PSI - Issue 5

Volume 5 • 2017

ISSN 2452-3216

ELSEVIER

2nd International Conference on Structural Integrity, ICSI 2017, 4-7 September 2017, Funchal, Madeira, Portugal

Guest Editors: Francesco I acoviello P edro M . G .P. Moreira P aulo J. S . T avares

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www.elsevier.com/locate/procedia 2nd International Conference on Structural Integrity, ICSI 2017, 4-7 September 2017, Funchal, Made r , Portugal Editorial XV Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal Thermo-mechanical modeling of a high pressure turbine blade of an airplane gas turbine engine P. Brandão a , V. Infante b , A.M. Deus c * a Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal b IDMEC, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal c CeFEMA, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal Abstract During their operation, modern aircraft engine components are subjected to increasingly demanding operating conditions, especially the high pressure turbine (HPT) blades. Such conditions cause these parts to undergo different types of time-dependent degradation, one of which is creep. A model using the finite element method (FEM) was developed, in order to be able to predict the creep behaviour of HPT blades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation company, were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were obtained. The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D rectangular block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The overall expected behaviour in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a model can be useful in the goal of predicting turbine blade life, given a set of FDR data. 2nd International Conference on Structural Integrity, ICSI 2017, 4-7 September 2017, Funchal, Madeira, Portugal Editorial Pedro Moreira*, Paulo J. Tavares INEGI / Faculty of Engineering Porto University, Portugal © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ICSI 2017. Research activity in Structural Integrity has seen an emer ing increase in recent years and spread throughout a number of exciting areas. ICSI focuses on all aspects and scales of structural integrity. This ranges from basics t future trends, with special emphasis on multi-scale and multi-physics approaches, and applications to new materials and challenging environments. Current research topics in the realm of Structural Integrity targeted by ICSI2017 include, but are not limited to Fracture and Fatigue, Stress Analysis, Damage Tolerance, Durability; Crack Closure, Nanoscale Damage, Material Ageing, Coatings Technology, Environmental Effects, Joining Technologies; Image processing fo SHM, New materi ls, Structural Integrity in Biomechanics and many other excitin res arch topics. In 2017, ICSI is proud to host the Second Multi-Lateral Workshop on Fracture and Structural Integrity, jointly organized by the Portuguese, Spanish and Italian groups on fracture. The Portuguese Structural Integrity Society and the Italian, and Spanish Groups of Fracture are strenuous scientific associations involved in several activities, under the umbrella of both the European Structural Integrity Society and the International Congress on Fracture. The second multilateral workshop is expected to increase the level of cooperation amongst these groups and increase the awareness to the research work done in the Iberian-Latin region of Europe on fractur and structural integrity relat d issues. This y ar, the ICSI organiz rs made an effort to return to the delegates part of their dedication and enthusia tic support from the previous editions, in the shape of increased visibility to the conference and scientific impact. ICSI2017 therefore launched a number of invitations to prominent researchers all over the globe to lecture on their own research fields, such as Prof. Alfonso Fernández-Canteli, Prof. Antonio Martín-Meizoso, Prof. Francesco Iacoviello, Prof. John W. Hutchinson, Prof. Pedro Camanho, and Prof. Manuel Freitas. ICSI2017 also started the organization of dedicated symposia and hosted the organization of ESIS Technical Committees annual meetings. Apart from the publication of the proceedings in Procedia Structural Integrity and a special issue in the International Journal 2nd International Conference on Structural Integrity, ICSI 2017, 4-7 Septe ber 2017, Funchal, Madeira, Portugal it rial Pedro oreira*, P ulo J. Tavare INEGI / Faculty of En ineering Porto University, Portugal © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ICSI 2017. Research activity in Structural Integrity has seen an emerging increase in recent years and spread throughout a number of exciting areas. ICSI focuses on all aspects and scales of structural integrity. This ranges from basics to future trends, with special emphasis on multi-scale and multi-physics approaches, and applications to new materials and challenging environments. Current research topics in the realm of Structural Integrity targeted by ICSI2017 include, but are not limited to Fracture and Fatigue, Stress Analysis, Damage Tolerance, Durability; Crack Closure, Nanoscale Damage, Material Ageing, Coatings Technology, Environmental Effects, Joining Technologies; Image processing for SHM, New materials, Structural Integrity in Biomechanics and many other exciting research topics. In 2017, ICSI is proud to host the Second ulti-Lateral orkshop on Fracture and Structural Integrity, jointly organized by the Portuguese, Spanish and Italian groups on fracture. The Portuguese Structural Integrity Society and the Italian, and Spanish Groups of Fracture are strenuous scientific associations involved in several activiti s, under the umbrella of both the European Structural Integrity Society and the International C ngress on Fr cture. The second multilateral workshop is expected to increase the level of cooperation amongst these groups and increase the awareness to the research work done in the Iberian-Latin region of Europe on fracture and structural integrity related issues. This year, the ICSI organizers made an effort to return to the delegates a part of their dedication and enthusiastic support from the previous editions, in the shape of increased visibility to the conference and scientific impact. ICSI2017 therefore launched a number of invitations to prominent researchers all over the globe to lecture on their own esearch fields, such as Prof. Alfo so Fernánd z-Canteli, Prof. Antonio artín- eizoso, Prof. Francesco Iacoviello, Prof. John . Hutchinson, Prof. Pedro Camanho, and Prof. anuel Freitas. ICSI2017 also started the organization of dedicated symposia and hosted the organization of ESIS Technical Committees annual meetings. Apart from the publication of the proceedings in Procedia Structural Integrity and a special issue in the International Journal Pedro Moreira*, aulo J. Tavares INEGI / Faculty of Engineering Porto University, Portugal © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ICSI 2017. Research activity in Structural Integrity has seen an emerging increase in recent years and spread throughout a number of exciting areas. ICSI focuses on all aspects and scales of structural integrity. This ranges from basics to future trends, with special emphasis o multi-scale and multi-physics approaches, and applications to new materials and challenging environments. Current research topics in the realm of Structural Integrity targeted by ICSI2017 include, but are not limited to Fracture and Fatigue, Stress Analysis, Damage Tolerance, Durability; Crack Closure, Nanoscale Damage, Material Ageing, Coatings Technology, Environmental Effects, Joining Technologies; Image processing for SHM, New materials, Structural Integrity in Biomechanics and many other exciting research topics. In 2017, ICSI is proud to host the Second Multi-Lateral Workshop on Fracture and Structural Integrity, jointly organized by the Portuguese, Spanish and Italian groups on fracture. The Portuguese Structural Integrity Society and the Italian, and Spanish Groups of Fracture are strenuous scientific associations involved in several activities, under the umbrella of both the European Structural Integrity Society and the International Congress on Fracture. The second multilateral workshop is expected to increase the level of cooperation amongst these groups and increase the awareness to the research work done n the Iberian-Latin region of Europe on fracture and structural integrity related issues. This y ar, the ICSI organizers made an effort to return to the delegates a pa t o their de ication and enthusiastic support from the previous editions, in the shape of increased visibility to the conference and scientific impact. ICSI2017 therefore launched a number of invitations to prominent researchers all over the globe to lecture on their own research fields, such as Prof. Alfonso Fernández-Canteli, Prof. Antonio Martín-Meizoso, Prof. Francesco Iacoviello, Prof. John W. Hutchinson, Prof. Pedro Camanho, and Prof. Manuel Freitas. ICSI2017 also started the organization of d dicated symp sia and hosted th organization of ESIS Technical Committees annual meetings. Apart from the publication of the proceedings in Procedia Structural Integrity and a special issue in the International Journal * Corresponding author. T l.: +351 225 082 151; fax: +351 229 537 352. E-mail address: pmoreira@inegi.up.pt © 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of PCF 2016. © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ICSI 2017 Keywords: High Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation.

