Chiodi - A Performance-Based Design Approach for Viaduct Seismic

8/19/2019 Chiodi - A Performance-Based Design Approach for Viaduct Seismic

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Fédération Internationale du BétonProceedings of the 2

nd International Congress

June 5-8, 2006 – Naples, Italy

ID 8-2 Session 8 – Seismic design of new concrete structures

A Performance-Based Design Approach for Viaduct SeismicDesign

Chiodi, L.Scott Wilson, Scott House, Basing View, Basingstoke, RG21 4JG, United Kingdom

Stroscio, R. Tony Gee and Partners, TGP House, 45-47 High Street, Cobham, KT11 3DP, United Kingdom

INTRODUCTION

Most of the world population resides in regions characterised by high earthquake activity, hence worldeconomy requires the development of major infrastructure projects in areas with high seismicity. The high seismic demand imposes significant design challenges to bridge designers where the primarypurpose of earthquake design is to safeguard against major failures and loss of life. Therefore the seismicloading represents generally the governing load combination for the design of viaducts.To achieve economical designs and enhance structural efficiency, a new concept has been introduced, theperformance-based design. According to this concept, design codes tend to specify multi-level designearthquakes with corresponding performance requirements, to obtain performance-based objectives thatcorrespond to desired levels of service. The structure has to meet different post event conditions whereaccurate evaluation of the earthquake forces and careful application of the design principles are required for

safe and economic design.The paper presents a performance-based design methodology founded on the force-strength base approachfrom a designer’s perspective and in relation with the current standards. Detailed examples from recentseismic design experience of high-speed rail viaducts in Far-East Asia and to AASHTO standards areincluded.

Keywords: viaduct design, seismic design, capacity design, overstrength, performance-based

THE CONCEPT OF PERFORMANCE-BASED DESIGN

Seismic design has been concerned until recently with the structural damage an earthquake can cause inorder to provide for life safety. The structural design has been therefore driven by the necessity to limit the

damage without paying attention to the actual response of the structure, in particular with respect to itscapability to remain serviceable after a seismic event.The need to reduce the high costs associated with loss of use and repair of heavily damaged structures hasled to the introduction of a new design paradigm in which the focus is on the performance response of thestructure rather than just safeguard against collapse. Performance-based seismic design can be defined asdesign to reliably achieve targeted performance objectives. In performance-based seismic design, thestructure functionality is as important as the structural damage.Performance objectives are levels of acceptable damage of the structure for an earthquake of given severity.The performance target can represent specified limits on any response parameter such as stress, strains,displacements and so on. Performance-based design allows a structure to perform in a manner that meetsthe owner’s economic and safety goals. A single performance objective that requires a structure to remainoperational even in the most severe event will result in extraordinarily high costs. Conversely, a designwhere life safety is the only requirement may not adequately meet the economic interest of the structure

owners. Due to many sources of uncertainties, the performance levels can be assessed only in probabilisticterms.Obviously, the idea to design the structure based on performance objective is not entirely new. A limit staterepresents a form of performance objective. However, performance-based earthquake engineering is a more


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June 5-8, 2006 – Naples, Italy Seismic design of new concrete structures

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encompassing concept that tries to adapt design and construction to the required performance levels of thestructure.The general methodology for performance-based design may have different approaches and much researchis needed, and is indeed under way, to obtain a general design process for multiple performance and hazardlevels.

In the following, a performance-based methodology for viaduct seismic design is described wheredisplacement limits and damage levels are imposed. The structures are analysed with the traditional force-based approach to verify the corresponding performance objectives. The procedure can be presented withfour main design steps (Fig. 1).

Fig. 1. Viaduct performance-based seismic design methodology

DESIGN METHODOLOGY

Seismic design is an iterative process where engineers need to understand dynamic behaviour and predictthe effects from various parameters in order to make the appropriate design decisions to build safe andeconomic structures. Furthermore, the recent performance-based objectives have introduced multi-leveldesign earthquake where the structure has to meet different post-earthquake conditions in line with a desired

level of service. An appropriate methodology is therefore important to prevent excessive design and analysisiterations.


