Structural Concrete 1/2013

1 Volume 14 March 2012 ISSN 1464-4177

- fib MC2010: mastering challenges, encountering new ones - Service life design – incorporating fib MC2010 rules in ISO 16204 - Reliability-based non-linear analysis to fib MC2010 - Global safety format for non-linear analysis of RC structures - Towards efficient structures: construction of an ellipsoidal concrete shell - Lattice equivalent continuum method for 3D FE analysis - Experimental appraisal of large circular RC columns in compression - How cover, φ/ρs,ef and stirrup spacing affects cracking – tests and theory

Structural Concrete

Volume 14 2013 No. 1

Contents

The photograph shows a newly completed mall in Chiasso, Switzerland. The shell has the form of an ellipsoid (93 × 52 × 22 m) and its thickness varies between 100 and 120 mm. The shell was built using sprayed concrete and also ordinary concrete in some regions. A number of tailored solutions were also adopted, such as post-tensioning, addition of fibres and shear studs, to ensure satisfactory performance at both the serviceability and ultimate limit states. More information is provided on pages 43–50 of this issue (Photo: Aurelio Muttoni)

Structural Concrete Vol. 14 / 1

March 2013 ISSN 1464-4177 (print) ISSN 1751-7648 (online) Wilhelm Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG www.ernst-und-sohn.de

fédération internationale du béton International Federation for Structural Concrete www.fib-international.org

Journal of the fib

Peer reviewed journal Since 2009, Structural Concrete is indexed in Thomson Reuter’s ISI Web of Science.

Impact Factor 2011: 0.270

www.wileyonlinelibrary.com, the portal for Structural Concrete online subscriptions

Editorial 1

Joost Walraven, György L. Balázs fib Model Code for Concrete Structures 2010: a landmark in an ongoing development Technical Papers

3

Joost Walraven Model Code for Concrete Structures 2010: mastering challenges and encountering new ones

10

Steinar Helland Design for service life: implementation of Model Code 2010 rules in the operational code ISO 16204

19

Vladimir Cervenka Reliability-based non-linear analysis according to Model Code 2010

29

Diego Lorenzo Allaix, Vincenzo Ilario Carbone, Giuseppe Mancini Global safety format for non-linear analysis of reinforced concrete structures

43

Aurelio Muttoni, Franco Lurati, Miguel Fernández Ruiz Model Code 2010: mastering challenges and encountering new ones

51

Syed Ishtiaq Ahmad, Tada-aki Tanabe Three-dimensional FE analysis of reinforced concrete structures using the lattice equivalent continuum method

60

Tai-Kuang Lee, Cheng-Cheng Chen, Austin D.E. Pan, Kai-Yuan Hsiue, Wei-Ming Tsai, Ken Hwa Experimental evaluation of large circular RC columns under pure compression

69

Alejandro Pérez Caldentey, Hugo Corres Peiretti, Joan Peset Iribarren, Alejandro Giraldo Soto Cracking of RC members revisited: influence of cover, φ/ρs,ef and stirrup spacing – an experimental and theoretical study

79 80 81 81 81 82 83 84 85

fib-news fib days in Chennai, India fibUK Technical Meeting in recognition of Andrew Beeby Design of Concrete Bridges: fib short course in Ankara, Turkey New fib officers Gordon Clark visits Japan Short notes Congresses and symposia fib membership benefits Acknowledgement

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Products and Projects

Bautechnik 81 (2004), Heft 1

3

Imprint The journal “Structural Concrete”, the official journal of the International Federation for Structural Concrete (fib – fédération internationale du béton), provides conceptual and procedural guidance in the field of concrete construction, and features peerreviewed papers, keynote research and industry news covering all aspects of the design, construction, performance in service and demolition of concrete structures.

“Structural Concrete” is published four times per year completely in English.

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Publisher fib – International Federation for Structural Concrete Case Postale 88, CH-1015 Lausanne, Switzerland phone: +41 (0)21 693 2747, fax: +41 (0)21 693 6245 e-mail: fib@epfl.ch, Website: www.fib-international.org Publishing house Wilhelm Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG Rotherstraße 21 12045 Berlin/Germany phone: +49 (0)30/47031-200 fax: +49 (0)30/47031-270 e-mail: info@ernst-und-sohn.de, Website: www.ernst-und-sohn.de Editor Dr.-Ing. Dirk Jesse, Verlag Ernst & Sohn Rotherstraße 21, D-10245 Berlin phone: +49 (0)30/47031-275, fax: +49 (0)30/47031-227 e-mail: dirk.jesse@wiley.com Technical editor Francisco Velasco, Verlag Ernst & Sohn Rotherstraße 21, D-10245 Berlin phone: +49 (0)30/47031-277, fax: +49 (0)30/47031-227 e-mail: francisco.velasco@wiley.com Advertising manager Fred Doischer, Verlag Ernst & Sohn phone: +49 (0)30/47031-234 Advertising Annekatrin Gottschalk, Verlag Ernst & Sohn Rotherstraße 21, D-10245 Berlin phone: +49 (0)30/4 70 31-2 49, fax: +49 (0)30/4 70 31-2 30 e-mail: annekatrin.gottschalk@wiley.com Layout and typesetting: TypoDesign Hecker GmbH, Leimen Printing: Meiling Druck, Haldensleben

Structural Concrete 14 (2013), No. 1

Editorial board Editor-in-Chief ß Luc Taerwe (Belgium), e-mail: Luc.Taerwe@UGent.be Deputy Editor ß Steinar Helland (Norway), e-mail: steinar.helland@skanska.no Members ß György L. Balázs (Hungary) ß Josée Bastien (Canada) ß Mikael Braestrup (Denmark) ß Tom d’ Arcy (USA) ß Michael Fardis (Greece) ß Stephen Foster (Australia) ß Tim Ibell (UK) ß S.G. Joglekar (India) ß Akio Kasuga (Japan) ß Gaetano Manfredi (Italy) ß Pierre Rossi (France) ß Guilhemo Sales Melo (Brazil) ß Petra Schumacher (Secretary General fib) ß Tamon Ueda (Japan) ß Yong Yuan (China) Current prices The journal Structural Concrete has four issues per year. In addition to “Structural Concrete print”, the PDF version “Structural Concrete online” is available on subscription through the online service Wiley Online Library. print print print + online (personal) (institutional) (personal) 125.00 €

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Products & Projects

Accelerated and safe construction with system components The Rotterdam-based architect, Rem Koolhaas, has given his high-rise ensemble a huge “jolt” – and as a result has placed high demands on the construction work. Therefore, the supporting structure concept for realizing the cantilevers at a height of 86 m is an essential part of the comprehensive PERI overall solution.

De Rotterdam will be the largest building in the Netherlands – situated in the immediate vicinity to other architectural highlights such as the Erasmus Bridge by Van Berkel & Bos, the inclined high-rise building by Renzo Piano and the World Port Center by Sir Norman Foster. Once completed, the 150 m high multi-storey ensemble on Rotterdam´s Wilhelminapier peninsula on the south bank of the river Maas, will consist of three complex designed towers standing side by side and connected to each other. The West Tower has 45 residential levels, the 41-storey Central Tower is designed to be used as office facilities only whilst the 43 floors of the East Tower feature both office space as well as a hotel tract. In total, around 250 apartments, 280 hotel rooms and 60,000 m² of office space will be realised.

The five-storey base section of the building has retail stores, restaurants, conference rooms and a fitness centre – as well as three parking decks on the ground floor and two basement levels.

A native of Rotterdam, renowned architect Rem Koolhaas has given his high-rise complex a huge “jolt” – shifting the upper half of the building to the side with a horizontal offset to the west and north. In so doing, at a height of 86 m, the 24th and 26th floors respectively along with the remaining upper storeys cantilever outwards up to 9 m. The construction site crew of Ed. Züblin AG, Stuttgart, has vast experience in realising high-rise buildings and the structural work is scheduled to be finished in early 2013 whilst the de Rotterdam CV project group plans to have all construction work completed by the end of the year. The rapid construction progress is supported through the use of comprehensive and ideally combined PERI system solutions. In particular, the supporting formwork solution for the cantilevered sections is an important component of the PERI overall concept.

Supporting structure with system For realizing the huge cantilevers at the great heights, PERI engineers developed a supporting formwork solution on the basis of the VARIOKIT engineering construction kit. For this, rentable system components are being used to a large ex-

tent, supplemented by a project-specific bracing construction. The flexible arrangement of the shear frames is carried out here whilst taking into account the respective geometry and loads of the structure as well as the range of mounting parts through to the masts of the tower cranes positioned in the building itself.

For dimensioning the beam heights in the West Tower, transferring the large loads from the 8.88 m cantilevers for two complete floors of the building and the low 3.52 m height of the storey below, had to be taken into consideration. For the Central and East Towers, a double-storey can be used for this purpose – here, the supporting formwork solution not only serves for transferring the loads from the cantilevers but also as a supporting structure between the floors.

Extensive PERI know-how is used to good effect especially in the beam extensions when the inherent load-bearing capacity of the building has been reached.

The fact is that due to reasons of space, the shear frames cannot be simply retracted and disassembled within the storey itself without requiring direct crane support. For this purpose, the construction site crew is using the PERI lifting carriage that is normally used in connection with SKYTABLE large slab tables. The advantage of the PERI method – which was developed in and has been used for many years in North America – is that the shear frame is pulled horizontally from the building by means of a crane lift, a special chain block system and rear carriage.

Faster working through enhanced safety With the RCS P climbing protection panel from PERI, the two topmost floors under construction are completely enclosed each time. As a result, site personnel are prevented from falling at all times and protected from strong winds at great heights – this means that forming operations are accelerated and work performance is greatly enhanced. Züblin requires only eight days for one complete standard floor.

Already during the planning phase, the geometrical changes of the towers were taken into consideration so that those protection panel units affected by the offset could be moved to other sections without requiring any extensive modification work. The RCS solution demonstrated its high level of flexibility in the areas close to the slab edge where anchoring was not an option. In this situation, too, the slab shoes are securely fixed and ensure fast climbing procedures due to the continuing rail guidance.

Products & Projects

Fig. 1. The three towers of the 150 m high De Rotterdam multi-storey ensemble are positioned very close to each other and are offset halfway up.

Fig. 3. The systematic assembly sequence along with the lightweight system components of the SKYDECK slab formwork accelerate construction progress; even obstructions are easily shuttered within the system itself without requiring any additional formworking measures. (© PERI)

in particular, no additional storage facilities and assembly area are required.

Further Information: PERI GmbH, Schalung Gerüst Engineering, Rudolf-Diesel-Straße 19, 89264 Weißenhorn, Tel. +49 (0)7309.950-0, Fax +49 (0)7309.951-0, info@peri.com, www.peri.com

Design of Precast Concrete Components with RSTAB and RFEM Fig. 2. The striking procedure is an important component of the PERI solution: with the help of the SKYTABLE moving technique, the truss girders can be pulled horizontally from the building.

Crane-independent forming operations With the SKYDECK panel slab formwork, floor slabs can be formed without the need of a crane. System components made of aluminum to facilitate the transport and, in particular, shuttering and striking can be carried out manually. The systematic and therefore easy to-understand assembly sequence accelerates the construction processes and also ensures that time requirements can be accurately estimated. In addition, through the use of the drophead and the possibility of early striking, this also reduces the amount of panels and main beams required on site.

For the floors in the base section, the systematic assembly sequence and the high degree of safety for each standard bay has already been achieved using the SKYDECK platforms and the cantilevered 375 SLT main beams, also at the slab edges. For the large supporting heights reaching over several floors, the construction crew have combined SKYDECK with the MULTIPROP load-bearing system. The lightweight aluminum individual props can be vertically connected to each other by means of the MULTIPROP connector – and joined together using MULTIPROP frames to form extremely stable shoring towers.

De Rotterdam is encircled on all sides – longitudinally between the road and the Maas river as well as between two neighboring buildings at the ends. The narrow construction site therefore has very limited storage space. As a result, PERI supplied the RCS protection panel units and VARIOKIT shear frames already pre-assembled to the construction site. This means that these are lifted directly from the truck by crane and taken immediately to the designated place of use. This saves valuable crane time;

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Structural Concrete 14 (2013), No. 1

Due to their numerous advantages, precast parts consisting of reinforced concrete have become indispensable at construction sites because they can be applied in various ways. Precast single foundations, columns, girders, floors, etc., allow for quick mounting, regardless of weather conditions. Thus, construction periods are short. Furthermore, accuracy of precast parts is given in millimeters and they have very smooth surfaces that are difficult to be produced in comparison to cast-inplace concrete components.

The design of such precast parts can be performed with RSTAB and RFEM in combination with the appropriate add-on module according to Eurocode, ACI, DIN or SIA. Members and surfaces (only available in RFEM) for example can be designed in the

Fig. 1. Reinforcement output shown in table and graphic in CONCRETE

Responsible for Products & Projects: Publishing House Ernst & Sohn

Products & Projects add-on module RF-/CONCRETE, columns are designed in the add-on module RF-/CONCRETE Columns.

Nonlinear Calculation in CONCRETE The RSTAB add-on module CON-CRETE offers you the option to perform also non-linear calculations in cracked sections (state II). Moreover, it is possible to apply the effect of Tension-Stiffening (tension stiffening of concrete between cracks).

When you want to design girders, a variety of cross-sections like T-beams, rotated floor beams, rectangle-hollow cross-sections and I-beams are available for selection.

The calculated required reinforcement is shown by members and surfaces in the individual add-on modules. The provided reinforcement for members and columns can be viewed in 3D rendering mode. In this way, you can compare reinforcement drawings created later with the calculation so that data can be checked.

In addition, individual cross-sections can be created and designed in the stand-alone program SHAPE-MASSIVE.

Fig. 2. Column reinforcement in CONCRETE Columns in 3D rendering (© Dlubal)

BIM-Oriented Planning is Possible Because of numerous interfaces with other programs, concrete design of RSTAB/RFEM can be easily integrated into the BIM process. Models can be imported and exported in different file formats such as dxf, ifc, stp and dgn. Moreover, RSTAB and RFEM provide direct interfaces with Tekla Structures as well as Revit Structures and Auto-CAD by Autodesk, enabling a bidirectional data exchange (data transfer in both directions).

In addition, it is possible to transfer reinforcement specifications including geometry directly from RF-CONCRETE Surfaces to AutoCAD Structural Detailing where reinforcement plans are created.

Further Information and Demo Versions: Dlubal Engineering Software, Am Zellweg 2, 93464 Tiefenbach, Tel. +49 (0)9673 – 92 03-0, Fax +49 (0)9673 – 92 03-51, info@dlubal.com, www.dlubal.de

Products & Projects

Reminiscence of Bruno Taut The new headquarters of the French petroleum corporation Total will be the first building block of the so-called Europacity. The dominant feature of the slim and slightly bent building is its facade.

It consists of three-dimensional, sometimes very delicate curtain concrete elements. In their form and details, the façade elements remind of the famous architect Bruno Taut, who passed away in 1967. They offer an impressive display of the unique shaping possibilities of concrete – when design, execution, quality control and formwork facing set the highest standards. The 1395 precast concrete elements were manufactured by Dreßler Bau GmbH in their precast plant in Stockstadt. This is also where the formwork facing of Westag & Getalit AG, the East-Westfalian manufacturer of wood products, was implemented.

The blueprint was developed by architects and then fine-tuned in several workshops procedures, together with a panel of developers, users, external experts and representatives of the City and the State of Berlin. In the end, concrete was preferred as building material, for reasons of durability and appearance, to the detriment of a less expensive façade version made of steel.

The architects developed the so-called “K module”, as a basic element of the facade of the 17-storey Tour Total building. Each of the 400 modules consists of two three-dimensional elements. A “K module” extends over two floors and measures 7.35 m × 2.40 m. The individual modules differ in the layout of their diagonal edge which forms the “K” shape. The maximum depth of

Fig 1. The dominant feature of the slim and slightly bent building is its façade. It consists of three-dimensional, sometimes very delicate curtain concrete elements.

Fig 2. 450 of the almost 1395 elements were pre-produced within eight weeks, until the beginning of August 2011, and then stored on the premises under weatherproof conditions. Magnoplan DU= 360 formwork panels were used to meet the very tight tolerance levels. (© Westag & Getalit)

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Structural Concrete 14 (2013), No. 1

an element varies by up to 25 cm. The three-dimensional structure of the entire facade is created by the mirrored, staggered positioning the modules.

Greatest imaginable challenge Economist Daniel Stanik, manager of the Dreßler precast plant: “In addition to the design and the manufacture of classic precast concrete elements, we have successfully expanded the manufacture of special concrete facades into a stand-alone production line for multi-purpose architectural concrete. The Tour Total façade, however, was the greatest possible challenge for the Dreßler team. Every single production stage – statics, production particularities, logistics and assembly – was defined in minute detail. The timely production and the high architectural requirements were supported by rigorous quality controls. Formwork manufacturing and logistics presented unusual challenges for the team. For example, a new turning beam was bought for improving the production process.”

The basic elements of the facade were cast in a T-form. The vertical pilaster strip and the horizontal parapet were formed simultaneously, thus preventing the twisting of the pilaster strips under the influence of horizontal wind loads.

Manufacturing tolerances of less than three millimeters Peter Zahn, carpentry and formwork technician at the pre-cast plant Stockstadt: “Because of the dimensional accuracy, a lot of the difficult pointed forms, partly converging to 0, had to be cut out with the circular hand saw, from the 21 mm thick Magnoplan panels. From our experience, the high requirements in terms of concrete surface quality were best met using this DUO 360 5 ply plywood sheet”. The perfect sealing of the edges, the assembly, the thorough cleaning of the form and the precise insertion of the reinforcement were well documented. Manufacturing tolerances have to be under three millimeters, as the general joint pattern had to have a deviation of maximum +/–1.5 mm.

“The abrasion-resistant film facing of the formwork also contributed to the outstanding results in terms of finish and lifespan”.

The white cement-based architectural concrete of the modules was produced in a specially designed mixing plant, built on the premises of the Stockstadt plant. The pouring and the subsequent compaction of the concrete were done by means of vibration tables and bottles but also by trowel, which required exquisite craftsmanship, due to the sometimes extreme geometries.

The final procedure was the souring of the entire surface of ca.

7.500 m2. The final souring gives the structure made of white cement and quartz sand an elegant marble appearance.

450 of the almost 1395 elements were pre-produced within eight weeks, until the beginning of August 2011, and then stored on the premises under weatherproof conditions. Subsequently, they were transported to the building site on trailers, fastened and padded, in special loading boxes. Subcontractors then started the assembling under the supervision of Dreßler Bau. The remaining façade elements (column claddings, parapets, Tcolumns, attics, etc.), were produced by the end of 2011. The assembling took place until early summer 2012.

The specifications require that the dynamic façade should act as a medium, linking the building and the city. “Repetition and variation of a precast concrete module breaks the rigidity of the grid-like facade. The bright concrete elements cover the building in a three-dimensional line pattern, which enhances the effects of light and shadow on the facade”.

Further information: Westag & Getalit AG, Hellweg 15, D-33378 Rheda-Wiedenbrück, Tel. +49/5242/17-0, Fax +49/5242/17-75000, zentral@westag-getalit.de, www.westag-getalit.de

Responsible for Products & Projects: Publishing House Ernst & Sohn

Products & Projects

Doka has won another landmark, the super-high-rise Lokhandwala Minerva building in Mumbai Looming out of a 12-storey parking podium, the skyscraper will top out at 300 m and feature 82 storeys in two separate towers.

Named the “Minerva” after the Roman goddess of wisdom, the design for the tower comes from Hafeez Contractors, and bears a similarity to an oversized letter “M”.

The tower will be for residential use only and aims to be one of the most luxurious addresses in Mumbai. For the core walls, automatic climbing formwork SKE50 and SKE100 will be in use.

In order to guarantee an optimal construction workflow, each core will be split into two individual working zones. This increases productivity and guarantees a smooth work-flow. Construction of the building is scheduled to be finished in 2014.

With this project Doka continues its expansion strategy in the segment of the world’s tallest buildings.

Further Information: Doka GmbH, Josef-Umdasch-Platz 1, 3300 Amstetten, Austria, Tel. +43 (0)7472 605-0, Fax +43 (0)7472 64430, www.doka.com

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The Minvera Tower in Mumbai will be formed with Doka’s automatic climbing formwork. (© Doka)

Responsible for Products & Projects: Publishing House Ernst & Sohn

Provider directory products & services

anchor channels

fastening technology

reinforcement technologies

software

anchored in quality JORDAHL GmbH Nobelstraße 51 D-12057 Berlin Tel. (0 30) 6 82 83-02 Fax (0 30) 6 82 83-4 97 e-Mail: info@jordahl.de Internet: www.jordahl.de JORDAHL® anchor channels JORDAHL® screws Shear Reinforcement Shear Connector

bridge accessories

HALFEN Vertriebsgesellschaft mbH Katzbergstraße 3 D-40764 Langenfeld Phone +49 (0) 21 73 9 70-0 Fax +49 (0) 21 73 9 70-2 25 Mail: info@halfen.de Web: www.halfen.de concrete: fixing systems facade: fastening technology framing systems: products and systems

post-tensioning Maurer Söhne GmbH & Co. KG Frankfurter Ring 193 D-80807 München Phone +49(0)89 32394-341 Fax +49(0)89 32394-306 Mail: ba@maurer-soehne.de Web: www.maurer-soehne.de Structural Protection Systems Expansion Joints Structural Bearings Seismic Devices Vibration Absorbers

DYWIDAG-Systems International GmbH Max-Planck-Ring 1 40764 Langenfeld/Germany Phone +49 (0)21 73/7 90 20 Mail: dsihv@dywidag-systems.com Web: www.dywidag-systems.de

prestressed concrete

literature

Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG Rotherstraße 21 10245 Berlin Phone +49 (0) 30 4 70 31-2 00 Fax +49 (0) 30 4 70 31-2 70 E-mail: info@ernst-und-sohn.de Web: www.ernst-und-sohn.de

HALFEN Vertriebsgesellschaft mbH Katzbergstraße 3 D-40764 Langenfeld Phone +49 (0) 21 73 9 70-0 Fax +49 (0) 21 73 9 70-2 25 Mail: info@halfen.de Web: www.halfen.de concrete: fixing systems facade: fastening technology framing systems: products and systems

Max Frank GmbH & Co. KG Technologies for the construction industry Mitterweg 1 94339 Leiblfing Germany Phone +49 (0)94 27/1 89-0 Fax +49 (0)94 27/15 88 Mail: info@maxfrank.com Web: www.maxfrank.com

sealing technologies Paul Maschinenfabrik GmbH & Co. KG Max-Paul-Straße 1 88525 Dürmentingen/Germany Phone +49 (0)73 71/5 00-0 Fax +49 (0)73 71/5 00-1 11 Mail: stressing@paul.eu Web: www.paul.eu

Max Frank GmbH & Co. KG Technologies for the construction industry Mitterweg 1 94339 Leiblfing Germany Phone +49 (0)94 27/1 89-0 Fax +49 (0)94 27/15 88 Mail: info@maxfrank.com Web: www.maxfrank.com

Ing.-Software DLUBAL GmbH Am Zellweg 2 93464 Tiefenbach Phone +49 (0) 96 73 92 03-0 Fax +49 (0) 96 73 92 03-51 Mail: info@dlubal.com Web: www.dlubal.de

stay cables

DYWIDAG-Systems International GmbH Max-Planck-Ring 1 40764 Langenfeld/Germany Phone +49 (0)21 73/7 90 20 Mail: dsihv@dywidag-systems.com Web: www.dywidag-systems.de

vibration isolation

BSW GmbH Am Hilgenacker 24 D-57319 Bad Berleburg Phone +49(0)2751 803-126 Mail: info@berleburger.de Web: www.bsw-vibration-technology.com under-screed impact sound insulation with European Technical Approval, PUR foam & PUR rubber materials for vibration isolation

Structural Concrete 14 (2013), No. 1

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Editorial

fib Model Code for Concrete Structures 2010: a landmark in an ongoing development The design and analysis of concrete structures has a remarkable history. This starts with the concrete material itself, which has undergone a revolutionary metamorphosis, especially during the last decades. Only a few decades ago, the maximum concrete strength achievable on a building site was about 35 N/mm2. The mixes had to be designed with a sufficient amount of water to ensure workability. Nobody cared about properties such as permeability, diffusion and chemical reactions leading to deterioration. As admixtures were developed, so lower water/cement ratios became daily practice and higher strengths could be achieved. The discovery of silica fume as a reactive filler enabled the realization of concrete strengths up to C100, which was experienced as a sensation – and only 15 years ago. Self-compacting concrete and high-performance fibre concrete represented the next steps, which went hand in hand with a more careful study of the question as to why these mixes function and how we can replace empiricism by mix design methods based on knowledge about the interactions of the components. By virtue of the ongoing insight into aspects such as particle packing, optimizing the design of performance-based concrete became reality. In this respect, further leaps forward are expected in the forthcoming years.

We have also witnessed considerable advances in the design and analysis of concrete structures, in conjunction with remarkable changes in priority. In the eighties and early nineties of the last century, great effort was invested in developing viable models for structural safety and serviceability. Many current code rules go back to the work carried out in those days. A daring prognosis in that period was that durability of concrete structures would become a design issue of the same importance as structural safety and serviceability. Meanwhile, this is a matter of course: service life design is becoming the norm. In the early years of this century, major steps were taken to realize the international harmonization of building codes. Transparency and up-to-dateness of code rules were leading principles in this work. And, just a few years later, we have realized that the codes we have written focus on new structures only. Nowadays, we are confronted with an enormous legacy of existing structures, exhibiting different degrees of deterioration and exposed to loads larger than those for which they were initially designed. So the focus changes again, and new challenges beg serious consideration.

The Model Codes, published by CEB-FIP in the past and now by fib, testify very clearly to these changes in priority. The fib Model Code 2010, too, now brand-new, will in future only be seen as an intermediate landmark. Nevertheless, it will fulfil an important duty: the creation of a sound basis to facilitate new and nec-

Joost Walraven

György L. Balázs

© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Structural Concrete 14 (2013), No. 1

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Editorial

essary developments, which will help the engineers of the future in their responsibility towards meeting the demands of a changing society.

We see it as a privilege that we could work together with so many esteemed colleagues on the realization of fib Model Code 2010. It is a pleasure to announce a series of articles, starting in this issue, on various new aspects of the design and analysis of structural concrete as published in the latest Model Code.

Joost Walraven Convenor of fib SAG5 “New Model Code”

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Structural Concrete 14 (2013), No. 1

György L. Balázs President of fib 2011–12

Technical Paper Joost Walraven

DOI: 10.1002/suco.201200062

fib Model Code for Concrete Structures 2010: mastering challenges and encountering new ones The Model Code for Concrete Structures 2010 is a recommendation for the design of structural concrete, written with the intention of giving guidance for future codes. As such, the results of the newest research and development work are used to generate recommendations for structural concrete at the level of the latest state of the art. While carrying out this exercise, areas are inevitably found where information is insufficient, thus inviting further study. This paper begins with a brief introduction to the new expertise and ideas implemented in fib Model Code 2010, followed by a treatment of areas where knowledge appeared to be insufficient or even lacking and where further research might be useful.

cent years. During the preparation of fib MC 2010, new findings from research and application have been synthesized to form up-to-date design methods and new concepts in structural design. It is inevitable that during this process areas are found where information is incomplete or even missing, and where existing ideas seem to be conflicting. The following overview starts with a brief look at those areas in fib MC 2010 where progress has been made and innovations have been introduced. Subsequently, the overview turns to areas that can be seen as “white spots” that invite further investigation.

Keywords: concrete, structures, codes, recommendations, future developments, fib Model Code 2010

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Introduction

The fib Model Code for Concrete Structures is a set of recommendations for the design of reinforced and prestressed concrete which is intended to be a guiding document for future codes. Model Codes have been published earlier, in 1978 and 1990. A Model Code not only functions as a reference document for new codes, but also offers the latest state-of-the-art information about the various methods of design and analysis, in line with the real needs of society regarding the creation of an optimized living environment and infrastructure. When Model Code 1990 appeared, it focused primarily on structural safety and serviceability. An important new aspect in those days was the introduction of constitutive equations for concrete. This was inspired by the emergence of new, powerful non-linear finite element programs, which require preferably uniform input by users with regard to the relevant parameters. The maximum concrete strength class in MC 1990 was C80, which in those days was a significant step forward, but turns out meanwhile to be only a moderate step in the direction of the ultra-high-performance concretes we know today. fib Model Code 2010, the final draft of which appeared in 2012, not only presents updated methods of design and analysis, but also introduces new elements, the need for which has developed over reCorresponding author: jcwalraven@hotmail.com Submitted for review: 16 December 2012 Revised: 3 January 2013 Accepted for publication: 3 January 2013

New elements in fib Model Code 2010

Looking at fib Model Code 2010 [1], the final draft of which was edited in early 2012, we see quite a number of new aspects: – The most important new element in fib MC 2010 is the introduction of “time” as an important design criterion [2]. This not only applies to traditional concrete properties such as creep and shrinkage, but is aimed especially at design for service life. Whereas fib MC 1990 primarily focused on the design of concrete structures with sufficient safety and serviceability in the new state, the aim of fib MC 2010 is the design of concrete structures with sufficient safety and serviceability for a defined period of time after delivery. This means that the structure should be able to fulfil its function with low maintenance costs for the period specified, which in turn requires an adequate strategy to be adopted right from the design stage.

The structure of the code reflects this philosophy: the chapter on design is followed by chapters on construction, conservation and dismantlement. The approach in fib MC 2010 is considerably more analytical and mature than that of MC 1990, where only general statements were given.

– fib MC 2010 contains a chapter on conceptual design which provides many indications for realizing optimum design for given boundary conditions. Structures should not only be aesthetic in order to gain long-term acceptance; they should also be sustainable and be able to fulfil their duty without constraints for the period envisaged. Moreover, they should be robust and easy to maintain, fit well into their environment and respect local traditions (Fig. 1). Aspects such as adaptation, dismantlement and recycling should be considered at the

© 2013 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Structural Concrete 14 (2013), No. 1

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J. Walraven · fib Model Code for Concrete Structures 2010: mastering challenges and encountering new ones

Fig. 1. The Pantheon in Rome – an example of a structure that has survived for centuries

– Design principles for external reinforcement using fibrereinforced polymers (FRP) are given, respecting the upcoming need to strengthen an increasing number of existing structures to enable them to carry higher loads.

– fib MC 2010 deals with a wide scope of loads that can be relevant during the life of a structure. It treats the design of concrete structures under static, cyclic, impact and fatigue loads. Moreover, it deals with fire, seismic loads and imposed deformations in a harmonized way.

– fib MC 2010 gives principles for design by testing, not only based on the statistical analysis of series of tests on similar specimens, but also respecting the combination of short series of tests with numerical methods of analysis, including the reliability principles mentioned previously.

– fib MC 2010 specifies maintenance strategies as a part of the design for service life.

– A first introduction is given on the expected growing role of sustainability criteria in design. Only principles are given, based on the expectation that there will be considerable development in this field in forthcoming years, resulting in more specific methods.

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design stage, even if such aspects only become relevant far in the future. fib MC 2010 introduces – further to the partial safety factor format, which is generally used in daily practice now – the probabilistic safety format and the global resistance format. The probabilistic safety format is especially relevant to a new task in structural engineering which is very quickly gaining in importance: the assessment of the loadbearing capacity of existing structures which were designed to old codes but are now subjected to loads higher than those for which they were designed originally and are possibly in a state of developing or advanced deterioration. The global safety format should support the application of non-linear calculations, e.g. with finite elements, with defined reliability levels. fib MC 2010 offers methods of analysis with various “levels of approximation”. In this way a distinction is made between applications for daily use and applications that require a more accurate analysis because of, for instance, considerable financial consequences, see [3], for example.

A reliability concept is introduced for numerical calculations. Up to now, numerical calculations have been used with the input of personal choices for the basis of the calculation. In this way the results of the analysis, even carried out by experts, are to a certain degree subjective and can vary substantially. Therefore, authorities are often reluctant to accept the results obtained by this method since the reliability of the results is difficult to quantify. In fib MC 2010 a choice of methods is offered, which are linked to different levels of reliability.

A design method for steel fibre-reinforced concrete is given. This recognizes fibre reinforcement as a serious alternative or supplement to traditional reinforcing systems. The design method offered is valid over the full range between conventional fibre-reinforced concrete and ultra-high-performance concrete.

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Areas inviting further study Defined performance materials

In current codes, the properties of concrete are linked to its compressive strength. This is a very practical arrangement since cylinder or cube tests are carried out anyhow, and for most properties there is a reasonable correlation between compressive strength and properties such as creep, shrinkage, tensile strength, elastic modulus, coefficient of water permeability and diffusion coefficient. These relationships are valid for conventional concrete under certain restrictions such as the condition of a minimum cement content (e.g. 260–280 kg/m3). Recent years, however, have shown a considerable evolution with regard to designing concrete mixes. The knowledge about particle packing, fillers and admixtures has opened the door to a considerable spectrum of concretes with attractive properties. As an example, the development of low binder concretes is given. Research, e.g. that carried out by Fennis [4], has led to a method of designing low binder concretes with sufficient strength and workability based on packing density considerations, water demand and the so-called cement-space factor CSF (Fig. 2).

Concrete mixes with only 110 kg/m3 of cement showed a 28-day cylinder strength of 32 N/mm2. Shrinkage and creep tests showed lower values than obtained with conventional concretes of the same strength. Moreover, electric resistivity tests exhibited more favourable values, demonstrating that durability criteria are also satisfied. It is clear that for such innovative concretes, the link between properties and compressive strength is misleading and would prevent such mixes from being used. To give those mixes a chance, an appropriate system of testing not only strength, but also other properties should be devised. Mixes can be developed with particular properties, but should meanwhile meet other demands. The equivalent performance concept, as generally defined in the European standard EN 206-1, is promising but should be worked out further: the question is “equivalent to what?”, and how to demonstrate this by means of tests.

J. Walraven · fib Model Code for Concrete Structures 2010: mastering challenges and encountering new ones

packing

t en tm

φ

jus ad

mi / x α

t

re xtu Mi

water

CSF

strength

Fig. 2. Design procedure for developing low binder concrete based on packing density, water demand and cement-space factor ([4])

3.2

Creep of concrete bridges

The creep functions in section 5.1 “Materials” in fib MC 2010 have been upgraded to reflect the most recent state of the art. Nevertheless, it was claimed that those relationships would not be satisfactory because long-term deflection measurements on a substantial number of long-span concrete bridges showed that the measured deflections can reach values about twice as large as those calculated. An interesting discussion on this topic at the fib conference in Prague in 2011 showed that there are quite different points of view with regard to the reason for this difference. Prof.

Bazant (see [5], for example) argued that the creep expressions in fib MC 2010 were not correct, and proposed his own B3 model as an improvement. Others, however, disagreed on the statement that the formulation of the creep function is the reason for the difference between calculated and measured deflections. Several other potential reasons were suggested, such as the role of cracking in the stiffness, insufficient regard for the construction history and the underestimation of temperature effects. Another aspect mentioned was the definition of the notional size of the member assumed as Ac/u, where Ac is the cross-sectional area in mm2 and u is the perimeter of the member in contact with the atmosphere in mm. It should be noted that in a bridge built as a cantilever system, the lower flange of the cross-section at the central support often has a thickness of about 1 m, whereas the notional size factor has been verified on prismatic specimens with a cross-section no larger than 300 × 300 mm. A small error in the estimation of the creep of the concrete in this lower flange could have a large influence on the mid-span deflection because of the “multiplier” 0.5 l/h, where l is the span and h the depth of the cross-section at the support. Anyhow, this question invites further investigation.

