masonry Infill Walls (RETROFIT)
• Primary Components‐ masonry infill, concrete or steel frame‐ primarily RETROFIT applications
• Preferred Model: single or multiple diagonal struts
• Resources‐ ASCE 41, supplement 1 (2008)‐ FEMA 306/307, “Evaluation of earthquake
damaged concrete and masonry wall buildings,” (1998).
• Status of Models
‐ diagonal strut is an approximate model, whose properties are adjusted to consider several possible failure modes in mortar or masonry units
‐ SENSITIVITY analyses are recommended to improve confidence in analysis results
‐ need also to consider shear or splice failures in boundary frame members
Modeling of Structural Components: Braced Frames
50
Steel Braced Frames
• Primary Components‐ steel braces (buckling or BRB), steel frame
• Preferred Model: fiber beam‐column with geometric imperfection to simulate buckling
• Resources‐ ASCE 41‐06‐ Uriz, P., Mahin, S.A. (2008), “Toward Earthquake‐
Resistant Design of Concentrically Braced Steel‐Frame Structures,” PEER Report 2008/08.
• Status of Models
‐ when calibrated with appropriate imperfections, fiber beam‐column can simulate overall brace buckling under cyclic loads
‐ maximum drifts and/or brace deformations should be limited unless local buckling and fracture is considered in the model
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 26
Modeling of Structural Components: Response Modification Devices
51
Response Modification Devices
• Primary Components‐ Energy dissipaters (viscous or hysteretic dampers)‐ Seismic isolators
• Preferred Model: uniaxial models that employ the appropriate hysteretic rule (or combination of rules)
• Resources‐ ASCE 7‐10 (Chp. 17 and 18)‐ ASCE 41(Chp. 9)
• Status of Models
‐ Idealized hysteretic spring models are generally available that can be calibrated to data available from manufacturers of response modification devices
Outline
1. Introduction ‐ Background and Motivation
2. Nonlinear Demand Parameters and Model Attributes
3. Modeling of Structural Components
4. Foundation and Soil Structure Interaction
5. Nonlinear Static Analysis
6. Nonlinear Dynamic Analysis
52
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 27
Foundation and Soil‐Structure‐Interaction
53
“Direct Approach” “Substructure Approach”
Reference: Stewart, J.P., Tileylioglu, S., “Input ground motions for tall buildings with subterranean levels” PEER TBI Task 8.
ug: free‐field ground motionsuFIM: Foundation Input Motions
Foundation and Soil‐Structure‐Interaction
54
Direct Approach
• explicit modeling of soil, foundations, contact interfaces, and structure
• free‐field ground motions, adjusted for incoherence where appropriate
• advantage: general approach that is not subject to simplifying assumptions that may limit applicability
• disadvantages:
‐ challenges associated with defining model parameters and input ground motions
‐ computationally intensive
‐ data/model management can become intractable and difficult to assess sensitivity to modeling parameters
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 28
Foundation and Soil‐Structure‐Interaction
55
Substructure (soil‐spring) Approach
• approximate soil‐foundation spring and damper models
• for buildings with relative small footprints and embedment, free‐field motions are typically used as input
• disadvantages: approximate, challenges of characterizing soil‐foundation spring/damper properties (amplitude dependent)
• advantages:
‐ conceptually straightforward, practical, and computationally efficient
‐ amenable to sensitivity analyses to bracket design solution
Excitation with FIM, including foundation flexibility and damping
Simplified excitation with free‐field motions, including foundation flexibility and damping
Outline
1. Introduction ‐ Background and Motivation
2. Nonlinear Demand Parameters and Model Attributes
3. Modeling of Structural Components
4. Foundation and Soil Structure Interaction
5. Nonlinear Static Analysis
6. Nonlinear Dynamic Analysis
56
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 29
Nonlinear Static Analysis
57
Nonlinear Static Analysis (ASCE 41)
Equivalent Static Earthquake Load
‐ Force Distribution‐ Target Displacement
Demand Parameters
‐Member Forces & Deformations‐ Story Drift
Applicability of NSA Method
‐ Dynamic Stability (Rmax) Check‐ Higher Mode Check
Component Acceptance Criteria
‐ Force‐Controlled Elements‐ Deformation‐Controlled Elements
V
roofGlobal Pushover Response
t
FEMA 440 – Improved Target Displacement (aka “performance point”):
• Improved “Coefficient Method” (incorporated in ASCE 41)
• Improved Equivalent Linearization (Capacity Spectrum ATC 40) Method(s)
elastic roof displacement
Nonlinear Static Analysis
58
C1 = amplification for inelastic response
C2 = amplification for pinched hysteresis, cyclic stiffness and strength deterioration
Original ATC‐40, FEMA 356 Method New FEMA 440 Methods (A,B,C)
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 30
FEMA 440 ‐ Dynamic Stability Check:
Nonlinear Static Analysis
59
Nonlinear Static Analysis
60
Nonlinear Static Analysis – Virtues and Limitations
Virtues‐ straightforward to perform and interpret‐ computationally efficient‐ avoids complexities of dynamic analysis
Limitations‐ static approximation to dynamic response‐ inaccurate where higher mode effects are significant (above 5 stories)
Proposed Improvements – Inconclusive*‐ adaptive and Multi‐Mode Pushover‐ consecutive Modal Pushover
Useful with Nonlinear Dynamic Analysis‐ check and debug nonlinear analysis model‐ develop understanding of structural yield mechanisms‐ parametric studies for preliminary design
*NIST GCR 10‐917‐9 (2010), “Applicability of Nonlinear Multiple‐Degree‐of‐Freedom Modeling for Design”
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 31
Outline
1. Introduction ‐ Background and Motivation
2. Nonlinear Demand Parameters and Model Attributes
3. Modeling of Structural Components
4. Foundation and Soil Structure Interaction
5. Nonlinear Static Analysis
6. Nonlinear Dynamic Analysis
61
Nonlinear Dynamic Analysis
62
Nonlinear Dynamic (Response History) Analysis
Additional Considerations:
• Definition of Input Ground Motions
‐ Selection of Ground Motions‐ Scaling (or spectral matching) of Ground Motions‐ Soil‐Structure Interaction (?)
