MULTI-SPAN LARGE BRIDGES PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON MULTI-SPAN LARGE BRIDGES, 1–3 JULY 2015, PORTO, PORTUGAL Multi-Span Large Bridges Editors Pedro Pacheco & Filipe Magalhães Faculty of Engineering, University of Porto, Portugal Organized by: CRC Press/Balkema is an imprint of the Taylor & Francis Group, an informa business © 2015 Taylor & Francis Group, London, UK Typeset by MPS Limited, Chennai, India Printed and bound in Great Britain by CPI Group (UK) Ltd, Croydon, CR0 4YY All rights reserved No part of this publication or the information contained herein may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, by photocopying, recording or otherwise, without written prior permission from the publishers Although all care is taken to ensure integrity and the quality of this publication and the information herein, no responsibility is assumed by the publishers nor the author for any damage to the property or persons as a result of operation or use of this publication and/or the information contained herein Published by: CRC Press/Balkema P.O Box 11320, 2301 EH Leiden, The Netherlands e-mail: Pub.NL@taylorandfrancis.com www.crcpress.com – www.taylorandfrancis.com ISBN: 978-1-138-02757-2 (Hbk + CD-ROM) ISBN: 978-1-315-68719-3 (eBook) Multi-Span Large Bridges – Pacheco & Magalhães (Eds.) © 2015 Taylor & Francis Group, London, ISBN 978-1-138-02757-2 Table of contents Preface Acknowledgements Committees XV XVII XIX Keynote Lectures General presentation of the Keynote Lectures Large viaducts, some executions a few ideas J Manterola Design and construction of sea-crossing bridges – A review N Hussain 17 Viaducts with progressively erected decks J Strasky 27 Betwixt and between Portus and Cale A Adão da Fonseca 37 The Octavio Frias de Oliveira and Anita Garibaldi cable-stayed bridges C.F Ribeiro 51 Multi-span extradosed bridges A Kasuga 67 Multi-span large bridges – interaction between design and construction A.F Bæksted 83 Recent achievements in the design and construction of multi-span cable supported bridges in China A Chen, R Ma & X Zhang Multi-span large decks – the organic prestressing impact P Pacheco 93 103 Experts, Experiences & Landmark projects Crossing of Bjørnafjorden – Floating bridge B Villoria, J.B Wielgosz & S.M Johannesen 127 Rion-Antirion Bridge – Challenging earthquakes E Joly, P Moine & A Pecker 135 Innovative erection methods of steel cable-stayed bridges M de Miranda 143 Viaduct over river Ulla in the Spanish Atlantic high speed railway line: An outstanding composite steel-concrete truss bridge F Millanes, L Matute & M Ortega V 151 Juscelino Kubitschek Bridge, Brasília, Brazil F.B de Barros & J de Freitas Simões 159 Bridge over the Cádiz Bay, Spain J Manterola, A Martínez, J.A Navarro, S Criado, S Fuente, M.A Gil, L Blanco, G Osborne, M Escamilla & J.M Domínguez 167 Baluarte Bridge executive project G.R Argüelles 173 Queensferry Crossing: Role of concrete in the design and execution of the project P Curran 179 New Pumarejo Bridge over the river Magdalena in Barranquilla, Colombia J Manterola, J Muñoz-Rojas, S Fernández, J.A Navarro & S Fuente 187 Delivering the Padma Multipurpose Bridge project, Bangladesh W.K Wheeler & C.J Tolley 193 The tied arch bridge of the Saale-Elster-Viaduct W Eilzer, R Jung, T Mansperger & K Humpf 201 Construction and design features of the bridge over the Danube River, Bulgaria J Manterola, A Martínez, J.A Navarro, J.L Alvárez & J.I.D de Argote 209 TUNeIT – Towards a global World E Siviero, A.B Amara, M Guarascio, G Bella, M Zucconi, A Adão da Fonseca & K Slimi 215 The Russky Bridge: Pylons design approach optimization L.V Miklashevich & V.E Rusanov 223 Bridge across the Waschmühl Valley, Kaiserslautern, Germany: A harmonic symbiosis between a historic monument and a new innovative bridge K Humpf, V Angelmaier & W Eilzer 231 Viaduct over river Deba in the “Y-Basque” high speed railway line in the north of Spain F Millanes, M Ortega, P Solera, H Figueiredo & J Ugarte 239 Structural solutions and construction methods for the main crossing of the Mersey Gateway Bridge Project G.D Moir, S.H Jang, J Seo & P Sanders 247 Design of the long-span footbridge over the Bug River in Niemirów J Biliszczuk, J Onysyk, W Barcik, P Prabucki, K Ste˛pie´n, J Szczepa´nski, R Toczkiewicz, A Tukendorf, K Tukendorf & P Wo´zny Design and proof checking of foundation, substructure and superstructure of Rail cum Road Bridge at Munger, Bihar, India H.M Farook & G.S Babu 257 263 Multi-span bridge bypass over the Dziwna Strait J Hołowaty 271 Large multi-span bridges built in recent years in Poland J Biliszczuk, J Onysyk, P Prabucki & R Toczkiewicz 277 Kassuende Bridge over Zambezi River in Tete, Mozambique T Mendonỗa, V Brito & M Monteiro 285 VI Multi-span bridge crossings for improved road access to Szczecin sea port J Hołowaty 293 Armado Guebuza Bridge over Zambezi River in Caia, Mozambique T Mendonỗa, V Brito & M Almeida 301 Design and construction of a long-span continuous fin-back bridge Y Lu, M Fu, X He & C Zhou 309 Pinhal Interior Motorway