3.3

Role of maximum allowable crack width for durability

Throughout history there have been many discussions with regard to the question of which is the most appropriate crack width calculation model. However, it should be noted that in design, calculated crack widths are com-

Fig. 3. Storm surge barrier, Hook of Holland, The Netherlands, giving rise to interesting discussions on crack width control

pared with limit values in tables, the origins of which are somewhat vague. The maximum crack width values are formulated depending on the exposure class and the type of steel used (reinforcing or prestressing steel). Also, the definition of the load for which the maximum crack width should be calculated differs: some codes use the maximum service load, whereas other codes use the frequent load combination. All tabulated maximum crack width values are < 0.4 mm, whereas Schiessl [6], as long ago as 1986, demonstrated that crack widths < 0.4 mm are harmless as long as the thickness and quality of the concrete cover meet certain standards. Nowadays, new questions arise, associated with increased traffic loads on old bridges: e.g. “Is it acceptable if the crack width in a bridge under traffic load occasionally reaches a value of 0.5 mm?” Another interesting question was raised in relation to the crack width control in the storm surge barrier at the Hook of Holland in The Netherlands. The maximum crack width specified was 0.2 mm at maximum service load. The maximum service load is, however, only reached if the barrier is closed, which is expected to be once in 10 years, and for only a few days. In such a situation (see Fig. 3), the pressure of the high external water level is transmitted through the 237 m long steel trusses to two concrete foundation structures (length 30 m) through which this force is transferred into the soil. When the barrier is open, which is about 99.9 % of the time, the service load is zero. Therefore, the logical question asked was: Could, under this maximum service load, the maximum allowable crack width in the foundation structures be increased to a value of, for example, 0.6 mm because no large deterioration is expected to occur in the short period when the cracks are open? This would save a considerable amount of reinforcing steel. The answer from the experts in this particular case was that increasing the crack width to 0.6 mm would lead to significant microcracking in the concrete cover, which could impair the durability.

Anyhow, a sound basis for the definition of the maximum values of the allowable crack width, based on good arguments and test results, would be most welcome.

3.4

Shear capacity of solid slabs

Shear has been a topic of discussion for many decades already. As an estimation, about 8000–10 000 shear tests

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J. Walraven · fib Model Code for Concrete Structures 2010: mastering challenges and encountering new ones

have been carried out in the meantime. Nowadays, the shear capacity of solid slab bridges is under discussion, as a result of the increased traffic loads for which bridges were not designed originally. It turned out that despite the large number of tests mentioned, the answers required for the determination of the shear bearing capacity of solid slabs with large wheel loads near to line supports could not be found. Therefore, tests were carried out recently and these have formed the basis for a design recommendation introduced in fib MC 2010 (section 7.3.3.1), including an expression for the spreading of the load to the support and a multiplication factor to consider the positive effect of direct load transfer. Another remarkable observation is that the expressions for the shear bearing capacity of a slab have always been derived on the basis of tests on beams without shear links, assuming that slabs and beams behave similarly. However, slabs may be expected to have a better residual capacity since weak spots are compensated for by stronger areas and can carry the loads via an alternative loadbearing path. Special tests were recently carried out at TU Delft: solid slabs were tested which were intentionally weakened by strips with a much lower concrete strength than the basic concrete, Fig. 4. The slabs with a length of 4200 mm were supported on line supports at their ends and subjected to line loads at distances of 2.2d and 3.0d from the support.

The weak strips had no significant influence on the loadbearing capacity: the shear resistance agreed well with the resistance calculated using the mean concrete compressive strength. Another remarkable further observation was, however, that the shear capacity of the slabs tended to be significantly higher than that of comparable beams.

A higher mean value for the shear capacity of slabs in combination with a lower range of scatter of the results could lead to the introduction of a “slab factor” > 1.0, which would work out favourably for the assessment of existing slab bridges. This possibility should be investigated further.

Many old structures were reinforced with plain steel bars with a relatively low characteristic yield value (220–240 N/mm2). When the shear resistance of old bridges has to be assessed, the question comes up as to

Fig. 4. Geometry of a slab composed of high- and low-strength concrete strips 6

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whether the shear resistance of slabs reinforced with plain steel is reduced by the lower bond strength in comparison to ribbed steel. In this respect, very interesting tests were carried out by Leonhardt way back in the early 1960s [7].

His tests showed, surprisingly, that the shear capacity of beams reinforced with plain bars was substantially larger than that of similar beams with ribbed bars. This led to an interesting discussion about this phenomenon [8] that was denied by some authors, including even Leonhard himself!

A decade later, M. W. Kani [9] carried out shear tests on beams with reinforcement, the bond properties of which were reduced stepwise. Those tests clearly demonstrated the increasing effect of lowering the bond on the shear capacity. This effect can be explained by the fact that inclined cracks cannot occur if the reinforcement is smooth.

Current expressions do not take account of this effect, which is important for bridge assessment. Moreover, no shear tests are known on members with staggered plain reinforcement. In old structures with staggered plain bars, those bars often terminate in hooks, whose effect on the shear capacity is not known.

3.5

The effect of compressive membrane action on bending and shear capacity

An effect that is still generally ignored in design is compressive membrane action in slabs. Although this effect was demonstrated by Ockleston as long ago as 1955 [10], who tested the capacity of inner slabs in a large floor system of an old hospital that was about to be demolished, it has scarcely been introduced in codes. Fig. 5 shows the principle of compressive membrane action [11]. The slab (Fig. 5, left) is loaded by a concentrated load at mid-span.

This results in cracks under the load and at the supports.

If the steel in those cracks yields, a kinematic mechanism forms. At the support, the lower part of the slab cannot move horizontally because of the confinement by the adjacent part of the slab; this leads to the development of compression membrane action that substantially increases both the bending capacity and the punching shear capacity. In situ tests were carried out by Taylor et al. [12] on a bridge deck subjected to a concentrated wheel load. The

J. Walraven · fib Model Code for Concrete Structures 2010: mastering challenges and encountering new ones

Fig. 5. Principle of compressive membrane action [11]

160 mm thick deck was supported by prestressed beams spaced at 1500 mm c/c. Depending on the position of the concentrated load, the measured loadbearing capacity was a factor 1.6–5.2 times larger than the load predicted on the basis of the unconfined situation. The increase in the load due to compressive membrane action depends on the confining action of the adjacent part of the structure. At this moment, tests are being carried out at TU Delft on a 1:2 size model of a bridge deck in order to verify the effect of compressive membrane action on the loadbearing capacity. This bridge deck consists of prestressed beams with thin concrete slabs cast in between and connected by transverse prestressing. The concentrated load will be applied at various positions of the deck in order to quantify the effect of compressive membrane action on the capacity of this bridge prototype, representing 69 bridges in The Netherlands. The tests are being carried out in order to verify whether those decks should be strengthened or have a sufficient loadbearing capacity. General rules with regard to this phenomenon are of great importance for decision-making when it comes to strengthening existing structures.

3.6

Further development of the design recommendations for fibre-reinforced concrete

The provisions for the design of fibre-reinforced structures given in fib MC 2010 are a step forward in various respects. The recommendations are valid for the whole range between conventional fibre-reinforced concrete (FRC), with moderate strength and relatively low volumes of coarse fibres, to ultra-high-performance FRC, with a very high strength (180–200 N/mm2) and high volumes of fine steel fibres. Moreover, a classification of FRC has been introduced with regard to its mechanical properties. This means that design relationships can be assumed in advance for carrying out the design, which are verified later by tests on control specimens. Through this arrangement, the design of FRC basically follows the same pattern as the design of reinforced concrete, where the concrete strength class is chosen in advance and verified by cylinder or cube tests at a later stage. An objection that is sometimes raised against such a harmonized approach – valid for all types of FRC – is that it may be too conservative for

special FRC mixtures such as ultra-high-strength FRC. It might therefore be worthwhile comparing the results of the harmonized approach according to fib MC 2010 with those of tailor-made approaches in order to see if it makes sense to distinguish different levels of approximation, as introduced elsewhere in fib MC 2010. Another aspect that should be considered is the way in which the properties of FRC are tested. In order to determine the mechanical properties of FRC, in most cases a series of small control beams is subjected to a load at mid-span (RILEM test).

The stress-crack opening relationship is then derived from this series by inverse analysis. The tests show mostly a considerable scatter in load-deflection relations. This scatter, which is reflected as well by the stress-crack opening relationship and as a consequence affects the design stress-strain relation derived afterwards, is rather a property of the test series than it is representative of the behaviour of FRC in a structure. This should be given serious consideration. One possibility is to determine as accurately as possible the mean stress-crack opening relationship from tests with low variability, such as a bending test on a circular panel on three point supports (Fig. 6), where the scatter is small because of the compensating effect of the three yield lines, and combine the stress-crack opening or stress-strain relations obtained in this way with the scatter to be expected in the real structure. In a structure the scatter decreases as the cracked area involved in the loadbearing mechanism increases. General rules could be derived here.

3.7

Reliability of non-linear finite element calculations

As mentioned before, fib MC 2010 offers various strategies for introducing reliability into numerical calculations.

Three principles are given. The most practical strategy lies between the extremes of the “probabilistic method” and the “partial factor method” and is known as the “global resistance method”, and under this heading the “method of estimation of a coefficient of variation of resistance”. This method can be seen as a compromise between accuracy and practical applicability. Further case studies to optimize this method would be worthwhile. It is a step in the direction of tailor-made NLFEM analyses with the highest possible reliability.

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J. Walraven 路 fib Model Code for Concrete Structures 2010: mastering challenges and encountering new ones

Fig. 6. Bending test on 3 fibre-reinforced concrete circular slabs supported at three points [13]

3.8

Verification of limit states associated with durability

Since structural safety is expressed in terms of reliability, which should be maintained over the full service life of a structure, it is logical that reliability considerations enter the limit state conditions with regard to durability. A limit state of durability is reached when a specified criterion for a certain type of deterioration is reached. For chloride penetration and carbonation these criteria can be reasonably well specified. For other deterioration mechanisms, e.g. freeze/thaw attack, sulphate attack, alkali aggregate reaction and delayed ettringite formation, the deterioration mechanisms, and as such the limit state criteria, are less well defined. For a better specification of those criteria, an investigation of older structures with regard to their state of deterioration might be very instructive. Older structures offer an excellent opportunity to calibrate the results of theoretical deterioration models!

3.9

Introducing a sound basis for making decisions with regard to sustainability

When the draft version of fib MC 2010 was published and experts were invited to comment on it, several people wondered whether sustainability should really be a part of a modern code on structural concrete. This doubt was certainly stimulated by the circumstance that the recommendations given in the area of sustainability were quite general, which was partly due to the early stage of development of sustainability models. Actually, however, preliminary sustainability qualification models are already

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used in various countries in the process of tendering for new projects. It is therefore important that criteria in relation to concrete are introduced in an appropriate way in order to quantify the level of sustainability of designs for new concrete structures. Providing sets of suitable criteria can be a stimulus for the introduction of high-performance materials, as shown by Voo and Foster, Fig. 7 [14].

They compared a bridge in conventional concrete with an alternative in ultra-high-performance concrete (UHPC) with regard to sustainability, using the necessary volume of material, the embodied energy, the CO2 emission and the 100-year global warming potential (GWP). Remarkably, this comparison was definitely in favour of the UHPC solution, whereas a comparison on the basis of 1 m3 of

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Fig. 7. Comparison of a conventional bridge with an alternative in UHPC on the basis of sustainability criteria according to Voo and Foster [14]

J. Walraven · fib Model Code for Concrete Structures 2010: mastering challenges and encountering new ones

– During the work on fib MC 2010, a number of areas were found where consistent information was lacking, or no mature ideas had been developed at all.

– The exercise of writing a new Model Code made sure that structural engineering is an area that is still showing significant evolution.

References

Fig. 8. Part of a demountable office building in Delft, The Netherlands

Fig. 9. Priority of dismantlement for optimum flexibility

such concretes would erroneously give preference to the conventional material.

3.10 Dismantlement The chapter entitled “Dismantlement” in fib MC 2010 is relatively short. It marks the end of service life of a concrete structure and for that reason alone its implementation is justified in a document that tends to stimulate design for service life. The chapter could just as well have been called “Demolition”, but the term “Dismantlement” was preferred since it suggests a controlled process, which encourages designers to think about the end of service life right from an early stage of design. It is hoped that this might inspire the development of concepts for demountable and adaptable structures (Figs. 8 and 9). For further development, cooperation between structural engineers and architects might be fruitful.

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1. Model Code 2010, vols. 1 & 2, final draft, fib – Bulletins 65 & 55, fib, Lausanne, www.fib-international.org 2. Walraven, J. C., Bigaj, A. J., The 2010 fib Model Code for Concrete Structures: a new approach to structural engineering. Structural Concrete, Vol. 12, Nr. 3, pp. 139–147.

3. Muttoni, A., Fernández Ruiz, M., The levels-of-approximation approach in MC 2010: application to punching shear provisions. Structural Concrete 13 (2012), No. 1, pp. 32–41.

4. Fennis, S.: Design of Ecological Concrete by Particle Packing Optimization. PhD thesis, Delft University of Technology, 2011.

5. Bazant, Z. P., Hubler, M. H., Yu, Q.: Pervasiveness of Excessive Segmental Bridge Deflections: Wake-Up Call for Creep.

ACI Structural Journal, Nov–Dec 2011, pp. 766–774.

6. Schiessl, P.: Influence of cracks on the durability of reinforced and prestressed concrete members. Deutscher Ausschuss für Stahlbeton, No. 370, Beuth Verlag, Berlin, 1986 (in German).

7. Leonhardt, F., Walther, R.: Shear tests on simply supported reinforced concrete beams with and without shear reinforcement for the determination of the shear resistance and the upper limit of the shear stress. Deutscher Ausschuss für Stahlbeton, No. 151, Ernst & Sohn, Berlin, 1962 (in German).

8. Discussion of the paper by Kani, G. N. J.: The Riddle of Shear Failure and Its Solution. Journal of the ACI, Dec 1964, pp. 1587–1637 9. Kani, M. W., Huggins, M. W., Wittkopp, R. R.: Kani on Shear in Reinforced Concrete. University of Toronto, Department of Civil Engineering, 1979, 225 pp.

10. Ockleston, A. J.: Load tests on a three-storey reinforced concrete building in Johannesburg. The Structural Engineer, vol.

33, 1955, pp. 304–322.

11. Long, A. E., Basheer, P. A. M., Taylor, S. E., Rankin, B., Kirkpatrick, J.: Sustainable Bridge Construction Through Innovative Advances. Proc. of ICE Bridge Engineering, vol. 161, No. 4, Dec 2008, pp. 183–188.

12. Tailor, S. E., Rankin, B., Cleland, D. J., Kirkpatrick, J.: Serviceability of Bridge Deck Slabs with Arching Action. ACI Journal, Jan-Feb 2007, pp. 39–48.

13. Yang, Y.: Mechanical properties of steel fibre reinforced concrete tested by statically determinate round panel tests. Internal report, TU Delft, Section of Concrete Structures, 2008.

14. Voo, Y. L., Foster, S. J.: Characteristics of ultra-high performance ductile concrete and its impact on sustainable construction. IES Journal, Part A, Civil & Structural Engineering, vol. 3, No. 3, Aug 2010, pp. 168–187.

Conclusions

– fib MC 2010 offers modernized design recommendations for many aspects of the design and analysis of concrete structures.

– fib MC 2010 not only treats aspects of design and analysis, but also offers a more general philosophy, based on service life design.

Joost Walraven Delft University of Technology Faculty of Civil Engineering Section GCT PO Box 5048 2600 GA Delft, The Netherlands j.c.walraven@tudelft.nl

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Technical Paper Steinar Helland

DOI: 10.1002/suco.201200021

Design for service life: implementation of fib Model Code 2010 rules in the operational code ISO 16204 CEB/FIP Model Code 1990 (MC-1990) [1] did represent the technology and focus some 20 years ago. However, it soon became evident that the document had some notable lacunas. In 1995 the general assemblies of the two organizations endorsed CEB/FIP bulletin No. 228 [2], extensions to MC 1990 for high-strength concrete, and in 2000 a similar extension to MC 1990 for lightweight aggregate concrete as bulletin No. 4 [3].

The fib approved bulletin No. 34 Model Code for Service Life Design (MC SLD) [4] in 2006. All these three additions have since matured and are now incorporated in the new fib Model Code for Concrete Structures 2010 (MC-2010) [5, 6, 7].

The main purpose of an fib Model Code is to act as a model for operational standards. The obvious counterpart for a body such as fib operating worldwide is ISO. The initiative taken by MC SLD has therefore further matured in ISO TC-71/SC-3/WG-4 and it was accepted as ISO 16204 “Durability – Service Life Design of Concrete Structures” [8] during the summer of 2012.

According to the obligations given in the WTO Agreement on Technical Barriers to Trade [9], it is hoped that these principles will be further implemented in national and regional standards.

This article describes the need for a transparent methodology when dealing with service life design, and the process – originating from a group of enthusiasts one decade ago – through fib and finally reaching international consensus in ISO. Keywords: fib Model Code 2010, ISO 16204, service life design

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Background

Durability of concrete structures, and in particular the lack of such, has been in the focus of society in general over the last few decades. Excessive repair needs have challenged our industry.

The traditional approach in most national and regional concrete standards is to specify the provisions to ensure a certain design service life by limiting values for material composition and geometry based on the expert opinion of the code committee.

There are several weaknesses in this approach: – It is often unclear as to which condition represents the end of the service life.

– The required level of reliability for the design is often unclear as well.

– The criteria should be based on long-term field experience. Such experience is, however, not normally available for modern materials and design concepts, and concepts with service records > 50 years are seldom in use any more.

In 1998 a group of 19 European enthusiasts, all of us with a long record within CEB and FIP, signed a contract with the European Commission to develop a platform for durability design of concrete structures that contained the same elements and philosophy as that of modern structural design. This European network was named “Duranet”, and the contract lasted until 2001.

At DuraNet’s final workshop in Tromsø, Norway, in 2001, attendees from Europe and North America worked out a plan for how to progress to get this methodology standardized and implemented in the industry worldwide (Fig. 1). The obvious environment for this was ISO. Some of us therefore met at the ISO TC-71 meeting in Norway that autumn and presented our visions. TC-71, responsible for concrete-related standardization within ISO, endorsed the initiative, but quite correctly made us aware of the fact that ISO normally starts its work on the basis of existing documents. We therefore agreed to ask the International Federation for Structural Concrete, fib (formed by the merger of CEB and FIP) to work out such a model for a standard.

Corresponding author: steinar.helland@skanska.no Submitted for review: 03 August 2012 Revised: 23 August 2012 Accepted for publication: 23 August 2012

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Fig. 1. The “Duranet” workshop in Tromsø, 2001, which came up with a roadmap for how to implement limit state and reliability-based service life design in standards.

© 2013 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Structural Concrete 14 (2013), No. 1

S. Helland · Design for service life: implementation of fib Model Code 2010 rules in the operational code ISO 16204

Table 1. Comparison of some European durability requirements to ensure 50 years design service life (from [12])

Range of XC3 provisions for CEM I in Europe

UK → w/c < 0.55 and 25 mm minimum cover

Germany → w/c < 0.65 and 20 mm minimum cover

Range of XC4 provisions for CEM I in Europe

Netherlands → w/c < 0.50 and 25 mm minimum cover

Germany → w/c < 0.60 and 25 mm minimum cover

Range of XS2 provisions for CEM I in Europe

UK → w/c < 0.50 and 35 mm minimum cover

Norway → w/c < 0.40 and 40 mm minimum cover

Thereupon, fib set up Task Group 5.6 with experts from Europe, North and South America and Japan. In 2006 fib “Model Code for Service Life Design” (bulletin No. 34) was endorsed by the fib’s General Assembly in Naples, Italy. fib TG 5.6 was headed by Prof. Peter Schiessl from Germany. The other members were Gehlen (DE), Baroghel-Bouny (FR), Bamforth (UK), Corley (US) (present chair of ISO TC-71), Faber (DK), Helene (BR), Ishida (JP), Markeset (NO), Nilsson (SE), Rostam (DK) and Helland (NO).

The group decided early on to produce a document fully parallel with ISO 2394 “General principles on reliability for structures” [10]. This standard today forms the reference for fib MC-2010 and most modern standards for structural design. ISO 2394 is also the “parent document” for the European Eurocode 0 “Basis of structural design” (EN 1990) [11]. fib based its approach on a limit state (LS) and reliability-based concept. This approach recognizes that the nature of the deterioration of concrete structures over time must be treated in a statistical way. This is due to the natural spread in material characteristics and also to the spread in the mesoclimatic and microclimatic conditions a concrete structure is exposed to.

Since 2006 this initiative has progressed in close cooperation between fib’s group working on fib MC-2010, Special Activity Group No. 5 (SAG-5) and ISO TC-71/SC3/WG-4. fib MC-2010, including its elements for service life design, is currently being finalized. ISO 16204 “Durability – Service life design of concrete structures” achieved a positive international vote in summer 2012. These two documents are today – except for the cover and references – close to being identical when it comes to service life design.

2

How service life design is handled in most standards today

Provisions to ensure sufficient durability are today normally embedded in the concrete standards. In Europe durability is still regarded as coming under national authority and its provisions are expected to be given in a national annex to the European standard. In CEN TR 15868 [12], Tom Harrison has compared how the 31 European countries cooperating in CEN have solved the request in EN 1992/EN 13670/EN 206-1 [13, 14, 15] to give national provisions for a service life of 50 years based on requirements mainly linked to maximum w/c ratio, minimum cover to the reinforcement and cement type.

The spread of requirements for structures expected to be subject to similar conditions is striking. Some exam-

ples for exposure classes XC3 (exposed to carbonation – sheltered from rain), XC4 (exposed to carbonation – exposed to rain) and XS2 (submerged in sea water) for 50 years design service life are given in Table 1.

The differences in actual performance for these extremes are very large. Comparisons of durability-related provisions from other parts of the world demonstrate a similar spread.

Bearing in mind that the technical expertise on these matters is more or less at the same level in these countries, the explanation must be that the different national standardization bodies have different understandings of what actually represents the “end of service life” as well as the intended level of reliability.

3

Limit state concept for service life design

The limit state concept recognizes the need to be specific about what condition represents the “end of service life”.

The application of reliability-based and LS-based service life design is specifically excluded from both ISO 2394 and EN 1990. The task for fib TG 5.6 was therefore to come up with the amendments needed in these reference documents.

At first sight these ideas might be considered as revolutionary, but actually that is not true. All code writers in the past must have had some idea of what they considered to be the “end of service life” when they came up with their provisions. They must have known whether they were considering just rust stains or full structural collapse. They then applied a “limit state” concept. They must also have had in mind whether they expected the statistical average of the building population to stand this design service life length, or whether they expected the great majority of the population to meet this requirement.

They then applied a probabilistic approach. However, it is fair to say that these processes are very seldom applied in a transparent way.

ISO 2394 defines the serviceability limit state as “a state which corresponds to conditions beyond which specified service requirements for a structure or structural element are no longer met”. fib MC SLD, fib MC-2010 and ISO 16204 apply the same definition, but fib MC-2010 has a further group “Limit states associated with durability” as a separate category. In principle, this may be any condition that makes the building owner feel uncomfortable.

For concrete structures, corrosion of the reinforcement is often the critical deterioration process. The LS could then be depassivation, cracking, spalling or collapse (ultimate LS). Due to the problem of developing reliable time-dependent models for the rate of corrosion (after depassiva-

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Level of reliability – consequences of failure

fib MC SLD, fib MC-2010, EN 1990 and ISO 2394 all suggest a three-level differentiation of the consequences upon passing an LS: a) risk to life low, economic, social and environmental consequences small or negligible b) risk to life medium, economic, social and environmental consequences considerable c) risk to life high, economic, social and environmental consequences very great Based on the relevant consequence class, combined with a consideration of the cost of safety measures, a relevant level of reliability for not passing the LS during the design service life should be selected.

Within the limitations normally found in national building legislation, the reliability level used in the design should be agreed with the owner of the structure. fib and ISO suggest a probability of failure pf = 10–1 for depassivation of reinforcement (by carbonation or ingress of chlorides) in cases where the presence of oxygen and moisture makes corrosion possible. If collapse is the LS considered, pf = 10–4 to 10–6 may, as for traditional structural design, be the relevant level if the possible consequences are in classes b) and c).

Deterioration ((corrosion)

4

Collapse of structure pf ≈ 10 -4- 10 -6

20

15

Spalling

10

Formation of cracks Depassivation pf ≈ 10 -1

5

0 0

5

10

15

20

25

30

35

Time

Fig. 2. Various limit states and related reliability levels shown for corrosion of reinforcement

100

C 50% cumulative failure (%)

tion), LS depassivation is the choice of convenience for most engineers.

75

B 30%

50

A 2%

25

10%

0

5

End of service life

0

50

100

150

years

Based on the above, a main element in the fib and ISO documents is therefore an amended quantitative definition to the qualitative one we find in traditional standards such as the ones in ISO 2394 or EN 1990: Traditional qualitative definition: The design service life is the assumed period for which a structure or part of it is to be used for its intended purpose with anticipated maintenance but without major repair being necessary.

Quantitative amendment by fib and ISO: The design service life is defined by: – A definition of the relevant LS – A number of years – A level of reliability for not passing the LS during this period Fig. 2 indicates how various limit states may be associated with corresponding levels of reliabilities for not passing the LS within the design service life in the case where corrosion of reinforcement is the critical case.

In principle, the verification of the design has to demonstrate that the structure will satisfy all combinations of LS and pf. For practical design, however, we do not have time-dependent models with international consensus to predict the corrosion phase after depassivation.

The calculation therefore often has to be based on the time up to depassivation. The corresponding pf must then be sufficiently low to ensure that this LS results in equal or stricter requirements for material and depth of cover than the other combinations.

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Fig. 3. Time until depassivation of surface reinforcement (example derived from [16]). The Norwegian Standardization body applied a 10 % acceptance for depassivation as a criterion when determining its durability provisions, whereas countries A, B and C applied 2, 30 and 50 % respectively.

When considering the effect of corrosion of the reinforcement after its depassivation, splitting stresses in the cover zone from the reinforcement due to the effects of other mechanical actions/loads should also be considered. Wherever there are bond stresses in the reinforcement there are also “bursting stresses” in the concrete of the same nature as those from the expanding corrosion product, ultimately leading to the same type of cracking and spalling of the cover.

This is another argument for avoiding the minefields of using cracking and spalling as the LS for service life deign.

If we are pursuing the example of depassivation due to carbonation, all the characteristics that determine when the individual reinforcing bars will depassivate in a structure will have a statistical spread. This includes the actual depth of cover, the microclimatic conditions, the humidity of the concrete, its curing, etc. As a result, the initiation period will also exhibit a statistical spread.

Fig. 3, derived from Bamforth [16], indicates the accumulative time for depassivation of the surface rebars in a structure subjected to carbonation. To assess the actual service life of this structure, the depassivation LS has to be

S. Helland · Design for service life: implementation of fib Model Code 2010 rules in the operational code ISO 16204

cumulative e failure (%)

100

6

75

50

25

0 0

50

100

150

years Fig. 4. The same example as in Fig. 3, but with10 years of active corrosion added to reach cracking and spalling of the rebar cover. The limit state at 50 % probability for depassivation then implicitly results in an approx. 35% probability of failure for the limit state of cracking and spalling.

matched with a level of reliability. In fib Commission 5, TG.5.11, we are presently developing supporting documents to fib MC-2010/ISO 16204. The work has revealed that Norway applied a pf of 10–1 when working out its present deemed-to-satisfy requirement. In this case a service life of 70 years is reached. However, representatives from three other European countries stated that experts in their standardization bodies had in mind a pf of 2*10–2, 3*10–1 and 5*10–1 (2, 30 and 50 % respectively). This then gives a range of nominal service lives from 50 to 109 years for the same structure exposed to the same environment.

This lack of consistent use of the reliability-based limit state concept is probably a main reason for the aforementioned major differences in durability provisions among the European standards. The present lack of transparency must also be very confusing for the stakeholders when service life design is discussed.

In Fig. 4 I have included an assumption often used of 10 years active corrosion until cracking and spalling occurs. In this case the nation accepting a 50 % probability for depassivation implicitly also accepts an approx. 35 % probability of cracking and spalling.

Although it might be easy for a client to accept a high probability for passing an undramatic event such as depassivation during the design service life, it will be much harder to accept excessive cracking and spalling. The implicit consequences of linking an excessively high probability of failure for depassivation should therefore be clearly communicated.

What is the appropriate length of a design service life?

ISO 2394 gives guidance on the appropriate choice of the length of the design service life (Table 2).

The same guidance is referred to in the European standard EN 1990 and in practice dominates the application in many parts of the world. However, the table provides general guidance for all structural materials and should be used with utmost care for concrete structures.

This is particularly the case for class 3 comprising “buildings”. This is a very diverse group. Some buildings, e.g. factories, will often have an economic service life corresponding to the installed machinery. On the other hand, structural parts of residential buildings will, in general society, normally have an expected service life of much more than the 50 years indicated in the table.

ISO 16204 therefore strongly advises users to be more ambitions for at least those structural parts of a concrete building where repairing or replacing elements will be complicated and expensive.

7

Design of service life and its verification

“The design of a structure includes all activities needed to develop a suitable solution, taking due account of functional, environmental and economical requirements.” (definition in fib MC-2010) This implies that the flow of activities for service life design will follow the flowchart given in Fig. 5.

A similar graph is given in fib MC SLD and in text form in fib MC-2010.

The serviceability (performance) criteria have to be agreed with the owner within boundaries given in the legislation.

The documents are not specific regarding how the designer comes up with a general layout, dimensions and materials. However, the verification of the proposed design is strictly regulated. The fib and ISO documents offer four formats for verifying the service life design: The full probabilistic method: The time to reach the LS with the required level of reliability is calculated based on statistical data for the environmental load and structural resistance.

The partial factor method: As for the full probabilistic method, but the statistical data for load and resistance are substituted by characteristic values and partial coefficients.

Table 2. ISO 2394, Table 1 [10], gives examples of design service lives. The same table is given as guidance in EN 1990 [11]. ISO 16204 [8] states that class 3 should be used with care for structural parts of buildings where repair is complicated or expensive.

Class

Notional design working life

Examples

1 2 3 4

1 to 5 25 50 100 or more

Temporary structures Replacement structural parts, e.g. gantry girders, bearings Buildings and other structures, other than those listed below Monumental buildings and other special or important structures, large bridges

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S. Helland · Design for service life: implementation of fib Model Code 2010 rules in the operational code ISO 16204

Fig. 5. Flowchart for service life design (from [8])

The deemed-to-satisfy method: A set of requirements (normally w/c, cover to the reinforcement, crack width, air entrainment, etc.) that are prequalified by the code committee to satisfy the design criteria.

The avoidance-of-deterioration method: This method implies that the deterioration process will not take place due to, for instance: separation of load and structure by, for example, cladding or membrane, using non-reactive materials, suppressing the reaction with electrochemical methods, etc.

The fifth format offered by fib MC-2010 for verifying the structural capacity, the “global resistance”, is not mobilized for service life design.

The partial factor and deemed-to-satisfy methods both need to be calibrated, either by the full-probabilistic method or on the basis of long-term experience of building traditions.

Of these four options, the full probabilistic method is obviously the most complicated and sophisticated. For this reason, many academics have regarded it as the most prestigious and precise one. This is fundamentally wrong.

Due to the normal lack of good and representative data, and uncertainty in modelling, the full probabilistic method will seldom be feasible for the design of new structures; however, the method is well suited to assess the remaining service life of existing structures where data might be derived from the actual structure.

By assessing the remaining service life of existing structures by means of the full-probabilistic method, we al-

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Structural Concrete 14 (2013), No. 1

so have a powerful tool for verifying deemed-to-satisfy provisions for the design of new structures with similar exposure and design conditions.

The partial factor method is a semi-probabilistic approach where the calculation is deterministic and the statistical spread of the input parameters is taken care of by partial factors. The calibration of these partial factors for service life design for general use is very challenging, and its practical application is therefore not envisioned in the near future.

Both MC-2010 and ISO 16204 assume that the deemed-to-satisfy and avoidance-of-deterioration methods will continue to dominate the practical service life design of new structures in the future, but the provisions for the former will be linked to a specific LS and reliability. These two methods should be further verified by the code committee and communicated to the stakeholders.

8 8.1

Modelling General

We need models describing the deterioration process over time in order to be able to apply the full probabilistic and partial factor methods. There are not too many of models in our field which enjoy general international consensus.

In fib MC SLD, fib MC-2010 and ISO 16204 we have dared to suggest Fick’s 2nd law, modified by a time-dependent diffusion coefficient, for the ingress of chlorides, and the traditional square-root-of-time model for carbonation.

These two models, as described and explained in the three documents, are described in sections 8.2 and 8.3.

S. Helland · Design for service life: implementation of fib Model Code 2010 rules in the operational code ISO 16204

However, the documents are also open for the use of other models provided they are sufficiently validated through full-scale experience.

8.2

Carbonation

The ingress of the carbonation front might be assumed to obey the following equation: xc(t) = W · k √ ⎯t

(1)

where k is a factor reflecting the basic resistance of the chosen concrete mix (such as w/c ratio, cement type, additives) under reference conditions and the influence of the basic environmental conditions (such as mean relative humidity and CO2 concentration) against ingress of carbonation. It also reflects the influence of the execution.

W takes into account the varying mesoclimatic conditions for the specific concrete member during the design service life, such as humidity and temperature.

For the design of a new structure, the factors W and k might be derived from published data or existing structures where the concrete composition, execution and exposure conditions are similar to those expected for the new structure.

When assessing the remaining service life of an existing structure, the product of W and k might be derived directly from measurements on the structure.

8.3

α

Chloride ingress

The ingress of chlorides in a marine environment may be assumed to obey the following equation: ⎤ ⎡ x C(x, t) = C s − (C s − C i ) ⋅ ⎢erf ( )⎥ ⎢ 2 ⋅ Dapp(t) ⋅ t ⎥ ⎦ ⎣

(2)

In this modified Fick’s 2nd law of diffusion, the factors are: C(x,t) chlorides content in the concrete at depth x (structure surface: x = 0 mm) and time t [% by wt./binder content] Cs chlorides content at the concrete surface [% by wt./binder content] Ci initial chlorides content of concrete [% by wt./binder content] x depth with a corresponding chlorides content C(x,t) [mm] Dapp(t) apparent coefficient of chloride diffusion through concrete [mm2/year] at time t, see Eq. (3) t time of exposure [years] erf error function ⎛t ⎞ Dapp(t) = Dapp(t0 ) ⎜ 0 ⎟ ⎝t⎠ where: Dapp (t0)

α

(3)

apparent diffusion coefficient measured at a reference time t0

ageing factor giving the decrease over time of the apparent diffusion coefficient – depending on type of binder and micro-environmental conditions, the aging factor is likely to lie between 0.2 and 0.8

The “apparent” diffusion coefficient after a period t of exposure to chlorides Dapp(t) represents a constant equivalent diffusion coefficient giving a similar chloride profile as the measured one for a structure exposed to the chloride environment over a period t.

The decrease in the apparent diffusion coefficient is due to several reasons: – Ongoing reactions of the binder – Influence of reduced capillary suction of water in the surface zone over time – Degree of saturation of concrete – Effect of penetrated chlorides from seawater or de-icing salts (leading to ion exchange with subsequent blocking of pores in the surface layer) For the design of a new structure, the parameters Cs, Ci, α and Dapp (t0) may be derived from existing structures where the concrete composition, execution and exposure conditions are similar to those relevant for the new structure. When assessing the remaining service life of an existing structure, the factors, with the possible exception of α, may be derived directly from measurements on the structure.

For both the design of new structures and the assessment of the remaining service life of existing structures, the ageing factor α should be obtained from in situ observations of structures where the concrete composition, execution and exposure conditions are similar to those of the actual structure. Observations during at least two periods of exposure (with a sufficient interval between the observations) are needed for the calculation of the ageing factor.

8.4

Other deterioration mechanisms

For acid and sulphate attack, as well as for alkali-aggregate reactions, fib MC-2010 and ISO 16204 conclude that no time-dependent models with general international consensus are available and that full probabilistic and partial factor approaches for service life design are in these cases not feasible at present.

For these mechanisms, deemed-to-satisfy and avoidance-of-deterioration approaches have to be applied.

We have formulated a general time-dependent model for freeze-thaw cases, but this will hardly be usable due to the complexity of the input parameters. Therefore, deemed-to-satisfy and avoidance-of-deterioration will again be the practical approaches here.

As mentioned above, the fib and ISO committees did have problems with recommending time-dependent models for the rate of corrosion after the steel is depassivated.

Even if such models for predicting the total volume of corrosion products exist, they have problems in distinguishing between concentrated corrosion (pitting) and corrosion spread over a greater area with less severe consequences.

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S. Helland · Design for service life: implementation of fib Model Code 2010 rules in the operational code ISO 16204

8.5

Influence of cracks

Intuitively, we assume that cracked structures will deteriorate faster than uncracked structures. However, neither the fib nor the ISO committee was able to come up with any general model to take this effect into account.