2452-3216 © 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of PCF 2016. 2452-3216  2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ICSI 2017 10.1016/j.prostr.2017.07.195 * Corresponding author. Tel.: +351 218419991. E-mail address: amd@tecnico.ulisboa.pt 2452-3216 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ICSI 2017. 2452-3216 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ICSI 2017. * Corresponding author. Tel.: +351 225 082 151; fax: +351 229 537 352. E-mail address: pmoreira@inegi.up.pt 2452-3216 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ICSI 2017. * Corresponding author. Tel.: +351 225 082 151; fax: +351 229 537 352. E-mail address: pmoreira@inegi.up.pt

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of Fatigue, special issues on six other highly relevant journals in the field of Structural Integrity further supported the conference: Engineering Failure Analysis; Fatigue and Fracture of Engineering Materials and Structures; Journal of Strain Analysis for Engineering Design; Journal of Strain Analysis for Engineering Design; Bridge Structures, and; International Journal of Conservation Science. The response to these efforts has been overwhelming: Twelve symposia were proposed and accepted for organization; two ESIS Technical Committees annual meetings were hosted: TC10 on Environmentally Assisted Cracking and TC12 on Risk Analysis and Safety of Large Structures and Components; the number of abstract submissions nearly doubled from 2015: over 250 abstracts were approved for oral communication and nearly 200 full papers have been accepted for the conference proceedings. The biennial ICSI conferences, at the end of summer and resident in Funchal, the capital of the wonderful Madeira Island, were planned to be a referential source of inspiration for the researchers in the field that want to keep updated on the latest developments from reference researchers around the globe. The conference has seen an unprecedented growth in volume and quality and we welcome the reader to judge the excellence of the conference by himself and whether he should attend the next ICSI in 2019. Above all, the organizers believe the ICSI conferences disseminate excellent research and share worthwhile and beneficial knowledge for the enhancement of science and the prosperity of our society, and therefore actively contribute to the preservation and sustainability of our world.

