Bridge DynamicsBridge Dynamics

Suhasini Madhekar Suhasini Madhekar

College of Engineering PuneCollege of Engineering Pune

Faculty Development Program onFaculty Development Program on

Fundamentals of Structural Dynamics and Application to Fundamentals of Structural Dynamics and Application to

Earthquake EngineeringEarthquake Engineering

1212thth December 2015December 2015

Sanjay Sanjay GhodawatGhodawat Group of InstitutionsGroup of Institutions

AtigreAtigre, Kolhapur, Kolhapur 11

Presentation OutlinePresentation Outline

BridgesBridges aroundaround thethe worldworld

BehaviourBehaviour ofof bridgesbridges duringduring pastpast earthquakesearthquakes

MajorMajor componentscomponents ofof BridgeBridgeMajorMajor componentscomponents ofof BridgeBridge

BridgeBridge DynamicsDynamics andand BridgeBridge modelingmodeling

SeismicSeismic considerationsconsiderations forfor BridgesBridges

ConclusionsConclusions

22

Dynamic forces acting on BridgesDynamic forces acting on Bridges

WindWind

EarthquakeEarthquake

BlastBlast

Barge Impact / vehicle impactBarge Impact / vehicle impact

Flood : Buoyancy : Submersible bridges Flood : Buoyancy : Submersible bridges

33

Difference Difference Between WindBetween Wind--Resistant DesignResistant Design

and Earthquakeand Earthquake--Resistant DesignResistant Design

For Wind:For Wind:

Excitation is an applied Excitation is an applied pressure or force on the facade.pressure or force on the facade.

Loading is dynamic but response is nearly static for most Loading is dynamic but response is nearly static for most

structures.structures.structures.structures.

Structure deforms due to applied force.Structure deforms due to applied force.

Deformations are monotonic (unidirectional).Deformations are monotonic (unidirectional).

Structure is designed to respond elastically under factored loads.Structure is designed to respond elastically under factored loads.

The controlling life safety limit state is strength.The controlling life safety limit state is strength.

Enough strength is provided to resist forces elastically.Enough strength is provided to resist forces elastically. 44

Difference Between WindDifference Between Wind--Resistant DesignResistant Design

and Earthquakeand Earthquake--Resistant DesignResistant Design

For Earthquake:For Earthquake:

Excitation is an applied displacement at the base.Excitation is an applied displacement at the base.

Loading and response are truly dynamic.Loading and response are truly dynamic.

Structural system deforms as a result of inertial forces.Structural system deforms as a result of inertial forces.Structural system deforms as a result of inertial forces.Structural system deforms as a result of inertial forces.

Deformations are fully reversed.Deformations are fully reversed.

Structure is designed Structure is designed to respond to respond inelasticallyinelastically under factored under factored

loadsloads. Enough . Enough strength is provided to ensure that strength is provided to ensure that the the

structure withstands inelastic deformationsstructure withstands inelastic deformations

Demands Demands do not exceed deformation capacitydo not exceed deformation capacity

..

55

Bridge failures in Past Earthquakes Bridge failures in Past Earthquakes Bridge failures in Past Earthquakes Bridge failures in Past Earthquakes

66

Collapse of Collapse of NakazunoNakazuno Bridge : 1948 Fukui Earthquake, Japan Bridge : 1948 Fukui Earthquake, Japan 77

Failure of foundations due to soil liquefaction resulted Failure of foundations due to soil liquefaction resulted

in collapse of the bridge : in collapse of the bridge : NigataNigata Earthquake JapanEarthquake Japan88

Damage to SuperstructureDamage to Superstructure

Steel Steel superstructure failure and superstructure failure and collapse of Eastern collapse of Eastern

portion of portion of the San Franciscothe San Francisco––Oakland Bay Bridge Oakland Bay Bridge