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Project Specific Information and Requirements

Besides the information usually needed in bridge engineering - constraints definitions, ground conditions andtopographical survey - the design of seismic resistant viaducts requires the knowledge of concepts such asdesign earthquake and specific performance criteria.The design seismic events are defined with earthquake parameters that are specified by the codes ofpractice in the form of ground motion coefficients. Usually, these parameters consist of a peak groundacceleration related to a specific return period and a series of normalised response spectra that are functionof the structure location (soil type) and of the substructure type (damping ratio). The response spectrarepresent the peak response of a linear elastic single degree of freedom system with viscous damping whensubjected to a specific ground motion record. Conventionally, the response spectra curves are specified infunction of the structure’s natural period and are usually defined for both horizontal and vertical groundmotions.

The seismic performance criteria are the post-earthquake conditions that have to be met and are directlyrelated to the design seismic events definition. For economical and serviceability reasons, clients usuallyspecify multi-level design earthquakes with corresponding requirements.For example, a two-level earthquake event can be specified with the corresponding performance criteria asdescribed in the following:

A major earthquake event with a high peak ground acceleration equivalent to a very rare seismic event,return period in the order of 1000 years, where the performance requirements are such that structures areallowed to respond inelastically within specified ductility ratios and with reparable damages in postearthquake condition. The structures are hence detailed to provide the required ductility allowing sufficientreduction of the linear elastic seismic effects to permit economic design and providing adequate safety. Thecapacity design principles [1] are used to ensure a hierarchy of strengths in the structure and to avoid brittlefailure modes.

An operational earthquake event with lower peak ground acceleration, generally a fraction of the majorearthquake acceleration, corresponding to a frequent or occasional seismic event where the performance

criteria are such that structures must remain elastic (no yielding of the reinforcement and limited concretestrain) and with limited displacements during the event.

Conceptual Design

The conceptual design of the structural scheme represents one of the most creative and complex stages of thedesign process for any engineering structure. At this stage, a range of different constraints must be consideredwith the aim to find an optimal span arrangement for the most cost-effective seismic resistant structure.These constraints include non-seismic criteria such as the vertical and horizontal alignments, the soilconditions, the obstacles to cross (rivers, roads, railway lines, etc) and the suitable methods of construction,taking into account safety, construction programme, access, availability and economy, as well as the seismicrequirements where mass and stiffness distribution play fundamental roles.

At the same time the superstructure material is selected in relation to the structural arrangement adoptedand the chosen construction method with consideration to economical and durability aspects. In someinstance, where long-term durability and whole life cost are predominant criteria, concrete superstructurescan be preferred. On the other hand, steel superstructures present a weight advantage that can translateinto a reduction of the seismic effects and may give significant benefits in the design of the substructure.

The next critical step for the designer is the choice of the articulation arrangement and the degree ofconnection between piers and deck. In fact, for a given bridge site, the pier heights, the span lengths and thefoundation type are generally defined by the actual boundary conditions. The main design decision istherefore the definition of the deck degree of continuity and the support conditions at the piers andabutments.For long viaducts, where construction repetition plays a major role in the selection of the solution

(construction cost and construction programme), the choice of the articulation arrangement may begoverned by the preferred method of construction, particularly in a design and build contract. For example, aseries of repetitive simply supported spans can be build either with cast in-situ techniques using hydraulicmovable staging systems or made of precast concrete decks. The choice between these construction


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techniques could be governed by the bridge location, where the cast in-situ solution would be preferred forsites with difficult access. Arrangements with simply supported spans present several advantages in design simplification and speed ofconstruction but could lead to long term durability issues as the expansion joints represent the preferredroute for water infiltration causing rebar corrosion, concrete spalling and subsequent high maintenance

costs. Furthermore, the control of the relative movements between adjacent decks during an operationalearthquake could represent a critical performance design objective and may lead to the use of expensiveshock transmission units to limit relative movements. Adopting a continuous deck eliminates the expansion joints above the piers but requires more involvedconstruction techniques. This configuration would still require bearing assembly at deck-pier interface toresist large horizontal seismic effects and will need periodic inspection and maintenance.The next natural step in the articulation arrangement evolution is an integral connection between pier anddeck that eliminates bearings and expansions joints at the pier locations. Besides the whole life costadvantage, this option requires a review of the construction method and induces a fundamental difference inthe design concept. In fact, due to the portal-frame behaviour, longitudinal seismic effects introduce bendingmoments at the top of the piers and consequently in the deck. In terms of capacity design concepts, the fullstructural continuity requires the introduction of additional plastic hinges to generate the plastic mechanismnecessary to dissipate the seismic energy and to provide the required global ductility.