The committees therefore decided to stick to the simplified approach used by most operational concrete standards today. This implies that corrosion of the reinforcement is not influenced by crack widths below a certain size. Depending on the severity of the environment and sensitivity of the structure, this limiting crack width is normally given as a characteristic value (5 % upper fractile) in the range of 0.2 to 0.4 mm.

In harsh exposure conditions (e.g. exposure classes XD3/XS3 as defined in ISO 22965-1 [17] and EN 206-1), if functionality or structural integrity is affected, and if inspection and possible intervention is impossible, an avoidance-of-deterioration approach is recommended.

8.6

Uncertainties in model and data

As engineers, we should be humble and accept that the models we are applying are only approximations of how the real thing operates. As with traditional structural design, model uncertainties must be taken into account in our calculations, and their consequences should be reduced if possible. We also have an inherent problem when trying to characterize a structure’s long-term resistance by way of accelerated testing on young concrete specimens in the laboratory. fib MC-2010 and ISO 16204 therefore warn the user not to rely, uncritically, on predictions based on laboratory tests involving specimens just a few months old extrapolated to the end of the design service life without taking due account of the uncertainties in both model and data.

One obvious way of reducing these influences is to use the models to extrapolate observations from structures exposed in the field for a certain period. The Norwegian code committee used this approach when verifying the present deemed-to-satisfy requirements given in the Norwegian standards.

Maage and Smeplass [18] analysed and extrapolated in situ observations of carbonation in structures with an age of about one decade. Helland, Aarstein and Maage [19] analysed the remaining service life of 10 North Sea concrete structures based on 180 chloride profiles taken after 2 to 26 years of exposure (Figs. 6 and 7). Both studies were carried out according to the models and principles based on LS (depassivation) and level of reliability as described for the full probabilistic method in MC-2010 and ISO 16204.

9

Design assumptions concerning execution, maintenance and repair

Some important assumptions have to be made when designing a new structure (or redesigning an existing one).

The execution of the structure must ensure that the finished work achieves the properties on which the design is based. The quality level for the workmanship, and the quality management regime at the construction site, must

16

Fig. 6. Oseberg A platform in stormy weather [19]

Structural Concrete 14 (2013), No. 1

Fig. 7. An inspector assessing the condition of a concrete shaft on a North Sea petroleum installation [19]

therefore be at a certain level. fib MC-2010 and ISO 16204 have therefore assumed that the minimum requirements given in ISO 22966 “Execution of concrete structures” [20] are complied with. This standard is more or less identical to its European counterpart EN 13670.

It should be stressed that any special requirements regarding materials or execution that affect durability and are not already covered by the execution standard should be communicated from the designer to the constructor as part of the “execution specification”. It is further anticipated that the completed structure will be subject to an inspection.

It is advised that the design and construction be provided with “as-built” documentation. The part of this documentation containing the direct input parameters for the service life design, and therefore acting as a basis for condition assessments during the service life, is often called the structure’s “birth certificate”.

If inspections reveal deviations from the specifications outside the given tolerances, a non-conformity process should be initiated.

S. Helland · Design for service life: implementation of fib Model Code 2010 rules in the operational code ISO 16204

The assumptions concerning following up the structure during its use are given in fib MC-2010 in chapter 9 “Conservation”, and in ISO 16204 as the series of standards to be denoted ISO 16311 [21].

The ISO 16311 series for maintenance and repair of concrete structures is under development in ISO TC71/SC-7, chaired by Prof. Tamon Ueda, one of the main authors of chapter 9 of fib MC-2010. This is another example of fib MC-2010 provisions being implemented in operational ISO standards, and vice versa.

Another requirement is that the designer should communicate a “maintenance plan” to the organization that manages the structure. This plan should give the instructions on those activities assumed during the design, which may include activities such as general cleaning, ensuring that the drainage system works, applying sealants at regular intervals, etc.

The design work should also result in an inspection plan to be applied by the operator. This plan should state: – what types of inspection are required, – what components of the structure are to be inspected, – the frequency of the inspections, – the performance criteria to be met, – how to record the results, and – the actions to be taken in the event of non-conformity with the performance criteria.

Since the reliability level on which the verification of the design is based is chosen on the basis of the possible consequences if the structure does not satisfy the relevant LS, the extent of inspections during the service life is very important. If the structure will be subjected to frequent detailed inspections by qualified personnel, deficiencies will be noticed at an early stage, enabling strengthening/repair of the structure. Severe consequences will then be avoided. On the other hand, if the structure will not be subjected to any inspections (the case with many foundations), the possible consequences of underperformance will be much more severe. This must be reflected in the design.

10

Differences between fib MC SLD, fib MC-2010 and ISO 16204

In this suite of documents, the MC SLD was the first stage.

Due to its mission to introduce a new concept, it contains an extensive commentary as well as a number of informative annexes giving examples of applications. These examples have been very helpful for readers, but some have misinterpreted the examples and regarded them as generally valid. Such misuse has caused some disappointments as it often produced results that were regarded as unrealistic.

Some in our community have also incorrectly associated MC SLD only with the use of modelling using the full probabilistic method. It is for these reasons that there is some scepticism of the concept in the industry and the standardization bodies.

In contrast to the fib MC SLD, fib MC-2010 is a general document covering all aspects of design, execution, conservation and dismantling. The various elements of relevance for service life design here are spread and dealt with fully in parallel with structural design and design for

sustainability. The main element for service life design is, however, found in section 7.8 “Verification of limit states associated with durability”. fib MC-2010 does not include the informative annexes of fib MC SLD, but refers to this document for interested readers.

The text in fib MC-2010 is basically the same as in the normative part of fib MC SLD, but has somewhat matured based on experience with fib MC SLD and the fact that the core of the old fib TG.5.6 was reinforced with some additional 25 experts in the ISO committee working in parallel with fib SAG-5 preparing fib MC-2010.

ISO 16204 is close to an equivalent to the elements on service life design in fib MC-2010, but contains less commentary. Owing to the fact that ISO 16204 is an operational standard, its scope also differs from that of fib MC2010: “This International Standard specifies principles and recommends procedures for the verification of the durability of concrete structures subject to: – known or foreseeable environmental actions causing material deterioration ultimately leading to failure of performance; – material deterioration without aggressiveness from the external environment of the structure, termed self-ageing.

NOTE The inclusion of, for example, chlorides [in] the concrete mix might cause deterioration over time without the ingress of additional chlorides from the environment.

“This International Standard is intended for the use by national standardization bodies when establishing or validating their requirements for durability of concrete structures. The standard may also be applied: – for the assessment of remaining service life of existing structures; and – for the design of service life of new structures provided quantified parameters on levels of reliability and design parameters are given in a national annex to this International Standard; “In annex E to ISO 16204 we have given guidance for the content of such a national annex.”

11

Further fib activities regarding service life design

Commission 5 “Structural service life aspects” is the prime fib committee dealing with this theme.

The Task Groups currently working on documents providing direct support for fib MC-2010 and ISO 16204 are: – TG.5.08 “Condition control and assessment of reinforced concrete structures exposed to corrosive environment” – TG.5.09 “Model technical specifications for repair and interventions” – TG.5.10 “Birth and rebirth certificates and through-life management aspects” – TG.5.11 “Calibration of code deemed-to-satisfy provisions for durability” – TG-5.13 “Operational documents to support service life design”

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12

Conclusion

fib MC-2010 considers the design of a concrete structure for loadbearing capacity, service life and sustainability in parallel. The main author of the sustainability related elements in MC-2010 is Prof. Koji Sakai. He is also the chairman of the parallel ISO TC-71 subcommittee implementing these provisions in the ISO 13315 [22] suite of standards ensuring compatibility between these two sets of documents.

The design service life of a structure is the prime denominator in all calculations regarding cost and sustainability as applied by the owner and society.

As chairman of ISO TC-71/SC-3/WG-4, it is my hope that the LS and reliability-based concept developed by fib and implemented by ISO will improve the present situation and enable the industry to make more rational decisions. In Europe we have started the process of revising our main concrete-related standards. The result is expected to appear at the end of this decade.

The joint working group from CEN TC-104 (materials and execution) and TC-250/SC-2 (design) dealing with overlapping issues have already taken this methodology on board in their discussions. A similar intention to include the fib/ISO methodology on service life design was expressed by TC-250/SC-2 when starting the process of revising EN 1992 [23]. It is the author’s hope that this methodology will also be included in the “light” revision of the European standard for concrete production, EN 206, scheduled for 2013, thus enabling the 31 national standardization bodies in the CEN community to make their national annexes more harmonized and transparent than is the case today.

References 1. CEB/FIP Model Code 90. fib – fédération internationale du béton, International Federation for Structural Concrete.

Lausanne, 1993.

2. FIP/CEB Bulletin No 228. High Performance Concrete. Extensions to the Model Code 90. fib – fédération internationale du béton, International Federation for Structural Concrete. Lausanne, 1995.

3. fib Bulletin No. 4. Light Weight Aggregate Concrete – part 1: Recommended extensions to Model Code 90. fib – fédération internationale du béton, International Federation for Structural Concrete. Lausanne, 2000.

4. fib Bulletin No 34. Model Code for Service Life Design. fib – fédération internationale du béton, International Federation for Structural Concrete. Lausanne, 2006.

5. fib Bulletin No. 65. Model Code 2010, Final draft, vol. 1. fib – fédération internationale du béton, International Federation for Structural Concrete. Lausanne, 2012.

6. fib Bulletin No. 66. Model Code 2010, Final draft, Volume 2. fib – fédération internationale du béton, International Federation for Structural Concrete. Lausanne, 2012.

7. Walraven, J., Bigaj-van Vliet, A.: The 2010 fib Model Code for concrete structures: a new approach to structural engineering. Structural Concrete, Journal of the fib, vol. 12, No. 3, Sept 2011.

8. ISO 16204 Durability – Service Life Design of Concrete Structures. International Organization for Standardization, Geneva, 2012.

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9. WTO Agreement on Technical Barriers to Trade (TBT), Uruguay Round Agreement, World Trade Organization, https://www.wto.org/english/docs_e/legal_e/17-tbt_e.htm.

10. ISO 2394 General Principles on reliability for structures. International Organization for Standardization. Geneva, 1998.

11. EN 1990, Eurocode – Basis of structural design. CEN – European Committee for standardization, Brussels, 2002.

12. Harrison, T.: CEN/TR 15868 Survey of national requirements used in conjunction with EN 206-1:2000. CEN – European Committee for standardization, Brussels, 2009.

13. EN 1992-1-1, Eurocode 2: Design of concrete structures – Part 1-1: General – Common rules and rules for buildings.

CEN – European Committee for standardization, Brussels, 2004.

14. EN 13670 Execution of concrete structures. CEN – European Committee for standardization, Brussels, 2009.

15. EN 206-1 Concrete – Part 1: Specification, performance, production and conformity. CEN – European Committee for standardization, Brussels, 2000.

16. Bamforth, P.: Enhancing reinforced concrete durability.

Concrete Society Technical Report No. 61. The Concrete Society, 2004.

17. ISO 22965-1 Concrete – Part 1: Methods of specifying and guidance for the specifier. International Organization for Standardization, Geneva, 2007.

18. Maage, M., Smeplass, S.: Carbonation – A probabilistic approach to derive provisions for EN 206-1. DuraNet, 3rd workshop, Tromsø, Norway, June 2001. Reported in “Betongkonstruksjoners Livsløp”, report No. 19, Norwegian Road Administration, Oslo, 2001.

19. Helland, S., Aarstein, R., Maage, M.: In-field performance of North Sea offshore platforms with regard to chloride resistance. Structural Concrete, Journal of the fib, vol. 11, No. 2, June 2010.

20. ISO 22966 Execution of concrete structures. International Organization for Standardization, Geneva, 2009.

21. ISO/DIS 16311 Maintenance and repair of concrete structures. International Organization for Standardization, Geneva, 2011.

22. ISO 13315 Environmental management for concrete and concrete structures. International Organization for Standardization, Geneva, 2012.

23. CEN TC250/SC2 document N 833 Future development needs in EN 1992’s. Secretariat, DIN, Berlin.

Steinar Helland Skanska Norge as Post box 1175 Sentrum 0107 Oslo Norway

Technical Paper Vladimir Cervenka

DOI: 10.1002/suco.201200022

Reliability-based non-linear analysis according to fib Model Code 2010 The fib Model Code 2010 for Concrete Structures introduces numerical simulation as a new tool for designing reinforced concrete structures. The model of resistance based on non-linear analysis requires adequate model validation and a global safety format for verifying designs. The numerical simulations combined with random sampling offer the chance of an advanced safety assessment. Approximate methods of global safety assessment are discussed and compared in a case study. An example of a bridge design supported by non-linear analysis is shown.

Keywords: non-linear analysis, safety formats, reliability, fib Model Code 2010

1

Introduction

Advanced non-linear analysis is becoming a useful tool for the design of new and assessment of existing structures.

This development is influenced by the general impact of information technologies on society and the economy.

The fast-developing industry of concrete structures yields new structural solutions, which are often verified by numerical simulations based on non-linear analysis and the finite element method. Examples of such applications can be observed in integral bridge structures [1] and nuclear power plants [2]. This trend is confirmed by several recent conferences devoted to computational mechanics, such as Euro-C 2010 and WCCM 2012, where special sections were devoted to concrete structures. The subject was recently dealt with in fib Task Group 4.4 [3].

Non-linear finite element analysis can be used in the design of concrete structures as an alternative to linear analysis. The concept has been developed within the field of computational mechanics with the aim of simulating real structural behaviour. Although it was initially used in research studies to support experimental investigations and explain observed structural behaviour, it has recently become a powerful design tool.

In the design process, non-linear analysis offers the engineer a refined verification of a structural solution by simulating structural response under design actions. Such a simulation can be regarded as a virtual test and does not fit into the traditional scope of the design process. This is Corresponding author: cervenka@cervenka.cz Submitted for review: 06 August 2012 Revised: 20 November 2012 Accepted for publication: 25 November 2012

mainly due to the basic differences between linear and non-linear approaches. In traditional design, distribution of internal forces is carried out by linear analysis and safety is checked locally in sections. There are two important discrepancies worth mentioning in this approach. First, the elastic force distribution is one of the many possible states of equilibrium, which can be realistic at low load levels only. A significant force redistribution can occur due to inelastic response. Second, the local section safety check of limit states is made under the assumption of nonlinear material behaviour (cracking, reinforcement yielding, etc.), which is not consistent with the elastic analysis of internal forces. Furthermore, the local safety check does not provide any information about overall structural safety. Nevertheless, this approach represents a very robust design method verified through many years of experience, and is the basis of the partial factor design concept currently in use.

In order to support a more rational safety assessment, fib Model Code 2010 [4] reflects new developments in safety formats based on probabilistic methods. Chapter 4 “Principles of structural design” introduces the probabilistic safety format as a general and rational basis for evaluating safety. In addition to the partial factor format, which remains as the main safety format for most practical cases, a “global resistance format” is recommended for non-linear analysis. Section 7.11 “Verification assisted by numerical simulations” outlines a guide for using non-linear analysis for assessing resistance. This paper illustrates the background to these innovative approaches.

2

Numerical simulation

The finite element method is typically used for the numerical solutions to continuum problems. Depending on the type of formulation (stiffness, compliance and mixed methods), the results are, by definition, different from the exact solution. In the stiffness formulation a best possible equilibrium is found for a given approximation (finite element type and size). The finite element solution should satisfy the requirement of convergence to the exact solution by reducing the element size (and increasing the number of degrees of freedom). Thus, irrespective of the material model, the approximations introduced solely by the finite element formulation can be a significant source of errors in numerical analysis and these errors should be

© 2013 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Structural Concrete 14 (2013), No. 1

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V. Cervenka ﾂｷ Reliability-based non-linear analysis according to fib Model Code 2010

Fig. 1. Typical algorithm for non-linear finite element analysis

Fig. 2. Model of fracture energy-based crack band

adequately controlled. Non-linear analysis introduces additional effects, e.g. material behaviour approximation, large deformations (change of geometry), or time-dependent behaviour (e.g. creep). The most significant effect in concrete structures is the material behaviour.

The principles of non-linear analysis are illustrated in Fig. 1. The non-linear solution is performed by a predictorcorrector iterative process (variations of the NewtonRaphson method). In the predictor (1), the solution is estimated by a linear analysis based, optionally, on tangent or initial material stiffness. The solution is improved in the corrector (2), based on non-linear constitutive laws. The iterative process is stopped when the difference between predictor and corrector is acceptably small. Appropriate iterative techniques can be employed for chosen specific constitutive laws. A balanced approximation of numerical methods involved in all parts of the model, i.e. in structural discretization, element formulation and material laws, should be maintained.

vant features of material behaviour for the problem under consideration. Constitutive laws should be based on the principles of continuum and failure mechanics and must ensure the objectivity of the solution in the context of numerical methods.

Models for material softening, i.e. materials exhibiting a decrease in strength after reaching a certain ultimate stress value, should include appropriate regularization techniques in order to reduce the mesh sensitivity of strain-based formulations of constitutive laws. An example of such a technique is the crack band method used for modelling cracks in concrete as shown in Figs. 2 and 3. A discrete crack is modelled by a band of smeared cracks.

Owing to the softening of the stress窶田rack opening law, the strain localizes in a narrow band of elements but remains evenly distributed within one element. The crack band model ensures that the fracture energy required for crack formation is dissipated within the crack band. This technique significantly reduces the mesh effect [6, 7]. Examples of crack pattern simulations are shown in Fig. 4.

One important property of concrete is its sensitivity to the multi-axial stress state, i.e. a significant strength increase under hydrostatic stress, referred to as the confinement effect, see Figs. 5 and 6. Two well-known models re-

3

Constitutive models

The material models used for concrete, reinforcement and their interaction should capture all significant and rele-

P

P

Load P [kN] 400 Pu=309 kN

sym

300

200

100

0.

0.0

0.2

0.4

0.6

Displacement [mm] Fig. 3. Example of a crack band in a shear wall [5]

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V. Cervenka · Reliability-based non-linear analysis according to fib Model Code 2010

Fig. 4. Crack pattern simulation of beams (test by Braam [8]) -σ3

hydrostatic axis

σ0 -σ1

τ0

Strength [Mpa] σ3

-800 concrete 30

-700 -600 -500

Compression

-400 -300 Tension

-200 Eurocode 2

-100 0

deviatoric plane

0 -σ2

-100

-200

-300

-400

Confining stress [Mpa] σ2 = σ1

Fig. 5. Concrete failure surface in 3D stress state

Fig. 6. Example of confinement effect modelled by the Menetrey-Willam yield function

flecting this effect are those of Willam [9] and Ottosen [10]; both supply satisfactory results for a wide range of concrete strengths (including HSC).

In numerical implementations, various effects interact and, in general, can form a complex non-linear problem. Therefore, a strain decomposition method, where the total strain is the sum of strains due to fracture, plasticity, creep, etc., is often used in order to solve this problem. An example of such a constitutive model is the fracture-plastic model proposed in [11].

Only the most significant concrete properties were mentioned in the above discussion. However, there are some additional properties that are important as well, such as modelling of interfaces between two concrete surfaces, steel-concrete contacts, bond between reinforcement and concrete and reinforcement itself. All should be considered in practical applications.

to ensure adequate safety. Such a validation should cover the whole range of inherent approximations: constitutive models, numerical discretization and structural solution.

Basic material tests serve to validate the constitutive relations and are performed on simple structures, with the aim of reducing the influence of geometry and boundary conditions under well-defined stress and strain conditions.

Examples of such tests are compressive tests on concrete cylinders, fracture tests on concrete prismatic specimens subjected to three-point loading and tension stiffening tests in uniaxial tension for reinforcing bars embedded in concrete members. These tests are typically described in codes for materials testing, such as those recommended by RILEM. The aim of structural tests is to validate the ability of the algorithm or software to reproduce certain structural behaviour objectively. This is often accomplished by way of benchmark calculations. For example, if a shear wall is to be simulated, then validating the software by means of shear wall experiments should be ensured. Such studies can be considered to be a rational basis for choosing adequate material models and software for a given structure.

4

Model validation

Numerical models are more complex than simplified engineering methods and the associated uncertainty is potentially high. Therefore, numerical models must be validated

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V. Cervenka · Reliability-based non-linear analysis according to fib Model Code 2010

Experimental crack pattern

Analysis, mesh M20, cracks and compressive stress

140 120

Force P [kN]

100 80 60 Experiment 40

Mesh 5

20

Mesh 10 Mesh 20

0 0

1

2

3

4

5

Displacement [mm]

Fig. 7. How mesh size affects of shear panels

Mesh sensitivity tests should be performed in order to validate the finite element mesh of the numerical model. At least three mesh cases with different element sizes should be tested and their effect on the resistance evaluated. In the case of a significant mesh sensitivity, when at least two different mesh sizes do not provide sufficiently similar results, the numerical model should be considered as not objective. An example of a mesh sensitivity study of a shear panel tested by the author is shown in Fig. 7, (for more details see [3], p. 168). It can be seen that the mesh refinement has an opposite effect on resistance (stiffness) in the ranges of crack formation (increased stiffness) and maximum load (reduced strength). Thus, the principles from elastic analysis based on displacement methods, where refining the mesh always reduces the stiffness, cannot be simply extended into a non-linear analysis and should be applied with caution.

The errors of non-linear solutions are controlled by convergence criteria. The solution convergence is satisfied when the error lies within prescribed limits. In the case of the stiffness method, the most significant convergence criterion is the error in the force equilibrium (residual forces). In addition, increments in displacements or the residual energy can be checked. The choice of an adequate error tolerance is an important aspect of non-linear

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Structural Concrete 14 (2013), No. 1

analysis. The admissible errors must be appropriately validated, e.g. by a convergence study in which the results obtained with different tolerances are compared.

Finally, the model performance on the structural level should be checked. It should prove the capability of the chosen numerical model to reproduce the structural behaviour under consideration.

An example of validation based on a shear test from [7] is shown in Fig. 8. The beam size tested by Collins and Yoshida [12] exceeds the usual beam dimensions (span = 12 m, depth = 2 m). The failure was dominated by brittle response, which contributed to the size effect and which could be well reproduced by the numerical model based on fracture mechanics. More about this study will be show later in the examples of application.

5

Global safety format and model uncertainty

The usual design condition is considered as Fd < Rd

(1)

where Fd is the design action and Rd is the design resistance and both these entities cover safety margins. In this formulation the safety of loading and resistance are treat-

V. Cervenka · Reliability-based non-linear analysis according to fib Model Code 2010 500 450 400

Load [kN]

350 300 250 200 150 100

Experiment Y0

50

ATENA analysis

0 0

1

2

3

4 5 6 Displacement [mm]

7

8

9

10

Fig. 8. Comparison of load-displacement diagrams and crack patterns of large beams

Fig. 9. Safety formats for design resistance

ed separately, which is a certain approximation compared with a general probabilistic approach. In design practice (based on the partial safety factors) we accept this simplification and consider Fd = F(S,γG,γQ,γP,..) where the representative load S is factorized by partial safety factors γG,γQ,γP,.. for permanent load, imposed load, prestressing, etc.

In non-linear analysis Rd describes the global resistance (e.g. set of forces representing an imposed load, horizontal load, etc.). Note that in the partial safety factor method we assume failure probabilities of separate materials but do not evaluate the failure probability on the structural level. Unlike in sectional design, the global resistance reflects an integral response of the whole structure in which all material points (or cross-sections) interact. The safety margin can be expressed by the safety factor Rd =

Rm γR

(2)

where Rm is the mean resistance (sometimes referred to as nominal resistance). The global safety factor γR covers all uncertainties and can be related to the coefficient of variation of resistance VR (assuming a log-normal distribution according to Eurocode 2) as

γR = exp(αR β VR)

(3)

where αR is the sensitivity factor for resistance and β is the reliability index. It is recognized that variability included in VR depends on uncertainties due to various sources: material properties, geometry and resistance model. They can be treated as random effects and analysed by probabilistic methods. Owing to the statistical data available, the probabilistic treatment of materials and geometry can be performed in a rational way. However, a random treatment of model uncertainties is more difficult because of limited data.

A simplified formulation was proposed in fib Model Code 2010, where the denominator on the right-hand side of Eq. (2) is a product of two factors: γR = γmγRd (which follows from the determination of partial safety factors in fib Model Code 2010, section 4.5.2.2.3). The first factor γm is related to material uncertainty and can be established by a probabilistic analysis. The second factor γRd is related to model and geometrical uncertainties and recommended values are in the range 1.05–1.1 (as suggested by Eurocode 2-2).

Recent investigations by Schlune et. al. [13] found such values to be unsafe and proposed a more general method in which the overall coefficient of resistance variation can be determined as 2 VR = VG2 + Vm2 + VRd

(4)

where variability due to specific sources are identified: VG – geometry, Vm – material strength, VRd – model. This ap-

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V. Cervenka · Reliability-based non-linear analysis according to fib Model Code 2010

proach allows the inclusion of all uncertainties in a more rational way. Based on a survey of various blind benchmark studies, Schlune et al. concluded that the model uncertainties of non-linear analysis are much higher than in standard design based on engineering formulas and are strongly dependent on modes of failure. Reported coefficients of variation due to model uncertainty for bending failure are in the range 5–30 %, and 15–64 % for shear.

Schlune et al. concluded that due to the lack of data, the choice of the model uncertainty often depends on engineering judgment and can be subjective. However, these conclusions do not recognize the effect of model validation, which can decrease model uncertainties. Further research is needed to recommend appropriate values of the model uncertainty for numerical simulations.

The assessment of the design resistance according to Eq. (1) can be achieved by various methods, ranging from a full probabilistic analysis to the partial factor method, which differ in the level of approximations involved.

These safety formats are briefly characterized below and are illustrated in Fig. 9 by comparing how they represent failure probability.

5.1

Full probabilistic analysis

In general, probabilistic analysis is the most rational tool for assessing the safety of structures. It can be further refined by introducing non-linear structural analysis as a limit state function. The numerical simulation resembles real tests on structures by considering a representative group of samples, which can be analysed statistically for assessing safety. An approach applied in [16] will only be briefly outlined here. More information on probabilistic analysis can be found in [17].

The probabilistic analysis of resistance is performed by the LHS method, in which the material input parameters are varied in a systematic way. The resulting array of resistance values is approximated by a distribution function of global resistance and describes the random variation of resistance. Finally, for a required reliability index β, or probability of failure Pf, the value of design resistance Rd should be calculated.

However, full probabilistic analysis is computationally demanding and requires good information about random properties of input variables. It is usually applied in special cases where the consequences of failure justify the effort.

Probabilistic analysis based on numerical simulation with random sampling can be briefly described as follows: (1) Formulation of a numerical model based on the nonlinear finite element method. Such a model describes the resistance function and can perform a deterministic analysis of resistance for a given set of input variables.

(2) Randomization of input variables (material properties, dimensions, boundary conditions, etc.). This can also include some effects that are not in the action function (e.g. prestressing, dead load, etc.). Random material properties are defined by a random distribution type and its parameters (mean, standard deviation, etc.).

They describe the uncertainties due to the variation of

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the resistance properties. The randomization can be carried out by two methods: (1) random variables, where the parameter is constant within a sample (structure) but changes between samples; (2) random fields, where the parameter is randomly variable within a sample. A correlation of random variables should be considered appropriately.

(3) Probabilistic analysis of resistance. This can be performed by the numerical method of the Monte Carlotype of sampling, such as the LHS sampling method.

The results of this analysis provide random parameters of resistance, e.g. mean, standard deviation, etc., and the type of distribution function for resistance (PDF).

(4) Evaluation of design resistance based on the reliability index β or probability of failure. In this, a design point is found by extrapolating a point around a central region based on the probability distribution function (PDF).

The advantage of a full probabilistic analysis is that it is independent of a failure mode. The potentially higher safety margins of some failure modes, e.g. shear failure, is automatically included in the higher sensitivity of numerical resistance to a brittle failure. A disadvantage of this approach [16] is that the target value of design resistance is located in the tail of the PDF. This function is determined by the best fit from the available, and the design value is obtained by extrapolation and heavily depends on the choice of PDF. On the other hand, the approach is numerically robust, computationally efficient and feasible for practical application.

5.2

ECOV method – estimate of coefficient of variation

A simplified probabilistic analysis was proposed by the author [15], in which the random variation of resistance is estimated using two samples only. It is based on the idea that the random distribution of resistance, which is described by the coefficient of variation VR, can be estimated from the mean Rm and characteristic Rk values of resistance. The underlying assumption is that random distribution of resistance is in accord with a log-normal distribution, which is typical for structural resistance. In this case it is possible to express the coefficient of variation as

VR =

⎛R ⎞ 1 ln ⎜ m ⎟ 1.65 ⎝ Rk ⎠

(5)

The global safety factor γR of resistance is then estimated using Eq. (3).

Using the typical values β = 3.8 (50 years) and αR = 0.8 (which corresponds to the failure probability Pf = 0.001), the global resistance factor can be directly related to the estimated coefficient of variation VR as γR ≅ exp(3.04 VR), and the design resistance is obtained from Eq. (2).

The key element in this method is the determination of the mean and characteristic values of the resistance, Rm, Rk. It is proposed to estimate them using two separate non-linear analyses employing the mean and characteristic values of input material parameters respectively.

V. Cervenka 路 Reliability-based non-linear analysis according to fib Model Code 2010

Table 1. Case study description

No.

Description

1

Beam in bending

2

Deep beam in shear

3

Bridge pier

Scheme

Railway bridge test

5

Beam in shear without ties

6

Beam in shear with ties

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The method is general and the reliability level β and distribution type can be changed if required. It reflects all types of failure. The sensitivity to random variation of all material parameters is automatically included. Thus, there is no need for special modifications to the concrete properties in order to compensate for the greater random variation of certain properties as in the next method, EN 1992-2.

A similar and refined method with more samples was proposed by Schlune et al. [13].

5.3

Method based on EN 1992-2

Eurocode 2 for bridges introduced a concept for verifying global safety based on non-linear analysis. Design resistance is calculated from ∼ Rd = R(fym, fcm…)/γR

(6)

∼ where fym, fcm are the mean values of the material parameters of steel reinforcement and concrete fym = 1.1 fyk ∼ and fcm = 0.843 fck. Note that the mean value for concrete is reduced to account for the higher variability of the concrete property. The global factor of resistance should be γR = 1.27. The evaluation of the resistance function is accomplished using non-linear analysis assuming the material parameters according to the above rules.

5.4

Partial safety factors (PSFs)

The method of partial safety factors, which is used in most design codes, can be directly applied to global analysis in order to obtain the design resistance Rd = R(fd). The design values of the material parameters fd = fk/γM are used here, where fk are characteristic values and γM partial safety factors for materials.

It can be argued that design values represent extremely low material properties, which in turn do not represent real material behaviour and can thus lead to distorted failure modes. On the other hand, this method directly addresses the target design value and thus no extrapolation is involved. However, the probability of global resistance is not evaluated and is therefore not known.

6 6.1

Case study and applications Case study for safety formats

The author has initiated investigations with the aim of comparing the various safety formats. The study comprised the six cases described in Table 1. It included a wide range of structures, including simple beam, laboratory test of a shear wall, laboratory test of a deep beam, in situ test of a real bridge and a bridge pier design case. A variety of failure modes covered ductile bending mode, brittle shear modes and a concrete compression mode. Details of this investigation can be found in [15]. A summary of the results is shown in Table 2. Three approximate methods, namely the partial safety factors (PSF) method based on the estimate of coefficient or variation of resistance (ECOV) and the method according to EN 1992-2 are evaluated. The table shows the ratio of resistances Rd found

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Structural Concrete 14 (2013), No. 1

Table 2. Case study of safety formats

Rd/Rdprob.

Example 1 bending Example 2 deep beam Example 3 bridge pier Example 4 bridge frame Example 5 shear beam Y0 Example 6 shear beam Y4 average

PSF

ECOV

EN 1992-2

1.04

1.04

0.99

1.02

1.04

1.0

0.98

1.04

v

0.99

0.96

0.92

1.03

0.98

1.02

0.81

1.04

0.82

0.98

1.01

0.95

by approximate methods to the full probabilistic analysis (which is considered as the most exact for this purpose). It should be noted that the study does not reflect the model uncertainty in a consistent way. The PSF and EN 1992-2 methods include the model uncertainty as given by the Eurocode, whereas in the ECOV and full probabilistic analysis it is not considered in order to simplify the comparison. This could explain why the average results of the ECOV method are slightly higher than the other two methods.

The study confirmed the feasibility of the approximate methods for the safety assessment. The ECOV method is preferred since it relates the safety to the resistance random variation and is considered more rational when compared with the EN 1992-2 method.

Multiple failure modes, which are typical features of reinforced concrete structures, are inherently included in the numerical models and thus they are reflected in results of analysis and resistance variability. Therefore, the approximate methods of safety verification are generally applicable in design. In significant cases, if justified by the consequences of failure, a full probabilistic analysis should be applied.

6.2

Large shear beam

To illustrate this, two applications of design verification by non-linear analysis will be shown. The first example applies the safety formats discussed above to a large beam tested in the laboratory by Collins et al. [12] and already mentioned in Fig. 8. Its size is large and exceeds usual beam dimensions (span = 12 m, depth = 2 m). The shear failure is apparently influenced by its large size and is very brittle. The comparison of resistances obtained by various safety formats is shown in Fig. 10, which also shows the values of design resistance obtained with EN 1992-1 and ACI 318.

This case reveals two remarkable features of numerical simulation. First, a refined constitutive modelling based on fracture mechanics can capture the size effect of brittle shear failure and provide a safer model of resis-

V. Cervenka ﾂｷ Reliability-based non-linear analysis according to fib Model Code 2010

Fig. 10. Comparison of safety margins in shear failure

Fig. 12. Cracks and plastic strains at maximum uniform load

Fig. 11. Bridge under construction, built using the balanced cantilever method

tance. Second, the global safety formats offer consistent safety margins for the design verification.

6.3

Box girder bridge

The bridge over the River Berounka on the recently opened ring road around the city of Prague was designed with the help of numerical simulation. It is a box girder integral structure with complex geometry curved in three dimensions and supported on slender piers. During construction stages when the girder was not yet integrally connected with other spans, it was very sensitive to stability conditions, see Fig. 11. The safety of construction phases was verified by numerical simulation and global safety format.

For illustration only, a result of the load case with proportionally increased uniform load is presented in Fig. 12, showing cracks and plastic deformations. This helps to identify a mode of failure reached at the ultimate limit state. The evidence of structural resistance is provided by a load窶電isplacement diagram (Fig. 13). The relative load on the vertical axis is a non-dimensional overloading parameter representing the global safety factor ﾎｳR from Eq. (2). In this case the analysis confirmed the safety fac-

Fig. 13. Load-displacement diagram for bridge during construction

tor ﾎｳR = 1.7, which is well above the value of 1.27 required by the code. The global safety factors obtained for the other load histories due to the construction phases of the balanced cantilever method were 6.2 for wind action and 5.5 for formwork action during the cantilever construction. A sufficient safety margin was confirmed for all stages of construction.

The shape of a descending branch in the load-displacement diagram provides additional information about the ductile nature of the failure, which is an important measure of robustness. The case observed indicates a relatively brittle behaviour, which in this case is due to a compressive failure of the concrete, which occurs in the box girder following cable yielding and excessive rotation, and in some load cases in the concrete of the pier. More details can be found in [1].

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V. Cervenka · Reliability-based non-linear analysis according to fib Model Code 2010

7

Closing remarks

Verification by numerical simulation is a powerful tool for the design of concrete structures. It extends the range of application beyond the scope of engineering methods based on the elastic distribution of internal forces and cross-section safety check. Owing to its general approach, it overcomes the limits of standard design based on beams and columns. On the other hand, it introduces potentially higher model uncertainties. Therefore, the model validation becomes an important requirement for its application in engineering practice. fib Model Code 2010 outlines the framework of limit state verification by numerical simulations and introduces the global safety formats suggested for this purpose.

Further research is needed in order to improve the guide for the validation of numerical models and the classification of model uncertainties.

Acknowledgements The author would like to acknowledge the fruitful cooperation of the colleagues who contributed to the new fib Model Code. The financial support of Czech Science Foundation project P105/12/2051 is greatly appreciated.

References 1. Cervenka, V., Cervenka, J., Sistek, M.: Verification of global safety assisted by numerical simulation. fib Symposium, Prague, 8–10 June 2011.