Concession – IC3 – Section Condeixa – Coimbra – Special engineering structures – Construction processes T Nogueira, A Hipólito & N Amaro 317 Viaduct Araranguá – The alternative design of viaduct of 1661.59 meters in the BR-101/SC Brazil I.C Santos & F.P.S Nunes 325 Design and construction of flyovers in Outer Ring Road, Delhi K Ganesh & V Shanmugham 331 Haramain high speed railway line J.M.G Parejo, M.T Serrano, M.M Cueto, M.B García & F.J.M López 337 Design and construction of viaduct to Mumbai International Airport P.G Venkatram & K Ganesh 345 Meriỗ Bridge: Construction and quality control S Uluöz, S Düzbasan, T Uluöz, E Yakıt & U Akyazı 351 Design and construction of elevated viaduct at Nashik, India K Ganesh & P Murali 357 Conceptual design Development of a submerged floating tube bridge for crossing of the Bjørnafjord M Reiso, T.H Søreide, S Fossbakken, A.S Brandtsegg, S.A Haugerud, A Nestegård, J.H Sekse & A Minoretti 365 Three span floating suspension bridge crossing the Bjørnafjord J Veie & S.H Holtberget 373 Long railway viaducts with special spans: Part Arch construction by balanced cantilever with auxiliary cables J Manterola, A Martínez, B Martín, J.A Navarro, M.A Gil, S Fuente & L Blanco 381 Long railway viaducts with special spans: Part Arch construction by tilting J Manterola, J Moz-Rojas, A Martínez & S Fernández 389 Long railway viaducts with special spans: Part Precast girders J Manterola & A Martínez 395 Four spans continuous cable stayed bridges without extra cables J Romo 401 Particular design features for a long span cable-stayed bridge over the Harbour of Port Louis, Mauritius J Jungwirth, J Casper & A Baumhauer 409 A study on vehicular live load design based on actual vehicular load for a multi-span large cable-stayed bridge H Sugiyama, H Kanaji, H Watanabe & O Aketa 417 VII Comparison of variants for New Peljesac Bridge in Croatia J Radic, Z Savor, M Srbic & M Pipenbaher 427 Gebze–Orhangazi–Izmir Motorway, Izmit Bay Suspension Bridge N Güngör & F Zeybek 435 Construction of cable-stayed bridge over the Drava River on Corridor Vc, Croatia P Sesar, M.M Buhin, D Bani´c & S Kralj 443 Strait crossing of the Thermaikos Gulf with a mixed long-span bridge and subsea tunnel system M Malindretou-Vika & P Spyridis 451 Segmental prestressed concrete multispan large bridges V Barata, J.P Cruz & P Pereira 459 Experience of some long multi-span bridges in Queensland, Australia (Part 1) J.A Hart & E Kittoli 467 Experience of some long multi-span bridges in Queensland, Australia (Part 2) J.A Hart & E Kittoli 475 Multi-span bridges: The first Chilean experience and future challenges M.A Valenzuela, M Márquez & I Vallejo 483 Optimization of cable weight in multi-span cable-stayed bridges Application to the Forth Replacement Crossing A Baldomir, E Tembrás & S Hernández 491 Design parameters of suspension bridges: Updates of state of art and its application on multi-span typology I Vallejo, M.A Valenzuela & M Márquez 499 Comparative study of prestressing consumptions in different constructive methods for 75 m multi-span box girders A Ferreira, B Lima, F Lopes & P Pacheco 507 KaTembe Bridge over Espớrito Santo Estuary, in Maputo T Mendonỗa, V Brito & M Monteiro 513 The South Approach Viaduct of Izmit Bay Crossing Project N Güngör 521 Effect of hangers disposal on the steel consumption for bowstring arch bridges M Daraban & I.R R˘ac˘anel 527 Strategy for durability of structural concrete in Mega-Sealinks in tropical sea-waters V.K Raina Project Westgate – Lekki Beltway Bridge, Lagos, Nigeria C.M Bednarski & A Adão da Fonseca 533 549 Innovative construction methods High productivity in bridge construction – the OPS effect P Pacheco, H Coelho, A Resende, D Carvalho & I Soares 559 FlexiArch-Stress Ribbon combination for multi-span pedestrian bridges A.E Long, D McPolin, S Nanukuttan, A Gupta & D Robb 567 VIII Balanced lift method for the construction of bridges with two spans S Foremniak, W Weiss & J Kollegger An innovative system of precast segmental span-by-span construction for span lengths of above 100 m J Muñoz-Rojas, S Fernández, C Iglesias, P Pacheco, H Coelho & A Resende 575 583 Launching of fully welded steel long span bridges: Bogibeel bridge A.K Mathur, S.S Shukla & J Gupta 591 Swivel lowering operation of the viaduct over the River Tera F.J.M López, M.B García, M.M Cañueto, J.M.G Parejo & M.T Serrano 599 Deck forces of a cable-stayed bridge – “Analysis of the construction and the in-service phases” P Almeida & R.C Barros 607 Building the decks of the world’s largest high speed train arch bridges with movable scaffolding systems A.A Póvoas 615 The Patani Bridge (Nigeria): Innovative construction methods P Stellati & L Marenzi 625 Innovative spliced girder method for multi span bridges I.Z Stern 633 Innovative formwork systems in bridge construction – Case studies A Preuer, M Kamleithner, M Mihal & C Beer 641 Prestressed I-beams made of ultra-high performance concrete for construction of railway bridges ˇ P Tej, J Kolísko, P Bouška, M Vokáˇc & J Cech Preliminary assessment of