Conference Chairs,

Pedro M. G. P. Moreira Paulo J. S. Tavares INEGI – Institute of Science and Innovation in Mechanical and Industrial Engineering

Faculty of Engineering Porto University Manuel Freitas, (Multi-Lateral Workshop) IST Portugal

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Committees Chairmen

Pedro Moreira, INEGI, Portugal (ICSI2017) Paulo Tavares, INEGI, Portugal (ICSI2017) Manuel Freitas, IST, Portugal (Multi-Lateral Workshop) Organizing Committee

Virginia Infante, IST, Portugal José Correia, INEGI, Portugal Mário Vaz, University of Porto, Portugal Luís Reis, IST, Portugal Manuel da Fonte, ENIDH, Portugal Local Organizing Committee Lino Maia, UMA, Portugal Paulo Lobo, UMA, Portugal Behzad Farahani, INEGI, Portugal Daniel Braga, INEGI, Portugal Nuno Viriato, INEGI, Portugal Shayan Eslami, INEGI, Portugal Andreia Flores, INEGI, Portugal Joana Machado, INEGI, Portugal International Scientific Committee Abilio de Jesus, University of Porto, Portugal

Aleksandar Sedmak, University of Belgrade, Serbia Alexopoulos Nikolaus, University of Aagen, Greece Alfonso Fernandez Canteli, University of Oviedo, Spain Andrea Carpinteri, University of Parma, Italy Antonio Martin Meizoso, CEIT IK4, Spain António Arêde, University of Porto, Portugal António Torres Marques, University of Porto, Portugal Carlos Rebelo, University of Coimbra, Portugal Carmine Pappalettere, Politecnico di Bari, Italy Claudia Barile, Politecnico di Bari, Italy Constantinos Soutis, The University of Manchester, UK Daniel Kujawski, Western Michigan University, USA Dariusz Rozumek, Opole University of Technology, Poland

Donka Angelova, University of Chemical Technology and Metallurgy, Bulgaria Francesco Iacoviello, Università di Cassino e del Lazio Meridionale, Italy Grzegorz Lesiuk, Wroclaw University of Technology and Science, Poland Hannes Körber, Technical University of Munich, Germany Hernani Lopes, Instituto Superior de Engenharia do Porto, Portugal

Humberto Varum, University of Porto, Portugal Igor Varfolomeev, Fraunhofer IWM, Germany J Gordon G Williams, Imperial College London, UK Jesus Toribio, University of Salamanca, Spain Jidong Kang, CanmetMATERIALS, Canada John W. Hutchinson, Harvard University, USA

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José Correia, INEGI, Portugal José L. Ocaña, Centro Láser UPM, Spain José Xavier, University of Trás-os-Montes e Alto Douro, Portugal João Custódio, LNEC, Portugal Kim Long, The Boeing Company, USA Luca Susmel, University of Sheffield, UK Lucas da Silva, University of Porto, Portugal Luis Borrego, Instituto Superior de Engenharia de Coimbra, Portugal Luis Reis, Instituto Superior Técnico , Portugal Luis Simões da Silva, University of Coimbra, Portugal Malgorzata Kujawinska, Warsaw University of Technology, Poland Manuel Freitas, Instituto Superior Técnico , Portugal Marcelo Moura, University of Porto, Portugal Martins Ferreira, University of Coimbra, Portugal Mário Vaz, University of Porto, Portugal Mieczyslaw Szata, Wroclaw University of Science and Technology, Poland Milan Veljkovic, Delft University of Technology, Netherlands Nikolai Kashaev, Helmholtz-Zentrum Geesthacht, Germany Paulo Lobo, University of Madeira, Portugal Paulo Tavares, INEGI, Portugal Leslie Banks-Sills, Tel Aviv University, Israel Lino Maia, Universidade da Madeira, Portugal Pedro Areias, University of Évora, Portugal Pedro Camanho, University of Porto, Portugal Pedro Moreira, INEGI, Portugal Per Stahle, Lund Institute of Technology, Sweden Peter Horst, Technische Universität Braunschweig, Germany Raj Das, University of Auckland, New Zeland Rhys Jones, Monash University, Australia Rui Calçada, University of Porto, Portugal Rui Miranda Guedes, University of Porto, Portugal Sabrina Vantadori, University of Parma, Italy Satish kumar Velaga, Indira Gandhi Centre for Atomic Research, India Spiros Pantelakis, University of Patras, Greece Stefan Pastrama, University Politehnica of Bucharest, Romania Stéphane Sire, Université de Bretagne Occidentale, France Thierry Grosdidier, CNRS UMR, France Uwe Zerbst, BAM, Germany Valery Shlyannikov, Kazan National Research Technical University, Russia Virginia Infante, Instituto Superior Técnico , Portugal Volnei Tita, Universidade de São Paulo, Brasil Waldemar A. Monteiro, Instituto de Pesquisas Energéticas e Nucleares, Brasil Weidong Zhu, University of Maryland, USA Zhiliang Zhang, Norwegian University of Science and Technology, Norway