2. Cervenka, J., Proske, D., Kurmann, D., Cervenka, V.: Pushover analysis of nuclear power plant structures. fib Symposium, Stockholm, 11–14 June 2012, pp. 245–248, ISBN 978-91-980098-1.

3. Foster, S. (ed.), Maekawa, K. (convenor), Vecchio, F. (deputy chair): Practitioners’ guide to finite element modelling of reinforced concrete structures. State of the art report by fib Task Group 4.4, Bulletin No. 45, 2008, ISBN 987-3-88394085-7.

4. Walraven, J. (convener): Model Code 2010. Final draft, vols.

1 & 2, 2012. fib Bulletin Nos. 65 & 66, ISBN 978-2-88394105-2.

5. Asin, M.: The Behaviour of Reinforced Concrete Continuous Deep Beams. PhD dissertation, Delft University Press, Netherlands, 1999, ISBN 90-407-2012-6.

6. Cervenka, V., Pukl, R., Ozbold, J., Eligehausen, R.: Mesh Sensitivity Effects in Smeared Finite Element Analysis of Concrete Fracture, Proc. Fracture Mechanics of Concrete Structure II, (FRAMCOS 2), Wittmann, F. H. (ed.). Zurich, 25–28 July 1995, vol. II, pp. 1387–1396, ISBN 3-90508812-6.

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7. Cervenka, J., Cervenka,V.: On the uniqueness of numerical solutions of shear failure of deep concrete beams: comparison of smeared and discrete crack approaches. EURO-C 2010. Computational Modeling of Concrete structures – Bicˇanicˇ et. al. (eds.). Taylor & Francis Group, London, ISBN 978-0-415-58479-1.

8. Braam C. R.: Control of crack width in deep reinforced beams. Heron 4 (35), 1990.

9. Menétrey, P., Willam, K. J.: Triaxial failure criterion for concrete and its generalization. ACI Structural Journal 92 (3), pp. 311–318.

10. Ottosen, N.: A Failure Criterion for Concrete, Journal Engineering Mechanics Division, ASCE, vol. 103, EM4, Aug 1977.

11. Cervenka, J., Pappanikolaou, V.: Three-dimensional combined fracture-plastic material model for concrete. Int. J. of Plasticity, vol. 24, 12, 2008, pp. 2192–2220, ISSN 0749-6419.

12. Yoshida, Y.: Shear Reinforcement for Large Lightly Reinforced Concrete Members, MS thesis under supervision of Prof. Collins, University of Toronto, 2000.

13. Schlune, H., Plos, M., Gylltoft, K.: Safety Formats for Nonlinear Analysis of Concrete Structures. Engineering Structures, Elsevier, vol. 33, No. 8, Aug 2011.

14. Novak, D., Vorechovsky, M., Lehky, D., Rusina, R., Pukl, R., Cervenka, V.: Stochastic nonlinear fracture mechanics finite element analysis of concrete structures. Proceedings of 9th Int. conf. on Structural Safety & Reliability, Icossar, Rome, 2005.

15. Cervenka, V.: Global Safety Format for Nonlinear Calculation of Reinforced Concrete. Beton- und Stahlbetonbau 103 (2008), special edition, Ernst & Sohn, pp. 37–42.

16. Cervenka, V. (ed.): SARA – Structural Analysis and Reliability Assessment. User’s manual. Cervenka Consulting, Prague, 2003.

17. Vrouvenwelder, A. C. W. M.: Conclusions of the JCSS Workshop on Semi-probabilistic FEM calculations, Delft, 1–2 Dec 2009.

Vladimir Cervenka, President, Cervenka Consulting Na Hrebenkach 55, 15000 Prague 5, Czech Republic Tel. +420 220 610 018, e-mail: vladimir.cervenka@cervenka.cz

Technical Papers Diego Lorenzo Allaix* Vincenzo Ilario Carbone Giuseppe Mancini

DOI: 10.1002/suco.201200017

Global safety format for non-linear analysis of reinforced concrete structures Semi-probabilistic safety formats for the non-linear analysis of reinforced concrete structures are of practical interest for structural designers. The safety format proposed in EN 1992-2 enables a safety assessment through a non-linear structural analysis and the application of a global safety factor, which is defined as the ratio between the representative and design values of the material resistances. A more realistic estimate of the global safety factor can be obtained from the distribution of the structural response. This paper proposes a safety format based on the mean values of the material resistances and a global resistance factor.

Its practical application in the structural design of concrete beams and columns is also presented.

Keywords: safety format, non-linear analysis, reinforced concrete structures, global resistance factors, Monte Carlo method

1

Introduction

According to EN 1990 [1], the verification of structures against failure due to lack of structural resistance is indicated at section level by the following inequality: Ed ≤ Rd

(1)

where Ed is the design value of the effects of actions and Rd the corresponding resistance. EN 1992-1-1 [2] allows the designer of concrete structures to determine the design value Ed by means of a linear elastic analysis, a linear elastic analysis with limited redistribution or a non-linear analysis. The non-linear analysis is the most accurate method of those proposed because it makes use of the realistic constitutive laws of the materials and is based on the concepts of equilibrium and compatibility of deformations. Furthermore, it can be used to predict the structural response at each load level, from serviceability to ultimate conditions.

As observed in [3], the non-linear analysis of concrete structures should be performed using the mean values of

* Corresponding author: diego.allaix@polito.it Submitted for review: 17 July 2012 Revised: 20 September 2012 Accepted for publication: 30 September 2012

the material resistances. The comparison of experimental could occur tests and non-linear finite element analyses has shown that the actual structural behaviour can be reproduced only if the mean values of the material properties are considered in the structural analysis. The use of the design values in the structural analysis leads to an erroneous assessment of the load bearing capacity; for example, an unrealistic redistribution of internal actions could occur in the case of beams. An even worse effect could be observed in the case of slender columns. In fact, the design values of the material properties lead to an overestimation of the deformability of a structure.

So for the sake of the accuracy of the distribution of internal forces, the term Ed should be estimated with the mean values, whereas the semi-probabilistic approach requires an assessment of the resistance Rd using the design values. Therefore, the left- and right-hand sides of Eq. (1) should be determined using different values for the material properties.

Several safety formats have been proposed to solve this inconsistency. A safety format based on the mean values of the material resistances and a safety check in the domain of the internal actions are proposed in this paper.

The safety format is intended to be consistent with the Eurocodes. The procedure is developed and applied to beams and columns subjected to a combination of axial force and bending moment.

The safety formats already available in the literature are analysed first. This is followed by a description of the new proposal. Finally, examples of applications are presented.

2

Safety formats in fib Model Code 2010

The design condition used in the safety format for non-linear analysis proposed in fib Model Code 2010 [4] is written in the domain of the actions: Fd ≤ Rd

(2)

where Fd is the design value of the actions and Rd the design resistance. Three different approaches can be used for evaluating the resistance Rd in Eq. (2): – the probabilistic method – the global resistance methods – the partial factor method

© 2013 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Structural Concrete 14 (2013), No. 1

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D. L. Allaix/V. I. Carbone/G. Mancini · Global safety format for non-linear analysis of reinforced concrete structures

2.1

fcmd = 0.85 fck

Probabilistic method

The design value Rd of the actual resistance is derived from the distribution of the resistance R of the structure, which can be represented by the ultimate load. In general terms, the design value Rd is expressed as Rd =

(

)

R −1 ⎡Φ −α Rβ ⎤ ⎣ ⎦ γ Rd

(3)

where R resistance predicted by a mechanical model αR resistance sensitivity factor β reliability index γRd model uncertainty factor.

As an example, the values αR = 0.8, β = 3.8 and γRd = 1.06 can be considered for the ultimate limit states, moderate consequences of failure and a reference period of 50 years [1]. The two-parameter log-normal distribution is normally used to model the resistance of concrete structures. Hence, Eq. (3) may be rewritten as Rd =

(

μ R exp −α Rβ VR

)

γ Rd

(4)

where μR and VR are the mean value and the coefficient of variation of the distribution respectively of the resistance predicted by the model. These two parameters can be estimated by means of a Monte Carlo simulation. As described in [4], the probabilistic assessment of the structural resistance is based on two models; a non-linear finite element model is suggested to represent the response of the structure and a probabilistic model is required to account for the uncertainty of the model parameters, e.g. material properties, geometrical dimensions, boundary conditions, or other effects, e.g. prestressing.

2.2

Global resistance methods

The aim of the global resistance methods is to estimate the design resistance Rd by dividing the resistance computed with properly chosen representative values frep for the material resistances and the global resistance factor γR: Rd =

( )

R frep

γ Rγ Rd

(5)

Two alternative methods are mentioned in [4]: the global resistance factor method and the method of estimating a coefficient of variation of resistance (ECOV). These methods differ in their derivation of the global resistance factor.

In the former, the global resistance factor is defined as the ratio between the representative and the design values of the material properties. The mean value of the yield stress fym is considered for the reinforcing steel: fym = 1.1 fyk

(6)

where fyk is the characteristic yield stress. A reduced value fcmd for the concrete compressive strength is used to take into account a reduction in the material resistance due to concrete uncertainty:

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Structural Concrete 14 (2013), No. 1

(7)

where fck is the characteristic compressive strength. A value of 1.2 is proposed in [4] for the global resistance factor γR. In the ECOV method, the global resistance factor is estimated from

γR = exp(αRβ VR)

(8)

This relationship, too, relies on the hypothesis that the resistance R is modelled by a log-normal random variable.

The coefficient of variation VR of the resistance is estimated by means of two non-linear analyses performed using the mean and characteristic values of the material resistances. The coefficient of variation VR is derived under the hypothesis that the resistance follows a two-parameter lognormal distribution: VR =

⎛R ⎞ 1 ln ⎜ m ⎟ 1.65 ⎝ Rk ⎠

(9)

where Rm and Rk are the values of the structural resistance based on the mean and characteristic values of the material resistances respectively. The design resistance is then calculated from Rd =

Rm γ Rγ Rd

(10)

Although not included in fib Model Code 2010, the safety format proposed by Schlune et al. [5, 6] could be considered as an improved ECOV method. Schlune et al. present an investigation concerning beam sections subjected to a combination of bending moments and shear forces. The design resistance Rd is derived from the global resistance factor γR and the resistance is computed using the mean yield stress of the steel fym, the mean in situ concrete compressive strength fcm,is and the nominal values of the geometrical dimensions anom: Rd =

(

)

R fym, fcm,is , anom

γR

(11)

where:

γR =

(

exp α Rβ VR

θm

)

(12)

and θm is the bias factor, which is defined as the mean ratio of experimental to predicted resistance. Its value varies between 0.7 and 1.2 for failure in compression, bending and shear. It is important to note the distinction between the bias factor θm and the model uncertainty factor γRd, although both take into account model uncertainties.

Firstly, they correspond to different fractiles of the corresponding distribution. The bias factor is a mean value, whereas the model uncertainty factor is a design value.

Secondly, they describe different types of uncertainties. The bias factor is directly related to the difference be-

D. L. Allaix/V. I. Carbone/G. Mancini · Global safety format for non-linear analysis of reinforced concrete structures

tween the experimental and the model results. The model uncertainty factor also takes into account uncertainties related to the position of the reinforcing bars in concrete members.

The coefficient of variation VR is written by Schlune et al. [5] as follows: VR = Vg2 + Vm2 + Vf2

Rm

Δfc, Δfy RΔfc, RΔfy

(14)

standard deviations of the concrete compressive strength and the yield stress of the steel respectively finite variations of the material resistances results of non-linear analyses performed using the values fcm – Δfc for the concrete compressive strength and fym – Δfy for the yield stress

The coefficient of variation VR can be estimated by means of three non-linear analyses: one performed with the mean values of the material resistances, the other two with the values fcm – Δfc and fym – Δfy. As observed in [8], the parameters Δfc and Δfy should be chosen with particular care in order to avoid unsafe results.

The most important improvement in this method with respect to the ECOV method is that the uncertainty related to the numerical model can be taken into account directly. This model uncertainty is taken into account in both the numerator and the denominator of Eq. (12), which defines the global resistance factor γR. As observed in [7], these two approaches lead to design resistance values that do not differ significantly from the results of the probabilistic method.

2.3

Partial factor method

According to this method, the design resistance Rd is estimated by means of a non-linear analysis with the design values of the material resistances. However, it was mentioned in the introduction that the choice of the design values should be avoided when evaluating the left-hand side of Eq. (1) [3].

3

as the compressive resistance value. A bilinear constitutive law is adopted for the reinforcing steel. The mean values of the yield stress fym and the tensile strength ftm are fym = 1.1 fyk

(16)

ftm = 1.1 ftk

(17)

where fyk and ftk are the characteristic values of the yield stress and tensile strength respectively. Once the non-linear analysis has been performed, the following inequality in terms of external and internal actions is checked for the critical regions of the structure:

2

2

⎛ Rm − RΔ f ⎞ ⎛ Rm − RΔ f ⎞ y c 2 +⎜ ⎟ σ2 ⎟ σ fc ⎜ ⎜⎝ Δ fc ⎟⎠ Δ fy ⎟ fy ⎜⎝ ⎠

where σfc, σfy

(15)

(13)

where Vg, Vm and Vf are the coefficients of variation of the geometrical, model and material uncertainties respectively. Suggestions for Vg and Vm are also proposed in [5, 6].

When the main material parameters are the concrete compressive strength and the yield stress of the steel, the coefficient of variation Vf can be estimated by means of

Vf ≈

fc,rep = 0.843 fck

Safety format in EN 1992-2

According to the safety format proposed in EN 1992-2 [8], a non-linear analysis is performed using the following assumptions for the material properties. The concrete in compression is described by the Sargin constitutive law, assuming

(

E γ GGk + γ QQk

)

⎛q ⎞ R⎜ u⎟ ⎝γ O⎠ ≤ γ Rd

(18)

The left-hand side is the load effect evaluated for the design load, where γG and γQ are the partial factors to be applied to the characteristic values of the permanent actions Gk and variable actions Qk respectively. The resistance R corresponding to the load effect E is evaluated at the load level qu/γO, where qu is the ultimate load level and γO is the global safety factor. Suggested values for γO and γRd are 1.20 and 1.06 respectively [8]. Alternatively, the safety check can be written as ⎛q ⎞ E γ GGk + γ QQk ≤ R ⎜ u ⎟ ⎝ γ O′ ⎠

(

)

(19)

where γO′ = γO γRd = 1.27 [8]. The inequality (18) can be also rewritten as follows:

(

γ Ed E γ gGk + γ qQk

)

⎛q ⎞ R⎜ u⎟ ⎝γ O⎠ ≤ γ Rd

(20)

where γEd is the load effect uncertainty factor and γg and γq are the partial factors for the permanent and variable actions respectively.

Concerning the evaluation of the action effects Ed, it should be noted that the expression Eq. (20) is the most general. The relationships of Eqs. (18) and (19) are approximations that may be unsafe if the action effects are under-proportional functions of the actions [9].

Fig. 1 shows an application of this safety format for the case of a scalar problem (i.e. beam in bending) using Eq. (19).

The term R(qu/γO′) is the point on the internal actions path corresponding to the load level qu/γO′. The structure is safe if the point on the internal path at load level γGGk + γQQk is below the point corresponding to R(qu/γO′).

The value γO′ = 1.27 is proposed in EN 1992-2 [8].

This value is obtained as the ratio of the representative to the design values of the material resistances. In the case of concrete failure

Structural Concrete 14 (2013), No. 1

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D. L. Allaix/V. I. Carbone/G. Mancini · Global safety format for non-linear analysis of reinforced concrete structures

Following this idea, the probabilistic derivation of the global resistance factor γR has been developed in a few research papers [10–13]. This factor takes into account the effect of the uncertainties of the structural parameters on the global response and possibly the uncertainties related to the resistance model. For example, global resistance factors for reinforced concrete beams and columns have been derived recently [10–12] considering the axial force and bending moment resistance of the cross-section. Alternatively, the global resistance factor can be estimated in terms of the ultimate load level [13]. This approach is realistic because it also takes into account the type of failure.

5

Fig. 1. Application of the safety format of EN1992-2.

γ O′ =

fc, rep fcd

=

0.843fck ≈ 1.27 fck 1.5

(21)

fym fyd

=

1.1fyk fyk

≈ 1.27

(22)

1.15 the value of γO′ is not differentiated with respect to the limit state condition and type of failure. This compromise has the practical advantage that a single global safety factor has to be applied to the resistance R.

4

Discussion

Four safety formats for the non-linear analysis of concrete structures were presented in sections 2 and 3. The safety formats differ in terms of the values of the material properties used in the calculations and in terms of the domain where the safety check is performed.

A new safety format, which could be used in the context of the Eurocodes, is proposed below. Therefore, the proposal should be consistent with the EN 1990 [1]. In the structural design according to the STR limit state, the designer has to check that Eq. (1) is fulfilled. Hence, the proposed safety format is based on comparing the action effects and corresponding resistances, as in the approach of EN 1992-2 [6].

Concerning the material properties, the mean values of the resistances of steel and concrete should be used in the non-linear analysis in accordance with the suggestions of the CEB [3].

A comment is necessary regarding the global safety factor (or global resistance factor). The global safety factor used in EN 1992-2 is defined as the ratio between the representative values and the design values of the material properties. It would be more appropriate to derive this factor from the resistance at cross-section level or from the load-carrying capacity of the structure.

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Structural Concrete 14 (2013), No. 1

The safety format proposed in the present paper is based on the mean values of the material resistances and verifying safety in the domain of the internal actions. In order to be easily applicable, the safety format is based on the global resistance method.

The design resistance Rd is evaluated as follows: ⎛q ⎞ R ⎜ um ⎟ ⎝ γR ⎠ Rd = γ Rd

and in the case of steel failure

γ O′ =

Safety format based on mean values of material resistances

(23)

where qum is the ultimate load level reached in a non-linear analysis performed with the mean values of the material resistances. The global resistance factor γR is defined as the ratio between the mean value and the design value of the distribution of the ultimate load level:

γR =

μqu

(24)

qud

In the derivation of the global resistance factor γR it has been assumed that the mean value μqu of the ultimate load level can be approximated by the ultimate load level qum computed using the mean values of the material resistances. This assumption is an approximation because it corresponds to the truncation at the first term of the Taylor series expansion of the ultimate load level about the mean values of the material resistances: n

qu = qum +

i =1

+

1 2

n

∂q

∑ (Xi − μ X ) ∂Xui i

X=μX

n

∂2q

∑ ∑ (Xi − μ X ) ⎛⎝X j − μ X ⎞⎠ ∂Xi ∂uX j i =1 j =1

i

+…

j

(25)

X=μX

where Xi is one of the material resistances. Although qum is an approximation of μqu, the assumption is of practical use for designers.

Considering that the resistance of reinforced concrete members can be described by a two-parameter lognormal distribution, the design value qud is approximated by qud = μqu exp(–αRβ Vqu)

(26)

D. L. Allaix/V. I. Carbone/G. Mancini · Global safety format for non-linear analysis of reinforced concrete structures

Therefore, the global resistance factor γR can be easily derived from the coefficient of variation Vqu:

γR = exp(αRβ Vqu) ≈ exp(3.04 Vqu)

(

γ Ed E γ gGk + γ qQk

)

(28)

The model uncertainty factor γRd is applied to the resis⎛q ⎞ tance R ⎜ um ⎟ . According to the simplified level II ⎝ γR ⎠ method [14], the limit state function concerning a ULS problem is written as g(X,ϑR,ϑE) = ϑRR(X) – ϑEE(X)

1 exp −α Rβ Vϑ R

(

)

(

E γ GGk + γ QQk

)

(31)

or ⎛q ⎞ E γ GGk + γ QQk ≤ R ⎜ um ⎟ ⎝ γ R′ ⎠

(

)

(32)

The comparison between the action effects and the resistance in Eqs. (28), (31) and (32) automatically takes into account the structural behaviour. The internal actions path allows the designer to understand the structural behaviour, including the redistribution of internal actions.

Concerning the evaluation of the actions effects Ed, the relationships of Eqs. (31) and (32) are an approximation of Eq. (28), which may be unsafe if the action effects are an under-proportional function of the actions [9].

The global resistance factor γR′ can be estimated from the distribution of the actual ultimate load qu′: qu′ = ϑRqu

(33)

The coefficient of variation Vqu′ of the distribution of qu′ can be estimated by means of a set of Monte Carlo simulations that explicitly include the resistance model uncertainty. Assuming that qu and ϑR are independent random variables, then the coefficient of variation Vqu′ can be approximated as Vq ′ ≈ Vϑ2 + Vq2 u

R

(34)

u

The global resistance factor γR′ is derived as follows:

(

γ R ′ = exp α Rβ Vq

u′

) = exp ⎛⎜⎝α β R

⎞ Vϑ2 + Vq2 ⎟ R u⎠

(35)

Alternatively, γR′ can be written as follows [1]: (29)

where X is the vector of random parameters and ϑR and ϑE are the resistance and load effects uncertainties respectively. As can be seen, these model uncertainties multiply the resistance R and the load effects E. Furthermore, the model uncertainty factor γRd should account for the difference between the real behaviour of a structure and the results of its numerical model.

Therefore, its value should be derived from the comparison of experimental tests and numerical calculations. Given the distribution of the resistance model uncertainty ϑR, the model uncertainty factor γRd can be derived using the following expression [14]:

γ Rd =

⎛q ⎞ R ⎜ um ⎟ ⎝ γR ⎠ ≤ γ Rd

(27)

The coefficient of variation Vqu is estimated here using the Monte Carlo method. A non-linear analysis up to failure is performed using an FE model for each sample of the random variables in order to obtain the ultimate load qu.

The results of the investigation heavily depend on the assumptions underlying the models used in the nonlinear analysis. Clearly, the approach is meaningful if the structural model covers all relevant failure mechanisms.

It is suggested to make reference to EN 1992-1-1 [2] and EN 1992-2 [8] for the constitutive laws and models for specific situations, e.g. structures where the second-order effects are not negligible. In the case of beams and columns, the proper choice is to use the Sargin law for concrete in compression and a bilinear constitutive law with inclined top branch.

The probabilistic model used for the uncertainty analysis of the structural response mainly covers the material resistances (concrete compressive strength, yield stress and tensile strength of steel) and the model uncertainties. A probabilistic characterization of the geometrical dimensions of the cross-section and the positions of the reinforcing bars could also be considered.

The safety check becomes ⎛q ⎞ R ⎜ um ⎟ ⎝ γR ⎠ ≤ γ Rd

In accordance with EN 1990 [1], the safety check can be rewritten as

(30)

where α∼R = 0.4αR = 0.32 is the sensitivity factor for the resistance model uncertainty and VϑR is the coefficient of variation of the resistance model uncertainty ϑR.

γR′ = γRdγR

(36)

where γRd is defined in Eq. (30) and γR in Eq. (27). The global resistance factor γR′ can be expressed in terms of the coefficients of variation Vqu and VϑR:

γR′ = exp(α∼RβVϑR)exp(αRβVqu)

(37)

Eqs. (35) and (37) lead to slightly different expressions of the global resistance factor γR′. Eq. (35) is derived from the distribution of the actual ultimate load qu′. Hence, the uncertainties related to the resistance model uncertainty ϑR and the ultimate load qu are taken into account according to Eq. (34).

A simplified approach is presented in Eq. (37), which separates the effects of the resistance model uncertainty and the ultimate load on the global resistance factor. Given the probabilistic characterization of the resistance model uncertainty, the contribution of γRd to γR′ is the same irrespective of the uncertainty related to the ultimate

Structural Concrete 14 (2013), No. 1

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D. L. Allaix/V. I. Carbone/G. Mancini · Global safety format for non-linear analysis of reinforced concrete structures

Fig. 2. Structural scheme.

load. The advantage of this approach is that it is straightforward if global resistance factors have to be estimated for a class of structures, for examples according to the simplified level II approach [14].

The model uncertainty in Eq. (33) is related to the estimation of the ultimate load by means of a non-linear analysis. It has been observed [7] that the difference between the results of FE models and experimental tests heavily depends on the type of structural problem and the modelling approach chosen. As discussed in [8], insufficient data are available for quantifying the modelling uncertainty related to the results of a non-linear analysis in order to establish a probabilistic model. In the present paper, the uncertainty concerning the resistance model in Eq. (29) is also used for the ultimate load.

In the following section it is shown that the global resistance factors can be related to the critical regions of the structure, for concrete beams and columns subjected to axial force and bending moment. The case of a single failure mode is considered.

5.1

Continuous beams

A comparison between the values of the global resistance factors γR and γR′ obtained with respect to the distribution of the resistance at section and structure levels is proposed for a two-span continuous beam (Fig. 2).

The structure is loaded by a permanent load gk = 28 kN/m and a variable load qk = 12 kN/m. The beam is designed using C25 concrete and S500reinforcing steel. The cross-section is rectangular with a width b = 0.30 m and depth h = 0.45 m (Fig. 3). The reinforcement areas have been designed using a linear elastic analysis, leading to the areas As = 710 mm2 and As′ = 1137 mm2.

Fig. 3. Cross-section.

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Structural Concrete 14 (2013), No. 1

The global resistance factors are estimated with the Monte Carlo method. For each sample, a non-linear analysis up to failure is performed using an FE model in order to obtain the ultimate load (structural resistance). Moreover, the resisting bending moment (sectional resistance) at the critical cross-section (inner support section) is also evaluated. The coefficients of variation of the distributions of the ultimate load and resisting bending moment are computed at the end of the simulations. Two simulations are performed, as explained in the previous section.

In the first one, the resistance model uncertainty is not included in the probabilistic model in order to assess γR. In the second one, the model uncertainty is modelled as a random variable in order to estimate γR′.

A probabilistic model is derived from [15] for the compressive strength of the concrete, the yield stress and tensile strength of the steel and the resistance model uncertainty. Details of the probabilistic model are given in Table 1.

The results of the investigation are shown in Table 2.

The mean value μ, the standard deviation σ and the coefficient of variation V are estimated for the ultimate load and the resisting bending moment. The global resistance γR is evaluated with Eq. (27). In the case of the resisting bending moment, the coefficient of variation of the distribution of the ultimate load is replaced by the coefficient of variation of the resisting bending moment. The global resistance γR′ is evaluated in the same way as γR, but the resisting model uncertainty ϑR is considered directly in the Monte Carlo simulations, as expressed in Eq. (33).

It can be seen that the coefficients of variation of the distributions of the ultimate load and resisting bending moment coincide. Therefore, the global resistance factors γR and γR′ have the same value. This means that the structural behaviour, in terms of redistribution of internal actions, does not affect the global resistance factor. This factor is only influenced by the material non-linearity concerning the critical section, where failure occurs.

A parametric analysis of the global resistance factor γR′ has been performed for a section subjected to a bending moment with respect to the amount of reinforcement area. It was assumed that failure occurs with crushing of the concrete while the bottom reinforcement is in the plas-

D. L. Allaix/V. I. Carbone/G. Mancini · Global safety format for non-linear analysis of reinforced concrete structures

Table 1. Probabilistic model

Variable

Description

Distribution

Mean value

Std. dev.

C.o.v.

fc25 [MPa] fy [MPa] ft [MPa] ϑR [–]

Concrete compressive strength Yield stress Tensile strength Resistance model uncertainty

log-normal log-normal log-normal log-normal

33.7 560.0 644.0 1.1

5.7 30.0 40.0 0.077

0.17 0.05 0.06 0.07

Table 3. Reinforcement areas

Table 2. Results

Parameter

Ultimate load [kN/m]

Resisting bending moment [kNm]

μ (without ϑR) σ (without ϑR) V (without ϑR) γR μ (with ϑR) σ (with ϑR) V (with ϑR) γR′

86.9 4.2 0.05 1.16 95.4 8.3 0.09 1.31

249.8 12.9 0.05 1.16 274.1 24.0 0.09 1.31

tic range. The relative depth of the neutral axis x/d has been limited to 0.45 in order to ensure enough ductility in hyperstatic beams, as required by EN 1992-1-1 [2].

Seven values of the reinforcement ratio ρ = As/(bd) varying between 0.13 % and 4 % are considered in the design. The reinforcement areas are listed in Table 3. The probabilistic model [15] given in Table 4 has been used to evaluate the global resistance factors γR and γR′.

The behaviour of the coefficient of variation, the mean value and the standard deviation of the distribution of the resisting bending moment is explained below. The coefficient of variation VMR of the distribution of the resisting bending moment is plotted in Fig. 4. The relative variation of VMR is about 10 %. It induces a decrement in the global resistance factor γR amounting to 3 %, which is considered negligible. The reason for such behaviour of VMR is that the standard deviation and the mean value of the distribution increase with the reinforcement ratio with an approximately constant slope, as shown in Figs. 5 and 6.

The contribution MC of the concrete in compression is equal to the product of the resultant C of the stress in the concrete and the distance of this resultant from the centre of gravity of the cross-section. The mean value of the compressive resultant C increases in absolute values from ρ = 0.13 % to ρ = 1.0 %, with the same rate of

ρ [%]

As,btm [mm2]

As,top [mm2]

0.13 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

158 608 1215 1823 2430 3038 3645 4253 4860

– – – 126 733 1341 1948 2556 3163

increment in the resultant F for the bottom reinforcement in order to satisfy equilibrium of internal forces, as shown in Fig. 7. If a reinforcement ratio equal or larger than 1.5 % is adopted, the size of the concrete compression zone reaching the peak stress fc increases. Hence, the small increment in C is due to the gradual broadening of the area of the cross-section with a concrete deformation less than –0.002. Moreover, the distance bc decreases in the mean value for the same reason.

In terms of the standard deviation of the resultant C, a more significant increment can be observed between the reinforcement ratios ρ = 1.5 % and ρ = 4.0 % (see Fig. 8).

As previously mentioned, an increment in the reinforcement ratio leads to a larger number of fibres with deformation less than –0.002. Consequently, the standard deviation of C increases. An increment in the standard deviation of distance bc is observed at the same time. The coupling between the behaviour of the standard deviation of resultant C and the distance bc explains the increment in the standard deviation of the contribution MC to the resisting bending moment.

The contribution MF of the bottom reinforcement is a linear function of the reinforcement area and the steel stress. Whereas the reinforcement ratio ρ varies between 0.13 and 4 %, the bottom steel always yields because the increment in the reinforcement area leads to a linear in-

Table 4. Probabilistic model

Variable

Description

Distribution

Mean value

Std. dev.

C.o.v.

fc35 [MPa] fy [MPa] ft [MPa] ϑR [–]

Concrete compressive strength Yield stress Tensile strength Resistance model uncertainty

log-normal log-normal log-normal log-normal

40.6 560.0 644.0 1.1

5.4 30.0 40.0 0.077

0.13 0.05 0.06 0.07

Structural Concrete 14 (2013), No. 1

35

D. L. Allaix/V. I. Carbone/G. Mancini 路 Global safety format for non-linear analysis of reinforced concrete structures

Fig. 4. Coefficient of variation VMR.

Fig. 5. Mean value of the components of the resisting bending moment.

Fig. 6. Standard deviation of the components of the resisting bending moment.

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Structural Concrete 14 (2013), No. 1

D. L. Allaix/V. I. Carbone/G. Mancini · Global safety format for non-linear analysis of reinforced concrete structures

Fig. 7. Mean value of the internal forces.

Fig. 8. Standard deviation of the internal forces.

crement in both the values μMF and σMF due to the constant value of the coefficient of variation of the distribution of the area of the reinforcing bars.

The contribution MF′ of the top reinforcement is an increasing function of the reinforcement ratio. The increment in the reinforcement ratio leads to an increment in the strain in the top reinforcing bars in order to satisfy equilibrium of the axial forces acting in the cross-section.

Therefore, the stress in the reinforcing bars increases in absolute terms. If the mean value of the stress in the top reinforcing bars is considered, it is noticeable that it decreases due to the increment in the strain. For the same reason, the standard deviation is an increasing function of the reinforcement ratio.

After having performed the non-linear analysis with the mean material resistances, the structural designer knows the value of the bending moment due to the applied loads at the critical cross-section. By means of the proposed safety format, the designer performs the safety check according to Eqs. (28), (31) and (32). The global resistance factors γR and γR′ are plotted in Fig. 9. The difference between the two diagrams simply depends on the re-

sistance model uncertainty, which is not considered in the derivation of γR.

5.2

Columns

The columns of non-sway frames and isolated slender columns are considered here.

5.2.1 Columns of non-sway frames It is assumed that only the material non-linearity can affect the distribution of the internal actions, as in the case of continuous beams. The failure load is the load that leads to the attainment of the bending moment capacity at the critical section of the column. Indeed, the safety check is expressed by the following inequality: MEd ≤ MRd

for

NRd = NEd

(38)

where NEd and MEd are the design axial force and bending moment respectively. Given the interaction diagram (N, M) for the critical cross-section of the column, it is possi-

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D. L. Allaix/V. I. Carbone/G. Mancini · Global safety format for non-linear analysis of reinforced concrete structures

Fig. 9. Global resistance factors gammaR and gammaR’.

Fig. 10. Global resistance factor gammaR.

Fig. 11. Global resistance factor gammaR’.

ble to estimate the global resistance factors γR and γR′ with respect to the distribution of the resisting bending moment for different axial force values. As an example, a concrete column with a square cross-section is considered.

Concrete class C35 and reinforcing steel grade S500 are used in the design. The width of the cross-section is 0.30 m and the distance of the reinforcing bars from the concrete surface is 0.045 m.

It is interesting to investigate the variation in the global resistance factors for different values of NR and MR, which represent the resistance of a cross-section subjected to axial force and bending moment respectively. The area of reinforcement has been varied between As,min = 0.002 Ac and As,max = 0.04 Ac, where Ac is the concrete area. An interaction diagram (NR, MR) is computed for each reinforcement area, considering the mean values of the material properties. The global resistance factors are estimated for each point on this diagram. The probabilistic model listed in Table 4 has been used to

evaluate the global resistance factors γR and γR′. As a result, the global resistance factors are plotted in Figs. 10 and 11. With reference to the possible strain profiles, it could be observed that γR shows a significant variability in the part of the diagram where the steel deformation εs varies between zero and the deformation at yield, which is 0.0027.

The global resistance factor decreases with an increment in the reinforcement area for a fixed value of the axial force Ν. As the reinforcement area increases, so its contribution to the resisting bending moment also rises. The variability in the steel properties is limited and so an increment in the reinforcement area is associated with an increment in the mean value of the resisting bending moment, which is larger than the increment in the standard deviation. Therefore, the coefficient of variation and the global resistance factor decrease.

The structural engineer can plot the internal action path of the critical section of the column on this dia-

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D. L. Allaix/V. I. Carbone/G. Mancini · Global safety format for non-linear analysis of reinforced concrete structures

Fig. 12. Global resistance factor gammaR.

Fig. 13. Global resistance factor gammaR’.

gram and can easily find the values of γR and γR′ to be used in the safety check according to Eqs. (28), (31) and (32).

6

5.2.2 Slender isolated columns Let us consider a column fully restrained at the bottom, free at the top and bent in simple flexure subjected to the action of loads parallel with the axis, horizontal forces and moments at the top. Under these hypotheses, the critical section is at the base of the column. As the loadcarrying capacity of the structure is affected by the second-order effects, the global resistance factors should not refer to the ultimate section capacity because buckling occurs.

The effect of slenderness on the global resistance factors is analysed for a column with the same cross-section as that considered in the previous section. It has been assumed that the slenderness λ = 100, where λ is the ratio between the effective buckling length of the column and the radius of gyration of the concrete section. A parametric analysis of the global resistance factors with respect to the reinforcement area has been performed. As in the previous section, the reinforcement area has been varied between As,min = 0.002 Ac and As,max = 0.04 Ac. The reduced interaction diagram is computed using the mean values of the material resistances for different amounts of reinforcement. Given the axial force N, the bending moment M represents the maximum first-order moment that can be carried by the cross-section. This value decreases with respect to the resisting bending moment of the cross-section as the column becomes more slender, except for the case N = 0. The probabilistic model listed in Table 4 has been used to evaluate the global resistance factors γR and γR′.

The global resistance factors γR and γR′ are plotted in Figs. 12 and 13. The shape of the diagrams differs significantly from those of Figs. 10 and 11 due to the slenderness of the column. However, the global resistance factors vary over the same range as that observed in the case of columns of non-sway frames.

Comparison of safety formats

The safety formats proposed in EN 1992-2 and the one proposed in this paper can be compared directly because both are formulated in the domain of the internal actions.

The first example concerns a two-span continuous beam and the second one is related to a slender column.