The general rule of the capacity design concept [1,2] is that, under very rare seismic event, structures aregenerally allowed to respond inelastically, with the inelastic effects confined to predetermined regions of thestructure (plastic hinges), provided that ductility requirements are satisfied. The viaduct is then designed sothat a stable plastic mechanism can form in the structure. Plastic hinges are introduced in the structuralsystem to provide a hierarchy of strengths in the various structural components for the intended plasticmechanism and to avoid brittle failure modes. In bridge engineering context, the strong beam-weak columnapproach is usually adopted, where the bridge deck is designed to remain within the elastic range and thelocations of the plastic hinges are in the accessible parts of the piers for ease of inspection, maintenanceand repair.

For non-integral piers, the plastic hinges are designed at the base (Fig. 3). For integral connection betweenpier and deck, two plastic hinges are required, at either ends of the pier (Fig. 4). The internal forcedistribution is obviously influenced by the choice of the articulation and dictates the location of the plastichinges.

The different viaduct articulation arrangements are shown in Fig. 2, with the corresponding advantages anddisadvantages as described in Tab. 1.

Fig. 2. Longitudinal articulation: F=fixed, M=free


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Option Description Advantages Disadvantages

A - Simply Supported Bearings and expansion joints at every support

- Construction and Design repetition- Longitudinal Earthquake resistedat each support

- Whole life cost- Displacement control atevery support- Non optimal deck design

B - Continuous Bearings at everysupport - expansion joints at abutments only

- Expansion joints at abutment only- Longitudinal restraint at mostslender pier- Optimal deck design

- Displacement control atabutments- Whole life cost

C - Integral Bearings and expansion joints at abutments only

- Whole life cost- Number of plastic hinges/degreeof redundancy- Optimal deck design

- Complex constructionmethod- Thermal effects

Note: the optimal span arrangement varies for each option.

Tab. 1. Comparison of articulation arrangements (Fig. 2)

Analysis

An initial analysis with the equivalent static method can be undertaken to assess the conceptual design - pierdimensions, pier reinforcement, and foundation stiffness - before a complete dynamic analysis. For eachpier, the first mode can be calculated assuming a single degree of freedom system where the deck massdistribution is simply based on the arrangement of spans and articulation. The effects at the base of the piersare then calculated for the desired level of earthquake in correlation with the response spectra, the soil type,the design ground acceleration and the seismic force reduction factors [2]. The validity of this preliminaryanalysis is generally dependent on the viaduct regularity [3] but provides a suitable initial design.Response spectra are defined in the form of normalised acceleration response spectra for member forcesand for displacements. Each response spectrum is tabulated for different soil profiles and are used toquantify the horizontal and vertical components for very rare seismic event and for operational earthquake.Since the bridge deck is generally designed to remain within the elastic range, the deck outline designshould be confirmed before starting any substructure detailed design, as any subsequent deck mass change

would result in a re-design of the bridge substructure.

The full structural analysis can be carried out using three dimensional, linear elastic, distributed mass orlumped mass space frame models. Spring supports are generally modelled at the base of the foundations tosimulate the soil-structure interaction effects. The mass of the structure is generally distributed withsuperimposed loadings and live loadings represented by lumped masses at node points applied along thespans. Element section properties are assumed on the basis of gross concrete sections, with the exceptionfor the very rare seismic analysis where cracked section properties are used over the plastic hinge regions,the equivalent flexural stiffness corresponding to a fraction of the gross concrete section properties.

Current available design standards allow the viaduct structural models to be analyzed using the multi-moderesponse spectrum method. Sufficient vibration modes are required such that the sum of the effective modelmasses for each analysis performed is greater than ninety percent of the total mass modelled.