wind actions in large span MSS A Resende, H Coelho & P Pacheco 649 655 Cabriel River Viaduct in Cofrentes (Valencia, Spain) bypass at N-330 Construction design J.F.M Soriano, J.I.C Vázquez & B.D Santana 663 Segmental precast technology for multi-span bridges (production, transportation and launching) V.N Heggade 673 Construction of Panipat Elevated Expressway on NH-1 on BOT basis P.N.S.S Sastry 701 Mold for full span method M Kye 707 Special foundations and geotechnical site investigations Offshore pile driving foundations monitored by PDA® Test at Puente Nigale M Rojas, I Miquilena & A Souza Ceira bridge foundations: Combined Micropile and Footing Foundations (CMFF) Static load tests J.M.S Cruz, M.S Neves & S Gil IX 715 721 Tresfjord Bridge – Foundation of main span on 40 m caisson on soil seabed K.B Dahl, L Toverud & D.E Brekke 729 Chiapas Bridge G.R Argüelles 737 Life cycle Life-cycle costs of bridge bearings – Key considerations for bridge designers and owners T Spuler, N Meng & G Moor 743 Application of the Monte-Carlo method to calculate the life-cycle costs of bridges C Hofstadler & M Kummer 751 Selective use of non-corrosive rebar to increase concrete durability A.E.C Borderon 759 Monitoring, maintenance and management Dynamic characterization and continuous dynamic monitoring of long span bridges E Caetano, A Cunha, C Moutinho & F Magalhães Investigation and countermeasures for fatigue cracks that emerged on the finger joint of the cable-stayed bridge T Kosugi, M Takahashi, Y Nakamura & H Dobashi Management of the Severn Bridge Suspension Bridge C.R Hendy, C Mundell & D Bishop Surveillance of continuous precast concrete bridge decks supported by monitoring-based techniques H Sousa, C Sousa, A.S Neves, J Figueiras & J Bento Implementation of a B-WIM system in a centenary steel truss bridge F Cavadas, B.J.A Costa & J Figueiras A novel inspection method for orthotropic steel decks using phased array ultrasonic testing T Makita, H Sakai, T Suzuki & N Yagi Self-evaluating smart expansion joints of multi-span and long bridges K Islami & N Meng 771 781 789 799 807 815 823 Evaluation of fatigue crack formation in cantilever brackets of a multi-span railway steel box girder bridge L.R.T Melo, R.M Teixeira, A.P da Conceiỗóo Neto & T.N Bittencourt 831 Investigations of post tensioned bridges with critical prestressing steel regarding hydrogen induced cracking (HIC) A.W Gutsch & M Walther 841 Fatigue management of the midland links steel box girder decks C.R Hendy & S Chakrabarti Improved structural health monitoring strategies for better management of civil infrastructure systems J Winkler, C.R Hendy & P Waterfall X 847 855 Figure Piers and their respective foundations with their points of failure Table Computed results for spring rotational constants Spring rotational constant c1 c2 11 m foundation m foundation 9.29 × 1012 2.095 × 1012 pier 1.0125 × 1012 first structural member with the respective spring constant c2 regardless the number of structural members (or storys) Hence, during the design process it is quite easy to assess a future behavior, since it is quite easy to determine c1 , c2 , h1 , P1 , , Pn From these values, one may compute the deflection angle ratio ψ1 , ψ2 that prevails in the structural failure assessment It is also found that when the rotational spring constant ratio is c1 /c2 ≤ that means c2 > c1 then, a smaller deflection angle ratio results and hence, the convergence of the values for the homogeneous system ψ1 , ψ2 , , ψn is achieved at a safer and faster rate EXAMPLE A paper (Drosos & Georgakos & Anastasopoulos & Gazetas, 2010), presents the behavior and the points of failure of two piers with respect to their foundations as tested in different experiments that took place in the National Technical University of Athens (see Fig below) Now, for this case study an effort is made to explain why the pier in the first case and the foundation on the other case failed the way they did using the term Plimit load discussed in this paper Assume that the pier and its respective foundation act as a two member model, where the foundation is member and the pier is member Also, consider as a given that the superstructure’s loads are 12,000 kN and the pier’s loads are 2200 kN First, the spring rotational constants are found using the formula below (Petersen, 1982): where c = rotational spring constant; a = foundation length; b = foundation width; E = soil elastic modulus; i = foundation depth to foundation width variable; and k = foundation length to foundation width variable Next, the respective Pcritical joint load values are determined using equations (5) and (6) Note that the actual computations are not presented (due to space limitation) It follows that equations (5) 1282 and (6) become: And the following 2nd order equations result: 0.296 · h2 · P − 0.142 · h · P + 0.11 · c2 = for the large foundation and 0.296 · h2 · P − 1.548 · h · P + 0.48 · c2 = for the small foundation Hence, for the large foundation: Pcritical joint load = 770,000 kN, ψ1 = 0.09945 ψ2 and ψ2 = 10.0548 ψ1 Similarly, for the small foundation: Pcritical joint load = 570,000 kN, ψ1 = 0.227 ψ2 and ψ2 = 4.403 ψ1 Next, the designer must check if the natural frequencies of the structure are close to the resonance frequency that produces additional dynamic loading The natural frequence equation shown below is applied: where ω = natural frequency; g = gravitational force; and h = height Thus, the following results are obtained: ω = 6.06 sec−1 for the large foundation and −1 ω = 4.95 √ sec for the small foundation.