6.1

Continuous beam

The non-linear analysis concerns the concrete beam already presented in section 5.1. The bending moment at the inner support section is plotted as a function of the load level in Fig. 14.

The design value Ed of the bending moment due to the applied loads is computed for γG = 1.35 and γQ = 1.5.

The ultimate load level is 89.3 kN/m and corresponds to a bending moment of –246 kNm at the inner support section.

Let us consider the design resistance Rd according to Eqs. (31) and (32) of the safety format proposed in the present paper. According to Eq. (31), the ultimate load is divided by γR and then the corresponding bending moment is divided by γRd. The global resistance factor γR = 1.16 according to Eq. (27), whereas γRd is assumed to be 1.09 from Eq. (30). If the safety check is performed using Eq. (32), the ultimate load is divided by γR′, which is 1.31.

The safety format according to EN 1992-2 is applied by means of Eqs. (18) and (19), which are analogous to Eqs. (31) and (32). According to Eq. (18), the ultimate load is divided by γO and then the corresponding bending moment is divided by γRd. The global safety factor γO and the model uncertainty factor γRd are equal to 1.20 and 1.06 respectively. The safety verification according to Eq. (19) requires that the ultimate load is divided by γO′, which is 1.27.

It can be seen in Fig. 14 that the safety formats according to Eqs. (19) and (32) lead to almost the same Rd value because the difference between γR′ and γO′ is negligible. Further, the difference between the Rd values obtained from Eqs. (18) and (31) is insignificant. Therefore,

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D. L. Allaix/V. I. Carbone/G. Mancini · Global safety format for non-linear analysis of reinforced concrete structures

Fig. 14. Example 1: Application of the safety format.

the two safety formats lead to similar results in this application example.

6.2

Slender column

A slender column is subjected to the vertical forces Ngk = 280 kN and Nqk = 80 kN, a horizontal force Hqk = 10 kN and two moments Mgk = 27 kNm and Mqk = 8 kNm. The column is 8 m high and the square cross-section is 0.45 m wide. Fig. 15 shows the structural scheme and the section.

The column is designed using C35 concrete and S500 reinforcing steel. The reinforcement areas As1 and As2 are both equal to 1527 mm2. The slenderness of this column is λ = 123.

The probabilistic model listed in Table 5 has been used to evaluate the global resistance factors γR and γR′.

The resistance model uncertainty is characterized by a larger mean and larger standard deviation with respect to the probabilistic model of the first example. The present model also takes into account the presence of the axial force.

The internal actions path is plotted in Fig. 16. It can be seen that the safety formats according to Eqs. (18) and (31) agree well. The global resistance factor γR and the

Fig. 15. Structural scheme.

Table 5. Probabilistic model

Variable

Description

Distribution

Mean value

Std. dev.

C.o.v.

fc35 [MPa] fy [MPa] ft [MPa] φ [rad] ϑR [–]

Concrete compressive strength Yield stress Tensile strength Out-of-plumb Resistance model uncertainty

log-normal log-normal log-normal normal log-normal

40.6 560.0 644.0 0.0 1.2

5.4 30.0 40.0 0.0015 0.18

0.13 0.05 0.06 – 0.15

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Fig. 16. Example 2: Application of the safety format.

model uncertainty γRd applied in Eq. (28) are 1.18 and 1.20 respectively.

The reader will notice a difference between the design resistances Rd computed using Eqs. (19) and (32).

The reason for this difference is the value of 1.61 used for the global resistance factor γR′, whereas γO′ = 1.27 is used in Eq. (19). The larger value of γR′ with respect to the previous one is explained by the different probabilistic model of the resistance model uncertainty ϑR.

7

Conclusions

This paper proposes a safety format for the non-linear analysis of concrete structures. The safety check is performed in the domain of the internal actions. Following the suggestions of previous papers, the mean values of the material resistances are used in the non-linear analysis in order to estimate the internal actions accurately. Two global resistance factors γR and γR′ are applied on the resistance side of the safety check.

The global resistance factors depend on the coefficient of variation of the actual resistance of the structure.

The uncertainty of the resistance is related to the structural layout, the randomness of the material properties and geometrical dimensions of the members and model uncertainties.

The results of the application examples are valid for the particular beam in bending and column investigated for the combination of axial force and bending moment.

The results presented in the paper cannot be directly extrapolated to other structures and failure modes. A broad numerical investigation would be necessary in order to assess global resistance factors that can be used for several

types of structure that may fail according to different failure modes.

The proposed safety format is compared with the one in EN 1992-2. Very close agreement for the resistance Rd is obtained in the first example (beam), whereas a discrepancy is observed in the second example (slender column) due to the different assumptions concerning the resistance model uncertainties. A detailed comparison between the method suggested in EN 1992-2 and the method proposed in this paper would require an investigation of several structures and failure modes.

References 1. CEN: EN 1990: Eurocode – Basis of structural design. CEN, Brussels, 2003.

2. CEN: EN 1992-1-1: Eurocode 2 – Design of concrete structures. Part 1-1: general rules and rules for buildings. CEN, Brussels, 2004.

3. CEB: New developments in non-linear analysis methods.

Bulletin d’Information No. 229. CEB, Lausanne, 1995.

4. fib: fib Bulletin 56: Model Code 2010, first complete draft, vol. 2, fib, Lausanne, 2010.

5. Schlune, H., Plos, M., Gylltoft, K.: Safety formats for nonlinear analysis tested on concrete beams subjected to shear forces and bending moments. Engineering Structures 33 (2011), pp. 2350–2356.

6. Schlune, H., Gylltoft, K., Plos, M.: Safety formats for non-linear analysis of concrete structures. Magazine of Concrete Research (2012), pp. 1–12.

7. Sykora, M., Holicky, M.: Safety format for non-linear analysis in the Model Code – Verification of reliability level. fib symposium proceedings, Prague, 2011.

8. CEN: EN 1992-2: Eurocode 2 – Design of concrete structures. Part 2: concrete bridges. CEN, Brussels, 2005.

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9. fib: fib Bulletin 55: Model Code 2010, first complete draft, vol. 1. fib, Lausanne, 2010.

10. Holicky, M.: Probabilistic approach to the global resistance factor for reinforced concrete members. In: Taerwe, Proske: 5th International Probabilistic Workshop, Ghent, Acco, 2007, pp. 209–218.

11. Allaix, D. L., Carbone, V. I., Mancini, G.: Global resistance factor for reinforced concrete beams. In: Taerwe, Proske: 5th International Probabilistic Workshop, Ghent, Acco, 2007, pp. 195–208.

12. Allaix, D. L, Mancini, G.: Assessment of a global resistance factor for reinforced concrete columns by parametric analysis. In: Shen, Li, Wu, Luo: International Symposium on Innovation & Sustainability of Structures in Civil Engineering, Shanghai, Southeast University Press, 2007, pp. 1–9.

13. Cervenka, V.: Global safety format for nonlinear calculation of reinforced concrete. In: Taerwe, Proske: 5th International Probabilistic Workshop, Ghent, Acco, 2007, pp. 183–194.

14. König, G., Hosser, D.: The simplified level II method and its application on the derivation of safety elements for level I. CEB, 1983.

15. Joint Committee on Structural Safety. Probabilistic Model Code, Internet publication, 2001, www.jcss.byg.dtu.dk.

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Diego Lorenzo Allaix Department of Structural, Building & Geotechnical Engineering Politecnico di Torino Corso Duca degli Abruzzi 24 10129 Torino, Italy e-mail: diego.allaix@polito.it Phone: +39 011 090 4825 Fax: +39 011 090 4899

Vincenzo Ilario Carbone Department of Structural, Building & Geotechnical Engineering Politecnico di Torino Corso Duca degli Abruzzi 24 10129 Torino, Italy e-mail: vincenzo.carbone@polito.it

Giuseppe Mancini Department of Structural, Building & Geotechnical Engineering Politecnico di Torino Corso Duca degli Abruzzi 24 10129 Torino, Italy e-mail: guiseppe.mancini@polito.it

Technical Papers Aurelio Muttoni Franco Lurati Miguel Fernández Ruiz*

DOI: 10.1002/suco.201200058

Concrete shells – towards efficient structures: construction of an ellipsoidal concrete shell in Switzerland Concrete shells have been widely used in the past as economical and suitable solutions for a number of structures such as roofs, silos, cooling towers and offshore platforms. Taking advantage of their single or double curvature, bending moments and shear forces are limited, and the structures develop mostly membrane (in-plane) forces, allowing them to span large distances with limited thicknesses (typically just a few centimetres). In recent decades, advances in numerical modelling, formwork erection and concrete technology have opened up a new set of possibilities for the use of concrete shells. This paper describes the design and construction of a shell in the form of an ellipsoid (93 × 52 × 22 m) and with thickness varying between 100 and 120 mm. The shell was built using sprayed concrete and also ordinary concrete in some regions. A number of tailored solutions were also adopted, such as post-tensioning, addition of fibres and shear studs, to ensure satisfactory performance at both the serviceability and ultimate limit states.

Keywords: shell, concrete structure, design, sprayed concrete, fibre-reinforced concrete, architecture

1

Introduction

Masonry arches and vaults The history of masonry arches and vaults is rich and embraces a number of building traditions. Detailed summaries and analyses can be consulted elsewhere [1–5]. Masonry arches were most probably the first structures invented by mankind to span significant distances across rivers or valleys. These structures, which might have been inspired by natural shapes, appeared as early as the 2nd millennium BC in Mesopotamia. They are composed of a set of prepared stones (voussoirs) arranged side by side in direct contact or with intermediate mortar. Taking advantage of the shape of the arch, external actions (gravity-induced forces and imposed loads) are carried by the compression forces that develop internally and at the interfaces between the voussoirs (and sometimes through the spandrel walls and filling at the extrados of the masonry works). The line defining the theoretical resultant of the compression forces equilibrating the external actions

* Corresponding author: miguel.fernandezruiz@mfic.ch Submitted for review: 8 December 2012 Accepted for publication: 12 December 2012

is usually called the “thrust line” (comprising its associated thickness referring to the material strength) and needs to remain inside the masonry since no tensile stresses are acceptable at the joints of such constructions [5]. The shape of the arch is thus decisive. Shapes where the thrust line does not remain inside the masonry are not in equilibrium with the external actions and lead to the collapse of the structure.

Vaults are double-curvature surfaces assembled from masonry voussoirs or bricks. They have traditionally been used as roofs or to cover underground constructions. As for masonry arches, vaults need to develop the thrust surface within the masonry work. However, loads can be carried in more than one direction due to the double curvature of the vaults. For classical dome shapes, with spherical soffits, the pressure surface can be kept within the masonry by significantly increasing its thickness in selected zones (e.g. Pantheon dome, Rome). In these cases the vaults exert a horizontal thrust at the bottom supports. Another possibility is to provide the vault with tangential tensile forces, keeping the pressure surface within the masonry. St. Peter’s basilica (Vatican City) was strengthened in the mid-18th century with four iron chains serving as a tension ring after large cracks in the dome were discovered [5].

Reinforced concrete shells The problems observed for masonry works, and in particular for vaults (adequacy of the form for the actions leading to significant thicknesses), can be mostly solved with the addition of reinforcement, whose tensile forces can deviate the thrust surface, allowing it to lie within the concrete. As a consequence, reinforced double-curvature structures develop mostly membrane forces (in-plane axial and shearing forces) and very limited bending and out-ofplane shear forces. As a consequence, the required thickness can be significantly reduced, leading to double-curvature thin concrete shells.

Following this principle of membrane behaviour, the first concrete shells were built expressing this potential in a clear manner [6]. Designers in Europe (F. Dischinger, E. Torroja, R. Maillart) and America (A. Tedesko) experienced the advantages of such constructions with thicknesses as low as 30–40 mm. These works, built mainly between 1910 and 1940, typically used shapes defined by analytical expressions (such as sections of spheres, cylin-

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A. Muttoni/F. Lurati/M. Fernández Ruiz · Concrete shells – towards efficient structures: construction of an ellipsoidal concrete shell in Switzerland

ders or hyperbolic paraboloids). They included stringers in the edges to ensure membrane behaviour as perfectly as possible. The difficulties encountered in the analytical treatment of thin shells explains the rather limited number of shapes used during this period and the low number of designers using them. Following this period, interesting new developments took place between 1940 and 1970 in America, instigated by the Spanish architect F. Candela and the Uruguayan engineer E. Dieste (the latter also involved with the development of masonry shells). Their approach consisted of performing analyses that were as simple as possible (Candela particularly) and combining different sections of previous shapes, preferring mostly hyperbolic paraboloids due to their plastic qualities and ease of construction. Their approach led to a larger and richer variety of forms. In Switzerland, H. Isler [7, 8], too, built an impressive number of unusual shells between the 1960s and 1980s whose shape was obtained and optimized by different mechanical analogies (pneumatic, gravity-shaped membranes, etc.). It should be noted that, actually, the different experiences with concrete shells were mostly linked to the skills of their designers rather than to a continuous evolution in concrete shell design.

In the 1980s and 1990s, concrete shells were seldom used as a consequence of the large number of man-hours required for building formwork and placing reinforcement with respect to the material costs, which typically gave priority to other structural solutions. In recent years, the situation has changed somewhat. The possibilities offered by new types of concrete (as fibre-reinforced concrete), reinforcement, numerical cutting of formwork and its positioning on the construction site as well as the new possibilities available for the analysis of these structures (related mostly to computer software) have allowed the development of a new approach to shells, with more freedom in the choice of shape. Nevertheless, an understanding of the role of double curvature, the load-carrying mechanisms and the governing limit states of these structures still remains essential to the design of shells. This is particularly relevant with respect to the analysis of the buckling behaviour of these structures. A state-of-the-art review of this topic was published in 1979 [9] by the International Association for Shell & Spatial Structures, providing guidance on such design. However, research is still being performed in this area [10, 11] and remains necessary.

In the following, the most significant aspects of the design and construction for concrete shells will be discussed with reference to a shell built recently in Switzerland, a project in which the authors of this paper were involved.

2

Design of a concrete shell for covering a mall at Chiasso, Switzerland

Why a concrete shell?

An ellipsoid-shaped roof was planned to cover a new mall to be constructed at Chiasso, Switzerland. This roof satisfied the requirements of the client in terms of usability, architectural needs and image. The thickness of the ellipsoid was decisive since it directly influenced the amount of floor area that could be let, see Fig. 1a. Solutions were

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(a)

(b)

Fig. 1. How the thickness of the roof influences the lettable floor area: (a) thick roof, and (b) thin concrete shell

investigated using timber and steel linear elements. Local buckling, however, was the governing factor for these solutions, requiring significant thicknesses in the most critical parts. This led to uneconomical solutions for the client, with significant reductions in the lettable floor area. By contrast, a concrete shell was shown to be a suitable solution. Its thickness was only 100 mm in the critical regions influencing the lettable floor area. This allowed the client to have sufficient space available and optimized the cost of the mall (Fig. 1b).

Geometry and main properties of shell The ellipsoid shell has axis dimensions of 92.8 m (major axis) and 51.8 m (minor axis) and is 22.5 m high. The ellipsoid is cut by a horizontal plane and is supported on a concrete basement composed of transverse walls, leading to a total height for the shell of 18.24 m, see Fig. 2. The thickness of the shell varied. A value of 100 mm was selected as the default thickness. This was governed by constructive issues (minimum thickness considering reinforcement cover necessary) and also ensured adequate safety against buckling.

Four layers of reinforcement were provided, two at the intrados and two at the extrados of the shell. The reinforcement layers were oriented following the radial (meridian) and tangential (parallel) directions. This was selected as the most effective layout for structural reasons.

The four-layer arrangement was needed to control the bending moments and shear forces that develop at the basement connection, near the prestressed zone, and for connecting to the steel structure at the zenith opening (Fig. 2). Bending moments and shear forces in other regions were very limited. Four reinforcement layers were nevertheless arranged in all regions for constructional reasons, to ensure suitable crack control (which may appear depending on the load cases) and to ensure adequate safety against buckling of the structure.

In addition to the ordinary reinforcement, 35 posttensioned tendons (0.6 inch monostrand tendons) were arranged near the equator of the shell (from level +5.50 m to level +12.60 m, see Fig. 1) to carry membrane tension in the horizontal direction. (They also presented a limited di-

A. Muttoni/F. Lurati/M. Fernández Ruiz · Concrete shells – towards efficient structures: construction of an ellipsoidal concrete shell in Switzerland (a)

(b)

Fig. 2. Main geometrical dimensions: (a) section along major axis, (b) section along minor axis

mension for the plastic duct, thus minimizing the disturbance in the compression field developing through the shell [12, 13].) The thickness of the shell was increased to 120 mm in this region (between levels +4.24 m and +13.35 m).

At the level of the connection to the concrete basement (between levels +4.24 m and +5.14 m), shear studs were also provided to ensure adequate shear strength and deformation capacity in this region (subjected to parasitic shear forces and bending moments).

The thickness of the shell was also 120 mm from level +21.60 m to the zenith opening. In the top part, the increased thickness allowed the concrete shell to be linked to a steel structure at the zenith opening (10.21 × 5.70 m); this allows daylight to reach the inside of the mall. In addition, between levels +4.81 m and +18.78 m, there are several circular openings (0.40 m dia.), see Fig. 2.

Concrete properties The structure was cast using sprayed concrete from level +4.24 m to level +19.90 m. This allowed conventional (one-sided) formwork to be used for the entire shell.

Where the slope was sufficiently limited (< 20°, from level +19.90 m to level +22.48 m), concrete was poured conventionally. For both concrete types, a characteristic compressive strength fck of 30 MPa at 28 days was specified.

Hooked metallic steel fibres (30 kg/m3) were used in the sprayed concrete region between level +4.24 m and level +13.36 m. The fibres have a length of 30 mm and a length-to-diameter ratio of 80. The fibres were arranged to enhance crack control (in the post-tensioned region) and to improve the ductility of concrete under high normal and shear forces (at the junction with the basement). The sprayed concrete contained 300 kg/m3 of cement and 25 kg/m3 of lean lime (to enhance the workability of the concrete). The aggregate sizes between 0 and 4 mm accounted for 70 % of the total, the rest ranging between 4 and 8 mm. Addition of water was performed at the spraying gun.

3

Design aspects

Apart from some aspects that were governed by constructional issues (e.g. shell thickness, as explained previously), the design of the shell and its reinforcement was governed by three structural aspects: the membrane (in-plane) inner forces in the shell, the second-order effects and the nonmembrane (parasitic) bending and shear forces at the junction with the concrete basement. The structure was modelled using a 3D finite element model (using the commercial program ANSYS) capable of performing linear and non-linear analyses. A comparison of the software re-

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A. Muttoni/F. Lurati/M. Fernández Ruiz · Concrete shells – towards efficient structures: construction of an ellipsoidal concrete shell in Switzerland (a)

(b)

Fig. 3. Membrane (in-plane) inner forces: (a) equator region, where maximum tensile forces develop, (b) diagram of unitary force intensity

(a)

(b)

(c)

Fig. 4. Deformed shapes at buckling failure: (a) reduced stiffness at zenith opening connection, (b) reduced flexural stiffness at top of post-tensioned region, and (c) overall reduced flexural stiffness

sults with some analytically solved cases such as spheres [14] was also performed in order to check the accuracy and relevance of the FEM results. This approach provided refined solutions but with a means to control them and check the suitability of the results obtained.

Membrane inner forces The membrane (in-plane) tensile inner forces were generally moderate or low and could be handled by the minimum reinforcement amount. The most significant exception to this rule was the large tensile forces occurring at the equator of the shell (see Fig. 3). Design was performed to ensure sufficient strength at the ultimate limit state as well as to control crack widths at the serviceability limit state. This required arranging post-tensioning in this region (monostrand tendons). In other parts of the structure it was noted that the delayed strains in the concrete (mainly shrinkage) led to tensile stresses in some regions (particularly at the connection to the concrete basement) which required the provision of sufficient reinforcement for crack control (spacing and crack opening).

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Buckling behaviour Buckling governed the design of the top region of the shell, with minimum curvature and largest compression forces. Design was performed according to IASS recommendations [9]. In order to determine the buckling behaviour, non-linear analyses were performed considering the initial imperfections, creep strains of concrete, the actual cracked stiffness and the non-linear behaviour [9]. In addition, a sensitivity analysis was performed by assuming large reductions in the stiffness in some selected cases (cracking in selected regions of the shell, local imperfections combined with snow cases or temperature). This modified the buckling modes (see Fig. 4), but with acceptable results in all cases.

Edge forces Non-membrane inner forces developed mostly at the concrete basement connection (edge forces due to compatibility). Also, non-membrane inner forces were observed in the post-tensioned region and zenith opening (nevertheless, with a lower intensity than at the basement).

A. Muttoni/F. Lurati/M. Fernández Ruiz · Concrete shells – towards efficient structures: construction of an ellipsoidal concrete shell in Switzerland (b)

(a)

Fig. 5. Comparison of non-membrane forces in vertical (radial) direction (normalized by maximum forces for a clamped case) as a function of the distance to the clamped edge (s normalized by thickness of slab): (a) bending moments, and (b) shear forces

(a)

(b)

(c)

Fig. 6. Shear and bending forces at the connection to the concrete basement: (a) location of theoretical thrust line, (b) behaviour of specimen tested with shear studs, and (c) behaviour of specimen tested without shear studs

The edge forces (bending and shear) typically appear at the boundaries of a shell and are well described in the scientific literature [14]. Both forces can be calculated on the basis of the shell geometry as vy = vy,0 · exp(–λ vs) ·cos(ω vs) my = my,0 · exp(–λ ms) ·cos(ω ms) where vy, my vy,0, my,0

λ v, λ m, λ v, λ m

unitary shear forces and bending moments at a distance s (perpendicular to the edge direction) unitary shear forces and bending moments at the clamped edge parameters depending on geometry of shell [14] (radius of curvature, thickness, Poisson’s coefficient, clamping conditions)

Both formulas lead to an exponential decay of the edge forces modulated by a harmonic function. For the present shell, the influence of the edge forces was almost negligible at a distance > 40 times the thickness of the shell (see Fig. 5). Accounting for the various imposed strains and load cases, the bending moments and shear forces at the free edges could act with both positive or negative values.

The significance of the edge forces of the boundary conditions should also be noted. For clamped edges, a bending moment appears (my,0,clamp), which becomes zero for a hinged shell at the edge line, but with a maximum thereafter (with lowest absolute value anyway). Also, with respect to the shear force, a shell supported on a clamped edge exhibits a maximum shear force (at the supported edge, vy,0,clamp) double that of a hinged shell at the edge line (vy,0,hinged). Fig. 5 plots the normalized inner forces in the region near the basement for two cases. The differences allow an appreciation of how the boundary conditions and deformation capacity influence these forces.

Different strategies are usually followed to provide suitable control of the edge forces. The first one consists of increasing the thickness of the shell locally so that the thrust line can be better accommodated (an analogous approach to that followed for stress ribbons [15]). Alternatively, the reinforcement can be designed at the serviceability limit state accounting for suitable crack control and at the ultimate limit state assuming a plastic redistribution of internal forces (plastic hinge, see Fig. 5, solution between clamped and hinged structures). This latter solution requires a certain level of deformation capacity in the edge region which is influenced by shear forces [16].

For the present shell, the second strategy was adopted to account for architectural and functional needs. The

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solution selected was tested in the laboratory, see Fig. 6.

Transverse reinforcement was provided (an amount equal to 0.5 % of the concrete transverse surface) allowing sufficient strength with a large deformation capacity (Fig. 6b).

This was instrumental and led to behaviour significantly better than that of a reference control specimen (Fig. 6c) tested without shear studs, which failed at a lower strength but most significantly with a quite limited deformation capacity.

4

Construction of the shell

Formwork was placed over timber falsework, Fig. 7a. The formwork was composed of panels bent in situ and screwed in their corresponding positions (Fig. 7b). Reinforcement was then placed and concrete was sprayed or poured in situ (Figs. 7c, 7d). Placing the reinforcement and concreting the shell took about three months in total.

Once concreting was finished, decentering of the shell was performed. This is probably the most critical phase, and in some cases has led shells collapsing [17]. For the present shell, the work was performed in a number of phases in order to avoid decentering being the governing design situation. Firstly, half of the post-tensioning force was applied (one out of two tendons post-tensioned).

Then, the timber falsework in contact with the post-ten-

sioned zone was removed, followed by the post-tensioning of all tendons. This operation ensured correct post-tensioning transfer to the concrete. Finally, the vertical struts of the falsework supporting the top region of the shell were gradually released, leading to complete decentering of the structure. Measured deflections were recorded during the process and were in good agreement with predicted values. Some pictures of the completed work can be seen in Fig. 8.

The cost of the concrete structure was 49 % for falsework and formwork, 21 % for ordinary reinforcement, 5 % for post-tensioning, 24 % for sprayed concrete and 1% for poured in situ concrete. This reveals the relatively large cost of falsework and formwork for this type of structure, and points to the need for future research on more efficient techniques.

5

Conclusions

This paper has provided a summary of the most relevant aspects related to the design and construction of a concrete shell built in Chiasso, Switzerland. Its main conclusions are: – Concrete shells are efficient structures and can be used as durable solutions for roofs or for covering large spaces.

(a)

(b)

(c)

(d)

Fig. 7. Construction of shell: (a) temporary falsework, (b) placing of prestressing tendons, (c) spraying of concrete, and (d) pouring of concrete

48

Structural Concrete 14 (2013), No. 1

A. Muttoni/F. Lurati/M. Fernández Ruiz · Concrete shells – towards efficient structures: construction of an ellipsoidal concrete shell in Switzerland

Fig. 8. Completed structure

– Concrete shells can be built with limited thicknesses, thus maximizing the space inside them. This fact also permits the amount of material and energy in their construction to be minimized, thus contributing to a sustainable construction approach.

– The design of concrete shells can be governed by aspects that are not always critical in other types of concrete structure, i.e. membrane forces, second-order effects and edge forces (for compatibility reasons), which are potentially governing criteria in different regions of the shell.

– Research and innovation are still required for formwork and falsework. Traditional approaches lead to good results in terms of shape and quality, but double-curvature surfaces lead potentially to excessively complicated (and expensive) systems.

– Design for buckling of concrete shell structures is a complex topic and is not suitably covered by codes of practice. A review and update of such design provisions should help and encourage designers in the use of concrete shell structures.

Credits Structural design and engineering: Aurelio Muttoni, Franco Lurati, Miguel Fernández Ruiz (Mendrisio and Lausanne, Switzerland) Architecture: Elio Ostinelli (Chiasso, Switzerland) Client: Centro Ovale 1 SA, (Chiasso, Switzerland) Contractor: Muttoni SA, (Bellinzona, Switzerland) Cost: SFr 5,300,000 (VAT and design costs included)

Structural Concrete 14 (2013), No. 1

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A. Muttoni/F. Lurati/M. Fernández Ruiz · Concrete shells – towards efficient structures: construction of an ellipsoidal concrete shell in Switzerland

References 1. Arenas de Pablo, J. J.: Bridges (in Spanish: Caminos en el aire: los puentes). Colegio de ingenieros de Caminos, Canales y Puertos, Madrid, 2 vols., 2002.

2. Boothby, T. E.: Analysis of masonry arches and vaults. Prog.

Struct. Engng. Mater., vol. 3, 2001, pp. 246–256.

3. Boyd, T. D.: The Arch and the Vault in Greek Architecture.

American Journal of Archaeology, vol. 82, No. 1, 1978, pp.

83–100.

4. Heyman, J.: The Stone Skeleton: structural engineering of masonry architecture. Cambridge University Press, 1995.

5. Muttoni, A.: The art of Structures – an introduction to the functioning of structures in architecture. EPFL Press, Lausanne, Switzerland, 2011.

6. Cassinello, P., Schlaich, M., Torroja, J. A.: Félix Candela. In memoriam (1910–97). From thin concrete shells to the 21st century’s lightweight structures (in Spanish: Félix Candela.

En memoria (1910–1997). Del cascarón de hormigón a las estructuras ligeras del s. XXI). Informes de la Construcción, vol. 62, No. 519, 2010, pp. 5–26.

7. Chilton, J., Isler, H.: Heinz Isler: The engineer’s contribution to contemporary architecture. RIBA Publications/Thomas Telford, 2000, pp. 20–29.

8. Kotnik, T., Schwartz, J.: The Architecture of Heinz Isler. Journal of the International Association for Shell & Spatial Structures, vol. 52, No. 3, 2011, pp. 185–190.

9. IASS (International Association for Shell & Spatial Structures), Working Group No. 5: Recommendations for reinforced concrete shells and folded plates. Madrid, Spain, 1979.

10. Espín, A.T.: Optimal design of shape and reinforcement in concrete shells (in Spanish: Diseño óptimo de forma y armado de láminas de hormigón). PhD thesis, Universidad Politécnica de Cartagena – Departamento de estructuras y construcción, Spain, 2007.

11. Mungan, I.: A conceptual approach to shell buckling with emphasis on reinforced concrete shells. In: Proc. of International Association for Shell & Spatial Structures (IASS), symposium, 2009, Valencia, pp. 39–50.

12. Muttoni, A., Burdet, O., Hars, E.: Effect of Duct Type on the Shear Strength of Thin Webs. ACI Structural Journal, Farmington Hills, USA, 2006, pp. 729–735.

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Structural Concrete 14 (2013), No. 1

13. Fernández Ruiz, M., Muttoni, A.: Shear strength of thinwebbed post-tensioned beams. American Concrete Institute, Structural Journal, vol. 105, No. 3, 2008, pp. 308–317.

14. Timoshenko, S., Woinowsky-Krieger, S.: Theory of plates and shells, 2nd ed., McGraw-Hill, 1959.

15. Schlaich, J., Engelsmann, S.: Stress Ribbon Concrete Bridges, Structural Engineering International, 1996, pp.

271–274.

16. Vaz Rodrigues, R., Muttoni, A., Fernández Ruiz, M.: Influence of shear on the rotation capacity of R/C plastic hinges.

American Concrete Institute, Structural Journal, vol. 107, No. 5, 2010, pp. 516–525.

17. Garlock, M., Billington, D.: Félix Candela. Engineer, Builder, Structural Artist. Yale University Press, New Haven, CT, 2008.

Aurelio Muttoni Muttoni & Fernández, ic SA Route du Bois 17, CH-1024 Lausanne, Switzerland aurelio.muttoni@mfic.ch

Franco Lurati Lurati Muttoni Partner SA Via Moree 3, CH-6850 Mendrisio, Switzerland franco.lurati@Impartner.ch

Miguel Fernández Ruiz Muttoni & Fernández, ic SA Route du Bois 17, CH-1024 Lausanne, Switzerland miguel.fernandezruiz@mfic.ch

Technical Paper Syed Ishtiaq Ahmad* Tada-aki Tanabe

DOI: 10.1002/suco.201100009

Three-dimensional FE analysis of reinforced concrete structures using the lattice equivalent continuum method The lattice equivalent continuum model (LECM) has proved to be very effective in analysing reinforced concrete structures in twodimensional cases. That model is extended here to three dimensions and is fitted to a finite element formulation for analysing three-dimensional reinforced concrete structures. In any of the three principal directions, the stress–strain behaviour of concrete will be affected by the stress state in the other two directions. Consequently, stress-strain curves for concrete will shift from a uniaxial pattern. This phenomenon is considered in this work by selecting concrete peak stresses in three alternative approaches. The effectiveness of those approaches is also evaluated. The results of the calculations show good reproduction of the test data, which indicates the validity of this proposed 3D modelling of reinforced concrete.

Keywords: finite element, three-dimensional model, simulation, reinforced concrete, ultimate strength, concrete structure, lattice, model

1

Introduction

Analysing reinforced concrete to simulate its three-dimensional behaviour under different types of loading has always been a challenging issue for researchers, engineers and academics due to its complexity arising from the heterogeneous concrete, reinforcement and presence of cracking. Many constitutive models have been proposed to simulate this complex 3D behaviour of reinforced concrete and are available in the literature. These constitutive models have used different approaches in their formulations. In one approach, some researchers have used lattice and particle models in which the continuum is replaced by a system of discrete elements. Van Mier et al. [1], Schlangen [2] and Niwa et. al. [3] were the first to use a lattice-type model for concrete. Further modification of this lattice-type model in later years can also be found elsewhere in the literature [4, 5, 6]. The smeared crack model, first introduced by Rashid [7] and Cˇervenka and Gerstle [8], is another approach that has been extensively used to develop constitutive models for reinforced concrete. It is based on the development of appropriate continuum material models in which cracks are smeared over a distinct

* Corresponding author: siahmad@ce.buet.ac.bd Submitted for review: 03 February 2011 Revised: 11 July 2012 Accepted for publication: 23 September 2012

area, typically a finite element or an area corresponding to an integration point of the finite element. Many recent, successful models are based on this smeared crack approach [9, 10]. Although a number of models are available in the literature, the authors of this paper feel that there is room for improvement in this area. The authors also believe that any research in this area should benefit the profession so that the existing gap between scientific activity and practice is narrowed. It is therefore of interest to develop constitutive laws for reinforced concrete which will not only give reasonably accurate results but will also provide a clear and easy understanding of the complex phenomenon occurring inside concrete elements with respect to stress and strain distribution, i.e. more engineering-oriented constitutive laws as opposed to the prevailing constitutive laws for reinforced concrete. To do this, the concept of the equivalent continuum of the lattice system [11, 12] is used and extended to three dimensions.

The lattice equivalent continuum model (hereinafter called “LECM”) has its origins in the successful use of discrete lattice modelling of reinforced concrete elements by Niwa et al. [3]. The continuum model essentially retains the features of the uniaxiality of stress-bearing materials; however, combining those features alters their fundamental characteristics from an initially orthotropic model and later even to a general, anisotropic model. Conceptually, this model begins with lattice-type idealization but ultimately the governing equations represent equivalent continuum of that lattice system, i.e. similar to a smear cracktype model. The concepts behind the formulation of the LECM are unique and different from other well-known uniaxial-type models such as Bazant’s microplane model [13]. For instance, the number of microplanes used in Bazant’s model is far more than the lattices used for modelling reinforced concrete in the LECM. Therefore, the present model is far easier to understand and apply. Furthermore, appropriate peak stress and strain criteria for individual lattices distinguish the LECM model from the microplane model, where the stress-strain laws are not the ones for macroscopic concrete elements.

The paper begins with a brief introduction to the formulation to derive the constitutive equation in the LECM. That is followed by the modelling of the stress transfer between cracked faces in concrete due to traction by introducing shear lattices into the system. Since the choice of the ultimate stress in the concrete lattice system influ-

© 2013 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Structural Concrete 14 (2013), No. 1

51

S. I. Ahmad/T. Tanabe · Three-dimensional FE analysis of reinforced concrete structures using the lattice equivalent continuum method

ences the results of the computations, the analysis is performed using three different ways of selecting peak stresses in a concrete lattice system, and a conclusion is drawn from the analysis results as to which system is closer to the actual concrete behaviour.

2

Formulation of the constitutive equation

The formulation of the lattice equivalent method is based on the assumption that reinforced concrete is cracked and composed of two sets of lattices. One set of lattices is parallel with the original discontinuous plane and lattices orthogonal to it. We call these main lattices. Fig. 1 depicts schematically the concept of main lattice idealization in reinforced concrete. The other set is the one that considers the shear transfer between main concrete lattices and will be introduced in the next section. The stresses and direction of the steel main lattices are those of the steel reinforcement itself, whereas crack directions in the concrete, which are in turn fixed by principal stresses, determine the concrete main lattices and their orientation.

We begin by assuming a uniformly strained 3D continuum strain, which has the global coordinates

{ε } = [ ε g

Fig. 1. Lattice idealization of reinforced concrete members

 {

l}

=

x

⎧ εx ⎪ ε ⎪ y ⎪ ε 2 2 2 εξ = [ a b c a b b c c a ] ⎨ z γ ⎪ xy ⎪ γ yz ⎪γ ⎩ zx

⎫ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎭

(2)

where a, b and c are the direction cosines of the lattice direction with respect to the x, y and z axes. For reinforced concrete, ξ, η and ζ are the directions of the principal strains and can be computed using basic continuum mechanics laws. If n number of lattices exists in the continuum, we can write L

{ g}

(3)

r1

l1



0







rj

=

lj



0

l1

(4)

lj

rnn

ln

(1)

The strain in a lattice member in this strain field is assumed to be identical with the strain of Eq. (1). Therefore, for an inclined lattice member for which local coordinates (ξ, η, ζ) are taken such that the ξ coordinate coincides with the lattice axis, the lattice strain εξ is

{ l} =

Steel lattices Concrete lattices

= Rn

ε y ε z γ sy γ yz γ zx ]T

Lattice idealization

RC block

ln

{ l}

where rj = ∂σj/∂εj denotes the tangential stiffness of individual lattices.