In applying the capacity design rules, elastic forces from the multi-mode response spectrum analysis aremodified using seismic force reduction factors, which make allowance for increased ductility arising from theformation of plastic hinges under very rare earthquake event. These reduction factors are dependent on theallowable ductility capacity, the soil type, the viaduct substructure arrangement and the fundamental naturalperiod of the structure in the direction under consideration. The seismic reduction factors are only applied tothe bending moments extracted from the elastic analysis in the plastic hinge regions under very rareearthquake events, for member forces resulting from horizontal loadings.

Since the multi-mode response spectrum analysis is an elastic method, the principle of superposition can beapplied where the three components of the seismic action (longitudinal, transverse and vertical) areextracted separately and combined using the 1.0/0.3/0.3 combination rule.

Each structural member is designed for the most adverse co-existent actions resulting from one of the three

above combinations.

The soil structure interaction and the pile group stiffness are generally computed using specific software,which usually assume the pile caps to be rigid, and piles within founding soils to be linear elastic. The soil


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stiffness is defined in terms of shear modulus and Poisson’s ratio with a linear increase in depth. The pilegroup arrangement with the soil properties is modelled and the stiffness is extracted (stiffness matrix) for thestructural analysis. In the global model, the supports are represented with equivalent elastic springsstiffness.

Performance Design and Verifications

The design process is iterative in the sense that the initial assumptions made for the stiffness of thesubstructure, foundations and piers, have significant impact on the distribution of the structure internalforces. The analysis and design are only complete after the compatibility between the model assumptionsand the design requirements have been satisfied.

It is advisable to complete the superstructure outline design prior, or in parallel to, the design of thesubstructure. This would avoid a change of the deck mass during the superstructure detailed design, whichwould result in a subsequent design-analysis iteration of the substructure.

A non-exhaustive list of performance design checks is shown in Tab. 2. The criteria to be met underoperational earthquake can be specified by the client, while those under very rare seismic event aregenerally based on the design standards.

Design Element VERY RARE EARTHQUAKE OPERATIONAL EARTHQUAKEPlastic Hinges sections(generally pier bases unlessintegral structures where piertop would also apply)

• ULS check of shear undereffects arising from capacitydesign

• ULS check of the reducedmoments with coexistent axial force

• Stress Strain limitation check forthe biaxial bending moments andcoexistent axial force

Expansion joints • Check for any loss of support

• Check for minimum dimensionrequired to accommodatemovements

• Maximum allowable movement(displacement and rotation) check

Foundations (structural design) • ULS check of shear undereffects arising from capacitydesign

• Displacement check (geotechnical)

Pier stem and pier top • ULS check of shear undereffects arising from capacitydesign

• N/A (generally not critical other than atULS)

Bearing Assembly • ULS check of shear undereffects arising from capacitydesign

• Elongations/displacements checks

Deck • ULS check of diaphragm undereffects arising from capacitydesign (Transverse design)

• ULS check of Longitudinal Design

• SLS check for Longitudinal andTransverse design (stress strainlimitation check)

• Deflection control check

Notes:1) ULS denotes Ultimate Limit State design2) SLS denotes Serviceability Limit State design

3) Shaded text denotes most critical checks

Tab. 2. Critical seismic performance design checks

For reinforced concrete sections, the overstrength plastic moment (Mos) is defined as the ultimate moment ofresistance of a section under the action of the applied axial load, when the actual material strengths (steelyield strength and concrete compressive strength) are greater than the specified design strengths.

The overstrength plastic moment Mos is calculated using a factor ϕ, which is applied to the plastic moment

Mp.

Mos = ϕ Mp


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With: Mp = ultimate moment of resistance of the section based on the specified design strength ofmaterials and under the action of applied axial load.

ϕ = overstrength factor (e.g. equal to 1.3 according to AASHTO [3])

All elements required to remain elastic are designed for capacity design effects resulting from equilibrium

conditions in the intended plastic mechanism.

The first elements to be designed are the reinforced concrete sections where plastic hinges occur. Theoperational earthquake could govern the reinforcing bars in these sections where the strains are limited toremain within the elastic range to avoid any damages under frequent earthquake conditions. Additionally, thesections must be checked at ultimate limit state under very rare seismic event using the reduction factorsthat make allowance for the ductility of the plastic hinge formation.