(1989 (1989 Loma Loma PrietaPrieta earthquake) earthquake) 99

Damage to BearingsDamage to Bearings

Bearing failure at several locations led to large

superstructure rotations 1010

1991 Costa Rica earthquake (1991)

Abutment rotated due to liquefaction and lateral spreading

(lateral sliding of gently sloping ground due to soil

liquefaction at relatively shallow depth ) 1111

Failure of 18 Span Viaduct in Kobe Earthquake Failure of 18 Span Viaduct in Kobe Earthquake

Damage resulted from insufficient consideration on ductility of Damage resulted from insufficient consideration on ductility of

columns and insufficient strength of bearings.columns and insufficient strength of bearings.

The most extensive damage occurred at a 18 The most extensive damage occurred at a 18 -- span viaduct. It span viaduct. It

collapsed due to failure of RC columns which resulted from the collapsed due to failure of RC columns which resulted from the

premature shear failure.premature shear failure.premature shear failure.premature shear failure.

Northridge earthquake: Costliest natural disaster in the history of Northridge earthquake: Costliest natural disaster in the history of

USA. Six bridges collapsed on the major freeways. USA. Six bridges collapsed on the major freeways.

The main failure types of bridges are classified in two groupsThe main failure types of bridges are classified in two groups

Failure of abutments and piersFailure of abutments and piers

Failure of superstructuresFailure of superstructures1212

First Tacoma Narrows Bridge, First Tacoma Narrows Bridge, USAUSA

CollapseCollapse ofof suspensionsuspension bridgesbridges duedue toto windwind :: TacomaTacoma

NarrowsNarrows BridgeBridge DisasterDisaster

BridgeBridge provedproved toto bebe veryvery sensiblesensible toto windwind forcesforces andand waswas

excitedexcited toto laterallateral asas wellwell asas verticalvertical vibrationsvibrations..excitedexcited toto laterallateral asas wellwell asas verticalvertical vibrationsvibrations..

OnOn NovemberNovember 77,, 19401940,, exposedexposed toto aa modestmodest laterallateral windwind ofof

1919 m/m/ ss thethe suspensionsuspension bridgebridge movedmoved inin longitudinallongitudinal waveswaves

upup andand downdown withwith aa twistingtwisting deckdeck andand eventuallyeventually thethe hangershangers

rupturedruptured.. TheThe centralcentral spanspan ofof 853853 mm fellfell downdown andand sunksunk intointo

thethe riverriver..1313

TheThe firstfirst TacomaTacoma NarrowsNarrows suspensionsuspension bridgebridge collapsedcollapsed duedue toto windwind--inducedinduced

vibrationsvibrations onon NovNov.. 77,, 19401940.. TheThe bridgebridge waswas engineeredengineered itit toto withstandwithstand hurricanehurricane

winds,winds, butbut thethe windwind thatthat dayday waswas onlyonly 4040 mphmph…… whatwhat happened!?happened!? 1414

Accidental Accidental overload and overload and impact of vehicles with main impact of vehicles with main

structural elements of bridge : structural elements of bridge : ship collisions with bridge ship collisions with bridge

piers.piers.

Causes of Bridge Causes of Bridge FailuresFailures

Structural Structural and design and design deficiencies deficiencies

Scour of foundations in river bedScour of foundations in river bed

Construction Construction and supervision and supervision mistakesmistakes

Lack Lack of maintenance and inspection.of maintenance and inspection.

1515

Causes of Bridge Causes of Bridge FailuresFailures

Under strong ground excitations, highway bridge structures

experience severe nonlinear behaviors : Yielding and plastic

deformation of pier members

The pounding between adjacent decks induced by the local

failure of hinge bearings

Bridges of the BMHWB kind are quite common on highway

river-crossings all over the world.

1616

Distribution of Bridges Collapse causesDistribution of Bridges Collapse causesEarthquakesEarthquakes

1717

Structural and Design DeficienciesStructural and Design Deficiencies

Incorrect assumption of loadsIncorrect assumption of loads. .