• Hysteretic Models and Parameters
‐ monotonic vs. cyclic skeleton curve‐ capabilities to simulate deterioration
• Modeling of Inertial Mass
• Specification of Viscous Damping
• Data Processing and Statistics
‐ “mean” vs. “mean + sigma” demands‐ acceptance criteria: “design”, “nominal” or “expected” values
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 32
Nonlinear Dynamic Analysis: Ground Motions
63
Definition of Input Ground Motions:
• Target Hazard Spectra
‐ service, DBE, MCE‐ uniform hazard spectra, or‐ conditional mean spectra (?)
• Dominant Earthquake Source
‐ Fault mechanism and proximity‐ characteristic EQ magnitude‐ site soil/rock properties
• Source Ground Motions (> 7 pairs)‐ recorded motions‐ spectrally matched‐ synthetic motions
Recorded Motions – typically scaled to target hazard spectra from 0.2T to 1.5T, where T is the first mode building period.
Viscous Damping with Nonlinear Dynamic Analysis
Raleigh (proportional) Damping:
Explicit Damping Elements
[c]i configured to represent likely sources of viscous and other incidental damping.
[c]i
Modal Damping:
Nonlinear Dynamic Analysis: Damping
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 33
Observations: 1. Measured damping in the range of 2% to 8% of critical2. Effective damping seems to decrease with increasing buidling height3. Difficult (impossible) to distinguish hysteretic and viscous damping
Nonlinear Dynamic Analysis: Damping
REF: Chopra/Goel
Recorded Strong Motion Data (US)
• Assume that energy dissipation at large deformations is primarily accounted for by hysteretic response
• Raleigh or modal damping is usually expressed as a percentage of critical damping (for first few modes) to reflect other sources of “un‐modeled” energy dissipation:
– SAC Joint Venture (1995): 2%
– FEMA P695 (2007): 5%
– Tall Buildings – PEER TBI (2010) and LATBSDC (2011): 2.5%
– CTBUH: 1 to 2% for buildings taller than 50 meters
• Suggested values:
– 1% to 5%, depending on building height, structural and architectural materials, and shaking amplitude (service EQ versus MCE)
– specify critical damping in first few modes (~0.2T to 1.5T)
– be aware how analysis software implements damping (check sensitivity of results to specified damping)
Nonlinear Dynamic Analysis: Damping
Recommendations for Damping
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 34
67
Limit States and Acceptance Criteria (assuming 7 record pairs)
Demand Parameters and Model Attributes
Limit ASCE 7 (2010) PEER TBI (2010) LATBSDC (2011)
Service EQ ‐‐ 50% in 30 yr. 50% in 30 yr.
Story Drift ‐‐ 0.5% 0.5%
Force‐Controlled ‐‐ mean < Fn,exp NA
Deform.‐Controlled ‐‐ little to no damage (IO per ASCE 41)
little to no damage (IO per ASCE 41)
Safety EQ DBE (=2/3 MCE) MCE MCE
Story Drift Mean 1.25 x 2% mean 3%; max 4.5% mean 3%; max 4.5%
Residual Story Drift ‐‐ mean 1%; max 1.5% mean 1%; max 1.5%
Force‐Controlled max < Fn(in place of o)
1.2 to 1.5mean < Fn,exp 1.5mean < Fn,exp
Force‐Controlled(non‐critical)
‐‐ mean < Fn,exp mean < Fn,exp
Deform.‐Controlled mean < 2/3 u mean < u(CP per ASCE 41)
mean < u(CP per ASCE 41)
Lateral strength ‐‐ < 20% loss < 20% loss
Nonlinear Modeling Assumptions and Criteria
8 Story RC Frame Example – Static vs. Dynamic Analysis
68
• Office occupancy
• Los Angeles Basin
• Design Code: 2003 IBC / 2002 ACI / ASCE7‐02
• Perimeter Frame System
• Maximum considered EQ demands:
– Ss = 1.5g; S1 = 0.9g
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 35
Nonlinear Dynamic Analysis: 8 Story Example
DBE
MCE
1.5MCE
8 Story RC Frame – Static vs. Dynamic Analysis
Nonlinear Dynamic Analysis: 64‐story RC Wall System
64 Story RC Wall System – Dynamic Analysis
Courtesy: Magnusson Klemencic Assoc.Story Drift Ratio
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 36
Nonlinear Dynamic Analysis: 64‐story RC Wall System
Courtesy: Magnusson Klemencic Assoc.
64 Story RC Wall System – Dynamic Analysis
Wall Shear Wall Moment
Nonlinear Dynamic Analysis: 64‐story RC Wall System
Courtesy: Magnusson Klemencic Assoc.
64 Story RC Wall System – Dynamic Analysis
Wall Segment ShearLongitudinal Bar Tensile Strains
PBEE Course 8/22/2011
Deierlein – RC Frame Benchmarking Study 37
Nonlinear Dynamic Analysis: 64‐story RC Wall System
Courtesy: Magnusson Klemencic Assoc.
64 Story RC Wall System – Dynamic Analysis
Coupling Beam Rotation Coupling Beam Rotation
74