analiza pushover

Push-over analysis for seismic performance evaluation of RC frame structures. Computer programsPush-over analysis for seismic performance evaluation of RC frame structures. Computer programs

22oo Ciclo de Palestras em Engenharia Civil-2003 Ciclo de Palestras em Engenharia Civil-200312 de Novembro de 200312 de Novembro de 2003

Universidade Nova de Lisboa-Centro de Investigaçao em Estruturas e Construção-UNICUniversidade Nova de Lisboa-Centro de Investigaçao em Estruturas e Construção-UNIC

Push-over analysis for seismic Push-over analysis for seismic performance evaluation of RC frame performance evaluation of RC frame

structures. Computer programsstructures. Computer programs

22oo Ciclo de Palestras em Engenharia Civil-2003 Ciclo de Palestras em Engenharia Civil-200312 de Novembro de 200312 de Novembro de 2003

Universidade Nova de Lisboa-Centro de Investigaçao em Estruturas e Construção-UNICUniversidade Nova de Lisboa-Centro de Investigaçao em Estruturas e Construção-UNIC

Push-over analysis for seismic Push-over analysis for seismic performance evaluation of RC frame performance evaluation of RC frame

structures. Computer programsstructures. Computer programs Dr. C. G. ChioreanDr. C. G. Chiorean

Technical University of Cluj-Napoca, RomaniaTechnical University of Cluj-Napoca, RomaniaBolseiro na UNL/FCT, Lisboa, PortugalBolseiro na UNL/FCT, Lisboa, Portugal


Part II. Part II. Computer programsComputer programsNEFCAD NEFCAD Computer program for large deflection elasto-plastic Computer program for large deflection elasto-plastic

analysis of spatial frame structuresanalysis of spatial frame structures

ASEPASEP Computer program for inelastic analysis of arbitrary Computer program for inelastic analysis of arbitrary reinforced and composite concrete sectionsreinforced and composite concrete sections

OutlineOutlineOutlineOutline

Part I. Part I. Push-over analysis for seismic Push-over analysis for seismic

performance performance evaluation of spatial RC evaluation of spatial RC frame structuresframe structures


Static NonlinearStatic Nonlinear analysis - analysis -Push-over AnalysisPush-over Analysis (aproximative solution) (aproximative solution)

Seismic performanceSeismic performance – – Inelastic Inelastic Types of Types of analysisanalysis

Seismic performanceSeismic performance – – Inelastic Inelastic Types of Types of analysisanalysis

Nonlinear dynamic analysis- time history (final solution)Nonlinear dynamic analysis- time history (final solution)

Vb

UN

Push-over CurveLoad vs Deflection

UN F

Vb


• Nonlinear static procedure: constant gravitational loads and monotonically increasing lateral loads

• Plastic mechanisms and P- effects: diplacement or arc length control

• Capacity curve: Control node displacement vs base shear force

• Lateral load patterns: uniform, modal, SRSS, ELF force distribution

• Estimation of the target displacement: elastic or inelastic response spectrum for equivalent SDOF system

• Performance evaluation: global and local seismic demands with capacities of performance level.

Key elements of the push-over analysisKey elements of the push-over analysisKey elements of the push-over analysisKey elements of the push-over analysis


Concentrated plasticity Distributed plasticity

• Dimensionless plastic hinge

• Interaction surface

• Return mapping plasticity algorithms

• Computationally efficient but limited accuracy

• Plastic zones

• Force-strain curves: quasi plastic hinge approach

• Stress-strain curves: fiber element approach

• Plastic flow rules

• High accuracy but computational expensive

Plastic hingePlastic zones

Elastic Elastic

Inelastic analysis modelsInelastic analysis modelsInelastic analysis modelsInelastic analysis models


IP4 IP3

IP2

j=IP5

iPI1

L/2

L/2

x

z

y

Concrete Steel

Z

Y x

vi, Tiy

y

wi, Tiz

z

zj,Mzj

xj,Mxj

uj, Nj vj, Tjy

yi,Myi

xi,Mxi

ui, Ni

zi,Mzi

X wj, Tjz

Mz

My

N z

y

• Flexibility-based nonlinear beam column element

•Iterative method to compute inelastic response at cross-sectional level (inelasatic flexural and axial rigidity)

• Gradual yielding along the member length and within the cross sections

• Distributed loads

• Uniform or nonuniform (tapered) members

• Variation of reinforcement bars along the member

One element/

member

3D RC Fiber Beam Column Element3D RC Fiber Beam Column Element3D RC Fiber Beam Column Element3D RC Fiber Beam Column Element