Many bridges Many bridges collapsed due to static and / or dynamic wind collapsed due to static and / or dynamic wind

forces : Tacoma Narrows (1940). forces : Tacoma Narrows (1940). forces : Tacoma Narrows (1940). forces : Tacoma Narrows (1940).

Besides Besides using long using long term statistics term statistics to reliably estimate the to reliably estimate the

wind force, nowadays wind wind force, nowadays wind tunnel tests tunnel tests are performed to are performed to

verify structures that are verify structures that are especially sensitive especially sensitive to wind forcesto wind forces..

1818

Superstructure FailuresSuperstructure Failures

1919

2020

2121

Buckling of bridge pier in HanshinBuckling of bridge pier in Hanshin--Awaji Awaji

earthquake : 17earthquake : 17thth January 1995January 1995

2222

Failure of Steel PiersFailure of Steel Piers

2323

Shear failure of RC columnsShear failure of RC columns

2424

Development of ClausesDevelopment of Clauses

Till 1948, seismic effects were not considered / poorly Till 1948, seismic effects were not considered / poorly

considered in design : Tilting, Overturning and settlement of considered in design : Tilting, Overturning and settlement of

foundations occurred.. Leading to extensive damages and foundations occurred.. Leading to extensive damages and

collapse..collapse..collapse..collapse..

Construction of massive & rigid piers with large sections Construction of massive & rigid piers with large sections

started. started.

In 1960In 1960--1970s : Importance of considering soil liquefaction 1970s : Importance of considering soil liquefaction

and unseating prevention devices was first recognised. and unseating prevention devices was first recognised.

2525

Development of Development of

Unseating prevention devicesUnseating prevention devices

2626

Damage resulted from Damage resulted from

insufficient ductility of insufficient ductility of

columns and strength of columns and strength of

bearingsbearings

2727

Ductile DetailingDuctile Detailing

2828

Seismic Design Practice in JapanSeismic Design Practice in Japan

2929

Extensive Damage of BearingsExtensive Damage of Bearings

3030

Performance of BearingsPerformance of Bearings

ChiChi––Chi Chi earthquake earthquake (1999, M7.3), Taiwan (1999, M7.3), Taiwan : Improper : Improper

functioning of bearings can lead to deckfunctioning of bearings can lead to deck--falling failure falling failure

The The gap of joints between decks can have a significant effect gap of joints between decks can have a significant effect

on the response of a bridgeon the response of a bridge

When When sliding and pounding occurs, accelerations of bridge sliding and pounding occurs, accelerations of bridge

decks may increase by a factor of decks may increase by a factor of 10, 10, as compared to that as compared to that

without pounding.without pounding.

The abrupt increase of accelerations can result in severe The abrupt increase of accelerations can result in severe

impact forces that damage structural members like the deck impact forces that damage structural members like the deck

or pier.or pier.3131

Design of BearingsDesign of Bearings

3232

Damage of Unseating Prevention Damage of Unseating Prevention

DevicesDevices

3333

Experience of 1995 Kobe EarthquakeExperience of 1995 Kobe Earthquake

3434

Change in Bridge codes..Change in Bridge codes..

IRC 112 (2011): Code of practice for concrete road bridges : IRC 112 (2011): Code of practice for concrete road bridges :

Based on Based on Limit state method Limit state method : Now mandatory: Now mandatory

IRC 18 Design criteria for PSC road (postIRC 18 Design criteria for PSC road (post--tensioned) Bridges tensioned) Bridges

and IRC 21 Code of practice for concrete road bridges) : and IRC 21 Code of practice for concrete road bridges) :

Both based on WSM are withdrawn. Both based on WSM are withdrawn.