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XV Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal Thermo-mechanical modeling of a high pressure turbine blade of an airplane gas turbine engine P. Brandão a , V. Infante b , A.M. Deus c * a Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal b IDMEC, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal c CeFEMA, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal Abstract During their operation, modern aircraft engine components are subjected to increasingly demanding operating conditions, especially the high pressure turbine (HPT) blades. Such conditions cause these parts to undergo different types of time-dependent degradation, one of which is creep. A model using the finite element method (FEM) was developed, in order to be able to predict the creep behaviour of HPT blades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation company, were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were obtained. The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D rectangular block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The overall expected behaviour in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a model can be useful in the goal of predicting turbine blade life, given a set of FDR data. 2nd International Conference on Structural Integrity, ICSI 2017, 4-7 September 2017, Funchal, Madeira, Portugal 45 years of cable-stayed SNP Bridge in Bratislava Ivan Ba áž a * , Yvona Koleková b a Department of Metal and Timber Structures, b Department of Structural Mechanics, Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, Bratislava, SK-81005, Slovak Republic Design, description and experience with 45 years old cable-stayed SNP Bridge over the river Danube in Bratislava, Slovak Republic. Imperfection measurements, i spections, calculation of rating factors and evaluation f load-carrying capacities, proposal for exception, strengthening and its influence. Local and global buckling combined with shear lag effects. Influence of torsion at box girders. Development of cable-stayed bridges and position of the SNP Bridge in the world rankings of the large span cable stayed bridges after 45 years from it opening. © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ICSI 2017. Keywords: Cable-stayed bridge; imperfection measurement; inspections; load-carrying capacities; strenghtening 1. Introduction When it was constructed in 1969, the SNP Bridge, with main span 303 m, was the world record holder in the category of cable-stayed bridges. The bridge was the fourth-longest cable-stayed bridge span when it was opened to traffic on August 29, 1972. It was the winner of the competition Structure of the Twentieth Century in Slovakia, organized in 2001. The original name of the bridge was Slovak National Uprising Bridge (In Slovak: Most Slovenského Národného Povstania = SNP). It was renamed, like other Bratislava Danube bridges, after the collapse of the communist regime in the beginning of the 1990s. The name “New Bridge” was valid only in the period 1993– 2012. Before and after this p rio the name s SNP Bridge. Today the NP bridge, 45 years from its opening, is with the main span 303 m on the 4 th place in the category of cable-stayed bridges with single tower and single cable plane 2nd International onference on Structural Integrity, I SI 2017, 4-7 Septe ber 2017, Funchal, adeira, Portugal rs f l -st ri i r tisl Ivan aláž a * , vona oleková b a Department of Metal and Timber Structures, b Department of Structural Mechanics, Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, Bratislava, SK-81005, Slovak Republic Abstract Design, description and experience with 45 years old cable-stayed SNP Bridge over the river Danube in Bratislava, Slovak Republic. Imperfection measurements, i spections, calculation of rating factors and evaluation of load-carrying capacities, proposal for exception, strengthening and its influence. Local and global buckling combined with shear lag effects. Influence of torsion at box girders. Development of cable-stayed bridges and position of the SNP Bridge in the world rankings of the large span cable stayed bridges after 45 years from it opening. © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ICSI 2017. Keywords: Cable-stayed bridge; imperfection measurement; inspections; load-carrying capacities; strenghtening 1. Introduction hen it as constructed in 1969, the S P Bridge, ith ain span 303 , as the orld record holder in the category of cable-stayed bridges. The bridge as the fourth-longest cable-stayed bridge span hen it as opened to traffic on ugust 29, 1972. It as the inner of the co petition Structure of the T entieth Century in Slovakia, organized in 2001. The original na e of the bridge as Slovak ational prising Bridge (In Slovak: ost Slovenského árodného Povstania = S P). It as rena ed, like other Bratislava anube bridges, after the collapse of the co unist regi e in the beginning of the 1990s. The na e “ e Bridge” as valid only in the period 1993– 2012. Before and after this period the na e is S P Bridge. Today the S P bridge, 45 years fro its opening, is ith the ain span 303 on the 4 th place in the category of cable-stayed bridges ith single to er and single cable plane © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ICSI 2017 © 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of PCF 2016. Keywords: High Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation. Abstract

2452-3216 © 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of PCF 2016. 2452-3216  2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ICSI 2017 10.1016/j.prostr.2017.07.071 * Corresponding author. Tel.: +351 218419991. E-mail address: amd@tecnico.ulisboa.pt 2452-3216 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ICSI 2017. 2452-3216 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ICSI 2017. * Corresponding author. Tel.: +0-421-2-59274379; fax: +0-421-2-52494116. E-mail address: ivan.balaz@stuba.sk * Corresponding author. Tel.: +0-421-2-59274379; fax: +0-421-2-52494116. E-mail address: ivan.balaz stuba.sk

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after the bridges: Flehe, Germany, 368 m, 1979, Kao-Pin Hsi, Taiwan, 330 m, 1999, Vansu Bridge, Latvia, 312 m, 1981. Ranking of cable-stayed bridges with single tower a nd multi towers in (Baláž, 2014 , pp. 1314-1316).

Fig. 1. SNP Bridge over Danube river in Bratislava, the capital of Slovak Republic

Nomenclature R

factored resistance (e.g. R = R d )