√Hence, for a dynamic loading with a frequency greater than = × 6.06 = 8.54 sec−1 and = × 4.95 = 7.00sec−1 respectively, the structure is not be affected by dynamic loading due to resonance Only static loads act upon the structure Moreover, the response of the structure to dynamic loading results in oscillations with an amplitude, sdynamic , that are lesser in comparison to the amplified oscillations due static loading (sdynamic < sstatic ) 4.1 Evaluation of the deflection angle interval under a certain loading: Large foundation The largest deflection ψ1 of the system occurs when the axial force resultant will cause the soil stresses greater than the allowable ones From boundary limits such as the allowable soil stresses one may estimate the possible size of the deflection angles for that particular structural loading Assume an allowable soil stress of 250 kN/m2 Since the resultant lies beyond the internal core of the foundation, but within the external core then solving further for the eccentricity e, results in: e∗ = a/2 − e = 11/2 − 3.44 = 2.07 m therefore, the allowable moment capacity for this foundation for that given soil stress is: M = (12000 + 2200) · 2.07 = 29394 mkN The respective deflection angle α∞ for circular section foundations is obtained from following equation found in DIN 4019 Part where e ≤ r/3 and solving results in α∞ = 0.004627 This is the maximum allowable system deflection for loads found using first order theory (a nondeflective system) However, due to second order theory (deflective system) the iteration should be confined to an interval between zero and maximum allowable deflection, otherwise surcharge pressure prevails and failure occurs If one now wishes to narrow down this interval to shorten the iteration process, then the deflection angle that develops due to the actual must be evaluated Assume axial loading with an eccentricity: i.e 1.83 meters This means that the axial loading lies near of edge of the internal core of the section and as such, a moment M equal to 26023 mkN is produced It follows that, ψ1 = 0.004627 − 0.00028 = 0.004347 In other words, the deflection angle interval ranges from to 0.004347 and with the iteration method, after 12 loops it is obtained that: ψ1 = 0.00002 and ψ2 = 0.00020342 The additional second order theory moments are: M1 = c1 ψ1 = 1858 mkN, M2 = 2060 mkN and ψ1 /ψ2 = 10.1711 Thus, the total moments are: M1 = 26023 + 1858 = 27881 mkN < 2994 mkN Note, that they are less than the allowable moment found earlier and hence, there is no failure of the foundation as 1283 verified by the experiment On the other hand, for the pier the actual moment was found to be 20818 mkN The sum of the moments is 22878 mKN > 20818 mkN Thus, the pier fails due to a surcharge of second order theory moments 4.2 Evaluation of the deflection angle interval under a certain loading: Small foundation Acting accordingly, for comparison reasons assume the same type of loading on the structure and soil stress with a small foundation, inducing an eccentric axial loading then, e = a/6 = 7/6 = 1.1667 < 1.83 m < 2.3334 m These axial loads are found within the external section’s core and so the force resultant lies at a distance of 1.67 m from the edge of the section The moment produced is the same as before (26023 mkN) The soil stress was found to be 810 kN/m2 > 250 ⇒ unacceptable Therefore, the foundation fails as verified by the experiment, despite the fact that the deflection angles may be quite small The pier suffers from no damage whatsoever CONCLUSIONS It is concluded that special consideration must be given during the design of a structure to the evaluation of the deflection ratio This paper investigates a method for solving second order theory stability problems with the help of spring rotational constants, for loads smaller than Pcritical joint load , that due to the existence of second order deflections structural failure may result This method deals with actual loads that define the true load limits of a structure with compression members whose slenderness ratio (λ ≤25), i.e large shear walls or piers of large span bridges, commonly found in seismic regions due to regulations’ requirements From the investigation of equation (13) it is deduced that, in seismic regions where large axial accelerations may occur, i.e significant fluctuations of axial loads, structures fail at a greater extend That is because as observed from equation (13) a reduction in the axial loading results in an increase of the ψ2 /ψ1 ratio in relation to the increased lateral