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Seismic Behaviour and Analysis of IrregularBridges with Different Column Heights

Payam Tehrani

Supervisor: Prof. Denis Mitchell

Department of Civil Engineering and Applied MechanicsMcGill University

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INTRODUCTION

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Department of Civil Engineering and Applied Mechanics

Main Problems with Bridges with Different Column Heights

Deformation demands on columns are highlyirregular and excessive deformation demands occurin a few elements.

Stiffness irregularities cause concentration of seismicshear forces in the shorter columns, so brittle shearfailure is possible.

Sequential yielding of ductile members may causesubstantial deviations of the results from linearanalyses performed with assumption of a globalreduction factor.

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Concrete shear strength degradation according to the highductility levels

Shear strength in plastic hinge region based on CSA-S6-06 :

Minimum factored axial compression >

Minimum factored axial compression = 0

Effect of ductility on shear strength?!

2.5c c cr v vV f b d

0.1 c g f A 0.18

0

concentration ofhigh ductility demands

on short columns

Shear Strengthmay be overestimated

in design

cV

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BACKGROUND

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Reinforced Concrete Bridge Models (1:2.5 scale)

ELSA Laboratory

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http://slidepdf.com/reader/full/tehrani 7/35Department of Civil Engineering and Applied Mechanics

The absorbed energy in the irregular bridge wasconcentrated in the short middle pier, which dissipated

more than 70% of the total energy.

Safety against collapse of the irregular bridge was quitelow compared to the safety of the regular bridge.

The regular bridge was able to withstand twice thedesign loads while the irregular bridge suffered damagein the short column under a seismic input of 1.2 timesthe design earthquake.

Results from ELSA Tests

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Study by Calvi et al. [1994 and 1996]

Straight bridges were considered with 3 or 5 piers ofdifferent heights.

Results showed that EC8/2 design approach may resultin lower than expected safety levels, with higher thanexpected ductility demands.

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Parameters of Regularity

Measures of the difference between the mode shape of thewhole bridge and of the deck alone.

: Mode shapes of the bridge : Mode shapes of the deck

n : Number of modes considered

2

11

( )n

B Di j

j

M

Rn

1 1

2

[(1 ) ]1

n n

B Dij i ji j

M R

n

B

i

D

j

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Displacement Ductility Versus Regularity Factor

D i s p

l a c e m e n

t D u c

t i l i t y

Parameter of Regularity ( ) 2 R

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Modal PushoverAnalysis (MPA) forIrregular Bridges?

An extension of the ‘standard’

pushover analysis

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MPA Main Steps:Compute the natural periods,T n and modes, φ n

Carry out separate pushoveranalyses for each mode usingforce distribution, s n =m φ n

Calculate the earthquakedisplacement demand for eachmode (e.g. Capacity SpectrumMethod (CSM))

Combine the peak ‘modal’responses using the SRSS orthe CQC combination rule.

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Two Principal Assumptions:

The coupling among modes is essentially neglected.

SRSS or CQC combination rules are valid.

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Study by Kappos et al. on An Existing Bridge

Comparison between Modal Pushover Analysis ( MPA ), Single Pushover

Analysis (SPA ) and Inelastic Time History Analysis ( ITHA)

Design earthquake

Twice thedesign earthquake

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Pushover Analysis should be used with caution forfollowing cases :

Bridges with great eccentricity

Torsionally flexible bridges (eg., free abutments)

Bridges with a relatively flexible deck

Bridges with very stiff central pier

Bridges with very stiff end piers

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CODEPROVISIONS

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Caltrans and the Proposed 2007 AASHTO GuideSpecifications

For any two bents within a frameor any two columns within a bent:

For adjacent bents within a frameor adjacent columns within abent:

The ratio of fundamental periodsof vibration for adjacent frames :

0.5ei j

e

j i

K m

K m

0.5eie

j

K K

0.75eie

j

K K

0.75ei j

e

j i

K m

K m

0.7i

j

T

T Oversimplified !!

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PRELIMINARYRESULTS

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Preliminary 4-Span Bridges

4-span bridges with different configurations and different abutmentconditions were studied.