R d specified material resistance R d = R y / γ m = 360 MPa / 1.25 = 290 MPa (280 MPa for thickness t > 25 mm for steel grade 52 (S355) R y specified yield stress γ m partial material safety factor D i nominal dead load effect of element i γ D,i dead load factor for element i L j nominal live load effects for load j other than the rated vehicle γ L,j live load factor for load j other than the rating vehicle L R nominal live load effects for the rated vehicle γ L,R live load factor for the rated vehicle n total number of elements contributing dead load to the structure m total number of live loadings contributing to the live load effects other than the rated vehicle δ factor used to approximate the dynamic effects of moving vehicles ψ c load combination factor ( ψ c = 1 for m = 0, ψ c = 0.9 for m = 1 and 2, ψ c = 0.8 for m > 2) σ c , σ b uniform and bending components of longitudinal compression direct stress in subpanel τ shear stress in subpanel ρ c , ρ b reduction factors of local buckling for subpanel under compression and bending ρ q reduction factor of local buckling for subpanel under shear SNP Bridge is the second permanent bridge over Danube River in Bratislava, the capital of the Slovak Republic. It is a steel cable-stayed bridge with a single backward inclined steel tower and a single cable plane. The asymmetrical position of the inclined 84.6 m high A-shaped tower, crowned by a circular restaurant with 32 m in diameter, creates a natural balance to the famous Bratislava Castle and the St. Martin Dome (Fig. 1). The restaurant UFO (previously called Bystrica; capacity 120 people) and the public observation deck on its roof offer a nice view of Bratislava. SNP Bridge is the only bridge registered in the World Federation of Great Towers, where the key criterion is to have a public observation deck. The bridge certainly looks distinctive and elegant. The bridge has three spans of 74.8 m + 303 m + 54 m with a total length of 431.8 m. Three cables support the 4.6 m high steel orthotropic box girder, dividing the main span into four segments of 51.5 m + 70.2 m + 82.6 m + 98.7 m = 303 m. The main span is 80.2% of the total length of two stayed spans (74.8 m + 303 m). The reason for the major span being longer than usual is that the bridge has a single back stay anchored to the abutment rather than several back stays distributed along the side span. The navigation opening was prescribed to be 10 m × 180 m. 2. SNP Bridge description

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The bridge superstructure consists of a steel orthotropic two-cell box girder supported by a single plane fan cable system. Nevertheless, along the length 86 m + 54 m = 140 m, the cross section was originally a single-cell box steel girder because the middle web of the box girder was omitted from the point of the last, most-inclined cable anchorage till the Bratislava end of the bridge (Fig. 1). Cables in one vertical plane along the bridge middle axis are used. The bridge has four traffic lanes. There are two pedestrian walk ways of 3 m on both sides of the bottom flange. The steel box girder has a width of 21 m (Fig. 2). The orthotropic deck plate is mainly of 12 mm thick and increased to 16 mm, 20 mm, 25 mm, and 30 mm at the areas of the cable anchorages. The plate thicknesses are rather small due to preloading. The bottom flange plate thickness varies between 12 mm and 22 mm and three vertical web plates are 12 mm thick (Fig. 2). Cross frames are spaced at 3 m. The system of longitudinal stiffeners is as follows: closed trapezoidal ribs with 600 mm spacing made of 6 mm and 8 mm thick plates are used in the bridge deck, while the three vertical web plates (spacing 6.3 m, height 4.6 m) and the bottom flange of the box girder are stiffened by L profiles.

Fig. 2. Half of the SNP Bridge cross section used in calculation.

3. Imperfection measurements

In 1984 measurements of deflections at the centre of subpanels and deflections of longitudinal stiffeners of bottom flange of the SNP Bridge were made (Chladný, Baláž, Nádaský, 1985); the deflection taken at mid -point of the gauge length. A mechanical system consisting of a bar carrying two fixed probes and a central dial gauge was used for measuring ripples in plate panels. The gauge length were b and 2b , where b is the spacing of the longitudinal stiffeners. A builder`s level was used for measuring ripples of the longitudinal stiffeners. The gauge length was a , where a is the spacing of the transverse stiffeners. Initial deflections in the unloaded were computed from the well known formula of linear theory, in which signs “–“ ( “ + ” ) are used for a panel in compression (tension).   cr measured o w w   / 1   (1) The results of imperfection measurements indicated that the deflections of the bottom plate of the SNP Bridge are much lesser than on the other bridges which were investigated in Czechoslovakia and Germany (Massonnet, 1980; Chladný, Baláž, 1990). There were altogether 2288 measurements of plate panels imperfections using gauge length b = 787.5 mm and 1560 measurements of plate panels imperfections using gauge length 2 b = 1575 mm. Both measurements consisted of 17 sets differing in: a) plate panel thickness 12, 14, 16, 18 and 20 mm, b) kind of stresses in plate panel: compression or tension stresses, c) existence or not existence of transverse field butt weld in measured section. The obtained values were compared with the value b/200 = 3.94 mm. This value was exceeded only in the set TW 12-12, where 95 % fractile (176 measurements) was 5.825 mm ( b / 135) and in the set TW with 5.303 mm ( b / 149). T means panel in tension, W weld in panel between 12 mm and 12 mm parts of panel. TW means in all tension panels with welds (352 measurements). And there were altogether 92 measurements of positive imperfections of