loading Hence, it goes without say that the ψ2 /ψ1 ratio is the principle factor for evaluating structural failures A case study was used to present the application of this proposed methodology for dealing with stability problems The experimental outcomes obtained from the National Technical University of Athens were verified by the analysis presented in this paper Namely, in the case of a large foundation, the pier failed at the base due to a large second order moment that created a respective large deflection, although Pcritical joint load was not reached There was no failure of the soil (only small stresses developed) On the contrary, for the case with the small foundation, the soil crushed due to the formation of large stresses, while smaller moments formed at the base of the foundation and yet again, Pcritical joint load was not reached REFERENCES Drosos, V & Georgarakos, P & Anastasopoulos, I & Gazetas, G 2010 Experimental Validation of Bridge Pier Seismic Design Employing Soil Ductility Karatazas, Elisabeth & Karatzas, Velvet & Karydis, George & Konsttigatantakopoulos, Theodore IBSBI 2014 Investigation on Stability Problems as a Second Order Theory Problem for Piers with Practically Infinite Stiffness, Greece Karatzas, Velvet & Karatzas, Elisabeth, fib 2010 Instability Problems – Investigation of P critical joint load under moment loads Karatzas, Velvet & Karatzas, Elisabeth & Karydis, George, STESSA 2012 Investigation of structures whose slenderness ratio is λ ≤25 and is based on P critical joint and the eigenvalue ratio Petersen, Christian 1982 Statik und Stabilität der Baukonstruktionen, Vieweg: pp 910–912 1284 BIBLIOGRAPHY Drosos, V & Georgarakos, P & Anastasopoulos, I & Gazetas G, 2010 Experimental Validation of Bridge Pier Seismic Design Employing Soil Ductility, Volos Greece Karatazas, Elisabeth & Karatzas, Velvet & Karydis, George & Konsttigatantakopoulos, Theodore IBSBI 2014 Investigation on Stability Problems as a Second Order Theory Problem for Piers with Practically Infinite Stiffness, Greece Karatzas, Velvet & Karatzas, Elisabeth, fib 2010 Instability Problems – Investigation of P critical joint load under moment loads, USA Karatzas, Velvet & Karatzas, Elisabeth & Karydis, George, STESSA 2012 Investigation of structures whose slenderness ratio is λ ≤25 and is based on P critical joint and the eigenvalue ratio Petersen, Christian 1982 Statik und Stabilität der Baukonstruktionen, Wiesbaden: Vieweg 1285 Multi-Span Large Bridges – Pacheco & Magalhães (Eds.) © 2015 Taylor & Francis Group, London, ISBN 978-1-138-02757-2 Suspension cables bridge and arches L.M Laginha Instituto de Engenharia de São Paulo, Divisão de Estruturas, Brasil ABSTRACT: The behavior of Suspension Bridges without stiffness girder under action of a moving load is analyzed theoretically and with experimentation The traditional assumption of the inextensibility of the suspension cable is replaced by the Equality of the Areas, explaining what really happens with this formulation The length of the parabolic cable is calculated in an original way, only by his forces, solving the problem with the compatibility of deformations The behavior of the arches is analyzed together with the cables, generalizing the application of the formulation Equality of the Areas INTRODUCTION This paper is a summary of the Master’s Thesis of the author supervised by Prof Hideki Ishitani at the Polytechnic School of the University of São Paulo in 1997 We define the reference configuration as corresponding to the balance of the permanent load w, and after the cable receive accidental load P, the displaced configuration The balance of the suspension cable in the reference configuration (Fig 1) in the generic x section: results in the cable equation in the reference configuration: The above equation represents the reference setting, that is, the function of the position of the dead load and the horizontal component Hw from Tw , the tensile force By hypothesis, the cable’s own weight was considered evenly distributed horizontally and added to the own weight of the board, resulting the dead load w Figure The reference configuration 1287 Figure The offset configuration where kl is the abscissa of equilibrium of the load P This is the study of the suspension cable only submitted to a concentrated load P on the general equilibrium abscissa kl (Fig – offset configuration) For this, we use two Cartesian systems oriented vertically from a line linking the anchors down, and horizontally, the anchors to the concentrated load, respectively EQUALITY OF THE AREAS Assuming zero the work of the permanent load w to be applied to accidental concentrated load P (Fig 2), it follows the classical expression for the HP value In fact, consider null the work of the dead load w along the cable, implies that the integral of displacement v = yw − y is zero Mathematically: This implies that the Aw area, enclosed by the reference configuration, and the area A, encompassed by the displaced configuration, are equal Therefore, matching Aw = A we obtain the classical