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Adaptive Nonlinear Analysis as Applied to Performance based Earthquake Engineering. Dr. Erol Kalkan, P.E. United States Geological Survey TUFTS , 2008. This study is based on a paper published in the Journal of Structural Engineering , and winner of the

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adaptive nonlinear analysis as applied to performance based earthquake engineering

Adaptive Nonlinear Analysis as Applied to Performance based Earthquake Engineering

Dr. Erol Kalkan, P.E.

United States Geological Survey

TUFTS, 2008

slide2

This study is based on a paper published in the

Journal of Structural Engineering,

and winner of the

2008 ASCE Raymond Reese Research Award

outline
Outline
  • Seismic Analysis Methods of Structures
  • Nonlinear Static Analysis
    • Fundamental Theory
    • Conventional Methods (FEMA and ATC)
    • Limitations
  • Adaptive Nonlinear Static Analysis
    • Methodology Developed
    • Comparative Results
  • Summary & Conclusions
seismic analysis methods of structures
Seismic Analysis Methods of Structures
  • Linear static procedures
    • Equivalent static analysis
  • Linear dynamic procedures
    • Modal analysis
    • Direct time-history analysis
  • Nonlinear static analysis
    • - Nonlinear static procedures (NSPs)
      • Capacity spectrum analysis (ATC-40, FEMA-440)
      • Displacement coefficients method (FEMA-273-274,356,440)
    • - Improved NSPs
      • Modal pushover analysis (MPA) (Chopra & Goel, 2002)
      • Adaptive Modal Combination (AMC) (Kalkan & Kunnath, 2006)
  • Nonlinear dynamic analysis

Most common in

routine applications

slide6

Multi-degree-of-freedom (MDF) system seismic behavior can be approximated with certain accuracy

by

equivalent SDF systems.

MDF

ESDF

Equivalent SDF (ESDF) system properties are computed by conducting

pushover analyses…

conventional nonlinear static pushover analysis
Conventional Nonlinear Static (Pushover) Analysis
  • Choose height-wise distribution of lateral forces
  • Monotonically increase lateral forces till the “control node” reaches a “target displacement” i.e., increasing load factor while fixing load pattern.
  • Develop pushover (capacity) curve: Plot of base shear vs. roof displacement

ur

Vb

summary of nonlinear static analysis

D

V

Fsn/Ln

D

Dn

ut

V

uj

dj

Summary of Nonlinear Static Analysis

ESD System

Force-Deformation Relation

Pushover Analysis

Target Displacement

of MDF System ut

Inelastic

SDF System

Capacity estimation at

target displacement

Participation Factor, Gn

slide9
Fundamental Assumptions:
  • The response of the multi-degree-of-freedom (MDF) structure can be related to the response of an equivalent SDF system, implying that the response is controlled by a single mode and this mode shape remains unchanged even after yielding occurs.
  • The invariant lateral force distribution can represent and bound the distribution of inertia forces during an earthquake.
two important components of nonlinear static analysis
Two Important Components of Nonlinear Static Analysis
  • Construct loading vector shape
  • Determine target roof displacement
height wise distribution of lateral forces fema recommendations
Height-wise Distribution of Lateral Forces: FEMA Recommendations

ELF and SRSS distributions intended to consider higher mode responses

fema recommended force distributions
FEMA Recommended Force Distributions

Each force distribution pushes all floors in same direction

higher mode response
Higher Mode Response

Yielding

Initial

Yielding

Initial

Yielding

Initial

Yielding

Initial

two important components of nonlinear static analysis14
Two Important Components of Nonlinear Static Analysis
  • Construct loading vector shape
  • Determine target roof displacement
target displacement estimation displacement coefficient method
Target Displacement Estimation(Displacement Coefficient Method)

f

f

Elastic SDF System

Inelastic MDF System

u

u

f

u

Inelastic SDF System

C0 = Constant to relate elastic deformation of SDF and MDF system

displacement coefficient method
FEMA-356: Cinel =C1C2C3

C1 = Ratio of inelastic and elastic SDF systems

C2 = Constant to account for effects of pinching, stiffness degradation, and strength deterioration

C3 = Constant to account for P-Delta effects

ASCE-41: Cinel = C1C2

C1 = Ratio of inelastic and elastic SDF systems

C2 = Constant to account for cyclic degradation of stiffness and strength

Upper limit on R to avoid dynamic instability

Displacement Coefficient Method
capacity spectrum method

Teq, zeq

f

f

u

Inelastic MDF System

Equivalent Linear Elastic SDF System

u

f

u

Inelastic SDF System

Capacity Spectrum Method
capacity spectrum method equivalent damping concept

Teq= Tsec

Sa

ESo

Sd

ED

Capacity Spectrum Method – Equivalent Damping Concept

For bilinear systems

Requires iterations to compute Teq and zeq

because of unknown ductility (uinel / uelas)

fema 440 capacity spectrum method
FEMA-440 Capacity Spectrum Method

A to K = Constants that depend on hysteretic behavior and post-yield stiffness ratio

limitations of conventional fema atc nonlinear static analysis procedures
Limitations of Conventional (FEMA & ATC) Nonlinear Static Analysis Procedures
  • Restricted to single mode response, can be reliably apply to 2D response of low-rise structures in regular plan.
  • Gives erroneous results in case of:

Higher Mode Effects

Plan Irregularities (i.e., Torsion, Vertical Irregularities)

  • No established procedure for 3D pushover analysis yet.
slide24

T=10.6 sec T=8.44 sec T=11.24 sec T=8.96 sec T=8.96 sec T=8.86 sec

Instantaneous inertia profiles when story maxima take place

  • ‘T’ indicates the time-instance in the time-history
  • Filled square marker indicates the critical story at T
adaptive modal combination amc kalkan kunnath 2006
Adaptive Modal Combination (AMC) (Kalkan & Kunnath, 2006)
  • Basic Elements of the Procedure
    • Establishing Target Displacement: An energy-based procedure is used in conjunction with inelastic displacement spectra at a set of pre-determined ductility levels to progressively establish the target displacement as the modal pushover analysis proceeds.
    • Dynamic Target Point: This concept is analogous to the performance point in CSM, however, it represents a more realistic representation of demand since inelastic spectra are used to target this demand point.
    • Adaptive Modal Combination: The method recognizes the need to alter the applied lateral load patterns as the system characteristics change yet retain the simplicity of combining the response measures at the end of the analysis.
energy based incremental modal displacement
Energy Based Incremental Modal Displacement
  • The basic limitation of current non-adaptive procedures is that elastic modal properties are used to compute the inelastic system parameters
  • This approach may necessitate several iterations for convergence of target displacement computed from inelastic dynamic analysis.
  • The roof displacement is approximated from the maximum deformation of an ESDF system. Such an approach is only meaningful for the first mode, while for higher modes, the roof displacement does not proportionally change with the other story deformations
energy based esdf system representation of nth mode mdf system capacity curve
Energy-based ESDF system representation of nth-mode MDF system capacity curve

MDF

Level

SDF

Level

performance point evaluation using system ductility through a set of inelastic spectra
Performance point evaluation using system ductility through a set of inelastic spectra

Capacity Side

Demand

Side

validation studies
Validation Studies
  • Several regular and irregular building frames of varying height were developed used for validation studies.
  • Different suite of records were compiled from near-fault forward directivity, near-fault fling and far-fault recordings.
  • Each building model was also subjected to a series of ground motions to generate benchmark results.
  • Engineering demand parameters considered are roof drift ratio, inter-story drift ratio in global level and member plastic rotations and story ductility in local level for cross comparisons.
slide31
The structural system is essentially symmetrical.

Moment continuity of each of the perimeter frames is interrupted at the ends where a simple shear connection is used to connect to the weak column axis.

Moment resisting connection

Simple hinge connection

Structural Details of 6-story Building

structural details of 13 story building

Moment resisting connection

Simple hinge connection

Structural Details of 13-story Building
  • The exterior frames of the building are the moment resisting frames and interior frames are for load bearing.
  • The foundation consists of piles, pile caps and grade beams.
  • The corner columns of outer frames are composed of box sections.
analytical modeling in opensees open source finite element software
Analytical Modeling in OpenSEES (Open source Finite Element Software)
  • Centerline dimensions were used in the element modeling.
  • A force-based nonlinear beam-column element that utilizes a layered ‘fiber’ section is utilized to model all components
  • One half of the total building mass was applied to the frame distributed proportionally to the floor nodes.
  • The simulation of special features such as local connection fracture did not accounted for; consequently, the modeling of the members and connections was based on the assumption of stable hysteresis derived from a bilinear stress-strain model.
  • The columns were assumed to be fixed at the base level (No SSI).
recorded earthquake data from 6 story building
Recorded Earthquake Data from 6-Story Building

The building performed well in all these earthquakes with no visible signs of damage. Recorded data indicates an essentially elastic response in each case.

recorded earthquake data from 13 story building
Recorded Earthquake Data from 13-Story Building

Approximately 12% of the connections on the west perimeter of the North-South frame fractured during the Northridge earthquake.

summary conclusions
Summary & Conclusions
  • Developed AMC offers a direct multi-mode technique to estimate seismic demands and integrates concepts incorporated in:
      • Capacity spectrum method recommended in 3

ATC-40 (1996)

      • Direct adaptive method originally proposed by

Gupta and Kunnath (2000)

      • Modal pushover analysis advocated by

Chopra and Goel (2002)

  • AMC procedure accounts for higher mode effects by combining the response of individual modal pushover analyses and incorporates the effects of varying dynamic characteristics during the inelastic response via its adaptive feature
summary cont
Summary (cont.)
  • A novel feature of the procedure is that the target displacement is estimated and updated dynamically during the analysis by incorporating energy based modal capacity curves in conjunction with constant-ductility capacity spectra.
  • AMC method has shown promise in predicting inelastic displacement demands for a range of regular and irregular buildings.
  • Validation studies under 3D models (including torsion) are currently underway.