3535

Optimal performance achieved Optimal performance achieved by by

�� Providing Providing competent load pathcompetent load path

�� Providing Providing redundancy redundancy

�� Avoiding Avoiding configuration irregularitiesconfiguration irregularities

�� Proper Proper consideration of “consideration of “non non -- structural” elements structural” elements and and �� Proper Proper consideration of “consideration of “non non -- structural” elements structural” elements and and

componentscomponents

�� Avoiding Avoiding excessive massexcessive mass

�� Detailing Detailing for controlled energy dissipationfor controlled energy dissipation

�� Limiting Limiting deformation demandsdeformation demands

3636

Natural Natural and Added Dampingand Added Damping

3737

Reduction in Seismic DamageReduction in Seismic Damage

3838

Seismic Analysis of Structures with Passive EnergySeismic Analysis of Structures with Passive Energy

Dissipation SystemsDissipation Systems

3939

Objective of Bridge ModelingObjective of Bridge Modeling

To provide a simple mathematical formulation of

the true structural behavior, which satisfies a the true structural behavior, which satisfies a

particular assessment or design requirement for

a quantitative response determination

40

Types of modelsTypes of models

� Lumped parameter model:

Very simple ; but requires significant knowledge and

experience – Deformation relationship of few idealized

elements to represent the prototype bridge

� Structural component model:

Based on idealized Structural subsystems that are connected

to resemble the prototype

� Detailed FE Model: Huge computational effort required –

nonlinear analysis – cyclic response

41

42

43

44

General Modeling IssuesGeneral Modeling Issues

The model is to describe :

Geometric domain

Seismic mass

Connection

Boundary conditions

Loading of the prototype

…..as closely as possible to facilitate the engineering

interpretation of numerical response quantities.

45

General Modeling IssuesGeneral Modeling Issues

� With the earthquake loading, the soil structure interface

may also be important.

� When soft soils, massive foundations, and /or

liquefaction potential are present , soil structure

interaction (SSI) should be modeled through description

of appropriate soil springs

� Alternatively actual soil modeling in the form of a

continuous half-space or a portion thereof.

46

Bridge Structural SystemBridge Structural System

� The total structural bridge system consists of the

superstructure and the substructures

� To reflect the importance and differences of different

individual subsystems in terms of the analytical modeling for

seismic bridge response quantification

(1) global models, (2) frame models, and (3 ) bent models.

47

Individual Structural MembersIndividual Structural Members

� The three groups of structural members or

elements used in bridge models are

(1) line elements

(2) plates and shells and

(3) solid elements

48

49

50

51

Bridge FoundationsBridge Foundations

Most common footing types for bridge piers and

abutments :

(1) spread footings for stiff soil sites

(2) pile-supported cap footings for soft soil sites or

soil layers with liquefaction potential

(3) well foundations

52

Damage to FoundationsDamage to Foundations

5353

Pile Damage Pile Damage by by Lateral Spread Lateral Spread

1964, Niigata, Japan1964, Niigata, Japan

5454

Spread and Pile FootingsSpread and Pile Footings

Spread or pile footings are typically considered to be rigid

bodies that allow support conditions to be modeled at a

single point with boundary springs at the bottom of the

column or pier model at the end of the effective length

extension link into the footing.extension link into the footing.

For pile footings rotational stiffness is of greater significance

than lateral stiffness on overall bridge response.

The rotational stiffness and capacity of pile footings are

largely related to pile axial stiffness and the pile axial

capacities in compression and uplift.55

56

Shock Transmitting DevicesShock Transmitting Devices

� STU : Also known as ‘Lock Up’ Device (LUD)

� First use of STU : By Steinman, the designer of the

Carquinez Bridge in California, US (1927)

� STU : Forms a rigid link under rapidly applied loads � STU : Forms a rigid link under rapidly applied loads