value of literature: The Equality of the Areas has the same meaning as the vertical immobility of the center of gravity of the dead load In Figure are shown plots of vertical displacement of the cable to a concentrated load obtained from experimental forms EXPERIMENTAL ANALYSIS Two experiments were conducted in the Laboratory of Structures and Structural Materials of the Polytechnic School of the University of São Paulo A cable with 1.5 mm nominal diameter formed by 19 galvanized steel wires of 0.3 mm was charged with 19 weights of 0.625 kgf = 6.25 N Resulted in a load w uniformly distributed horizontally 0.10 kgf/cm = N/cm, simulating the dead load 1288 Figure Layout and experimental structure with dial mm hundredth LEM-EPUSP, 1994 Figure 1994 Layout and experimental structure with electromagnetic transducers “HP DC-DT” LEM-EPUSP, of the board The range of 125 cm was divided into ten segments, resulting in stations for the measurement of displacements in the model The adopted fw construction sag was 12.5 cm, φ = P/W and W = wl With the hypothesis of Equality of the Areas, there are points whose abscissas have no vertical displacement (Fig 5) and depend only on the equilibrium position x = kl of the load P Fixed 1289 Figure The theoretical fixed points in the central graph, and the experimental vertical displacements v 1290 Figure Point is defined as a point of reference yw setting where it crosses setting the shifted y (yk or yj ) These abscissas, result v = 0, does not correspond more to the same physical point on the wire The abscissas that locate the Fixed Points obey the following law: NEW FORMULATION OF THE SUSPENSION CABLE LENGTH 4.1 The length formula deduction To determine the suspension cable length, we adopt the notation: T – traction force on the cable support; R – vertical component of T on support; H – horizontal component of T , invariant in x and w – vertical load evenly distributed horizontally Below, we will calculate the length of the cable only submitted to w dead load, which is why we will omit the indices w (T indicates Tw , H indicates Hw , V indicates Vw , etc.): this is the exact parabolic cable length formula, highlighting the reaction forces in the funicular polygon 4.2 The elastic deformation of the cable After applying the concentrated load P, each cable element ds, will bring with it a ds end deformation, due to the final traction force T installed on the cable Thus, the total stretch in the cable s is: calculating, results in: 1291 Figure Comparison of Central Displacement with the Equality of Areas, Elastic, Elastic with EA/2 and Inextensible 1292 where sw is the total elongation of the cable in the reference configuration As sP is the deformation due to the load P, we have: sP = s − sw Applying the above deducted formulations and Aw = wl /(12Hw ) results: where sP is the deformation increased due solely to the application of the load P The elastic elongation was calculated by the expression (7) It was solved by the program “Mathematica”, and obtained the value of HP = βHw – The problem of compatibility of the axial deformation of the cable is resolved equaling the length difference sP = s − sw ; – The effect of varying the cable EAc axial stiffness was verified by comparing the values obtained with EAc and EAc /2; – The vertical displacements was calculated with the hypothesis of Equality of Areas; – Finally, determined the displacement obtained under the assumption of inextensibility with: s = sP − sw = through the Mathematica program Adopted for the cable: E = 1.6 E6 kgf/cm2 Ac = 0.013 cm2 and EAc ∼ = 20.000 kgf CONCLUSIONS 5.1 The term Equality of the Areas exactly means the area encompassed by the reference configuration and the displaced configuration, respectively, or also the immobility of the center of gravity of w, the dead load It should be noted, that this is not the cable inextensibility condition, usually adopted by the literature; 5.2 Analyzing the curves shown in Figure 8, it can be said: the vertical displacements of the suspension cable are mainly due to the change of cable equilibrium line, with little influence of the variation of axial stiffness EAc We can conclude that the analyzed phenomenon shows little sensitivity to changes in the value of the axial stiffness of the cable; 5.3 The formulation of the Equality of Areas can be applied to solve the Biarticulated Arc So HP is obtained, equation (4), ignoring the compatibility of the axial deformation of the cable or arch The values of “Leveraged Moments by Displacement” vH in the cable are identical to the values of the bending moments M in the analogue biarticulated arc Cables Arches Equation of displacement: (9) MP = yw HP + vH where v is the vertical displacement of the cable Integrating the equation along the span l: ∫ MP dx = ∫ yw HP dx + ∫ vHdx Apply Equality of Areas for the displacements: ∫ vHdx = Equation of flexural moments: MP = yw HP + M (10) where M are the flexural moments on the arch Integrating the equation along the span l: ∫ MP dx = ∫ yw HP dx + ∫ Mdx Apply Equality