(NA)

y

x

22

yx

yxuxyu

• Arbitrary cross-sections under biaxial bending moments and axial force

• Arc length icremental iterative method with tangent stiffness strategy

• Green´s theorem: domain integrals are evaluated in terms of boundary integrals

• M-N- curves, N-Mx-My interaction diagrams and axial force ultimate curvature

Inelastic analysis of cross-sectionsInelastic analysis of cross-sectionsInelastic analysis of cross-sectionsInelastic analysis of cross-sections


• Large deflection and large rotations

• Geometrical local effects (P-) including bowing effect, shear deformations

• Concentrated and distributed plasticity (fiber and M-N- aproaches)

• Consistency between linear and nonlinear models (one element/member)

• Local geometrical and material imperfections

• Flexible (semi-rigid) and finite joints

• Complete non-linear behavior (pre and post crtical response: snap-back and snap-through)

Model capabilitiesModel capabilitiesModel capabilitiesModel capabilities


Elastic spectrum response: Type 1

Ground Type: A

Design ground acceleration: PGA=0.3g

Mass=40 (80) tones/level

Case study (Six story RC frame building)Case study (Six story RC frame building)Case study (Six story RC frame building)Case study (Six story RC frame building)

60 x60

30 x50

Structural configuration

Control node


Pushover loads “mode 1 transv.”

Effective modal mass=65%

Pushover loads “mode 1-longit”

Effective modal mass=76%

Base shear forces:

• Transversal (mode 1): Fz= 348 kN

• Longitudinal (mode 1):Fx= 482 kN

T1=1.5s T1=1.27s

Seismic force evaluationSeismic force evaluationSeismic force evaluationSeismic force evaluation


Plastic hinge analysis Plastic zone analysis

Interaction surface equation: Stress-strain curves for concrete and steel bars (Eurocodes)

7 Gauss-Lobatto IP/member

Interaction N-M

-2000

0

2000

4000

6000

8000

10000

12000

0 200 400 600 800 1000 1200

Bending moment (kNm)

-2000

0

2000

4000

6000

8000

10000

12000

0.00 0.01 0.02 0.03 0.04 0.05

Ultimate curvature

Axia

l fo

rce

(kN

)

-1000.00

0.00

1000.00

2000.00

3000.00

4000.00

5000.00

0.00 100.00 200.00 300.00 400.00

Bending Moment (kNm)

Major axisbending

Minor axisbending

0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

0.00 0.05 0.10 0.15 0.20

Ultimate curvature

Major axisbending

Minor axisbending

01

6.16.1

zp

z

py

y

M

M

M

M

820

30x50cm

Inelastic analysis dataInelastic analysis dataInelastic analysis dataInelastic analysis data

1625

60x60cm

Unconfined concrete

Confined concrete


Plastic zone analysis Plastic hinge analysisPushover curves-Longitudinal direction

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0.00 20.00 40.00 60.00 80.00 100.00 120.00Displacement X (cm)

Ap

lied

load

fac

tor

Plastic zone, Plim=1.12

Plastic hinge, Plim=1.11

Pushover analysis: Longitudinal directionPushover analysis: Longitudinal directionPushover analysis: Longitudinal directionPushover analysis: Longitudinal direction

Plastic hinge: CPU time: 1.5 min

(120 load cycles)

Plastic zone: CPU time: 8.3 min

(150 load cycles)

One element/physical member


Plastic hinge analysisPlastic zone analysisPushover curves-Transversal direction

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

0.00 20.00 40.00 60.00 80.00Displacement Z (cm)

Ap

lied

lo

ad f

acto

r Plastic zone, Plim=1.21

Plastic hinge, Plim=1.11

Pushover analysis: Transversal directionPushover analysis: Transversal directionPushover analysis: Transversal directionPushover analysis: Transversal direction


Bending moments Flexural rigidities

Plastic zone analysis: Longitudinal directionPlastic zone analysis: Longitudinal directionPlastic zone analysis: Longitudinal directionPlastic zone analysis: Longitudinal direction


Bending moments Flexural rigidities

Plastic zone analysis: Transversal directionPlastic zone analysis: Transversal directionPlastic zone analysis: Transversal directionPlastic zone analysis: Transversal direction


Pushover curves-Transversal direction

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40


Ap

lied

loa

d f

ac

tor Plastic zone (modal pattern), plim=1.21

Plastic zone (uniform acceleration), plim=1.19

Modal vs Uniform force distributionModal vs Uniform force distributionModal vs Uniform force distributionModal vs Uniform force distribution


Pushover curves-Longitudinal direction

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40


Ap

lied

loa

d f

ac

tor

Plastic zone (modal pattern), Plim=1.12

Plastic zone (uniform pattern),Plim=1.28

Modal vs Uniform force distributionModal vs Uniform force distributionModal vs Uniform force distributionModal vs Uniform force distribution