The pier sections must also be checked, at ULS, to resist the significant shear forces arising from very rareearthquake. In the case of ductile columns, the shear forces (Vos) are calculated based on the overstrengthmoments, on the pier geometry and on the articulation arrangement as shown in Fig. 3, which includes thepier stem reinforcement curtailment and lapping details following the rules of capacity design.

For integral piers (Fig. 4), the derivation of the overstrength shear in the plane of the frame requires aniterative procedure. The overstrength shear is a function of the overstrength moment, which is related to acoexisting axial load in the column that varies from column to column under an applied horizontal load. Thecalculation is done incrementally starting with a first estimate of overstrength shear per column (Vos,I) basedon axial loads from structural self weight only. The sum of all columns overstrength shear (V os,I ) is thenapplied to the structural frame and the overstrength effects re-calculated based on the new derived axialloads. The procedure is repeated until a reasonable convergence is achieved in the calculation of the sum of(Vos,I).

To ensure sufficient ductility is provided in the plastic hinge regions to achieve reliable plastic deformations,confinement reinforcement must be provided in the form of closely spaced horizontal bars and cross tieswhich link the vertical bars on opposite faces of the pier.

Fig. 3. Derivation of overstrength shear (Vos) for cantilever pier


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The capacity design effects are calculated for different configurations depending on the earthquake direction.For instance, in order to cover all possible conditions, the overstrength effects for a pier section are analysedfor 3 possible directions in relation to the viaduct centre line (longitudinal, transverse and diagonal) as shownin Fig. 4.

Fig. 4. Overstrength for integral pier

Another criteria to be verified are the relative displacements at the expansion joints and at the supportlocations. To comply with the performance design requirements, the movements are to remain within theallowable specified values under operational earthquakes and any loss of support during very rareearthquake must be avoided. Sufficient room is to be provided between two adjacent structures to preventany impact during very rare seismic event. The displacement criteria should be verified at the initial designstage, as it is directly dependent on the substructure stiffness. Any stiffness change would result in astructural response modification, requiring new design-analysis iteration.

Subsequently the foundations are to be detailed, piles and pile caps, the critical governing structural designeffects usually provided by the very rare earthquake loading. The seismic effects at the base of the pile capsare a combination of overstrength effects from the plastic hinge and of elastic unreduced effects from themass of the pile cap, including overburden soil.

For non-integral piers, piercaps are required to resist large concentrated loads and cannot respond in aductile manner. The significant horizontal loads arising from seismic effects can well be beyond the capacityof conventional bridge bearing systems. The common alternative to mechanical bearings is the provision ofconcrete shear keys to resist horizontal loads and standard pot bearings to transfer vertical loads from thesuperstructure to the substructure.For simply supported articulation arrangement, the shear key can only restrain the deck when it is movingtowards the fixed pier. When the deck movement is in the opposite direction, tie bars can be used to provide

the required restrain. To comply with the seismic performance criteria relative to the movements betweenadjacent decks, these tie bars are generally pre-tensioned to prevent any elongation under operationalearthquake.


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To prevent damage to the deck and/or to the concrete shear key during the deck rotations, replaceableelastomeric bearings are introduced at the deck-shear key interface. The mechanical pot bearings aredesigned to resist uplift and a typical plan view of bearing assembly is shown in Fig. 5.

The piercap detailing takes into account the bearing compression and uplift forces as well as horizontal

loads applied to the shear keys, designed for allowable concrete pressure and idealized as corbels.

Fig. 5. Plan view of bearing assembly

For the deck, the longitudinal design is done conventionally except for integral structures where theoverstrength moments have to be taken into account. In the transverse direction the deck diaphragms mustbe designed to transfer the load from the system centre of mass to the level of support. The combination ofhigh horizontal loads and significant eccentricities result in the diaphragm section to be heavily reinforced,particularly for prestressed concrete decks where room for the tendon anchorages has also to be provided.

A particular aspect of viaduct deck seismic design is related to the consideration of the torsional effects fromimposed earthquake loads. The torsion can arise from two sources: equilibrium torsion due to externallyapplied loading and necessary for the stability of the structure; compatibility torsion due to the differentiallateral displacement at the top of adjacent piers. To satisfy the seismic performance criteria, the compatibilitytorsion is considered under operational earthquake, while equilibrium torsion is taken into account undervery rare seismic event.