of Areas for the moments: ∫ Mdx = 5.4 With respect to stiffness, the heavier the deck bridge, i.e., the greater the span l or w dead load, the cable will be more rigid The vertical displacements are directly proportional to fw construction sag in the formulation of the Equality of the Areas In this approach, the vertical displacements not depend directly on the span l (l, the span, is hidden in the load factor ϕ = P/W , since W = wl), as can be seen in the following formula for the displacement of the central point: 1293 5.5 The formulation for the length of the parabolic cable, according to its reaction forces (6), does not need the geometry of the cable REFERENCES Ammann, O.H 1923 Possibilities of the Modern Suspension Bridge for Moderate Spans Engineering NewsRecord, 21/06 Cullimore, M.S 1986 The Clifton Suspension Bridge-Preservation for Utilisation IABSE ProceedingsAugust: 100-86 Ferry Borges, J.; Arantes e Oliveira, E.; Silva Lima, C 1966 International Symposium on Suspension Bridges, LNEC Franco, M 1983 Apostila PEF-602/FAU-USP Gravina, P.B.J 1951 Teoria e Cálculo das Pontes Pênseis, EPUSP Hardesty, S.; Wessman, H.E 1939 Preliminary Design of Suspension Bridges, Transactions, ASCE, Paper N◦ 2029 Honshu – Shikoku Bridge Authority The Akashi Kaikyo Bridge Horton, T 1983 Superspan – The Golden Gate Bridge, Squarebooks Hudson, Ralph G 1977 Manual Engenheiro, Livros Técnicos e Científicos Johnson, J.B.; Bryan, C.W.; Turneaure F.E 1911 The Theory and Practice of Modern Framed Structures, John Wiley & Sons, 9a Ediỗóo Jones, V & Howells, J 2008 Manual of Bridge Engineering, ICE Judd, B.J., Wheen, R.J 1978 Nonlinear Cable Behaviour, Proceedings ASCE, Vol 104, No ST3, March, p 567–575 Kerensky, O.A 1959 The Maitland Lecture, ISE Laginha, L.M 1997 O Equilíbrio Cabo Pờnsil, Dissertaỗóo de Mestrado EPUSP Laginha, L.M 2006 Nova Formulaỗóo para o Comprimento Cabo Parabólico, Revista Engenharia, N◦ 576 Langendonck, T 1936 Prova de Carga das Pontes de São Vicente e de Jacarehy, Boletim 16, IPT Norris, C Head; Wilbur, J Benson; Utku, S 1976 Elementary Structural Analisys, McGraw-Hill Kogakusha Ltd., 3a Ediỗóo OConnor, C 1976 Pontes Superestruturas, Vol.2, LTC/EDUSP Peters, T.F 1987 Transitions in Engineering, Birkhäuser Verlag Pippard, A.J.S 1947 The Experimental Study of Structures, Edward Arnold p Pippard, A.J.S & Baker, J 1968 The Analysis of Engineering Structures, Edward Arnold 4a Ediỗóo Pugsley, A.G 1949 Some Experimental Work on Model Suspension Bridges, The Structural Engineer, Aug., Vol 27, N◦ 8, p 327–347 Pugsley, A.G 1952 The Gravity Stiffness of a Suspension Bridge Cable, Quarterly Journ Mech and Applied Math., Vol 5, p 384–394 Pugsley, A.G 1968 The Theory of Suspension Bridges, Edward Arnold, 2a Ediỗóo Ramm & Wagner 1967 Praktische Baustatik, Stuttgart 4a Ediỗóo Steinman, D.B 1929 A Practical Treatise on Suspension Bridges, John Wiley & Sons, 2a Ediỗóo Steinman, D.B 1918 A Generalized Deflection Theory For Suspension Bridges, Transactions ASCE, No, 1935, p 1133–1170 Steinman, D.B., Grove, W.G 1926 The Eye-Bar Cable Suspension Bridge at Florianópolis, Brazil, Transactions ASCE, N◦ 1662, Jan., p 267–393 Steinman, D.B & Watson, S.R 1941 Bridges and Their Builders, G P Putnam’s Sons, Nova York Timoshenko, S.P 1983 History of Strength of Materials, Dover Timoshenko, S.P & Young, D.H 1945 Mecânica Técnica – Estática, Editora Gertum Carneiro, p.123 Timoshenko, S.P & Young, D.H 1965 Theory of Structures, McGraw-Hill Kogakusha 2a Ediỗóo Vogel, R 1983 Building Brooklyn Bridge, The Design and Construction: 1867–1883, Smithsonian Institution, Civil Engineering, May Widmer, U 1979 IABSE Bulletin, B11 Williams Jr., J.W 1977 J.B Eads and his St Louis Bridge, Civil Engineering, Oct 1294 Multi-Span Large Bridges – Pacheco & Magalhães (Eds.) © 2015 Taylor & Francis Group, London, ISBN 978-1-138-02757-2 Author index Adão da Fonseca, A 37, 215, 549 Aketa, O 417 Akyazı, U 351 Albuquerque, C.M.C 1091 Almeida, M 301 Almeida, P 607 Alvárez, J.L 209 Amara, A.B 215 Amaro, N 317 Angelmaier, V 231 Apaydin, N.M 1169 Argüelles, G.R 173, 737 Arici, M 1137 Astaneh-Asl, A 1169 Babu, G.S 263 Baldomir, A 491 Bani´c, D 443 Barata, V 459 Barcik, W 257 Barros, R.C 607, 1181 Barthélémy, J.-F 871 Bastien-Masse, M 1001 Bastos, R 1181 Baumhauer, A 409 Bednarski, C.M 549 Beer, C 641 Begg, D 1107 Bella, G 215 Benko, V 975 Bento, J 799 Biliszczuk, J 257, 277 Bishop, D 789 Bittencourt, T.N 831 Blanco, L 167, 381 Bondonet, G 871 Borderon, A.E.C 759 Bordin, F 879 Bouška, P 649 Brandtsegg, A.S 365 Brekke, D.E 729 Brito, V 285, 301, 513 Brock, C.T 887 Brühwiler, E 1001 Buhin, M.M 443 Bæksted, A.F 83 Caetano, E 771 Calado, L 895 Calỗada, R 1091, 1099, 1143 Calvo, M 1137 Caủueto, M.M 337, 599, 1057 Caprani, C.C 1029 Cardoso, A.M.L 1197 Carvalho, A 1001 Carvalho, D 559 Carvalho, M.T.M 955 Casper, J 409 Castro, L.G 1181 Castrodale, R.W 985 Cauvin, B 871 Cavadas, F 807 ˇ Cech, J 649 Chakrabarti, S 847 Chen, A 93 Chernyshova, L.A 1115 Chung, J.Y 1217 Coelho, H 559, 583, 655 Costa, B.J.A 807 Crémona, C 895 Criado, S 167 Cruz, J.M.S 721 