- Braking and seismic forces

� Moves freely under slowly applied loads

- Temperature, creep and shrinkage

� The unit is connected between elements of bridge structures

- At expansion joints or near the bearings57

Shock Shock Transmitting DevicesTransmitting Devices

� Rapid passage of viscous fluid through the narrow gap, orifice

or part generates high resistance

� Simple dimensions and simple installation, no leakage

� Installation soon after the structure is completed

� STU’s connect superstructure to substructure elements :

according to space available between the soffit of deck and

the top of pier

� STU is connected by brackets and pins

� STUs: can reduce the seismic response of any part of the

structure 58

STU : AdvantagesSTU : Advantages

� Load sharing by means of an STU in new multi-span bridges

results in smaller design section for the substructure elements

� STUs can be made to strengthen supporting piers which have

been found inadequate due to increase in traction and been found inadequate due to increase in traction and

braking forces / seismic considerations

� Installation of STUs can be carried out without closing the

bridge traffic

� STU are maintenance free. Periodic visual inspection

necessary in order to check the corrosion protection system

59

Case Study of Jaitapur BridgeCase Study of Jaitapur Bridge

60

� Near Jaitapur

� Prestressed concrete box girder 2 span continuous unit

� span = 65m Thus unit is of 65 + 65

� Bridge length more than 500 m

� Concrete, steel

� Cast steel rocker - roller bearings

� Pier height : 6-8m, pier cap 7.0m x 3.0m x 3.0m depth

� Wells are all of different size ranging from 10m to 11.5 m dia 61

� Number of spans : 1 span of 20m , 2 span unit of 33m , 2 units of

65 m, 2 spans continuous units and 1 span of 30 m.

� Span length : 65 m + 65 m two span continuous

� Superstructure Type : PSC box girder

Well Foundation : Jaitapur Bridge Details Well Foundation : Jaitapur Bridge Details

62

� Superstructure Type : PSC box girder

� Pier Type : Solid Circular

� Bearing : Rocker Roller

� Location : Near Jaitapur Konkan

� Seismic Zone : IV (Ah = 0.066)

Components of well FoundationComponents of well Foundation

AccordingAccording toto thethe constructionconstruction sequencesequence ::

1) Cutting edge

2) Well Curb

3) Well Steining

4) Bottom plug4) Bottom plug

5) Sand filling

6) Top Plug

7) Well cap

Island for grounding cutting edgeIsland for grounding cutting edge

Without STU With one STUWithout STU With one STU

Forces on Single Well Forces on Single Well Foundation Foundation

Dead load = 6820.00 kN

Bearing = 5.00 kN

Chairs = 25.00 kN

Shaft + sand = 1051.9 kN

Well Cap = 2106.4 kN

Dead load = 6820.00 - 2371.70

= 4448.30 kN

Bearing = 5.00 kN

Chairs = 25.00 kN

Pier Cap = 681.7 kN

Shaft + sand = 1051.9 kN

74

Well Cap = 2106.4 kN

Stening = 11849.6 kN

Top Plug = 223 kN

Sand fill = 7386 kN

Total = 56053.14 kN

Shaft + sand = 1051.9 kN

Well Cap = 2106.4 kN

Stening = 11849.6 kN

Top Plug = 223 kN

Sand fill = 7386 kN

Total = 53681.44 kN

Dimensions Dimensions of of Well Well Foundation (without STU)Foundation (without STU)

Outer diameter : 10.00 m

Inner diameter : 6.71 m

Height of steining : 26.06 m

Bottom plug thickness : 2.70 mBottom plug thickness : 2.70 m

Top plug thickness : 0.30 m

Well cap thickness :1.20 m

Total cost of one well foundation ~ 90 LakhTotal cost of one well foundation ~ 90 Lakh

Diameter with STU : 7m75

Dimensions Dimensions of of Well Well Foundation (with STU)Foundation (with STU)

Outer diameter : 7.00 m

Concrete Quantities (cubic meter):

without STU with STU

Well cap : 188.65 105.16Well cap : 188.65 105.16

Top Plug 10.63 4.88

Stening 2644.74 1568.14

Kerb 375 168.87

76

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