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longitudinal stiffeners and 14 measurements of negative imperfections of longitudinal stiffeners. Both measurements consisted of 12 sets differing in: a) thickness of bottom flange plate 12, 14, 16, b) kind of stresses in plate panel: compression or tension stresses, c) positive or negative imperfections. Negative means on the stiffener side of plate. The gauge length was spacing of the transverse stiffeners a = 3000 mm. The obtained values were compared with the value a / 500 = 6 mm in the case of positive imperfections and with the value a / 750 = 4 mm in the case of negative imperfections. The value 6 mm valid for positive longitudinal stiffeners imperfections was exceeded in the sets with 95 % fractiles in T12 (18 measurements, a / 388 = 7.738 mm), in T14 (14 measurements, a / 395 = 7.589 mm), C14 (13 measurements, a / 390 = 7.694 mm), in T (47 measurements, a / 417 = 7.199 mm), in 12 (34 measurements, a / 427 = 7.033 mm|, in 14 (27 measurements, a / 395 = 7.586 mm), in all 92 measurements ( a / 432 = 6.938 mm). More details may be found in (Chladný, Baláž, 1993). In 1989 and 1993 the first author took part in the inspections of SNP Bridge led by Professor Chladný (Chladný, Tesár et al., 1989; Chladný, Dutko et al., 1993). The management of all highway bridges in Czechoslovakia was controlled by two codes: (i) ON 73 6220 Register of Bridges on Motorways, (ii) ON 73 6221 Maintenance of Bridges on Motorways, Highways and Urban Roads. According to these codes the physical condition of the bridge is classified in seven rating levels: perfect, very good, satisfactory, bad, very bad and poor. The principal inspections of the SNP bridge were carried out by the Department of Metal and Timber Structures in 1983, 1989 and 1993.The results of the principal inspection was performed in 1989 visually and with device for corrosion measurement. The main results of this inspection are presented in (Chladný, Baláž, 1993). Maintenance of the bridge structure during the period 1983 1989 was to be better than during previous maintenance period. Recommendations for maintenance and repairs were as follows: a) suitable expansion joints are needed, b) Special measures must be taken to protect the structure of the box girder, tower and anchor chamber against the corrosion due to rain water leakage, c) many parts of the bridge structure need cleaning and protection paint, d) general repainting inside the box girder is also needed. The classification of states of all Slovak bridges related to the year 2011 divided in seven grade groups may be found in the Table 17.3 on page 762 in (Baláž, 2014 ). 4. Inspection In the Czechoslovak standards there were specifications for three types of variable actions for the determination of load-carrying capacities: (i) the normal action V n : six two-axle vehicles in two lanes or three in one lane for narrow bridges with legal weights of vehicle for classes A / B bridges 320 kN / 220 kN, (ii) the exclusive action V r : one four axle vehicle 800 kN / 400 kN, (iii) the exceptional action V e : special set for heavy loads with two three-axle tractors (840 kN) and one 14-axle trailer (1960 kN). Rating factors values were calculated from the formula (2). In calculation of the rating factor values the following values were considered: (i) normal load: j = 1 – uniformly distributed carriageway loading 2.5 kN / m 2 , j = 2 – uniformly distributed sidewalk loading 4 kN / m 2 along the length 100 m and 2.5 kN / m 2 on the remaining part of length if it was longer than 100 m, j = 3 – wind loading was neglected ( m = 2), γ L,R = γ L,1 = γ L,2 = 1.4, δ R = δ 1 = 1.1, δ 2 = 1.0; (ii) exclusive load: m = j = 1 – the sidewalk loading as for (i); (iii) exceptional load: m = 0, γ L,R = 1.1, δ R = 1.05, ψ c = 1.0. The loading with of the carriageway is 2 x 8.5 m = 17 m and of the two footpaths 2 x 3 m = 6 m. 5. Load-carrying capacity evaluation

n

m

c       D i i , D 

R

L







L j j j ,

i

j

1

1

R F

. .



(2)

c L R R R    , L

Detailed calculation was done in (Chladný, Dutko, 1989). It was found that the critical section (Fig. 3) of the box girder governs in computing rating factors values. The very low effective breadth ratio and missing middle web of the box girder cross-section in the critical section are responsible for this controlling condition. The obtained rating factors

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were very low (Chladný, Baláž, 1993, Table 3). There were six reasons for the very low and zero values of the rating factors: a) The SNP Bridge was designed according to the older codes with lower loading actions. The shear lag phenomenon was not taken into account in its design in 1969; b) The loaded length of the bending moment influence line for the critical section is 303 m + 54 m = 357 m. Czechoslovak standard (ČSN 73 6205: 1986) did not recognize the principle that as the loaded length of unique large span bridges increases the average load per unit length may be decreased. Load models defined in EN 1991-2 also should be used only for the design of road bridges with loaded lengths less than 200 m; c) The load and resistance factor concept applied to the calculation of the dead load internal forces, which were computed as the sum of the extreme values from 23 erection steps, leads to their unrealistic very high factored values; d) Uncertainty of the code in the question of the impact factor for long-span and cable- stayed bridges. In this case (ČSN 73 6205: 1986) prescribed a dynamic calculation. The value δ = 1.1 was taken as a minimum value from the code; e) According to the British code (BS 5400: part 3, 1982) a maximum of 60 % of the bending moment and/or the axial force in the web may be redistributed to the flanges, provided that the assumed stress distribution, after such shedding, is such that the whole of the applied bending moment and axial force is transmitted and equilibrium is maintained. No shedding is permitted by the Czechoslovak code. The following condition had to be satisfied according to (ČSN 73 6205: 1986) fo r each subpanel of the longitudinally stiffened plate panel: The interaction formula (3) does not recognize the plastic redistribution of bending moment stresses at ultimate state and for the critical web subpanel (shaded area of the web bottom subpanel in Fig. 3) leads to very low rating factors. The critical web subpanel has a thickness 12 mm and can be deemed to restrained. The adjacent bottom flange subpanel is, for construction reasons, 36 mm thick and therefore it is not critical. The very low rating factors were the reason that in (Chladný, Baláž, at al., 1991) the proposal for exception allowance relating to standard for load-carrying capacity calculation of SNP Bridge was justified. Based on this exception the following changes in calculation of load-carrying capacities were done: a) in agreement with (Buckland, 1981) the uniformly distributed carriageway loading for the loaded length 357 m was decreased to 1.94 kN/m 2 ; b) for loaded length 357 m the decreased sidewalk loading 1.5 kN/m 2 was taken into account according to (OHBDC, 1983). See also study (Baláž, Ároch, 1982); c) The load factors γ D,i = 1.0 were used in computing the dead load internal forces related to 23 erection steps; d) factor used to approximate the dynamic effects of moving vehicles δ = 1.0 was taken into account, because it was recognized that for long-span bridges the maximum loading occurs with the stationary traffic; e) it was decided that the left side of the verification condition (3) can be greater than 1.0, but must be less than the value 1.375, which corresponds to the condition under the test loading. The loading tests were performed in 1972 (Harasymiv, 1973). The loading test results (direct stresses in the critical section symbolized by 6 black points) relating to the loading test load 73 kN/m placed in the spans 303 m and 54 m long are shown in Fig. 3. The theoretical direct and shear stresses in Fig. 3 were obtained with computer program SEKTOR. The cross-section of the critical section of SNP Bridge used in calculation consisted of 296 points describing the real geometry including all longitudinal stiffeners (Fig. 2 and 3). For the purpose of SNP Bridge the original SEKTOR was modified taking into account non-linear direct stress distribution in the both cross-section flanges (Fig. 3). The direct stress distribution was calculated from the formula. 6. Comparison of theoretical results with loading test of SNP Bridge 1.0 0.6 2 2                  d q  b d R R  c d  b c  R   (3)