Cruz, J.P 459 Cunha, A 771 Curran, P 179 Custúdio, J 1121 da Conceiỗóo Neto, A.P 831 da Silva Araújo, S 955 Dahl, K.B 729 Daraban, M 527 de Argote, J.I.D 209 de Barros, F.B 159 de Boer, A 1107 de Freitas Simões, J 159 de Jesus, A.M.P 1091 de Miranda, M 143 1295 Defaucheux, L 863 Desprets, H 863 Diniz, S.M.C 1073 Dobashi, H 781 Domínguez, J.M 167 Düzbasan, S 351 Eilzer, W 201, 231 El-Belbol, S 887 Escamilla, M 167 Failla, I 1189 Farook, H.M 263 Fernández, S 187, 389, 583 Ferreira, A 507, 1151 Ferreira, J.R 1073 Ferreira, P.S 1163 Figueiras, J 799, 807 Figueiredo, H 239 Filho, H.R 955 Fillo, L’ 975 Foremniak, S 575 Fossbakken, S 365 Fu, M 309, 1175 Fuente, S 167, 187, 381 Ganesh, K 331, 345, 357 García, M.B 337, 599, 1057 Gil, M.A 167, 381 Gil, S 721 Gorkos, P 879 Granata, M.F 1137 Guarascio, M 215 Güngör, N 435, 521 Gupta, A 567 Gupta, J 591 Gutsch, A.W 841, 1009 Haixue, L 1065 Hajar, Z 863 Halvoník, J 975 Hart, J.A 467, 475 Haugerud, S.A 365 He, X 309 Heggade, V.N 673 Hendy, C.R 789, 847, 855, 887 Hernández, S 491 Hipólito, A 317 Hofstadler, C 751 Hołowaty, J 271, 293 Holtberget, S.H 373 Humpf, K 201, 231 Hussain, N 17 Iglesias, C 583 Imam, M 927, 937, 967 Ishitani, H 1197 Islami, K 823 Jang, S.H 247, 1217 Johannesen, S.M 127 Joly, E 135 Jung, R 201 Jungwirth, J 409 Jurado, C 1247 Kalný, M 993 Kamleithner, M 641 Kanaji, H 417 Karatzas, V 1279 Karydis, G 1279 Kashefi, K 1239 Kasuga, A 67 Kattenstedt, S 1203 Khairussaleh, N.A.M 937 Kilic, S.A 1169 Kim, S.B 1217 Kittoli, E 467, 475 Kolísko, J 649 Kollegger, J 575 Konstantakopoulos, T 1279 Körfgen, B 1169 Kosugi, T 781 Kralj, S 443 Kulakowski, M 879 Kummer, M 751 Kye, M 707 Lacort, A.G 1271 Laginha, L.M 1287 Lasa, I 1065 Laube, M 1009 Li, G.P 1255 Li, X 1175 Lima, B 507, 1151 Liu, C 919 Liu, Y 1037 Löker, E 1263 Long, A.E 567 Long, Q.Q 1019 Lopes, F 507 López, F.J.M 337, 599, 1057 Lu, D.G 1037 Lu, Y 309, 1211 Ma, R 93 Magalhães, F 771 Makita, T 815 Malindretou-Vika, M 451 Malveiro, J 1143 Manjure, P.Y 1049 Mansperger, T 201 Manterola, J 9, 167, 187, 209, 381, 389, 395 Marenzi, L 625 Márquez, M 483, 499 Martín, B 381 Martínez, A 167, 209, 381, 389, 395 Mathur, A.K 591 Matute, L 151 Maurer, R 1203 McPolin, D 567 Melo, L.R.T 831 Mendonỗa, T 285, 301, 513 Meng, N 743, 823, 1081 Mihal, M 641 Miklashevich, L.V 223, 1115 Millanes, F 151, 239, 1129 Minoretti, A 365 Miquilena, I 715 Moine, P 135 Moir, G.D 247, 1217 Monteiro, M 285, 513 Moor, G 743, 1081 Moutinho, C 771 Mundell, C 789 Muñoz-Rojas, J 187, 389, 583 Murali, P 357 Nakamura, Y 781 Nanukuttan, S 567 Navarro, J.A 167, 187, 209, 381 Nebreda, J 1129 Nestegård, A 365 Neves, A.S 799, 1099 Neves, M.S 721 1296 Ni, Y.S 919 Nicholls, A.D.J 887 Nie, Z 1175 Niu, X.J 1019 Nogueira, T 317 Nolte, T 1009 Nunes, F.P.S 325 Nunes, S 1001 Ökte, E 1263 Olamigoke, O.A 927, 967 Onoufriou, T 947 Onysyk, J 257, 277 Orcesi, A 895 Ortega, M 151, 239 Osborne, G 167 Oshiro, R.A 1197 Oyamada, R.N 1197 Öztürk, B.D 1263 Pacheco, P 103, 507, 559, 583, 655 Palacio, C.D.U 955 Paolacci, F 1037 Parejo, J.M.G 337, 599, 1057 Parke, G.A.R 927, 937, 967 Paulík, P 975 Pavi, S 879 Pecker, A 135 Peng, G.F 1019 Pereira, P 459 Pimentel, M 1001 Pipenbaher, M 427 Póvoas, A.A 615 Prabucki, P 257, 277 Preuer, A 641 Raatschen, H.J 1169 R˘ac˘anel, I.R 527, 1223, 1231 Radic, J 427 Raina, V.K 533 Recupero, A 1137, 1189 Rees, J 1217 Reiso, M 365 Resende, A 559, 583, 655 Ribeiro, A.B 1121 Ribeiro, C.F 51 Ribeiro, D 1143 Ribeiro, F 1001 Ricciardi, G 1189 Robb, D 567 Rojas, M 715 Romo, J 401 Roussou, E.K 1279 Ruan, X 1029 Runtemund, K 903 Rusanov, V.E 223, 1115 Saitta, F 1189 Sakai, H 815, 911 Sanders, P 247 Santana, B.D 663 Santos, I.C 325 Santos, J 895 Sastry, P.N.S.S 701 Savor, Z 427 Schreppers, G 1107 Sekse, J.H 365 Sellin, J.-P 871 Seo, J 247 Seo, J.H 1217 Serrano, M.T 337, 599, 1057 Servant, C 863 Sesar, P 443 Shanmugham, V 331 Sheikh, A.H 1239 Shen, Y 1255 Shi, Y.X 1019 Shukla, S.S 591 Silva, A.L.L 1091 Silva, A.S 1121 Silveira, P 895 Simões, R.S 955 Siviero, E 215 Slimi, K 215 Soares, I 559 Solera, P 239 Song, T.Y 1255 Søreide, T.H 365 Soriano, J.F.M 663 Sousa, C 799, 1099, 1143 Sousa, H 799 Souza, A 715 Spuler, T 743, 1081 Spyridis, P 451 Srbic, M 427 Stellati, P 625 Ste˛pie´n, K 257 Stern, I.Z 633 Strasky, J 27 Sugiyama, H 417 Sun, L.J 919 Suzuki, T 815 Szczepa´nski, J 257 Takahashi, M 781 Talıblı, E 1263 Tang, Z 1175 Tantele, E.A 947 Teixeira, R.M 831 Tej, P 649 Tembrás, E 491 Tian, F 1211 Toczkiewicz, R 257, 277 Tolley, C.J 193 Torrenti, J.-M 871 Toverud, L 729 Tukendorf, A 257 Tukendorf, K 257 Ugarte, J 239 Uluöz, S 351 Uluöz, T 351 Urdareanu, V.D 1231 1297 Valenzuela, M.A 483, 499 Vallejo, I 483, 499 Vázquez, J.I.C 663 Veie, J 373 Venkatram, P.G 345 Veronez, M 879 Villoria, B 127 Virlogeux, M 863 Virtuoso, F 1163 Vítek, J.L 993 Vokáˇc, M 649 Votsis, R.A 947 Walther, M 841 Watanabe, H 417 Waterfall, P 855 Weiher, H 903 Weiss, W 575 Wheeler, W.K 193 Whitmore, D 1065 Wielgosz, J.B 127 Winkler, J 855 Wo´zny, P 257 Xu, D 919 Yagi, N 815 Yakıt, E 351 Yang, J 1019 Zeybek, F 435 Zhang, X 93 Zhou, C 309 Zhou, J.Y 1029 Zhu, P 1211 Zucconi, M 215