Continuum local stresses transformed into global coordinates have the following form: ⎧ Δσ x ⎪ ⎪ Δσ y ⎪ Δσ z ⎨ Δτ ⎪ xy ⎪ Δτ yz ⎪ ⎪⎩ Δτ zx

⎫ ⎪ ⎪ ⎪ ⎬= ⎪ ⎪ ⎪ ⎪⎭

⎡ a2 ⎢ j ⎢ bj2 ⎢ 2 ⎢ cj ⎢ab ⎢ j j ⎢ b jc j ⎢c a ⎢⎣ j j

⎤ ⎥ ⎥ ⎥ ⎥ Δσ l ⎥ ⎥ ⎥ ⎥ ⎥⎦

{ }

Summing over all lattices gives us the expression

{Δσ } g

where

⎧ Δσ x ⎪ ⎪ Δσ y ⎪ Δσ z =⎨ Δτ ⎪ xy ⎪ Δτ yz ⎪ ⎪⎩ Δτ zx

⎫ ⎪ ⎪ ⎪ ⎬= ⎪ ⎪ ⎪ ⎪⎭

⎡ a2 ⎢ 1 ⎢ b12 ⎢ 2 ⎢ c1 ⎢ab ⎢ 11 ⎢ b1c1 ⎢c a ⎢⎣ 1 1

 a2j  an2 ⎤ ⎥  bj2  bn2 ⎥ ⎥  c 2j  cn2 ⎥ Δσ l  a jbj  anbn ⎥ ⎥  bjc j  bncn ⎥  c j a j  cnan ⎥⎥ ⎦

{ }

a12 b12 c12 a1b1 b1c1 c1a1       L

= a 2j b2j c2j a jb j b jc j c ja j       a 2n b2n c2n a n bn bncn cna n

Multiplying the strains by the stiffness of each lattice, the incremental stresses of the replaced continuum can be evaluated as

52

Structural Concrete 14 (2013), No. 1

which can be written as T

{Δσ } = ⎡⎣L ⎤⎦ {Δσ } g

l

ε

T

{ }

= ⎡⎣Lε ⎤⎦ ⎡⎣Rn⎤⎦ ⎡⎣Lε ⎤⎦ Δε g = ⎡⎣Dkin⎤⎦ Δε g

{ }

(5)

S. I. Ahmad/T. Tanabe · Three-dimensional FE analysis of reinforced concrete structures using the lattice equivalent continuum method

where n n n n ⎡n ⎢ ∑ rj a4j ∑ rj a2j bj2 ∑ rj a2j bj2 ∑ rj a3j bj ∑ rj a2j bj cj 1 1 1 1 ⎢1 n n n n ⎢ 4 2 2 3 ∑ rj aj ∑ rjbj cj ∑ rjbj aj ∑ rjbj3cj ⎢ 1 1 1 1 ⎢ n n n ⎢ 4 2 ∑ rjcj ∑ rj aj bj cj ∑ rjc3j bj ⎢ 1 1 1 ⎡⎣Dmain⎤⎦ = ⎢ n n ⎢ ∑ rj a2j c2j ∑ rj aj bj2cj ⎢ 1 1 ⎢ n ⎢ Sym. ∑ rjbj2c2j ⎢ 1 ⎢ ⎢ ⎢⎣

n ⎤ ∑ rj a3j cj ⎥ 1 ⎥ n ⎥ 2 ∑ rj aj bj cj ⎥ 1 ⎥ n ⎥ 3 ∑ rjcj aj ⎥ 1 ⎥ n 2b2c ⎥ r a ∑j j j j⎥ 1 ⎥ n ∑ rjc2j bj aj ⎥ ⎥ 1 ⎥ n ∑ rjc2j a2j ⎥ ⎥⎦ 1

Two lattices are introduced in each of the local coordinate directions parallel with the cracked plane as shown in Fig. 2c. Of these two, the lattice that is activated to transfer the stresses depends on the negative or positive traction direction as shown in Fig 2d. Now, incremental stresses in the shear lattice direction of S1 and S2 (in plane ξ – η) and S3 and S4 (in plane η – ς, not shown in the figure) can be evaluated using the following relation:

{Δσ sl}

(6)

3

Crack surface modelling with shear lattices

The formulation developed here decomposes the incremental strain {ε} into the uncracked or elastic strains {εe} and the crack strain {εcr} in order to accommodate singularities in the strain field caused by cracking while using the continuum-based formulation.

{Δε} = {Δε e} + {Δε cr}

(7)

Interlocking stress transfer between adjacent concrete main lattice faces in a crack will depend on the actual contact area between them. Contact surface is a complex function of height of protruding elements, i.e. roughness in a cracked face and crack width. For simplicity, a relative contact density factor t is introduced in this work and is linearly correlated with the tension strain softening curve of concrete.

For zero or no crack strain εcr, relative contact density is unity or, in other words, complete contact is assumed. As εcr increases, density factor t decreases linearly. An additional factor α is added to t to account for the effect of steel in the RC zone. These factors are illustrated in Figs. 2a and 2b. Experience shows that an α value of 0.0001~0.0005 is sufficient and 0.0002 has been used in this work.

To model this contact zone on a cracked face, four lattices are introduced for one cracked plane surface at any sampling point as shown in Figs. 2c and 2d. However, a modification factor in the form of a shear controlling matrix [Ω] is necessary in Eq. (7) to account for the limited volumetric characteristics of these shear lattices around the interlocking region. Therefore, we get, from the crack strain,

{ε cr}

{

= ⎡⎣Ω⎤⎦ ε ξ εη − ε e ες γ ξη γ ης γ ςξ

{

= 0 εηcr 0 γ ξη γ ης 0 where ⎡0 ⎢0 ⎢ ⎡⎣Ω⎤⎦ = ⎢ 0 ⎢0 ⎢0 ⎢⎣ 0

0 1 0 0 0 0

0 0 0 0 0 0

0 0 0 1 0 0

0 0 0 0 1 0

0⎤ 0⎥ 0 ⎥⎥ 0⎥ 0⎥ 1 ⎥⎦

T

}

⎡E 0 0 0 ⎢ s1 0 E 0 s2 0 =⎢ ⎢ 0 0 E s3 0 ⎢ 0 0 0 Es4 ⎢⎣ = ⎡⎣Dshear,uni ⎤⎦ Δε cr

{ }

⎡⎣σ l ⎤⎦ = ⎡⎣Ω⎤⎦ ⎡Tσ , S1,.., S4 ⎤ ⎣ ⎦

(9)

−1

{Δσ sl}

(10)

where [Tσ1,S1,..,S4] is the matrix for transforming stress from the shear lattice direction to the local coordinate direction. Therefore, we get a constitutive matrix for the shear lattice in global coordinates: ⎡⎣Dshear ⎤⎦ = t ⎡⎣Tσ ⎤⎦

−1

⎡⎣Dshear ⎤⎦ ⎡T ⎤ ξηζ ⎣ ε ⎦

(11)

where [Tσ] and [Tε] are transformation matrices from the local stress and strain to global direction respectively, and t is determined according to the procedure described before. Further, ⎡⎣Dshear ⎤⎦ = ⎡⎣Ω⎤⎦ ⎡⎣Tσ , S1,.., S4 ⎤⎦ ξης

−1

⎡D ⎤⎡ ⎤⎡ ⎤ ⎣ shear,uni ⎦ ⎣Tε , S1,.., S4 ⎦ ⎣Ω⎦ (12)

For a number of cracks n at a sampling point we get −1

n

⎡⎣Dshear ⎤⎦ = (8)

{ }

where [Tε,s1,..,S4] is the matrix for transforming stress from the local direction to the shear lattice direction. This matrix is dependent on the angle of the protruding part of the crack surface θ, normally 45° as shown in Fig. 2d.

In the matrix, ESi is the tangent elastic modulus from the uniaxial stress–strain relation of individual shear lattices. In this work the shape of the stress–strain curve for the shear lattice is taken to be elastic – completely plastic, as shown in Fig. 2e. The peak stress fs of this curve is taken as to be equal to 18fc0.33, which is in line with the research findings of Okamura et al. [14]. The local stress increment can be evaluated using the following relation:

T

}

⎤ ⎥ ⎥ ⎡T ⎤ Δε cr ⎥ ⎣ ε , S1,.., S4 ⎦ ⎥ ⎥⎦

∑ 1

ti ⎡⎢Tσ ⎤⎥ ⎣ i⎦

⎡D ⎤ ⎢⎣ shear,unii ⎥⎦ξης

⎡T ⎤ ⎢⎣ ε i ⎥⎦

(13)

Therefore, the completed constitutive equation will be that of the combined influence of main and shear lattices, i.e. ⎡⎣Dtotal ⎤⎦ = ⎡⎣Dmain ⎤⎦ + ⎡⎣Dshear ⎤⎦ or ⎡⎣Dtotal ⎤⎦ = ⎡⎣Dmain⎤⎦ +

n

∑ ti ⎡⎣Tσ i⎤⎦ i

−1

⎡D ⎤ ⎣ shear i ⎦ξηζ

⎡T ⎤ ⎢⎣ ε i ⎥⎦

Structural Concrete 14 (2013), No. 1

(14)

53

S. I. Ahmad/T. Tanabe · Three-dimensional FE analysis of reinforced concrete structures using the lattice equivalent continuum method

Fig. 2. Shear lattice on a crack surface

Eq. (14) denotes the final form of the constitutive matrix for reinforced concrete in the LECM.

ft

σpt

4

Ultimate strength criterion for concrete lattices

i

σpc

i

E1 E1/

fc

Fig. 3. Concrete lattice stress–strain laws

54

Structural Concrete 14 (2013), No. 1

In the 3D stress field, stress–strain behaviour in any principal direction of the concrete will shift from its uniaxial behaviour due to the influence of stresses in the other two directions. This means that a point may reach a failure surface that is different from the uniaxial strength of concrete due to stresses in other directions. But exactly where the stress state of a point will reach the failure surface is unknown beforehand. Additionally, changes in peak stress will result in overall changes to the shape of the concrete

S. I. Ahmad/T. Tanabe · Three-dimensional FE analysis of reinforced concrete structures using the lattice equivalent continuum method

σ2 (σ

p1

,σ

p2

,σ

p3

)

fc

(σ 1 , σ 2 , σ 3 )

ft

ft σ3

ft

fc

σ1

fc

(a) Case1 of peak stress selection Fig. 4. Stress path showing current stress state relative to failure stress

σ3

B

σ1

lattice stress–strain curve and, consequently, the tangent modulus to be incorporated in Eq. (14). Fig. 3 shows the concrete lattice stress–strain diagram with modified tangent modulus and peak strains due to changes in peak stress. Since the tangent modulus to be incorporated in Eq. (14) varies due to changes in peak stress, in the analysis it is important to predict correctly beforehand the probable peak stress that a point will reach from the current stress state. However, it should be noted that there are infinite paths in which the failure stress state (σp1, σp2, σp3) can be achieved by varying the current stresses (σ1, σ2, σ3) of three principal or lattice directions. Fig. 4 shows one of the numerous stress paths in which the current stress state may reach the eventual failure stress. To overcome this problem, in this work three fundamentally different ways of relating failure stresses to the current stress condition are considered, a concept that was first used by Ottosen [15]. These are: Case 1: Concrete lattice peak stresses are taken as equal to the uniaxial stresses of concrete (Fig. 5a).

Case 2: Peak stresses are taken as the point on the failure surface that is attained by proportionally increasing and/or decreasing the current stresses in all three principal stresses, i.e. the lattice direction.

This is elaborated in Fig. 5b, where point A represents stresses at the current loading step in the numerical computation. Point B is achieved by proportionally increasing the stresses up to the failure surface.

Case 3: The failure stress of any principal stress or lattice direction is taken as the one achieved by decreasing (for tension, increasing) it up to the failure surface parallel with the axis system. This means that stresses in the other two directions are kept unchanged while the peak stress is evaluated in any direction. This is illustrated in Fig. 5c, where point A (σ1, σ2, σ3) represents the stress state at the current loading step in the numerical computation. Point B (σ1, σ2, σpc3), which lies on the failure surface, is achieved by drawing a straight line from point A parallel with the σ3 direction, and σpc3 is the corresponding peak stress for the lattice in the direction of σ3. The same procedure is used to determine σpc1 and σpc2, the peak stresses in the other two lattice directions. The failure surface used in this work is the one proposed by Kang and Willam [16].

(σ p1 , σ p 2 , σ p 3 )

A

(σ 1 , σ 2 , σ 3 )

σ2

(b) Case 2 of peak stress selection σ

(σ p1 , σ p 2 , σ p 3 )

p3

B

σ1

σ2

A

(σ 1 , σ 2 , σ 3 )

σ3

(c) Case 3 of peak stress selection Fig. 5. Concrete lattice stress–strain diagram with peak stress criteria

5 5.1

Analysis of reinforced concrete test specimen RC cantilever column

First, a simple case of an RC cantilever column is analysed using the proposed LECM model. This column was tested

by Hirasawa et al. [17]. The dimensions of and reinforcement in the column are shown in Fig. 6. The column was 1440 mm high and supported on an RC block 400 mm deep and 610 mm wide having a concrete compressive strength of fc = 36.97 MPa. Other material properties are: Ec = 26 100 MPa, ft = 2.03 MPa and steel fy = 361 MPa. The mesh selected is shown in Fig. 7a and is composed of 8-noded solid elements. Due to symmetry, only half of the 230 D6 @ 50

Actuator

250

D10

1190 25

100

1840

25

150 610

400

Fig. 6. Dimensions of specimen RC cantilever column

Structural Concrete 14 (2013), No. 1

55

S. I. Ahmad/T. Tanabe · Three-dimensional FE analysis of reinforced concrete structures using the lattice equivalent continuum method

80.5

300 0

30

275

150

113.9

80.5

(a) FE mesh

(b) Deflected shape

80.5

113.9

80.5

275

Fig. 7. Finite element mesh and deflected shape of RC cantilever column

Slab thickness h = 230 mm, effective depth d = 195mm (all dimensions in mm)

1.5

Fig. 9. Dimensions of test specimen for slab in punching

1 Load (tf)

Test Case 1 Case 2 Case 3

0.5

0 0

20

40 Deflection (mm)

60

Fig. 8. Experimental and analytical load-deflection behaviour of RC cantilever column

section need be considered in the analysis. At the line of symmetry, the horizontal direction facing the other part is restrained for all points. For each element, at the calculation point, three concrete lattices are formed in the direction of the principal stresses as soon as cracks appear in the concrete. Reinforcement in an element is smeared across the section. The direction of these rebars is in effect the direction of the steel lattices. Shear lattice parameters θ and α are taken as 45° and 0.002 respectively.

Stress–strain behaviour for the concrete lattice in compression is taken to be parabolic. For tension, two types of behaviour are considered. Owing to the bond between concrete and the reinforcing bars, the concrete will continue to support part of the tensile force even after cracking has taken place. To account for this phenomenon, the tension stiffening model proposed by Okamura et al. [14] is taken as representative of concrete lattice behaviour in those elements where a steel lattice is present. For other elements, concrete lattice behaviour in tension is considered to follow softening model. The column assem-

bly is then analysed with a finite element analysis platform. Fig. 8 shows the load-deflection behaviour found from both the test and the FE analysis. Three analysis results were found using three peak stress criterions as described in the previous section. For Case 1, i.e. uniaxial concrete strength for concrete lattices, the peak load is overestimated by about 15 %. For Case 2 and Case 3, the peak load estimation is much closer to the experimental results. Of the three response curves, it can be seen that fixing two directions and considering peak stress in the third direction produces the most reasonable result (i.e.

Case 3).

5.2

Slab in punching

The simulation of slab punching behaviour, which is a truly three-dimensional phenomenon, is presented in this section. The slab taken considered was tested by Hoeggar and Beutel [18] and is shown in Fig. 9. The hexagonal specimen was vertically supported by 12 tie rods and loaded on the centre column with a hydraulic jack. After reaching the service load, the slab was unloaded and reloaded twice. The material properties and arrangement of the reinforcement are summarized in Table 1. No shear reinforcement was provided in the slab.

The finite element mesh used in the simulation is shown in Fig. 10. For reasons of symmetry, only a quarter of the test slab was modelled. The spatial discretization was performed by 8-noded solid elements as in the previous example. Load was applied by controlling the vertical displacement of the nodes at the bottom of the column area. To account for the confining effect, nodes adjacent to the column were kept fixed in the horizontal directions.

Table 1. Material Properties of Test Slab

Concrete

Tension reinforcement

Compression reinforcement

fc

ft

E

GF

fy

Number

Spacing

fy

Number

Spacing

MPa 21.0

MPa 1.73

MPa 21697

N/mm 0.10

MPa 569

– ϕ14

mm 10

MPa 569

– ϕ10

mm 17.5

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S. I. Ahmad/T. Tanabe ﾂｷ Three-dimensional FE analysis of reinforced concrete structures using the lattice equivalent continuum method

Deformed Zon ne

Vertical supports

Colum mn Load application 20 x 20 cm, 25 nodes

Fig. 12. Deflection pattern of the mesh representing the slab in punching

Fig. 10. Finite element mesh

Test Case 1 Case 2 Case 3

600

400 Load (kN)

200

0

0

10

20

Deflection (mm)

Fig. 11. Experimental and analytical load-deflection behaviour of slab in punching

The support points were exactly at the same location as that of the experiment. To avoid local damage, the elements around the supporting nodes were defined as linear elastic. Fig. 11 shows the comparison between calculated and experimentally measured load-deflection curves with three peak stress criteria. The load corresponds to the ver-

Columnn

tical column force and the deflection is monitored on the column loading surface. For Case 1, i.e. lattice peak stress equal to uniaxial concrete strength, the response curve predicts a higher peak load with a steep decline in load窶電isplacement response in the post-peak region, whereas the Case 2 and Case 3 response curves show good representation of the experimental load-displacement behaviour. Case 3 exhibits the closest approximation to the test data. Therefore, it can said that the proposed constitutive laws are able to predict the load-deformation response of a slab in punching with a good degree of accuracy provided the peak stress criterion is chosen appropriately.

The exaggerated deformed mesh of the simulated crack is shown in Fig. 12, which verifies the punching mode of failure as the deflections are localized along the inclined band of the element near the column. Fig. 13 shows the simulated crack pattern at failure obtained in the analysis for Case 3. The cracks are plotted in the direction of and in proportion to the principal strains. The crack pattern of the experiments is also superposed in this figure. As in the experiment, failure is obtained in the analysis due to punching shear with the formation of the characteristic punching cone, thus verifying the ability of the proposed constitutive laws to capture the three-dimensional behaviour of reinforced concrete accurately. Fig. 14a shows calculated and measured vertical deflections of the slab tension surface plotted for different load levels. Furthermore, Fig. 14b shows the calculated and measured tensile strains in the tension reinforcement. The tangential and radial strains in the concrete compression zone around the column for different load levels are shown in

Experimental punching cracck

Fig. 13. Crack pattern at failure for slab in punching

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S. I. Ahmad/T. Tanabe · Three-dimensional FE analysis of reinforced concrete structures using the lattice equivalent continuum method

10

Tensile Reinforcement Strain

Deflection (m m)

2 E xperim ent, P =3 4 5 E xperim ent, P =5 2 0 E xperim ent, P =6 1 5 C alcu latio n, P =3 4 5 C alcu latio n, P =5 2 0 C alcu latio n, P =6 1 5

5

0 1000 (a)

500 Distance from Slab Center

Radial Concrete Strain

Tangential Concrete Strain

500 1000 Distance from Slab Center (mm) 0

-0.5

800 (b)

0

(a)

0

-1

1

0

0

Experiment, 375 KN Experiment, 520 KN Experiment, 615 KN Calculation, 375 KN Calculation, 520 KN Calculation, 615 KN

E xperiment, P=375 E xperiment, P=520 E xperiment, P=615 C alculation, P =375 C alculation, P =520 C alculation, P =615

700 600 500 400 300 Distance from Column Center (mm)

-0.5 Experiment, P=375 Experiment, P=520 Experiment, P=615 Calculation, P=375 Calculation, P=520 Calculation, P=615

-1

200

200

300

(b)

400 500 600 700 Distance from Slab Center

800

Fig. 14. Comparison of calculation and experiment: (a) deflection, (b) strains in tension reinforcement

Fig. 15. Comparison of calculation and experiment: (a) tangential strains, (b) radial strains in concrete compression zone

Figs. 15a and 15b respectively. All of these graphs represent Case 3, where the response was closest to the test data. Fig. 14a shows that the analysis is close to predicting the vertical displacement distribution characterized by pronounced rotation at the column face and small rotation away from that face (Fig. 12). The calculation predicts the maximum deflection at peak load effectively, but at service load the calculated values are slightly lower. An improved prediction of the deflection at service load could be achieved by using a finer FE mesh. Since reinforcement is smeared out, the calculated strain in the tension reinforcement shown in Fig. 14b is that of steel lattices at sampling points at the level of the reinforcement. It can be seen that at peak load in particular, the predicted distribution agrees well with the experimental data. The tangential and radial strains in concrete are shown in Figs. 15a and 15b at the level of the compression reinforcement. From these figures it can be seen that calculation and experiment exhibit good agreement. Whereas the calculated radial strains are slightly lower, strains in tangential direction are slightly higher compared with the test results.

From the comparison between calculated and test results presented here it can be concluded that the lattice equivalent continuum method is able to provide a realistic prediction of the loadbearing behaviour, the deformations and the failure mechanism of flat slab punching behav-

iour, which is a truly three-dimensional reinforced concrete behaviour.

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Structural Concrete 14 (2013), No. 1

6

Conclusion

The application and effectiveness of the simple, engineering-oriented three-dimensional LECM for analysing reinforced concrete structures is presented in this paper. Basic input parameters of the model include concrete uniaxial compressive and tensile strength for construction of the failure surface, reinforcement yield strength and initial stiffness for both concrete and steel. These can be obtained from standardized tests on concrete and steel specimens. Apart from these primary parameters, two secondary input parameters for the shear lattice part of the constitutive matrix are θ and α. A crack angle θ value of 45° is a good approximation for the average of all crack surface roughnesses. For α, a value within 0.0002~0.0005 may be used. From the analysis results it is clear that loaddeflection and other behaviour are influenced by the choice of peak stress criterion for a concrete lattice system. Analysis results show keeping two directions fixed and checking for the peak stress in the third direction reproduces actual concrete behaviour reasonably (Case 3 in this paper). Two examples provided in this paper show that the LECM can capture the deformation characteris-

S. I. Ahmad/T. Tanabe · Three-dimensional FE analysis of reinforced concrete structures using the lattice equivalent continuum method

tics, load-displacement relationship and cracking behaviour of real three-dimensional reinforced concrete structures effectively.

References 1. Van Mier, J. G. M., Vervuurt, A., Schlangen, E.: Boundary and size effects in uniaxial tensile tests: a numerical and experimental study. Fracture and Damage in Quasibrittle Structures, E&FN Spon, London, 1994, pp. 289–302.

2. Schlangen, E.: Computational aspects of fracture simulations with lattice models. Fracture mechanics of concrete structures (Proc., FraMCoS-2, Zurich), Wittmann, F. H. (ed.), pp. 913–928. Aedificatio Publ., Freiburg, Germany, 1995.

3. Niwa, J., Choi, I. C., Tanabe, T.: Analytical Study for Shear Resisting Mechanism using Lattice Model. JCI Int. Workshop on Shear in Concrete Structures, 1994, pp. 130–145.

4. Van Mier, J. G. M., Van Vliet, M. R. A., Wang, T. K.: Fracture Mechanisms in Particle Composites: Statistical aspects in Lattice Type Analysis. Mech. Mater., vol. 34, No. 11 (2002), pp. 705–724.

5. Lilliu, G., Van Mier, J. G. M.: 3D Lattice type Fracture Model for Concrete. Eng. Fracture Mech., vol. 70, No. 7–8 (2003), pp. 927–941.

6. Cusatis, G., Bazant, Z. P., Cedolin, L.: Confinement-Shear Lattice Model for Concrete Damage in Tension and Compression: I. Theory. Journal of Engineering Mechanics, ASCE, vol. 129, No. 12 (2003), pp. 1439–1448.

7. Rashid, Y. R.: Ultimate Strength Analysis of Pre-stressed Concrete Pressure Vessels. Nuclear Engineering and Design, vol. 7 (1968), pp. 334–344.

8. Cervenka, V., Gerstle, K.: Inelastic Analysis of Reinforced Concrete Panels: Part I. Theory, Part II: Experimental Verification. IABSE, Zurich, Part I: vol. 31 (1971), pp. 32–45, Part II: vol. 32 (1972), pp. 26–39.

9. Rots, J. G., De Borst, R.: Analysis of concrete fracture in ‘direct’ tension. International Journal of Solids and Structures 25 (1989), pp. 1381–1394.

10. Barzegar, F., Maddipudi, S.: Three-dimensional Modeling of Concrete Structures II: Reinforced Concrete. Journal of Structural Engineering, vol. 123, No. 10 (1997), pp.

1347–1356.

11. Tanabe, T., Ahmad, S. I.: Development of Lattice Equivalent Continuum Model for Analysis of Cyclic Behavior of Reinforced Concrete, Modeling of Inelastic Behavior of RC structures under Seismic Loads, ASCE (2000), pp. 297–314.

12. Ahmad, S. I., Tanabe, T.: Development of Concrete Constitutive Laws Based on 3D lattice Equivalent Continuum.

Journal of Materials, Concrete Structures and Pavements, JSCE, vol. 58, No. 725 (2003), pp. 293–304.

13. Bazant, Z. P., Prat, P. C.: Microplane Model for Brittle-Plastic Material-parts I and II. Journal of Engineering Mechanics, ASCE, vol. 114, No. 10 (1988), pp. 1689–1702.

14. Okamura, H., Maekawa, K.: Nonlinear Analysis and Constitutive Models of Reinforced Concrete, Gihodo-Shuppan, Tokyo, 1991.

15. Ottosen, N. S.: Constitutive Model for Short-Time Loading of Concrete. Journal of the Engineering Mechanics Division, ASCE, vol. 125, No. EM1 (1979), pp. 127–141.

16. Kang, H. D., Willam, K.: Mechanical Properties of Concrete in Uniaxial Compression. Materials Journal, American Concrete Institute, vol. 94, No.6 (1997), pp. 457–471.

17. Hirasawa, I., Kanoh, M., Fujishiro, M.: Basic Test on the Dynamic Strength of R/C Square Columns under Biaxial Bending. Journal of the Society of Material Science, vol. 45, No. 4 (1996) pp. 423–429.

18. Hegger, J., Beutel, R.: Durchstanzen schubbewehrter Flachdecken im Bereich von Innenstutzen. Final report, AiF research project 10644N, Chair and Institute of Concrete Strctures, RWTH Aachen University, 1998.

19. Okamura, H., Maekawa, K.: Nonlinear Analysis and Constitutive Models of Reinforced Concrete, Gihod-Shuppan, Tokyo, 1991.

Ahmad, Syed Ishtiaq PhD, Professor, Department of Civil Engineering, Bangladesh University of Engineering and Technology, Dhaka 1000, Bangladesh.

E-mail: siahmad@ce.buet.ac.bd

Tanabe, Tada-aki PhD, Professor (retd.), Department of Civil Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8603, Japan.

E-mail: tanabe@civil.nagoya-u.ac.jp

Structural Concrete 14 (2013), No. 1

59

Technical Paper Tai-Kuang Lee* Cheng-Cheng Chen Austin D.E. Pan Kai-Yuan Hsiue Wei-Ming Tsai Ken Hwa

DOI: 10.1002/suco.201200012

Experimental evaluation of large circular RC columns under pure compression Eight sets of large, circular, short reinforced concrete columns were tested under monotonic axial compression. The primary variables are type of transverse reinforcement (spiral vs. circular tie), type of splice, end hook length and staggered length of adjacent circular ties. The tests confirmed the acceptable performance of the circular tie newly proposed in ACI 318M-11. In addition, the circular tie scheme in which the ends terminate with hooks that engage with a longitudinal steel bar and bend into the concrete core is acceptable for performance and ease of construction. The effectiveness of its end hook length and the staggered length of adjacent circular ties is also investigated.

Keywords: reinforced concrete, circular column, spiral, circular tie

1

Introduction

Concrete confinement of the column core is important for enhancing ductility, and transverse reinforcement plays an important role. The current provisions for spiral reinforcement require that the minimum volumetric ratios of such reinforcement ρs for non-seismic and seismic design of building columns are given by Eqs. (10-5) and (21-3) in ACI 318M-11 [5]: ⎛ A ⎞ f′ ρs = 0.45 ⎜ g − 1⎟ c ⎝ Ach ⎠ fyt

(ACI Eq. 10-5)

ρs = 0.12fc′/fyt

(ACI Eq. 21-3)

where fc′ specified compressive strength of concrete Ag gross area of concrete section Ach cross-sectional area of a structural member measured to outside edges of transverse reinforcement fyt specified yield strength of transverse reinforcement For circular bridge columns, only spirals or complete circular ties are permitted as confining steel in the USA [1].

* Corresponding author: E-mail: taikuang@abri.gov.tw Submitted for review: 21 May 2012 Revised: 7 November 2012 Accepted for publication: 6 December 2012

60

Some other countries, such as Korea [9] and Japan [8], permit lap-spliced confinement steel with adequate cross-ties.

Since the 1995 Kobe earthquake in Japan, interlocking spiral columns have been recommended in the design code [7]. Recently in Taiwan [6, 10, 11], a new type of fivespiral cage is approved as confining hoops for columns.

ACI 318M-08 [4] does not provide sufficient design details of transverse reinforcement for circular columns (unlike rectangular columns), especially for circular ties.

Recently, a new type of transverse reinforcement and the corresponding detailing of circular columns have been added by ACI [5]. In the additional section 7.10.5.4, a complete circular tie is permitted where longitudinal bars are located around a circular cross-section. The ends of the circular tie should overlap by not less than 150 mm and terminate with standard hooks that engage with a longitudinal column bar. Overlaps at ends of adjacent circular ties must be staggered around the perimeter enclosing the longitudinal bars. Alternatively, the design concept of the development of standard hooks in tension in section 12.5 in ACI 318M-11 may be adopted in the newly proposed complete circular tie. Table 1 summarizes the related design concepts for circular transverse reinforcement.

ACI 318M-11 does not provide any references to verify the performance of the new type of transverse reinforcement. Furthermore, design details such as splice type, end hook length and staggered lengths of adjacent circular ties still need to be clarified. To investigate these issues [2, 3], axial load tests were carried out on 16 large circular columns.

2 2.1

Experimental programme Test specimens

Eight sets of large circular concrete columns, each set with two identical specimens, were fabricated and tested under monotonic axial compression. All 16 specimens had the same cross-sectional dimensions, length, longitudinal bar arrangement and amount of transverse steel.

The cross-section of the circular specimens was 850 mm diameter with 24 metric No. 25 (nominal diameter 25.4 mm) longitudinal steel bars, as shown in Fig. 1(c).

This resulted in a longitudinal steel ratio of 2.2 %. Steel bars with a specified yield strength of 420 MPa and concrete with a specified compressive strength of 28 MPa were used. According to Eqs. (10-5) and (21-3) in ACI

© 2013 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Structural Concrete 14 (2013), No. 1

T.-K. Lee/C.-C. Chen/A. D.E. Pan/K.-Y. Hsiue/W.-M. Tsai/K. Hwa · Experimental evaluation of large circular RC columns under pure compression

Table 1. Design concepts for circular transverse reinforcement

ACI 318M-11 section

Class of transverse reinforcement

Type of transverse reinforcement splice

Length of lap splice or overlap

Extension length of 90° hook at end

Overlaps at ends of adjacent circular ties staggered?

7.10.4.5

spiral

lap splice

larger of (1) 300 mm (2) 48db

–

no

7.10.5.4

complete circular tie

overlap

≥ 150 mm

larger of (1) 6db (2) 75 mm

yes

12.5

complete circular tie

overlap

calculated development of standard hooks in tension

12db

no

7.10.5.3

rectilinear tie

–

–

larger of (1) 6db (2) 75 mm

no

Note: db is the nominal diameter of spiral or circular tie reinforcement.

850

850

10 @ 80 mm 14 @ 60 mm

2580

14 @ 60 mm

35 14 @ 60 mm 10 @ 80 mm 14 @ 60 mm

Test segment

Bottom segment

35

850

35

Top segment

850

Bottom segment

A

A

850

Test segment

850

A

Top segment

850

A

850

2580

A572 Grade 50 steel plate (850 mm Diameter)

35

A572 Grade 50 steel plate (850 mm Diameter)

A572 Grade 50 steel plate (850 mm Diameter)

Unit᧶ mm

A572 Grade 50 steel plate (850 mm Diameter)

Unit᧶ mm

(a) Spiral elevation

(b) Circular tie elevation 50

850 Concrete cover = 50 mm

24 Longitudinal reinforcement (No.25)

Spiral or circular tie 2-No.10 @ 80 mm Note᧶Spiral or circular tie 2-No.10 @ 60 mm for top and bottom segments

(c) Section A- A Fig. 1. Test specimens – dimensions and layout

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T.-K. Lee/C.-C. Chen/A. D.E. Pan/K.-Y. Hsiue/W.-M. Tsai/K. Hwa · Experimental evaluation of large circular RC columns under pure compression

500

mm

m 0m 2 1 (a) Type S1

(b) Type S2

main longitudinal rebar

auxiliary longitudinal rebar

(c) Type S3

(d) Type S4

m 0m 12 (e) Type S5

Fig. 2. Types of transverse reinforcement splice

318M-11, the required volumetric ratio of transverse steel ρs is 0.0085. For all specimens, two metric No. 10 (nominal diameter 9.5 mm) spirals or circular ties with a longitudinal spacing of 80 mm were used, as shown schematically in Fig. 1, the total volumetric ratio of transverse steel provided was nominally 0.0093.

Two classes of transverse reinforcement, class S and class CT, were used; class S represents “spiral” and class CT represents “circular tie”. Five types of transverse reinforcement splice were used, as shown in Fig. 2. For type S1, lap splice length was 500 mm, ≈ 48db, where db is the nominal diameter of a metric No. 10 steel bar. For type S2, 90° hooks at both ends bend directly into the concrete core. In addition, two 90° hooks for type S3 for all circular ties engage with the same auxiliary longitudinal rebar. For

type S4, similar to rectilinear ties, two 90° hooks engage with the same longitudinal rebar. For type S5, the circular tie overlaps with length 艎dh = 150 mm, where 艎dh is the required development length in tension with a standard hook.

The ends of the circular tie of type S5 terminate with hooks; one engages with a longitudinal steel bar and the other bends into the concrete core. For ease of construction, type S5 does not require that both hooks engage with a longitudinal rebar like the newly proposed type in ACI 318M-11. The nominal extension length of 90° hooks is 120 mm or 12db for all types except type S1. The overlap locations of adjacent circular ties except type S3 follow the same rotation direction along the longitudinal reinforcement axis with designated staggered length. The nominal staggered length is approx. 艎dh, 160 mm.

Table 2 lists set designations, class of transverse reinforcement, type of transverse reinforcement splice, length of lap splice or overlap, extension length of 90° hook and staggered length of each set of specimens. For set CT-S56db, the extension length of the 90° hook is 60 mm, 6db.

For CT-S5-2L, the staggered length is 320 mm. In each set there were two identical test specimens designated as “a” and “b” following the set designation.

The length of the columns (2550 mm) was three times the cross-sectional width. Each specimen was divided into three segments, as shown in Figs. 1(a) and 1(b).

The top and bottom segments were strengthened by providing higher concrete confinement achieved by reducing the longitudinal spacing of transverse reinforcement from 80 to 60 mm. As a result, the main failure of the column was then limited to the test segment. A 15 mm thick steel end plate capped each end of each column, and all the longitudinal steel bars were welded to these end plates.

Three sets of steel forms were used for concrete placement. The specimens were cast in an upright position and ready mixed concrete was used. The final level of concrete placement was set to 20 mm below the top end plate. The remaining 20 mm gap was filled with nonshrink cement grout with a nominal compressive strength of 56 MPa. The actual concrete compressive strength of each specimen can be found in Table 3. The actual yield and tensile strengths of the steel bars are listed in Table 4.