I M N y

 

N

  f y

z

 



(4)

A

  z

y



ef

w

z

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where N = 0 kN in the critical section, ρ w (z) = W y,ef / W y is effective section modulus ratio, which depends on the reduction due to the local buckling of the plate between stiffeners and in the parts of longitudinal stiffeners, the global buckling of the whole bottom flange in compression combined with reduction due to the shear lag in the bottom flange and on the reduction of the upper flange due to the shear lag. Details of ρ w (z) calculation may be found in (Baláž, 1990). Details of shear lag calculation at SNP Bridge were published in (Baláž, Chladný, 1991, 1992). f (y) is transverse direct stress distribution according to (ČSN 73 6205, 1984) and (BS 5400, Part3, 1982) described by 4 th order parabola; f (y ) = 1.0 for the vertical webs points and f (y ) < 1.0 for the other upper and bottom flanges points. Good correlation between theoretical and loading test values may be seen in Fig. 3.

Fig. 3. Comparison of theoretical direct and shear stresses distributions taking into local buckling, global buckling and shear lag effects due to loading test action 73 kN/m in the critical section with the measured loading test values of direct stress in the upper flange

7. Strengthening of SNP Bridge

As it was written above the cross section of SNP Bridge was originally a single-cell box steel girder from the point of the last, most-inclined cable anchorage till the Bratislava end of the bridge, because the middle web of the box girder was omitted in this part of SNP Bridge. The proposal for the bridge strengthening was made in (Chladný,

Table 1. Rating factors of SNP Bridge parts for normal, exclusive and exceptional actions. Part of the bridge Normal action rating factors = V n / 320 kN Exclusive action rating factors = V r / 320 kN

Exceptional action rating factors = V e / 3 20 kN

a) ON736220

b) exception

c) exception, strengthe ning

a) ON736220

b) exception

c) exception, strengthe ning

a) ON736220

b) exception

c) exception, strengthe ning

Box girder Tower leg

< 0 < 0 < 0

0.82 1.92 1.49

> 1.0

< 0 10.

1.0

1.0

0.58 7.09 1.29

1.7

1.8

– –

– –

– –

19.6

8.66 4.38

Cables

0.14

15.

Key: the sign “– “ means that rating factor was not necessary to calculate (> 1.0), the rating factor 0.82 means that instead of required V n = 320 kN, only 0.82 x 320 kN = 262.4 kN was obtained

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Baláž, Ároch, 1991) and realised in 1993. In this proposal took part also one of the best Slovak structural engineer Ing. Ján Bustin, PhD., (*17.02.1926, † 11.02.2017). The bridge was strengthened by adding a Warren-type truss as a middle web to make a two-cell box girder along the whole length of the bridge. Six- meter spacing of the “nodes’’ and a diagonal area of 12,000 mm 2 provide fictitious wall shear thickness t s = 2.73 mm (Fig. 4). Adding a truss middle web along the length 140 m has increases the effective breadth when taking into account shear lag phenomenon caused by live (variable) loading at the support in the form of a framed pendulum wall (critical section in Fig. 1) on the Bratislava side. Table 1 shows rating factors calculated according to (ON 73 6220, 1976) and relating standards (ČSN 73 6203, 1986) and (ČSN 73 6205, 1984): a) without any changes, b) taking into account proposal for exception, c) taking into account proposal for exception and strengthening.

Fig. 4. Strengthening by adding the middle truss web along the length 140 m at Bratislava end of the bridge.

Fig. 5. Stress distributions in the critical section: a) before strengthening (left), b) after strengthening by inserting middle truss web (right) for the internal forces: N = – 370 kN, M y = – 255 956 kNm, V z = – 14656 kN, B = – 6142 kNm 2 , T t = – 10151 kNm.