Equivalent SDOF and target displacementEquivalent SDOF and target displacementEquivalent SDOF and target displacementEquivalent SDOF and target displacement


Target displacements (Plastic zone)-Transversal direction

Dt=7.80 cm

Dt=15.77 cm

Dt=31.54 cm

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40


Ap

lied

loa

d f

ac

tor Computed pushover curve (plastic zone)

Idealized elaso-perfectly plastic (EC8)

Target displacements: transversal directionTarget displacements: transversal directionTarget displacements: transversal directionTarget displacements: transversal direction


Target displacements (plastic hinge)-Transversal direction

7.45

14.91

29.83

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0.00 10.00 20.00 30.00 40.00 50.00 60.00Displacement Z (cm)

Ap

lied

loa

d f

ac

tor

Computed pushover curve (plastic hinge)

Idealized elasto-perfectly plastic (EC8)

PGA=0.15g

PGA=0.3g

PGA=0.6g

Target displacements: transversal directionTarget displacements: transversal directionTarget displacements: transversal directionTarget displacements: transversal direction


Target displacements (plastic zone)-Longitudinal direction

11.65 cm

23.3 cm

46.64 cm

0.00

0.20

0.40

0.60

0.80

1.00

1.20


Ap

lied

loa

d f

ac

tor

Computed pushover curve (plastic zone)


PGA=0.15g

PGA=0.3g

PGA=0.6g

Target displacements: longitudinal directionTarget displacements: longitudinal directionTarget displacements: longitudinal directionTarget displacements: longitudinal direction


Target displacements (plastic hinge)-Longitudinal direction

11.27 cm

22.54 cm

45.08 cm

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0.00 20.00 40.00 60.00 80.00 100.00Displacement X (cm)

Ap

lied

loa

d f

ac

tor

Computed pushover curve (plastic hinge)


PGA=0.15g

PGA=0.3g

PGA=0.6g

Target displacementsTarget displacements – – longitudinal directionlongitudinal directionTarget displacementsTarget displacements – – longitudinal directionlongitudinal direction


Local seismic demandsLocal seismic demandsLocal seismic demandsLocal seismic demands

Curvatures along the member length

-0.0150

-0.0100

-0.0050

0.0000

0.0050

0.0100

0.0150

0.0200

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

Member length (m)

Cur

vatu

res

PGA=0.15g

PGA=0.3g

PGA=0.6g


Local seismic demandsLocal seismic demandsLocal seismic demandsLocal seismic demands

Curvatures along the member length

-0.0070

-0.0060

-0.0050

-0.0040

-0.0030

-0.0020

-0.0010

0.0000

0.0010

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50

Member length (m)

Cur

vatu

res

PGA=0.15g

PGA=0.3g

PGA=0.6g


Global seismic demandsGlobal seismic demandsGlobal seismic demandsGlobal seismic demandsPGA=0.15g

Dt=7.80 cm

PGA=0.3g

Dt=15.77 cm

PGA=0.6g

Dt=31.54 cm

Collapse

D=64.8 cm


PGA=0.3g PGA=0.6gPGA=0.15g Collapse

Plastic zone analysis

Plastic performance: Transversal directionPlastic performance: Transversal directionPlastic performance: Transversal directionPlastic performance: Transversal direction


PGA=0.3g PGA=0.6gPGA=0.15g Collapse

Plastic hinge analysis

Plastic performance: Transversal directionPlastic performance: Transversal directionPlastic performance: Transversal directionPlastic performance: Transversal direction

2 PH 7 PH 10 PH 13 PH


CollapsePGA=0.15g PGA=0.3g PGA=0.6g

Plastic zone analysis

Plastic performance: Longitudinal directionPlastic performance: Longitudinal directionPlastic performance: Longitudinal directionPlastic performance: Longitudinal direction


PGA=0.15g PGA=0.3g PGA=0.6g Collapse

Plastic hinge analysis

Plastic performance: Longitudinal directionPlastic performance: Longitudinal directionPlastic performance: Longitudinal directionPlastic performance: Longitudinal direction

7 PH 13 PH 15 PH 16 PH


• A computational efficient 3-D RC fiber beam-column element was developed and implemented in a nonlinear inelastic analysis computer program

• Plastic hinge analysis: limited accuracy

• A pushover example for spatial model was presented in conjunction with EC8 provisions

• Pushover analysis: good estimates of global and local inelastic deformations demands

• Limitations: for structures that vibrate primarily in the fundamental mode

• Overcomes: adaptive force distribution and modal pushover analysis procedures

• Nonlinear dynamic analysis: final solution

Concluding remarksConcluding remarksConcluding remarksConcluding remarks

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