Elastic Dynamic Analyses (EDA) were performed using SAP2000and the modal information, forces and displacements were extractedusing programmed excel sheets.

Modal Pushover Analyses (MPA) were performed using SAP2000and the results were extracted using programmed excel sheets

Inelastic Time History Analyses (ITHA) were performed inRUAUMOKO software using 7 records matched to the designspectra

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4-Span Bridges

Definition :

Bridge 213 has 3 piers with 14, 7 and 21 meters height respectively(from left to right)

Span length is 50 m

Bridge 213 (2x7, 1x7, 3x7)

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Modal Pushover AnalysisExample of capacity- demand curves

for 2 different modes

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Spectrum Matched Records For Inelastic Time HistoryAnalysis (ITHA)

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Bridges with Fixed Abutments

The results from 2 bridges will be presented:

Bridge 222 (Regular bridge with fixed abutments)

Bridge 213 (Irregular bridge with fixed abutments)

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Displaced Shape of the Bridge 222 (Regular bridge )Using Different Methods of Analysis

Displacem ent shapes

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 20 40 60 80 100 120 140 160 180 200

X (m)

L a

t e r a

l D i s p

l a c e m e n

t ( m )

Uniform load MPA ITHA ELASTIC

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Displaced Shape of theBridge 213 (Irregular Bridge)

Using Different Methods of AnalysisDisplacement shapes

00.02

0.040.060.08

0.10.120.140.16

0 50 100 150 200X (m)

L a t e r a

l D i s p

l a c e m e n

t ( m )

Uniform load MPA ITHA ELASTIC

Short Column

at x=100 m

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Comparison Between Deck

alone and Irregular BridgeMode Shapes

Mode Shape (1s t)

-1

-0.5

0

0.5

1

0 50 100 150 200

X

y

Deck Bridge

Mode Shape (2nd)

-1

-0.5

0

0.5

1

0 50 100 150 200

X

y

Deck Bridge

Mode Shape (3rd)

-1

-0.5

0

0.5

1

0 50 100 150 200

X

y

Deck Bridge

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Seismic Ductility Demand in ColumnsBridge 222 (Regular) and bridge 213 (Irregular)

Linear Analysis Nonlinear Analysis

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Rotational Demands on Columns ofRegular and Irregular Bridges

Regular

Irregular

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Bridges With Free Abutments

The results from 2 bridges will be presented:

Bridge 222R (Regular bridge with free abutments)

Bridge 213R (Irregular bridge with free abutments)

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Displaced Shape of the Bridge 222R(Regular bridge with free abutments)

Using Different Methods of AnalysisDisplacement shapes

0

0.1

0.2

0.3

0.4

0.5

0.6

0 20 40 60 80 100 120 140 160 180 200

X (m) L a t e r a

l D i s p

l a c e m e n

t ( m )

Uniform load SRSS ITH ELASTIC

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Displaced Shape of the Bridge 213R(Irregular bridge with free abutments)Using Different Methods of Analysis

Displacement shapes

00.1

0.2

0.3

0.4

0.5

0.6

0.7

0 20 40 60 80 100 120 140 160 180 200

L a

t e r a

l D i s p

l a c e m e n

t ( m )

Uniform Load MPA ITH ELASTIC

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Seismic ductility Demand in Columns(Bridge 222R and bridge 213R)

Linear Analysis Nonlinear Analysis

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OBJECTIVES

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Investigate the behaviour and safety level of bridges with varyingcolumn height designed based on the CAN-CSA-S6-06 code.

Compare the results from different methods of analysis includinglinear dynamic analysis, modal pushover analysis and nonlinear timehistory analysis and if possible determine criteria capable of

indicating which analysis methods are valid.

When can the seismic behaviour of a bridge be predicted by simplelinear dynamic analysis with application of a global reductionfactor?

Apply the Direct Displacement-Based Design (DDBD) method indesign of some selected critical bridges and compare the seismicbehaviour of the bridges designed with forced-based and DDBDmethod.

Research Objectives

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Thanks for your attention

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