8. Conclusion

Design, description and experience with 45 years old cable-stayed SNP Bridge over river Danube in Bratislava, Slovak Republic. Imperfection measurements, inspections, calculation of rating factors and evaluation of load carrying capacities, proposal for exception, strengthening and its influence. Local and global buckling combined with shear lag effects. Influence of torsion at box girders. Development of cable-stayed bridges and position of the SNP Bridge in the world rankings of the large span cable-stayed bridges after 45 years from it opening.

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Fig. 6. Development of the cable-stayed bridges. SNP Bridge, 1972, compared with the current world record span holders

Acknowledgements

Authors acknowledge support by the Slovak Scientific Grant Agency under the contract No. 1/0603/17.

References

Baláž, I., 1990. Efficient Calculation of Box Girder Section M odulus. Proceedings of International Colloquium, Budapest, April, pp. II/3-II/11. Baláž , I., Chladný E., 1991. Shear lag at SNP Bridge and at continuous girders. Sborník přednášek celostátní konference "Ocelové mosty ´91". ČSOK a SUDOP Hradec Králové, s.p., Hradec Králové, říjen 15 -16, pp. 210-217. (In Slovak). Baláž , I., Ároch., 1992. Actions on the large span bridges. Zborník referátov zo 4. konferencie "Teória a konštrukcia mostov". VŠDS Žilina. Donovaly, Nízke Tatry, 16.-17. júna, pp. 189-194. (In Slovak). Baláž, I., 2014. Chapter 17 Bridge Engineering in the Slovak Republic in: Chen, W.-F., Duan, L., (Eds.), Handbook of International Bridge Engineering, CRC Press, Boca Raton, London, New York, pp. 747-821. BS 5400, Part 3, 1982. Code of practice for design of steel bridges. Buckland, P. G. (ed.), 1981. Recommended Design Loads for Bridges. ASCE Journal of Structural Division. ČSN 73 6203, 1986. Actions on bridges. Czechoslovak standard based on Ultimate Limit States. (In Czech). ČSN 73 6205, 1984. Design of steel bridge structures. Czechoslovak standard based on Ultimate Limit States. (In Czech). Harasymiv, V., 1973. Loading test of steel SNP Bridge over the river Danube in Bratislava. Inženýrske stavby No.7, pp. 321 -334. (In Slovak). Chladný, E., Baláž, I., Nádaský, P., 1985. Die Bemessung und statistische Auswertung der Imperfektionen der SNP-Brücke über die Donau in Bratislava. 4th Conference on Steel Structures. Romania, Timisoara, pp. 232-239. Chladný, E., Tesár, A., Dutko, P., Schun, J. , Agócs, Z., Lapos, J., Vajda, J., Baláž, I., Voříšek, V., 1989. Main inspection of SNP Bridge over Danube river in Bratislava, Department of Metal and Timber Structures, Faculty of Civil Engineering, STU in Bratislava. (In Slovak).. Chladný, E., Dutko, P., Voříšek, V., Schun, J., Agócs, Z., Lapos, J., Vajda, J., Baláž, I., Nádaský, P., Tengler, M., Ároch, R., Agócs jun., Z., 1989. Bridge sheet of SNP Bridge over Danube river in Bratislava, Faculty of Civil Engineering, STU in Bratislava. (In Slovak). Chladný, E., Baláž, I., 1990. Geometrische Imperfektionen und ihr Einfluss auf die Tragfähigkeit des Untergurtes der SNP-Brücke über die Donau in Bratislava. Zborník vedeckej konferencie pri príležitosti jubilea 80 rokov prof. W. Boguckieg o. Politechnika Gdanska, Gdansk. Chladný, E., Baláž, I., Agócs jun. Z., Vajda, J., Belica, A., 1991. Proposal for exception allowance relating to standard for load-carrying capacity calculation of SNP Bridge over Danube river in Bratislava, Faculty of Civil Engineering, STU in Bratislava. (In Slovak). Chladný, E., Baláž, I., Ároch, R., 1991. Design of SNP Bridge strengthening by inserting of the middle truss web in bridge bo x-girder. Department of Metal and Timber Structures, Faculty of Civil Engineering, STU in Bratislava, pp.1-53. (In Slovak). Chladný, E., Dutko, P., Agócs, Z., Lapos, J., Baláž, I., Vajda, J., Brodniansky, J., Nádaský, P., Belica, A., Tengler, M., Ár och, R., Agócs jun., Z., Sandanus, J., Chladná, M., Florek, S., 1993. Report about main inspection of SNP Bridge over Danube river in Bratislava, Department of Metal and Timber Structures, Faculty of Civil Engineering, STU in Bratislava. (In Slovak). Chladný, E., Baláž, I., 1993 . Inspection, evaluation and strengthening of the SNP-bridge in Bratislava. Bridge Management 2. Inspection, Maintenance, Assessment and Repair. 2nd International Conference on Bridge Management, University of Surrey, Guilford, UK, on 18-21 April, Thomas Telford, London, pp. 407-417. OHBDC, 1983. Ohio Highway Bridge Design Code. ON 73 6220, 1976. Register of Bridges on Motorways, Highways and Urban Roads. (In Czech). SEKTOR. 1980. Computer program for cross section properties and stresses calculation for loading by axial force, bending, torsion and distortion Author of the program: Baláž, I, author of the graphical output: Ároch, R.