Table 2. Test specimen specifications

Set designation

Class of transverse reinforcement

Type of transverse reinforcement splice

Length of lap splice or overlap [mm]

Extension length of 90° hook [mm]

Staggered length of adjacent circular ties [mm]

S-S1 S-S4 CT-S2 CT-S3 CT-S4 CT-S5-6db CT-S5 CT-S5-2L

S S CT CT CT CT CT CT

S1 S4 S2 S3 S4 S5 S5 S5

500 – – – – 150 150 150

– 120 120 120 120 60 120 120

– – 160 – 160 160 160 320

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T.-K. Lee/C.-C. Chen/A. D.E. Pan/K.-Y. Hsiue/W.-M. Tsai/K. Hwa · Experimental evaluation of large circular RC columns under pure compression

Table 3. Average strengths of reinforced concrete column specimens

Measured concrete compressive strength [MPa]

S-S1a S-S1b S-S4a S-S4b CT-S2a CT-S2b CT-S3a CT-S3b CT-S4a CT-S4b CT-S5-6dba CT-S5-6dbb CT-S5a CT-S5b CT-S5-2La CT-S5-2Lb

28.7 29.9 29.9 28.0 29.2 28.7 31.4 28.0 28.7 24.3 29.0 26.8 28.8 29.0 22.0 22.0

850

Specimen

Loading plate

850

DT gripper DT DT

Supporting thread

850

Embedded threaded bar

Loading plate

2.2

Test setup and instrumentation

Unit᧶ mm

Specimens were tested using the 30 MN universal testing machine housed in the large-scale structure testing laboratory of the Architecture & Building Research Institute (ABRI) in Taiwan. The specimens were first centred and plumbed beneath the loading head. A monotonic compressive load was then applied using displacement control at a strain rate of 0.0009/min. The loading test was terminated when the post-peak load dropped below 50 % of the peak load.

The applied load was measured by the differential pressure Δ-p cell built into the machine. Axial deformation of the test segment of the specimen was measured by four displacement transducers (DT 1 to DT 4) installed uniformly around the specimen, as shown in Fig. 3. The displacement measured by the LVDT built into the machine was also recorded. Furthermore, transparent plastic sheet was wrapped around the specimen to retain the spalled concrete and thus protect the test segment deformation measuring system. Fig. 4 shows specimen CT-S5-2Lb during testing.

Fig. 3. Displacement transducer installation scheme

CT-S5-2Lb

19 MN

Fig. 4. Transparent plastic sheet wrapped around specimen CT-S5-2Lb

Table 4. Mechanical properties of steel bars used

Specimen

Steel bar

Yield strength [MPa]

Tensile strength [MPa]

S-S1(a,b), S-S4(a,b), CT-S3(a,b)

No. 25

458

676

No. 10

445

631

No. 25

485

711

No. 10

456

729

No. 25

447

658

No. 10

456

729

CT-S2(a,b), CT-S4(a,b), CT-S5a, CT-S5-2L(a,b)

CT-S5-6db(a,b), CT-S5b

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3

Experimental results

Measured Axial Load-Deformation Curve 25

A2

Pδ Spall

Axial load (MN) (MN) Axial Load

Since the specimen was wrapped in plastic sheet, failure of the specimens during loading was difficult to identify clearly by way of direct observation. However, the plastic sheet and the spalled concrete were removed after the loading test in order to inspect the specimen.

Fig. 5 shows specimen CT-S2a after removing the plastic sheet. Significant concrete spalling, longitudinal steel bar buckling and core concrete crushing could be seen in the test segment for all test specimens. In the top and bottom segments of the specimens, significant concrete spalling could be observed, but there were no signs of steel bar buckling. It was thus concluded that failure of all specimens occurred in the desired manner in the top and bottom segments. For all specimens, the steel buck-

ling and core concrete crushing were observed at approximately the same height around the circumference at the average column length location of 480 mm, as shown in Fig. 6. Tensile fractures occurred in the spirals or circular ties in all columns except specimens CT-S4b, CT-S5-6dba and CT-S5-6dbb. This observation signifies that some perimeter hoops could reach their tensile strengths.

Figs. 7(a) and 7(b) show the measured load vs. axial deformation curves of specimen S-S4a. The axial deformation data for curve A, designated δA, are the average values of DT 1 to DT 4. The axial deformation data for

20

Curve A 15

10

5 A1

0

δ Spall

0

5

10

15

20

25

30

35

40

45

Axial Displacement Axial Axial Deformation Deformationˡ ˡA(mm) (mm) A(mm)

(a) Definitions of axial load-deformation curve in the elastic range Measured Axial Load-Deformation Curve 25

Axial load (MN) (MN) Axial Load

Pδ Spall

CT-S2a

B2

20

Curve B

15 B3

10

5

Fig. 5. Failure of specimen CT-S2a

B1

0 0

5

(δ B )δ Spall

10

15

20

25

30

35

40

45

Axial Displacement Axial Axial Deformation Deformationˡ ˡ B(mm) (mm) B(mm)

(b) Definitions of axial load-deformation curve in the plastic range Approximate Axial Load-Deformation Curve 25

C2

Axial Load (MN) Axial load(MN) (MN) Axial load

Pδ Spall

20

15

Curve A

(a) Specimen S-S4b

(b) Specimen CT-S4b

Fig. 6. Typical test specimen failures

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Structural Concrete 14 (2013), No. 1

C3

C3’

30

35

5

0

C1

0

CT-S4b

ˡ ’

Shifted Curve B

10

CT-S5-2Lb S-S4b

Shifted & Corrected Curve B

δ Spall

5

10

15

20

25

40

Axial AxialDisplacement Deformation(mm) (mm)

(c) Specimen CT-S5-2Lb

(c) Axial load-deformation curve, (a) and (b) combined Fig. 7. Definitions of axial load-deformation curves

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T.-K. Lee/C.-C. Chen/A. D.E. Pan/K.-Y. Hsiue/W.-M. Tsai/K. Hwa · Experimental evaluation of large circular RC columns under pure compression

curve B, designated δB, are from the built-in LVDT of the testing machine. The axial deformation of the test segment, designated δ hereinafter, was expected to be equal to δA. Although the cracked concrete cover was retained by the plastic sheet to avoid damaging the displacement measuring system, δA started to become unreliable as the axial deformation of the test segment exceeded values ranging from 1.275 to 1.7 mm, expressed as δSpall, which is equivalent to an axial compressive strain of between 0.0015 and 0.002. This is mainly because the embedded threaded bars for mounting the DTs were distorted by the cracked concrete cover. Therefore, the axial deformation data had to be corrected to δB once axial deformations exceeded δSpall.

The measured δB included the deformation of the whole system, which included the three segments of the specimen and the loading system. The axial elastic stiffness of the column is designated KA and was obtained by linear regression of the P vs. δA data points within 20 to 70 % of P0 as calculated according to Eq. (1) with actual material strengths: P0 = 0.85fc′( Ag − Ast ) + fy Ast

(1)

where fc′ measured compressive strength of concrete in Table 3 Ast total area of longitudinal reinforcement fy yield strength of reinforcement The elastic stiffness of the whole system, designated KB, was obtained by linear regression of the P vs. δB data points in the range from 20 to 70 % of P0. Further, the elastic stiffness of the loading system KLS can be obtained from Eq. (2) by using the equivalent spring concept for 1 3 1 = + multiple springs in series : KB K A KLS KLS =

K AKB K A − 3KB

(2)

Once the axial deformation reaches δSpall, it is assumed that the top specimen segment, the bottom specimen segment and the loading system all remain in the elastic range with stiffnesses of KA, KA and KLS respectively. As the axial deformation increased, the load varied. Further, the differential axial deformation δ′ of the top specimen segment, the bottom specimen segment and the loading system can be calculated according to Eq. (3):

δ′ = 2 ×

(P − Pδ KA

Spall

) +

(P − Pδ

Spall

)

KLS

(3)

where PδSpall is the load reading at axial deformation equal to δSpall.

Consequently, δ beyond δSpall can be obtained by using Eq. (4):

δ = δ Spall + [δ B − (δ B)δ

Spall

] + δ′

where (δB)δSpall is δB corresponding to PδSpall.

(4)

The C1-C2-C3′ curve in Fig. 7(c) is the P vs. δ curve obtained for specimen S-S4a. The C1-C2 segment is taken directly from the A1-A2 curve of Fig. 7(a). By shifting the B2-B3 curve of Fig. 7(b) horizontally and connecting B2 to C2, we obtain the C2-C3 curve. The horizontal difference between C2-C3 and C2-C3′ is the δ′ calculated according to Eq. (3). The actual P vs. δ curve should be located somewhere between C1-C2-C3 and C1-C2-C3′. Curve C1-C2-C3′ is used in the following discussion.

The P vs. δ curve for all the specimens was obtained through the same procedure. Dividing δ by the length of the test segment (850 mm) enables the average strain in the test segment ε to be obtained. Fig. 8 shows the P/P0 vs. ε curve for all specimens. Table 5 shows a summary of the test results in which Ppeak is the maximum load reached, εpeak is the strain corresponding to Ppeak and εu is the strain corresponding to 0.8P/P0 in the descending state of the P/P0 vs. ε curve. It was found that the two specimens in the same specimen set exhibited fairly similar behaviour. Therefore, the average values of the two specimens – in the same set, e.g. Ppeak, ε–peak and ε–u, are used for the following discussion.

– The maximum load Ppeak is greater than P0 by 5–15 % for all specimens, which indicates that the full strength of the specimens was achieved. The strain εpeak is much greater than 0.004 for 11 specimens, which shows that these specimens regained strength after the concrete cover had spalled. Although five specimens (S-S1a, S-S4a, CT-S3b, CT-S4a and CT-S5b) did not show clear signs of regaining strength, those specimens still possessed a certain amount of plastic deformation capacity, as can be seen in Fig. 8. The significant difference in εpeak between two identical test specimens for all sets except CT-S5-6db and CT-S5-2L is also evident in Table 5. This indicates that the corresponding strains at peak axial load vary considerably in this research.

The transverse reinforcement used in this research seems to work satisfactorily. This suggests that the transverse reinforcement schemes investigated here are all acceptable for this specific column section. However, there are some apparent differences in performance among the transverse reinforcement schemes and they are discussed below.

The strain ε–u in CT-S5-6db is 48 % higher than that of S-S1. Therefore, it can be concluded that a type S5 splice is better than a type S1. The newly proposed type of circular tie in ACI 318M-11 should be acceptable because CTS5-6db matches the type proposed in ACI 318M-11 except that the ends of the circular tie of type S5 terminate with hooks that engage with a longitudinal steel bar and bend into the concrete core.

The difference in ε–u between S-S4 and CT-S5-6db is about 5 %. This indicates that the performance of type S4 for spirals could be as good as that of type 5. Hence, the improved ACI spiral splice type can provide a higher confining force than the traditional ACI spiral lap splice.

The difference in ε–u between CT-S5 and CT-S5-6db is about 3 %. It is apparent that the short extension length of the 90° hook did not lead to unfavourable results. Consequently, the extension length of six times the transverse reinforcement diameter for a 90° hook on a circular tie, in

Structural Concrete 14 (2013), No. 1

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T.-K. Lee/C.-C. Chen/A. D.E. Pan/K.-Y. Hsiue/W.-M. Tsai/K. Hwa · Experimental evaluation of large circular RC columns under pure compression

Axial Load-Deformation Curves 0 1.2

Axial Strain (mm/mm) Axial Strain (mm/mm) 0.01 0.02 0.03 0.04 0.05 0.06 0.01 0.02 0.03 0.04 0.05 0.06 1.2

1

1

0.6

0.6 S-S1a S-S1b

0.4

CT-S4a CT-S4b

0.4

0.2

0.2 (a)

1.2

(e)

1

0.6 CT-S5-6dba

S-S4a S-S4b

P/P 0

0.6

0.4

CT-S5-6dbb

0.2

0.2 (b)

1.2

(f)

1

1.2 1

0.8

0.8

0.6

0.6 CT-S2a CT-S2b

0.4

CT-S5a CT-S5b

P/P 0

P/P0

0.8

0.4

P/P 0

1.2 1

0.8

0.4

0.2

0.2 (g)

(c)

1.2 1

1.2 1

0.8

P/P0

P/P0

0.8

0.8

0.6

0.6

CT-S5-2La CT-S5-2Lb

CT-S3a CT-S3b

0.4

P/P 0

P/P 0

0.8

0.4

0.2

0.2

(d)

0 0

(h)

0

0.01 0.02 0.03 0.04 0.05 0.06 0.01 0.02 0.03 0.04 0.05 0.06 Axial Strain (mm/mm) Axial Strain (mm/mm)

Fig. 8. Axial load-displacement curves for all specimens

accordance with stirrup and tie hooks in ACI, is appropriate.

The strain ε–u of CT-S5-2L is 16 % higher than that of CT-S5. Accordingly, it can be concluded that the larger overlap staggered length for type S5 can provide a higher confining force. At the same time, the ACI 318M-11 recommendation that overlaps at ends of adjacent circular ties should be staggered around the circumference enclosing the longitudinal bars is reasonable.

The difference in ε–u between CT-S2 and CT-S3 is about 5 %. But it is obvious that CT-S2 and CT-S3 are better than S-S1 and close to S-S4.

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Structural Concrete 14 (2013), No. 1

The strain ε–u of CT-S4 is 10 % higher than that of CT-S5-6db and 16 % higher than that of S-S4. Therefore, it can be concluded that a type CT-S4 splice is better than CT-S5-6db and S-S4.

The performance of CT-S5-6db, CT-S5 and CT-S5-2L is in each case better than that of S-S1. Therefore, a type S5 splice layout is acceptable for performance and ease of construction.

In this paper, S-S1 is the only set that used the lap splice type for the spiral, whereas the other sets used 90° hooks at both ends. Both spiral and circular ties were bent into the concrete core. According to the results shown in

T.-K. Lee/C.-C. Chen/A. D.E. Pan/K.-Y. Hsiue/W.-M. Tsai/K. Hwa · Experimental evaluation of large circular RC columns under pure compression

Table 5. Summary of test results

Specimen set

Specimen

Ppeak/P0

εpeak

εu

S-S1

S-S1a

1.07

0.0027

0.028

S-S1b

1.07

0.0084

0.026

S-S4a

1.17

0.0021

0.033

S-S4b

1.12

0.0077

0.043

CT-S2a

1.14

0.0080

0.034

CT-S2b

1.10

0.0103

0.040

CT-S3a

1.06

0.0083

0.028

CT-S3b

1.07

0.0022

0.041

CT-S4a

1.06

0.0037

0.043

CT-S4b

1.10

0.0189

0.044

CT-S5-6dba

1.05

0.0155

0.038

CT-S5-6dbb

1.04

0.0157

0.042

CT-S5a

1.10

0.0095

0.042

CT-S5b

1.14

0.0048

0.036

CT-S5-2La

1.13

0.0154

0.040

CT-S5-2Lb

1.17

0.0174

0.049

S-S4

CT-S2

CT-S3

CT-S4

CT-S5-6db

CT-S5

CT-S5-2L

Table 5, the performance of 90° hooks at both ends is significantly better than that of the lap splice. It can be reasoned that the 90° hooks bent into the concrete core are helped by the better confinement of the core after the concrete cover has spalled. Some evidence of this mechanical phenomenon is provided by the fact that even the 90° hooks bent directly into the concrete core without engaging any longitudinal rebar (CT-S2) also exhibited acceptable performance.

4

Conclusions and recommendations

The effectiveness of several transverse reinforcement schemes for columns was investigated by axial load tests on 16 large circular column specimens. Based on the test results reported here, the following conclusions can be drawn: (1) The circular tie newly proposed in ACI 318M-11, where the ends overlap by 150 mm and terminate with tie hooks that engage with a longitudinal column bar, exhibits acceptable performance.

(2) The improved ACI spiral splice type with two 90° hooks and an extension length of 12 times the transverse reinforcement diameter engaging with the same longitudinal rebar can provide a higher confining force than the traditional ACI spiral lap splice.

(3) The extension length of six times the transverse reinforcement diameter for a 90° hook on a circular tie, in accordance with tie hooks in ACI, is appropriate.

(4) The larger overlap staggered length of adjacent circular ties can provide a higher confining force. The ACI 318M-11 recommendation that overlaps at ends of

– P peak/P0

ε–peak

ε–u

ε–u/(ε–u)S–S1

1.07

0.0056

0.027

1.00

1.15

0.0049

0.038

1.41

1.12

0.0092

0.037

1.37

1.07

0.0053

0.035

1.30

1.08

0.0113

0.044

1.63

1.05

0.0156

0.040

1.48

1.12

0.0072

0.039

1.44

1.15

0.0164

0.045

1.67

adjacent circular ties should be staggered around the circumference enclosing the longitudinal bars is reasonable.

(5) The performance figures of circular ties with two hooks bending into the concrete core and engaging with the same auxiliary longitudinal rebar are very close, better than the traditional ACI spiral lap splice and close to the improved ACI spiral splice type.

(6) Circular ties with two 90° hooks and an extension length of 12 times the transverse reinforcement diameter engaging with the same longitudinal rebar splice are better than the improved ACI spiral splice.

(7) The circular tie scheme in which the ends terminate with hooks that engage with a longitudinal steel bar and bend into the concrete core, similar to the newly proposed type in ACI 318M-11, is acceptable for performance and ease of construction. It is recommended for practical design. However, the effectiveness under cyclic loading needs further study.

Acknowledgements The writers gratefully acknowledge the support of and contributions to this project from the Architecture & Building Research Institute.

Notation Ag Ast db

gross area of section longitudinal reinforcement area nominal diameter of spiral or circular hoop reinforcement

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T.-K. Lee/C.-C. Chen/A. D.E. Pan/K.-Y. Hsiue/W.-M. Tsai/K. Hwa · Experimental evaluation of large circular RC columns under pure compression

fc′ fy KA KB KLS 艎dh P P0 PδSpall Ppeak – Ppeak δ δA

δB δSpall (δB)δSpall δ′

ε εpeak εu ε–peak ε–u ρs

specified or measured compressive strength of concrete specified yield strength of longitudinal reinforcement elastic stiffness of three segments of specimen elastic stiffness of whole system elastic stiffness of loading system development length in tension of deformed bar with standard hook axial load axial maximum nominal strength load reading at axial deformation equal to δSpall maximum load average value of Ppeak axial deformation of test segment of specimens axial deformation of test segment of specimens (average values of four DTs) axial deformation of whole system (measured by LVDT built into 30 MN universal testing machine) axial compressive strain between 0.0015 and 0.002 δB corresponding to PδSpall axial deformation difference considering elastic effect of top specimen segment, bottom specimen segment and loading system strain in test segment of specimens strain corresponding to Ppeak strain corresponding to 0.8P/P0 in descending state of P/P0 vs. ε curve average value of εpeak average value of εu ratio of volume of spiral reinforcement to total volume of core confined by the spiral (measured outside-to-outside of spirals)

8. Japan Road Association: Seismic design specifications of highway bridges. Maruzen, Tokyo, Japan, 2002.

9. Korean Ministry of Construction & Transportation/Korean Society of Civil Engineers: Design specifications for highway bridges, Korea, 2000.

10. Weng, C. C., Yin, Y. L., Wang, J. C., Liang, C. Y.: Seismic cyclic loading test of SRC columns confined with 5-spirals.

Science in China Series E: Technological Sciences 2008: 51 (5), pp. 529–555, Chinese Academy of Sciences, Beijing, China.

11. Weng, C. C., Yin, Y. L., Wang, J. C., Liang, C. Y., Lin, K. Y.: Seismic cyclic loading test of RC columns confined with 5-spirals. Structural Engineering 2011: 26 (1), pp. 57–91, Chinese Society of Structural Engineering, Taipei, Taiwan (in Chinese).

Tai-Kuang Lee Researcher, Architecture & Building Research Institute, Ministry of the Interior, 13F, No. 200, Beisin Rd., Sect. 3, Sindian, New Taipei City, Taiwan

Cheng-Cheng Chen Professor, Department of Construction Engineering, National Taiwan University of Science & Technology, No. 43, Keelung Rd., Sect. 4, Taipei, Taiwan

Austin D.E. Pan Technical Services Division Manager, Western Region Infrastructure Sector, P.O. Box 50012, Madinat Zayed, Abu Dhabi, United Arab Emirates

Kai-Yuan Hsiue Formerly Research & Development Substitute Services (RDSS), Architecture & Building Research Institute, Ministry of the Interior, 13F, No. 200, Beisin Rd., Sect. 3, Sindian, New Taipei City, Taiwan

Wei-Ming Tsai Formerly Research & Development Substitute Services (RDSS), Architecture & Building Research Institute, Ministry of the Interior, 13F, No. 200, Beisin Rd., Sect. 3, Sindian, New Taipei City, Taiwan

Ken Hwa Associate Professor, Department of Architecture, Taoyuan Innovation Institute of Technology, No. 414, Sect. 3, Chung-Shang E. Rd., Chungli, Taoyuan, Taiwan

References 1. AASHTO: AASHTO LRFD bridge design specifications.

American Association of State Highway & Transportation Officials, SI Units, 3rd ed., Washington, D.C., USA, 2005.

2. ABRI, Ministry of the Interior: Axial ductile performance of large-scale circular reinforced concrete columns with different design details. ABRI report 098301070000G2026, Taipei, Taiwan, 2009 (in Chinese).

3. ABRI, Ministry of the Interior: Axial ductile performance of large-scale circular reinforced concrete columns with circular ties. ABRI report 099301070000G2020, Taipei, Taiwan, 2010 (in Chinese).

4. ACI Committee 318: Building code requirements for structural concrete (ACI 318M-08) and commentary. Farmington Hills, Michigan: American Concrete Institute, 2008.

5. ACI Committee 318: Building code requirements for structural concrete (ACI 318M-11) and commentary. Farmington Hills, Michigan: American Concrete Institute, 2011.

6. Chang, K. C., Yin, Y. L., Wang, J. C., Wang, B. S.: Experimental study of spiral application to rectangular columns. Engineering 2005: 78 (3), pp. 101–124, Chinese Institute of Engineers, Taipei, Taiwan (in Chinese).

7. Japan Road Association: Seismic design specifications of highway bridges. Maruzen, Tokyo, Japan, 1996.

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Structural Concrete 14 (2013), No. 1

Articles Alejandro Pérez Caldentey* Hugo Corres Peiretti Joan Peset Iribarren Alejandro Giraldo Soto

DOI: 10.1002/suco.201200016

Cracking of RC members revisited: influence of cover, φ/ρs,ef and stirrup spacing – an experimental and theoretical study This article describes an experimental programme aimed at studying the effect of cover, ratio between diameter and effective reinforcement ratio (φ/ρs,ef) and the influence of stirrup spacing on the cracking behaviour of reinforced concrete elements. The experimental programme was conceived in order to contribute to the debate – fuelled by the publication in recent years of Eurocode 2 EN1992-1-1 and the revision of the Model Code under way when the tests were carried out (and now published as a finalized document) – regarding the influence of these parameters on cracking. Important theoretical aspects are discussed, including where the crack width is estimated by current code formulations and what relevance this may have on the correlation between crack opening and durability of RC structures, especially with regard to structures with large covers. The effect of stirrup spacing, a variable absent from current codes, is also discussed.

Keywords: cracking, φ/ρs,ef, cover, influence of stirrups

1

Introduction

There has been a long-lasting debate regarding models for the calculation of crack width design. Borosnyói and Balázs [1] compiled a total of 23 different mathematical formulations for the calculation of crack spacing and 33 different formulae for the calculation of crack width.

These figures provide an idea of how far consensus goes in the modelling of cracking of concrete structures. Furthermore, in 2004 Beeby [2] agitated the debate by publishing an article heavily defending the thesis that crack spacing is independent of parameter φ/ρs,ef and depends only on the distance from the nearest reinforcing bar. This was a very controversial statement, since the dependence of crack spacing on φ/ρs,ef is a direct consequence of theory, whereas dependence of crack spacing on cover and bar distance is more empirical. Despite a database with more than 300 tests from various researchers [3–10], it was not possible to obtain conclusive evidence that could settle this question.

For this reason, with a view to proposing a cracking formulation for Model Code 2010 [11], and working from the joint effort of fib Task Group 4.1, an experimental study was undertaken with the financial support of

* Corresponding author: apc@fhecor.es Submitted for review: 26 June 2012 Revised: 2 October 2012 Accepted for publication: 10 December 2012

COMSAEMTE. The aim of this was to distinguish the effect on cracking of cover, φ/ρs,ef and stirrup spacing. The results of this experimental programme are presented for the first time in this paper.

Another very important issue addressed in this paper, and which has been the subject of much confusion, is: Where do cracking models provide crack width? At the surface of the reinforcement or at the surface of the concrete?

2 2.1

Experimental programme Description of tests

An experimental programme involving 12 beam specimens was carried out at the Structures Laboratory of the Civil Engineering School of the Polytechnic University of Madrid from May to October 2009. The tests featured point loading with a constant moment span of 3.42 m.

Fig. 1 shows the test setup. All beams had a rectangular cross-section 0.35 m wide and 0.45 m deep. All specimens were concreted at the same time using the same concrete of strength class C25/33. Table 1 shows the results of the compression tests carried out at seven and 28 days.

The parameters studied were cover (20 and 70 mm), φ/ρs,ef ratio (diameter / amount of reinforcement per effective area of concrete), for which bar diameters of 12 mm and 25 mm (four bars in tension) were considered, and stirrup spacing sw. To do this, three configurations were considered: no stirrups in the constant bending moment span, stirrups spaced at 10 cm and stirrups spaced at 30 cm. Stirrup diameter was 8 mm. The specimens were coded XX-YY-ZZ, with XX referring to bar diameter (12 or 25), YY referring to cover (20 or 70) and ZZ referring to stirrup spacing (00 for no stirrups, 10 and 30, for 10 cm and 30 cm spacing respectively). The cross-sections of the specimens are shown in Fig. 2.

Table 2 shows the cover c, φ/ρs,ef ratio and stirrup spacing sw of each specimen. The effective area is calculated according to the definitions of EN 1992-1-1 (or MC 2010, which are the same), according to which the effective depth of the effective concrete tensile zone is the lesser of 2.5(h-d), h/2 and (h-x)/3, where h is the total depth of the cross section, d the effective depth and x the depth of the neutral axis for the cracked cross-section. In specimens 25-70-ZZ, the depth of the effective zone hef is limited by the third condition, i.e. that it be smaller than one-

© 2013 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Structural Concrete 14 (2013), No. 1

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A. Pérez Caldentey/H. Corres Peiretti/J. Peset Iribarren/A. Giraldo Soto · Cracking of RC members revisited: influence of cover, φ/ρs,ef and stirrup spacing – an experimental and theoretical study

Fig. 1. Test setup

Table 1. Compressive strength of concrete at seven and 28 days; specimens concreted on 26 March 2009

Specimen

Date of Test

Age of concrete [days]

Density [t/m3]

Measured compressive stress fc [MPa]

1 2 3

04/02/2009 04/02/2009 04/02/2009

7 7 7

2.29 2.28 2.27

21.3 22.3 22.0

21.9

4 5 6

04/23/2009 04/23/2009 04/23/2009

28 28 28

2.29 2.28 2.29

26.2 27.1 27.4

26.9

Fig. 2. Beam cross-sections

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Structural Concrete 14 (2013), No. 1

Mean Value [fcm]

A. Pérez Caldentey/H. Corres Peiretti/J. Peset Iribarren/A. Giraldo Soto · Cracking of RC members revisited: influence of cover, φ/ρs,ef and stirrup spacing – an experimental and theoretical study

Table 2. Main characteristics of the tested beams

Beam ID

φ [mm]

c [mm]

φ/ρs,ef [mm]

sw [mm]

25-20-00 25-20-10 25-20-30

25 25 25

20 20 20

460 460 460

– 100 300

12-20-00 12-20-10 12-20-30

12 12 12

20 20 20

882 882 882

– 100 300

25-70-00 25-70-10 25-70-30

25 25 25

70 70 70

473 (*) 473 (*) 473 (*)

– 100 300

12-70-00 12-70-10 12-70-30

12 12 12

70 70 70

1172 1172 1172

– 100 300

* hef = (h-x)/3

the beam, using a digital extensometer with a base of 20 cm – Strain along the tension face in correspondence with the location of longitudinal reinforcement in the top of the beam, using a digital extensometer with a base of 20 cm

2.3

Test results

A summary of test results in terms of mean sr,m and maximum sr,max crack spacing is given in Table 3. Fig. 3 shows the crack patterns of the 12 beams tested. The observed effects of cover c, φ/ρs,ef ratio and stirrup spacing on crack spacing are presented in the following paragraphs.

2.3.1 Measuring crack width The conceptual equation for the calculation of crack width can be written as wm =

third of the depth h of the member minus the depth of the neutral axis x.

All beams were loaded until failure so that the serviceability working area could be fully explored. More details can be found in [12], corresponding to the research project report.

2.2

σs s TS Es r,m

(1)

where wm mean crack width sr,m mean crack spacing σs theoretical stress in reinforcing steel at crack Es longitudinal elastic modulus of steel TS effect of tension stiffening

Measurements

The following data were measured for each beam: – Applied load – Support reactions – Deflections at cantilever ends, mid-span and quarterspan points – Strain along the compression face in correspondence with the location of longitudinal reinforcement in the side of the beam, using a digital extensometer with a base of 20 cm – Strain along the tension face in correspondence with the location of longitudinal reinforcement in the side of

The tension stiffening effect takes into account the fact that in between cracks, part of the tensile force carried by the steel at the crack is taken by the concrete, thus reducing the stress in the concrete and increasing the strain in the concrete. This effect reduces the crack width by reducing the mean difference in strain between steel and concrete. This equation allows an experimental value for the crack spacing to be derived, based on the measured value of wm: sr, m =

wmEs σ sTS

(2)

Table 3. Measured mean and maximum crack spacing

Beam ID

φ [mm]

c [mm]

φ/ρs,ef [mm]

sw [mm]

sr,m [mm]

sr,max [mm]

25-20-00 25-20-10 25-20-30

25 25 25

20 20 20

460 460 460

– 100 300

131 114 152

234 230 258

12-20-00 12-20-10 12-20-30

12 12 12

20 20 20

882 882 882

– 100 300

173 182 274

269 320 358

25-70-00 25-70-10 25-70-30

25 25 25

70 70 70

473 473 473

– 100 300

227 189 200

423 460 442

12-70-00 12-70-10 12-70-30

12 12 12

70 70 70

1172 1172 1172

– 100 300

236 260 281

412 381 383

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Fig. 3a. Effect of stirrup spacing on crack spacing in specimens with 12 mm dia. rebar

Fig. 3b. Effect of stirrup spacing on crack spacing in specimens with 25 mm dia. rebar

It has been argued, most notably by Beeby [13], that this is a better estimate of the crack spacing than the actual spacing, which can be obtained from counting the number of cracks and dividing the length of the constant bending

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Structural Concrete 14 (2013), No. 1

moment span by this number, due to the fact that it can never be stated that cracking is stabilized. However, it is the authors’ experience that these values indeed differ in many tests reported in the literature, but it seems that this

A. Pérez Caldentey/H. Corres Peiretti/J. Peset Iribarren/A. Giraldo Soto · Cracking of RC members revisited: influence of cover, φ/ρs,ef and stirrup spacing – an experimental and theoretical study

discrepancy can also be attributed to errors in measuring the crack width, and not only to non-stabilized cracking. It is well known that direct crack measurement by visual means carries with it a strong subjective component regarding the exact position in which the measurement is taken. Cracks open and close during a test, their width varies along their length, they divide and converge at different load steps and in many cases do not form perpendicularly to the reinforcement. Further, direct visual measurement of the crack width is very difficult due to the strain it puts on the eyes of the person reading the instrument. For this reason, the crack width was estimated in this study by measuring the mean strain along the tensile chord in correspondence with the reinforcement both in the side of the beam and in the top of the beam. The mean crack width was determined by dividing the mean strain by the number of cracks. This measurement already includes the effect of tension stiffening. Crack spacing was determined by direct observation. It was also observed that the crack pattern became fairly stable after a certain point in the test, so that it can be said that a stabilized crack pattern was reached in all tests.

Eq. (3) shows the expressions used to estimate the mean and maximum crack widths.

ε tension × L =

(

w = ∑ w + ε c × L → wm = n∑ cracks

= ε tension − ε c

)n L

cracks

≈ ε tension

L ncracks

wmax ≈ ε max × l where εtension mean strain in tension chord L length of constant moment zone εmax maximum measured strain in tension chord

(3)

l

Σw ncracks

measurement length of extensometer (20 cm) sum of crack openings within constant moment span number of cracks located within L

The above expressions take into account the fact that the stress in the reinforcement is reduced between cracks due to the contribution of the concrete, but ignore the effect of the tensile strain in the concrete and therefore slightly overestimate the crack width. However, this error is small.

An example can be considered to support this statement.

Assuming a relatively large 30 cm crack spacing, a tensile strength of 3.2 MPa, a modulus of elasticity of concrete of 30 000 MPa and a parabolic law for the tensile strain variation in the concrete, the tensile elongation of the concrete would result in a reduction in the crack width of only 2/3 × 0.3 × 3.2/30 000 = 0.02 mm.

2.3.2 Influence of cover The influence of cover, irrespective of the value of φ/ρs,ef, can be best appreciated by comparing the results from tests 25-20-XX and 25-70-XX. This is because these tests have almost the same φ/ρs,ef ratio due to the fact that the depth of the effective concrete area is limited, as shown in table 2 (both in EN 1992-1-1[14] and MC90 [15]), by the value of (h-x)/3.

Fig. 4 shows very clearly how cover increases crack width. This increase is clearly related to an increase in crack spacing (and therefore crack width), as can be seen in Fig. 5. The mean crack spacing increased from 13.1 cm in beam 25-20-00 (28 cracks) to 22.7 cm in beam 25-70-00 (16 cracks). These results confirm that cover is an important factor in the development of the cracking pattern and that models that do not consider this variable, such as

Fig. 4. The effect of cover on crack width: a very clear influence is observed in specimens having nearly the same effective concrete area

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Fig. 5. The effect of cover on crack spacing: beam 25-20-00 has a mean crack spacing of 13.1 cm, whereas beam 25-70-00 has a crack spacing of 22.7 cm

Model Code 90 [15], are incomplete. From a theoretical point of view, the effect of cover on crack spacing can be understood by the need to transmit tension stresses generated at the bar-concrete interface to the effective concrete area surrounding the bar in order to generate actual cracking. However, this is only part of the explanation of how cover affects crack spacing. Another aspect of the influence of cover on crack spacing has to do with secondary cracks and whether or not these cracks eventually become passing cracks. This topic is addressed in more detail in section 3.2.

2.3.3 Influence of φ/ρs,ef The influence of the φ/ρs,ef ratio on crack spacing is a direct consequence of the definition of the transfer length and can be easily derived from the equilibrium of the bar between a crack and the zero slip section and from the equilibrium of the two sections. The influence of this factor on crack spacing can easily be compared by counting the number of cracks in specimens having the same cover.

Fig. 6 shows this comparison. A clear influence can be

Fig. 6. Influence of φ/ρs,ef on mean crack spacing

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seen as the crack spacing increases with the value of φ/ρs,ef. These results seem to show a larger influence of this parameter for a smaller cover. This seems logical since crack spacing can be modelled as the sum of the effect of cover and the effect of φ/ρs,ef, as shown in Eq. (4): sr,m = k1c + k2

φ ρs, ef

(4)

As the cover c increases, so the relative importance of the second term in φ/ρs,ef becomes smaller. In Eq. (4), k1 and k2 are constants.

2.3.4 Influence of stirrup spacing Most cracking tests carried out avoid the presence of stirrups, because they influence the cracking pattern. A good example of this can be seen in the tie cracking tests carried out by Gómez Navarro [16] in Lausanne, shown in Fig. 7. It can be very clearly seen in these tests that cracks form every 10 cm on the sides where stirrups are placed at this distance and at 20 cm in the central part of the tie,

A. Pérez Caldentey/H. Corres Peiretti/J. Peset Iribarren/A. Giraldo Soto · Cracking of RC members revisited: influence of cover, φ/ρs,ef and stirrup spacing – an experimental and theoretical study

Fig. 7. Crack pattern governed by stirrup spacing in a test carried out by Gómez Navarro

which also coincides with stirrup spacing and location.