APPLICATIONS AND DETAILS

The following examples and details are based on seismic design and construction of high-speed rail viaductsin Far East Asia where the specified design ground acceleration was 0.34g with a two level designearthquake. Under major earthquake, with a return period of 950 years, the design was based on reparabledamage criterion and structures were allowed to respond in the inelastic range in accordance with thecapacity design rules. During an earthquake with horizontal ground acceleration equal to one-third of themajor earthquake acceleration, the structures were designed for safe operation where yielding ofreinforcement was not permitted and where relative displacement between decks had to remain within 25millimetres allowing the trains to brake safely from the full design speed of 350 km/h. These performance criteria presented challenging and conflicting requirements between the high-speed rail

demand and the seismic effects. On one hand, the high-speed rail required stiffness to control displacementand ensure safe operation; on the other hand earthquake design needed adequate flexibility to reduceseismic structural response. A complex compromise between stiffness and flexibility was therefore requiredto meet all structural performance requirements.


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Most of the articulation arrangement is made of simply supported spans, preferred to increase constructionrepetion and meet the design and build contracts deadlines. Typically, the prestressed concrete box girderspan between 30m and 45m and are designed to satisfy the high-speed rail deflection requirements.Construction repetition was achieved by standardisation of geometry for decks, piers and foundations as well

as reinforcement arrangement.

Typical pier base reinforcement arrangement is included in Fig. 6 showing the pier cross section at theplastic hinge region where confinement reinforcement is indicated. The curtailment and lapping of pier starterbars is shown in Fig. 7 and Fig. 8 gives an indication of the pier starter bars extent, a particularity of seismicdesign.

Fig. 6. Pier cross-section at plastic hinge: confinement reinforcement F1/G1/H1

Fig. 7. Pilecap reinforcement and pier starter Bars Fig. 8. View of Fig. 7


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The connection detail between piles and pilecap requires also particular attention. Generally, top of piles aredesigned to resist high axial loads either in tension or compression as well as significant shear forceresulting from the capacity design and local bending moments. Fig. 9 shows the typical extent of pilereinforcement into the pilecap.

Fig. 9. Pile/pilecap connection details

The general view of the bearing assembly is shown in Fig. 10 and 11, while detailing of the shear key isincluded in Fig. 12.

Fig. 10. Longitudinal section of deck supports

Fig. 11. Transverse section of deck supports

Plan View SectionFig. 12. Shear key reinforcement


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The typical deck diaphragm reinforced concrete details are shown in Fig. 13, showing the particularreinforcement required for load transfer between shear key and deck.

Fig. 13. Diaphragm reinforcement

CONCLUSIONS

Bridge response during earthquake is a complex phenomenon and methods for improving the structure’sperformance are constantly developed. The iterative aspect of viaduct seismic design has been presented

highlighting the interdependence between strength, stiffness and mass. The correlation among performanceobjectives, analysis, design, verifications and detailing has also been underlined. Specific bridge seismicdetails have also been included.

ACKNOWLEDGEMENTS

The examples presented result from the authors experience with Hyder Consulting Ltd, UK on the viaductsdesign for the Taiwan High Speed Rail Project. Opinions and views expressed are those of the writers.

REFERENCES

1. Park R., Paulay T., Reinforced Concrete Structures, John Wiley & Sons, 1975.2. Priestley M.J.N., Seible F, Calvi G.M.. Seismic Design and Retrofit of Bridges, John Wiley & Sons, 1996. 3. AASHTO, Standard Specifications for Highway Bridges, 16

th Edition, 1996.

4. Floren A., Mohammadi J., Performance-Based Design Approach in Seismic Analysis of Bridges, Journalof Bridge Engineering , January-February 2001.

5. Krawinkler H., Challenges and Progress in Performance-Based Earthquake Engineering, InternationalSeminar on Seismic Engineering for Tomorrow, Tokio, Japan, November 26, 1999.

6. Priestely M.J.N., Myths and Fallacies in Earthquake Engineering Revisited, The Mallet Milne Lecture,IUSS Press, 2003.

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