Nonlinear Analysis.greg Deierlein 8-24-11

PBEE Course 8/22/2011

Deierlein – RC Frame Benchmarking Study 1

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NEHRP Seismic Design Technical Briefs

Acknowledgements

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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.



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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

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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)

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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



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



• 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”





• 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



Revised RetrofitCourtesy: Degenkolb Engineers



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.



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 MotivationBackground and Motivation: Guidelines and Standards

Deformation Controlled Force Controlled

Generalized Component Response Curves




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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


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

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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)




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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


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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


242 pages



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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)

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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.



Outline







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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)



Demand Parameters and Model Attributes: Model Types

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Drift

Col

umn

She

arPhenomenological Fundamental

Accuracy – Feasibility - Practicality

Demand Parameters and Model Attributes: Wall Models

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Phenomenological Fundamental

Illustrative Wall Models



Demand Parameters and Model Attributes: Model Properties

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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



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



Demand Parameters and Model Attributes: Backbone Curves

Backbone Curves for Alternative Model Types (PEER TBI and ATC 72‐1 for details)

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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

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ASCE 41 (and related models)



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)



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

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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

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Above all: 1. Know the capabilities and limitations of the software2. Use capacity design to control response3. Apply judgment to assess the calculated response



Outline







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Modeling of Structural Components: RC Moment Frames

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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



Modeling of Structural Components: Beam‐Column Hinge

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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


Dispersion ~0.1 to 0.3 Dispersion ~0.6 to 0.8




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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

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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



Modeling of Structural Components: RC plastic rotation

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cap

Median:

Dispersion:

Haselton, et al. (2008)

Modeling of Structural Components: RC plastic and ultimate rotation



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

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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)


‐ 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



Modeling of Structural Components: RC Shear Walls

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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.


‐ 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

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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)



Modeling of Structural Components: Masonry Infill Walls

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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).


‐ 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

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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.


‐ 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



Modeling of Structural Components: Response Modification Devices

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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)


‐ Idealized hysteretic spring models are generally available that can be calibrated to data available from manufacturers of response modification devices

Outline







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Foundation and Soil‐Structure‐Interaction

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“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


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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




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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







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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


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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)



FEMA 440 ‐ Dynamic Stability Check:


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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”



Outline







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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



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



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


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)


Recommendations for Damping



67

Limit States and Acceptance Criteria (assuming 7 record pairs)


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



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






Wall Shear Wall Moment




Wall Segment ShearLongitudinal Bar Tensile Strains






Coupling Beam Rotation Coupling Beam Rotation

74