This type of result has made the fact that cracking models included in codes do not consider the presence of stirrups rather puzzling for some. For this reason, in the test series of the Polytechnic University of Madrid (UPM) it was decided to include stirrup spacing as a variable to be studied in cracking.

From the results in Table 4, which shows the mean and maximum crack spacing in each of the beams tested, it is difficult to make a clear-cut statement regarding how stirrups influence the formation of cracks. Despite the fact that cracks tend to develop at the stirrup positions, as shown by the experimental results of Gómez Navarro [16], it cannot be ruled out that cracks develop between stirrups, or sometimes fail to develop at stirrup locations. For a better understanding, in addition to the mean and maximum crack spacing, it is necessary to examine the surface of the beams in order to achieve a better interpretation of the results (Figs. 3a and 3b).

Table 4. Summary of results regarding separation between cracks

Beam ID

sr,m [mm]

sr,max [mm]

25-20-00 25-20-10 25-20-30

131 114 152

234 230 258

12-20-00 12-20-10 12-20-30

173 182 274

269 320 358

25-70-00 25-70-10 25-70-30

227 189 200

423 460 442

12-70-00 12-70-10 12-70-30

236 260 281

412 381 383

Figs. 3a and 3b show the cracks in each of the beams tested and the stirrup positions (black lines along the top of each beam).

It can be seen that the beams with 20 mm cover are the ones that have a better correlation between the positions of the cracks and the stirrups. Focusing on beam 1220-10, it can seen that the cracks have developed, in general, every two stirrups, approximately every 200 mm, and that they also correlate rather well with the observed mean crack spacing of 182 mm. In beam 12-20-30 it can be seen that each crack systematically coincides with a stirrup position. In this case the measured mean spacing of 274 mm is very close to the stirrup spacing of 300 mm.

Similarly, in beam 25-20-10 the cracks coincide with the stirrup positions (100 mm) and the mean separation obtained is 114 mm. In beam 25-20-30, cracks develop at the location of each stirrup and other cracks develop midway between stirrups, resulting in a mean crack spacing of 152 mm.

The beams with 70 mm cover also show, in a general manner, a tendency for cracks to coincide with the positions of stirrups, but in a less homogeneous way than in beams with 20 mm cover. The exception is beam 12-70-30, where cracks develop systematically at the positions of the stirrups (300 mm), resulting in a mean experimental separation of 281 mm.

From the above observations with respect to the effect of stirrups on crack spacing it can be stated that: – Stirrups induce the formation of cracks. This effect is stronger with smaller covers.

– It is not, however, correct to assimilate crack spacing and stirrup spacing. Cracks sometimes develop between stirrups and sometimes they do not develop at stirrup locations. Transfer length clearly still plays a role in crack formation.

– Although stirrup spacing has a significant effect on the mean crack spacing, the test results show that their influence on the maximum crack spacing is much less.

This is very clear in specimens with a 70 mm cover,

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where crack spacing is very similar in specimens with and without stirrups, and can also be observed in beams with 20 mm cover.

– Since what matters for crack control is maximum crack spacing and not mean crack spacing, excluding stirrup spacing from the cracking models of current and future standards seems justified.

3 3.1

Some theoretical observations Basic variables

Fig. 8. Diffusion of tensile forces is needed to crack concrete, thus explaining the dependence of crack spacing on cover from a theoretical point of view

As shown by the results of the experimental programme and some of the existing cracking models, crack spacing can be determined as a linear sum of two terms as expressed in Eq. (4). The second term corresponds to bond theory and, as stated above, can be derived from equilibrium of the bar and cross-sections located between the crack and the section of zero slip by applying the concept of transfer length, i.e. the length needed to transmit a tension force able to crack the concrete from the bar to the effective concrete area. The first term, dependent upon cover, can be explained by the need to transmit these tensile stresses from the bar surface to the centre of the effective area located on either side of the bar as shown in Fig. 8.

3.2

Differences between crack spacing at bar level and on the concrete surface

Experimental evidence supports the fact that a large increase in the crack width happens as the crack is measured further away from the bar. The work of Husain and Ferguson [17] (see Fig. 9) or, more recently, the work of Borosnyói and Snóbli [18] (see Fig. 10) can be cited as examples of such results. One possible explanation for this large increase would be that it is due to shear lag strain in the cover, since the concrete cover deformation is more restricted by reinforcement close to the bar than remote from it. However, a simple house number is enough to rule out shear lag as the reason behind crack width increase.

Indeed, the strain in free concrete after cracking can be estimated as fctm/Es∼10–4, so the crack opening due to shear lag would be equal to this value multiplied by crack spacing (which could be 30 cm as a generous estimate) minus slip occurring at bar level. This means that shear lag could be responsible for a crack width increase of much less than 0.03 mm, since slip will occur at the bar-concrete in-

Fig. 9. Tests of Husain and Ferguson, showing how crack width increases away from the bar surface (note the very small crack width at the bar surface)

terface. It is therefore clear that shear lag has a negligible effect. So why does the width of the crack increase?

An interesting observation taken from the experimental results mentioned above is that the crack opening at bar level is truly very small (approx. 0.05 mm). This provides the key to interpreting the phenomenon. It is well known, from the work of Goto [19], that secondary, nonpassing cracks occur near the bar surface. These secondary cracks help to distribute the slip and reduce the opening of the passing crack at bar level. As these internal cracks close, strain is concentrated in the passing crack, thus explaining the increase. This effect is similar to that observed in beam webs and is the origin for the need to provide web reinforcement, as has been incorporated in codes of practice for many years (see Fig. 11).

Fig. 10. Tests of Borosnyói and Snóbli, again showing how crack width increases away from the bar surface (again note the very small crack width at the bar surface)

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This argument allows a proposal to be made regarding crack width verification when durability is a concern.

Assuming crack width limits for durability reasons have been specified for a certain reference cover c0 (if the ENV 1992-1-1 [20] model is taken as a reference, then as in the cracking equation where the term 2c is given as 50 mm, c0 might be taken as 25 mm), if the crack opening is being limited for durability reasons, crack openings to be compared with admissible limits should be computed using this reference value c0. However, the client should be advised that the cracks actually appearing on the surface will be larger.

4 Fig. 11. Cracking in beam webs: need for web reinforcement to control cracking due to merging of smaller cracks (analogy with secondary cracking or Goto cracks)

Fig. 12. Relationship between increase in surface crack width and cover bearing on to the closure of secondary cracks

The consequence of this interpretation is that crack models provide the crack width at the surface of the concrete elements. The crack at the reinforcement level is much smaller.

With regard to this topic, if it is agreed that the increase in crack width as the distance from the bar increases is mainly due to the closing of secondary cracks, which seems reasonable, a strong case can be made against the current practice of demanding the same crack width limits for elements with large covers as for elements with smaller covers for durability reasons. This argument can be better understood by considering Fig. 12, which shows two elements with different covers: one with a large cover (top) and one with a smaller cover (bottom). It can be seen that in the one with a large cover, secondary cracks close before reaching the surface. Therefore, on the surface, crack width and crack spacing in the specimen with large cover are doubled with respect to the one with the smaller cover.

In the specimen with smaller cover, the secondary cracks in the beam with large cover actually become primary cracks and cracking would seem to be better controlled.

This is certainly the case if crack width is being limited for aesthetic reasons. However, from a durability point of view, the crack opening at the level of the reinforcement would be exactly the same and, if anything, the element with a large cover would be better protected.

Conclusions

From the above considerations, it is possible to draw the following conclusions: – The tests carried out at the Structures Laboratory of the Civil Engineering school of Madrid, designed to confirm, or discard, the effect of cover and parameter φ/ρs,ef on crack spacing, in the light of current controversy, have confirmed that both of these are important parameters affecting crack spacing.

– The tests have also confirmed that stirrup spacing has an influence on crack spacing. However, this influence is mainly relevant for mean crack spacing. Its influence on maximum crack spacing, which is the value relevant for the verification of the serviceability limit state of cracking, is much smaller. This fact would justify excluding this from the relevant parameters in current and future codes of practice.

– The large difference between crack spacing at the reinforcement surface and crack spacing at the concrete surface observed in tests can be attributed to internal cracking (or Goto cracks). At the bar surface, the differential strain between steel and concrete is distributed among the passing crack and the internal non-passing cracks. The increase in the width of the passing crack is only a reflection of the closing of the internal cracks.

– The effects of shear lag in the effective concrete area are negligible. For this reason it can be said that current crack models are actually providing an estimate of the crack width at the concrete surface.

– If it is agreed that the increase in the opening of cracks increasing with the distance from the bar is due to the closing of secondary cracks, it does not make sense to penalize cross-sections with large covers when crack width is being limited for durability considerations.

Large covers will result in larger superficial cracks due to the fact that a fewer internal cracks will make their way to the surface. However, at the bar level, the crack opening for small and large covers would be expected to be the same.

Notation εc tensile strain in concrete between cracks εs tensile strain in steel εtension mean measured tensile strain along constant moment span at level of reinforcement φ bar diameter ρs,ef effective reinforcement ratio σs stress in reinforcement at crack

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c d Es fctm h hef k1,k2 l L ncracks sr,m sr,max sw TS w wm wmax x

clear cover to longitudinal reinforcement effective depth of reinforcement modulus of elasticity of steel mean tensile strength of concrete depth of cross-section depth of effective concrete area model constants length used for strain measurement (l = 20 cm) span of constant bending moment zone number of cracks in constant moment span after stabilization of crack pattern mean crack spacing maximum crack spacing stirrup spacing factor (< 1) accounting for tension stiffening crack opening mean crack opening maximum crack opening depth of neutral axis assuming fully cracked section

Acknowledgements The tests carried out at the Structures Laboratory of the Civil Engineering School of UPM were performed within the framework of the Estudio de fisuración en muros pantalla research programme led by COMSAEMTE, S.A., with the participation of FHECOR Consulting Engineers. The tests were partly funded by Centro de Desarrollo Tecnológico Industrial (CDTI), a body of the Spanish Ministry of Science & Technology, under project No. IDI-20080937.

The authors also wish to thank the head of the laboratory, José Torrico, and visiting students from Politecnico di Milano as well as Francesco dal Pont and Andrea Facchini for their help in carrying out the tests.

References 1. Borosnyói, A., Balázs, G. L.: Models for flexural cracking in concrete: the state of the art. fib Journal Structural Concrete, vol. 6, No. 2, 2005.

2. Beeby, A.: The influence of the parameter φ/ρs,ef on crack widths. fib Journal Structural Concrete. vol. 5, No. 2, 2004.

3. Hogestad: Journal of PCI Research & Development Laboratories, 1962.

4. Rehm, G., Rüsch, H.: Versuche mit Betonformstählen, pt. I (1963), pt. II (1963), pt. III (1964). Deutscher Ausschuss für Stahlbeton, No. 140 (1963–64).

5. Krips, M.: Rissbreitenbeschränkung im Stahlbeton und Spannbeton. Doctoral thesis, 1984.

6. Hartl, G.: Die Arbeitslinie “Eingebetteter Stähle” bei Erstund Kurzzeitbelastung. Dissertation, 1977.

7. Rhem, G., Eligehausen, R., Mallée, R.: Rissverhalten von Stahlbetonkörpern bei Zugbeanspruchung, report, 1976.

8. Clark, A. P.: Cracking in Reinforced Concrete Flexural Members. ACI JOURNAL, Proc. vol. 27, No. 8, Apr. 1956, pp.

851–862.

9. Farra, B., Jaccoud, J.-P.: Influence du Beton et de l’armature sur la fissuration des structures en Beton. Rapport des essais de tirants sous deformation imposée de courte durée. Département de Génie Civil, Ecole Polytechnique Fédérale de Lausanne, Nov 1993, pub. No. 140.

10. Broms, B. B.: Stress Distribution in Reinforced Concrete Members with Tension Crack. Journal of the American Concrete Institute. Sept 1965.

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11. fib: Model Code 2010, final draft. Bulletin Nos. 65 & 66.

12. Pérez Caldentey, A., Corres Peiretti, H., Peset, J.: Estudio de fisuración en muros pantallas. Final report, research project No. IDI-20080937, funded by CDTI. Ministry of Science & Technology. Spain, 2010.

13. Beeby, A., Base, G. D., Read, J. B., Taylor, H. P.: An Investigation of the crack control characteristics of various types of bar in reinforced concrete beams. Cement & Concrete Association. Research report No. 18, pt. 1. Dec 1966.

14. CEN: EN-1992-1-1. Eurocode 2. Design of concrete structures – Part 1-1. General rules and rules for buildings, 2004.

15. CEB: Model Code 1990. Thomas Telford, 1993.

16. Gómez Navarro, M.: Concrete Cracking in the Deck of SteelConcrete Composite Bridges. PhD Thesis No. 2268, Lausanne, 2000.

17. Husain, S. I., Ferguson, P. M.: Flexural Crack Width at the Bars in Reinforced Concrete Beams. Research report No. 102-1F. Center for Highway Research. Austin, Texas, 1968.

18. Borosnyói, A., Snóbli, I.: Crack width variation within the concrete cover of reinforced concrete members. Epitoanyag (Building Materials, HU ISSN 00 13-970x) Journal of the Hungarian Scientific Society of the Silicate Industry. Hungary, 2010.

19. Goto, Y.: Cracks Formed in Concrete Around Deformed Tension Bars. ACI Journal. vol. 68, No. 4. Apr 1971.

Alejandro Pérez Caldentey Polytechnic University of Madrid – Mecánica de Medios Continuos y Teoría de Estructuras Calle Profesor de Arenguren, s/n Escuela Superior de Ingenieros de Caminos, Canales y Puertos Madrid Madrid 28040, Spain Fhecor Consulting Engineers, Calle de Barquillo, 23, 2, 28004 Madrid, Spain apc@fhecor.es

Hugo Corres Peiretti Polytechnic University of Madrid – Mecánica de Medios Continuos y Teoría de Estructuras, Madrid, Spain Fhecor Consulting Engineers, Calle de Barquillo, 23, 2, 28004 Madrid, Spain hcp@he-upm.com

Alejandro Giraldo Soto Polytechnic University of Madrid – Mecánica de Medios Continuos y Teoría de Estructuras, Madrid, Spain ags@he-upm.com

Joan Peset Iribarren Comsaemte – Gestión del Conocimiento e Innovación Tecnológica, S.A., Edificio Numancia 1. Viriato, 47, 08014 Barcelona, Spain

fib-news fib-news is produced as an integral part of the fib Journal Structural Concrete.

fib-days in Chennai, India Contents

fib President Gordon Clark and Immediate Past President György L. Balázs with students who attended the conference, in front of the Larsen & Toubro Engineering Design and Research Center.

In preparation for the 2014 fib Congress in Mumbai the Indian National Member Group of fib organised a series of “fib-days” over the past few years in major cities across India to assist in raising awareness of fib and to publicise the forthcoming Congress. The latest of these was held in Chennai, Tamil Nadu, on 10th and 11th January 2013 and was attended by about 350 engineers and students. It was hosted at the headquarters of Larsen & Toubro, one of India’s largest contractors and organised for the Institution of Engineers (India). L&T’s Engineering Design and Research Centre was the recipient of a Special Mention in the fib Awards for Outstanding Structures in 2002 and is a remarkable iconic concrete structure. fib President Gordon Clark and Immediate Past President György L. Balázs attended and presented keynote papers on “Recent Inspections of Post-Tensioned Bridges and lessons learnt” and “Fibres in Concrete”. Milan Kalny, Head of the

Czech National Delegation in fib and Frank Dehn, Chairman of Commission 8, also attended by invitation and presented keynote papers on “Rehabilitation of Concrete Bridges” and “Multifunctional Construction Materials”. The invited keynote speakers were given a very warm welcome by the audience and the organisers.

There were also several invited papers from experts from around India including: “Geopolymer concrete for sustainable development”

Issue 1 (2013)

fib-days in Chennai, India

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fibUK Technical Meeting

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Design of concrete bridges: fib short course in Turkey

81

New fib officers

81

fib Model Code book

81

Gordon Clark visits Japan

81

Short notes

82

Congresses and symposia

83

fib membership benefits

84

Acknowledgement

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(Dr Nagesh R. Iyer, CSIR-Structural Engineering Research Centre, Chennai), “Special concretes used in India – its future and way forward” (Dr Ravindra Gettu, Indian Institute of Technology, Madras), “U.S. experience with seismic design and construction of precast concrete xtructures” (S.K. Ghosh, California, USA), “Use of concrete in hydroelectric/irrigation projects” (S.K. Dharmadhikari, Chief Technical Officer, HCC Group), “Elevated corridors for road connectivity” (Vinay Gupta, CEO, Tandon Consultants, New Delhi), “Materials for sustainable concretes in India” (Dr M.R.

From left to right: Milan Kalny, Ravindra Gettu, Harshavardhan Subbarao (Chairman Construma Consultancy, Mumbai), Frank Dehn, V.N. Heggade (Head of Technical Management Gammon India, Mumbai), György L. Balázs

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fibUK Technical Meeting in recognition of Andrew Beeby Kalgal, UltraTech Cement), “Precast concrete construction” (Dr A. Ramakrishna, formerly of L&T), “Concrete construction for metros” (V.B Gadgil, L&T Metro Rail Hyderabad).

Additionally there were summaries presented of several noteworthy papers from the past two fib Symposia held in Prague in 2011 and in Stockholm in 2012.

On the evening of the first day there was a delightful cultural event for participants by two dancers who portrayed some traditional dancing of the region.

A hundred engineers gathered at the Headquarters of The Institution of Structural Engineers on the evening of 29th November to hear Andrew Beeby about Deflections in Concrete. This inaugural joint meeting of fibUK and The Institution of Structural Engineers was held to recognise the contributions of Professor Andrew Beeby to both organisations and to concrete engineering in general.

Prof Steve Denton (Chairman, fibUK) spoke for many by alluding to Prof Beeby’s mythical status to concrete designers. The three speakers were delighted to explain some of Prof Beeby’s contributions in the field of deflection.

Following the event Gordon Clark, György Balázs and Milan Kalny travelled to Mumbai, where they had each been invited to present to the conference “Concrete Futures” on 12th January organised by the Foundations Knowledge Initiative of Ambuja Cement, with an invited audience of about 200 engineers, architects and clients and where their presentations attracted lively debate during a closing panel discussion session.

It is anticipated that this sixth fibdays Conference in the important and successful series will strengthen interest in the Mumbai Congress (10-14 February 2014; see www.fibcongress2014 mumbai.com).

Gordon Clark

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Robin Whittle spoke about tension stiffening and the problems of determining deflections in the reality between uncracked and fully cracked behaviour. Prof Beeby’s early tension stiffening model had been incorporated into BS8110 Structural use of concrete and Robin had used this to predict deflections on a test slab – predictions that proved horribly wrong! It was only through a suggestion by Prof Beeby some years later that research was undertaken on the rate of decay of tension stiffening. This research showed that tension stiffening dropped 50% in 19 days – just as Prof Beeby had predicted – and much to the relief of the speaker.

Dr Richard Scott bumped into his friend Prof Beeby on a train: “Why don’t you do some work on service loads at Cardington?” Cardington was the full scale in-situ test building being built inside an airship hanger.

Funding was quickly arranged to enable measurement of in-situ strains in the 6th of 7 flat slabs. With the

help of Arup, different tension stiffening models were investigated and found to give very different answers.

With the caveats that only transient loads and one highly reinforced slab (1.7%) were investigated, Richard concluded that ICE Technical Note 372 appeared most appropriate – at least for slabs on the cusp of being cracked.

Dr Robert Vollum talked about span: effective depth (L/d) ratios, where Prof Beeby was a pioneer, developing rules for BS8110. Over time these rules proved to work very well. It became increasingly clear that tension stiffening has most influence on uncracked sections.

Therefore load history and cracking become very important in determining deflection. This was recognised in the background to the Eurocode 2 L/d rules. Unfortunately some of the assumptions made have now proved to be unconservative for lightly loaded slabs in multi-storey construction. Dr Vollum explained how improvements could be made and would be proposed.

Questions and discussion followed.

The chairman closed proceedings by leading a warm round of applause.

A recording of this lecture is available as a freely accessible webinar from the website of the Institution of Structural Engineers: www.istructe.org/resourcescentre/webinars Charles Goodchild

Editor’s note: Andrew Beeby, long-time member of CEB and fib, Model Code and Structural Concrete Textbook author, and first Editor in chief of fib’s Structural Concrete Journal, passed away on 28 October 2011.

fib-news

Design of Concrete Bridges: fib short course in Ankara, Turkey

New fib officers

Gordon Clark

fib, the Chamber of Civil Engineers of Turkey and Middle East Technical University (METU), organized a short course/workshop on design of concrete bridges, on October 15 and 16, 2012. The event took place at the Cultural and Convention Centre of METU, in conjunction with the Conference ACE2012 (Advances in Civil Engineering, 2012)) organized

by METU at the same venue, from October 17 to 20. The local organizers were Prof. Alp Caner, Associate Professor at the Civil Engineering Department, METU, and Prof.

Guney Özcebe, Professor and Chairman of the Civil Engineering Department, METU. The technical programme included the following presentations: – Conceptual design of bridges (Hugo Corres-Peiretti, fib) – General design concepts of concrete integral bridges (Murat Dicleli, METU) – Pinerolo bridge: Cast in situ bridge built on classical scaffolding (Giuseppe Mancini, fib) – Roccaprebalza bridge: Composite box girder bridge built by cantilevering (Giuseppe Mancini, fib) – Seismic design of concrete bridges according to Eurocode 8 (Michael Fardis, fib) – Bridges built with free cantilever method: Tajuña and Manzanal Bridge (Hugo Corres-Peiretti, fib) – Secondino Ventura bridge: Cast in situ launched bridge (Giuseppe Mancini, fib)

– Precast concrete bridges. (Hugo Corres-Peiretti, fib) – Verolengo bridge: precast on site assembled bridge (Giuseppe Mancini, fib) – Concrete viaducts for high speed railway lines: General concepts and examples using different construction methods. (Hugo CorresPeiretti, fib) – Ortakoy bridge, Artvin: LRFDbased design of segmental concrete bridge utilizing balanced cantilever construction (Alp Caner, METU) There were 45 registered participants, from Ankara and other cities in Turkey, as well as from neighbouring countries. They received copies of the presentations and certificates of attendance signed by Alp Caner, as main organizer of the course, M.N. Fardis on behalf of fib and Mr Taner Yüzgeç, President of the Chamber of Civil Engineers of Turkey.

fib is pleased to announce that Gordon Clark (Ramboll, UK) has taken office since 1st January as President of fib for the term 20132014. The new Deputy President is Harald Müller (Karlsruhe Institute of Technology, Germany). We wish them both a successful and rewarding time in their new roles.

Harald Müller

For the full list of fib Presidium members, visit http://www.fib-international.org/presidium.

Gordon Clark visits Japan fib President Gordon Clark was invited by NEXCO-RI (Nippon Expressway Company Research Institute, part of the former Japan Highways Authority, now privatised since 2005) to travel to Japan from 17 to 24 November 2012 to give two lectures and to visit some of their new post-tensioned bridges under construction using new tech-

On the occasion of the fib event, the co-sponsor, Turkish IABSE group, organized a dinner honoring Emeritus Professor Erhan Karaesmen, who had started his engineering career working at the CEB Secretariat in Paris, from 1962 to 1965.

For further information about fib Short Courses, visit: www.fib-international.org/courses.

Michael N. Fardis Lecture to JPCI

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Representatives of NEXCO plus Gordon Clark and Akio Kasuga (second from right) at the construction site of the Takubogawa bridge. On the far right is Keiichi Aoki, Head of Bridge Division, NEXCO-RI.

Gordon Clark commented on his visit: “Exchange of knowledge in the area of post-tensioned concrete bridges is very important as all countries of the world are faced with some repairs. It was impressive to see how Japan has embraced new technologies in construction of their new post-tensioned bridges.”

Short notes Birthdays of note nologies. The topics were “Grouting and durability of post-tensioned concrete bridges”, delivered to the Japan Prestressed Concrete Association which attracted an audience of about 120 from across Japan, and “Inspection and repair of post-tensioned concrete bridges”, delivered to NEXCO-RI with an audience of about 50 NEXCO staff from various bridge departments. Both lectures were interpreted into Japanese.

The various parts of NEXCO are responsible for management of about 9000 km of expressways across Japan and 20,000 bridges of which about 8,000 are post-tensioned, some dating back to the 1960’s.

Management and maintenance of these bridges is a specialist area where international expertise is developing and Gordon’s involvement in fib’s technical work on the state of the art of post-tensioning and international standards for grouting for over 20 years, together with Ramboll’s depth of experience, has given him significant knowledge and standing in this field.

During his visit Gordon visited the Takubogawa bridge construction site with representatives of NEXCO

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and Sumitomo Mitsui Construction.

The contractor got the whole site working for the occasion, even though it was a public holiday.

The Takubogawa bridge has precast fibre-reinforced pretensioned web panels and a combination of internal and external prestressing using epoxy coated strand. The features are described in the paper “Construction of a Butterfly Web Bridge”

by Kenichiro Ashizuka et al., published in the 2012 fib Stockholm symposium proceedings (www.fibstockholm2012.se).

He also visited the Toyota Arrows bridge – the world’s longest prestressed concrete bridge with corrugated webs.

While in Japan Gordon met several members of the Japanese fib group including Akio Kasuga, who organised the site visits, Presidium member Jun Yamazaki, and Shoji Ikeda, former member of the Japanese delegation and former Presidium member. Professor Hiroshi Mutsuyoshi of fib Commission 9 had arranged the presentation to JPCI at which Gordon met with the President of JPCI Professor Toyo Miyagawa.

Congratulations to Jacques Combault, who was awarded the fib Medal of Merit in 2004, on the occasion of his 70th birthday in February.

Congratulations also go Rüdiger Tewes, former CEB and fib Secretary General, who will celebrate his 70 years in March.

Congratulations go to Konrad Bergmeister (deputy chair of fib Commission 2, Head of Delegation for Austria) who was presented with an honorary doctorate by the Universität der Bundeswehr München on 1st February 2013, in recognition of his outstanding technical and personal achievements. The ceremony took place at the Faculty of Civil Engineering and Environmental Sciences and was presented by the faculty Dean Prof. Jürgen Schwarz and university President Prof.

Merith Niehuss, with a laudatory speech given by Prof. Manfred Keuser.

fib-news

Congresses and symposia Date and location

Event

Main organiser

Contact

4–5 April 2013 Rostov-on-Don, Russia

Development of large-panel housing construction in Russia

PATRIOT Engineering

kpd-conf@mail.ru mail@rifsm.ru

11–12 April 2013 Hamburg, Germany

Deutscher Bautechnik-Tag

Deutscher Beton- und.

Bautechnik- Verein E.V

www.betonverein.de/ bautechniktag2013.php

22–24 April 2013 Tel-Aviv, Israel

fib Symposium: Engineering fib group Israel a Concrete Future: Technology, Modeling and Construction

www.fib2013tel-aviv.co.il

27–29 May 2013 Tokyo, Japan

1st International Conference on Concrete Sustainability

JCI

www.jci-iccs13.jp

16–19 June 2013 Bergen, Norway

Sixth Symposium on Strait Crossings

Norwegian Public Roads www.sc2013.no Administration (NPRA)

26–28 June 2013 Guimaraes, Portugal

11th Int. Symposium on Fibre Reinforced Polymers for Reinforced Concrete Structures

University of Minho, ISISE

23–25 September 2013 Nanjing, China

7th International Conference on Concrete under Severe – Conditions (CONSEC13)

Hong Kong University of www.consec13.com Science and Technology

25–27 September 2013 Paris, France

Third International Workshop on Concrete Spalling due to Fire Exposure (IWCS 2013)

CSTB Paris, TU Delft, MFPA Leipzig

website to be announced

1–3 October 2013 Marseilles, France

2nd International Symposium on UHPFRC

AFGC

www.afgc.asso.fr

10–14 February 2014 Mumbai, India

4th International fib Congress and Exhibition

fib group India

18–20 February 2014 Neu-Ulm, Germany

58th BetonTage

FBF Betondienst GmbH

www.betontage.com

11–13 June 2014 Oslo, Norway

Concrete Innovation Conference (CIC2014)

Norwegian Concrete Assocation

www.cic2014.com

21–23 July 2014 Quebec, Canada

10th fib International Ph.D. Université Laval Symposium in Civil Engineering

www.fib-phd.ulaval.ca

10–18 September 2014 Beijing, China

10th International symposium on Utilization of HS/HP Concretes

www.hpc-2014.com

Beijing Jiaotong University

www.frprcs11.uminho.pt

www.fibcongress2014mumbai.com

The calendar lists fib congresses and symposia, co-sponsored events and, if space permits, events supported by fib or organised by one of its National Groups. It reflects the state of information available to the Secretariat at the time of printing; the information given may be subject to change.

Visit www.fib-international.org/events for a continuously updated online version of the events calendar and a link to the calendar of events of the Liaison Committee of International Associations of Civil Engineering.

Structural Concrete 14 (2013), No. 1

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fib-news

fib membership benefits fib has 41 National Member Groups as statutory members, and about 1000 individual or corporate members in about 60 countries. The objectives of fib are to develop at an international level the study of scientific and practical matters capable of advancing the technical, economic, aesthetic and environmental performance of concrete construction. These objectives shall be achieved by the stimulation of research, the synthesis of findings from research and practice, and the dissemination of the results by way of publications, guidance documents and the organisation of international congresses and symposia. The production of recommendations for the design and construction of concrete structures, and the information of members on the latest developments also belong to these objectives.

Individual membership is offered in two categories with the following benefits: Ordinary members receive the quarterly journal Structural Concrete and one technical publication (‘Bulletin’) of their choice per year at a discount rate. Students (persons under 30 years of age) receive the same benefits as ordinary members for the reduced fee of 90 CHF/year instead of 190 CHF/year. Subscribing members receive one copy of all technical publications (on average six Bulletins/year, plus the journal) and may order any quantity of publications at a discount rate (including former CEB or FIP publications). Furthermore, individual members receive discounts when attending official fib congresses or symposia.

Corporate membership is available in three categories with the following benefits: Associate members (libraries, companies, engineering offices, etc.) may nominate one representative to be registered as individual member of fib, and, in addition to the benefits described above for subscribing members, may request two copies of all technical publications at no extra charge. In addition to this, supporting members are entitled to nominate two representatives to be registered as individual members. They are also entitled to a special mention in the Directory and receive discount rates when advertising in the journal Structural Concrete. In addition to this, sponsoring members receive special mention on the fib website, including a link to their homepage. They may use fib's logo by stating ‘Sponsoring member of fib’ in their letterhead, and may nominate three representatives to be registered as individual members. They are entitled to nominate a member of a task group in one particular field or interest and may send a representative to the General Assembly.

In addition, all members receive the fib Directory free of charge and free access to the onlines services on fib's website.

Application Form I/my company want(s) to join fib as a: Ordinary Member (190 (90) CHF/year)

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remittance, free of charge for the receiver, to: fib—fédération international du béton, 1015 Lausanne, Switzerland, account No. 710.250.00 V, at the Union Bank of Switzerland (UBS), Case Postale 2950, CH-1211 Geneva 2, Dépôt (Swiftcode UBSWCHZH12A, IBAN: CH19 0024 0240 7102 5000 V, BIC: UBSWCHZH80A) Signature

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Structural Concrete 14 (2013), No. 1

fib-news

Acknowledgement fib – fédération internationale du béton – the International Federation for Structural Concrete – is grateful for the invaluable support of the following National Member Groups and Sponsoring Members, which contributes to the publication of fib technical bulletins, the Structural Concrete Journal, and fib-news.

National Member Groups AAHES – Asociación Argentina del Hormigón Estructural CIA – Concrete Institute of Australia ÖBV – Österreichische Bautechnik Vereinigung, Austria GBB – Groupement Belge du Béton, Belgium ABCIC – Associação Brasileira da Construção Industrializada de Concreto, Brazil ABECE – Associação Brasileira de Engenharia e Consultoria Estrutural, Brazil fib Group of Canada CCES – China Civil Engineering Society Hrvatska Ogranak fib-a (HOFIB) Croatian Group of fib Cyprus University of Technology Ceska betonarska spolecnost, Czech Republic DBF – Dansk Betonforening, Denmark Suomen Betoniyhdistys r.y, Finland AFGC – Association Française de Génie Civil, France Deutscher Ausschuss für Stahlbeton e.V., Germany DBV – Deutscher Beton- und Bautechnik- Verein e.V., Germany FDB – Fachvereinigung Deutscher Betonfertigteilbau e.V., Germany Technical Chamber of Greece Hungarian Group of fib The Institution of Engineers (India) Technical executive bureau, Iran IACIE – Israeli Association of Construction and Infrastructure Engineers Consiglio Nazionale delle Ricerche, Italy

Sponsoring Members JCI – Japan Concrete Institute JPCI – Japan Prestressed Concrete Institute Admin. des Ponts et Chaussées, Luxembourg fib Netherlands New Zealand Concrete Society Norsk Betongforening, Norway Committee of Civil Engineering, Poland Polish Academy of Sciences GPBE – Grupo Portugês de Betão Estrutural Society for Concrete and Prefab Units of Romania Technical University of Civil Engineering University of Transylvania Brasov, Romania ASC – Association for Structural Concrete, Russia Association of Structural Engineers, Serbia Slovak Union of Civil Engineers Slovenian Society of Structural Engineers Concrete Society of Southern Africa KCI – Korean Concrete Institute ACHE – Asociacion CientificoTécnica del Hormigon Estructural Svenska Betongföreningen, Sweden Délégation nationale suisse de la fib, Switzerland ITU – Istanbul Technical University, Turkey Research Institute of Building Constructions, Ukraine fib UK Group ASBI – American Segmental Bridge Institute PCI – Precast/Prestressed Concrete Institute PTI – Post Tensioning Institute

Preconco Limited, Barbados Liuzhou OVM Machinery Co., China CONSOLIS Technology, Finland FBF Betondienst GmbH, Germany FIREP Rebar Technology GmbH, Germany MKT Metall-Kunststoff-Technik GmbH, Germany VBBF – Verein zur Förderung und Entwicklung der Befestigungs-, Bewehrungs- und Fassadentechnik e.V., Germany Larsen & Toubro ECC Division, India ATP, Italy Sireg, Italy Fuji P. S. Corporation, Japan IHI Construction Service Co., Japan Obyashi Corporation, Japan Oriental Shiraishi Corporation, Japan P.S. Mitsubishi Construction Co., Japan SE Corporation, Japan Sumitomo Mitsui Construct. Co., Japan Patriot Engineering, Russia BBR VT International,Switzerland SIKA Services, Switzerland Swiss Macro Polymers, Switzerland VSL International, Switzerland China Engineering Consultants, Taiwan (China) PBL Group, Thailand CCL Stressing Systems, United Kingdom Strongforce, United Kingdom

Structural Concrete 14 (2013), No. 1

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Preview

Structural Concrete 2/2013 Hugo Corres Peiretti Conceptual design, the only procedure for achieving sound engineering proposals according to fib Model Code 2010 György L. Balázs et al.

Design for SLS according to fib Model Code 2010 Raphael Breiner, Harald Müller, Isabel Anders (nee Burkart), Michael Vogel Concrete: treatment of types and properties in fib Model Code 2010 Pierre Rossi, Jean-Louis Tailhan, Claude Boulay, Fabrice Le Maou, Eric Martin Compressive, tensile and flexural basic creep behaviours of a same concrete Jung-Chul Kim, Taeseok Seo Behaviour of concrete in a stress continuity region after cracking under restrained drying shrinkage Robert Lark, Ben Isaacs, Tony Jefferson, Robert Davies, Simon Dunn Crack healing of cementitious materal using shrinkable polymer tendons

Conceptual design is the approach that creates an idea in order to find a solution to a new proposal for a structure or solve a detail in a specific structure. It is a personal approach that is learned over time and with experience. It is not normally dealt with at university, but is vitally important for producing sound structures. The fib Model Code 2010 introduced this concept in the first section of chapter 7 “Design”. The content of that section explains the general approach to developing conceptual design.

The picture shows the final proposal for a footbridge competition (Dr. Techn. Olav Olsen + FHECOR Ingenieros Consultores + OKAW + Gullik Gulliksen)

Tian Sing Ng, Stephen J. Foster Development of a mix design methodology for high performance geopolymer mortars

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Miguel Fernández Ruiz, Thibault Clément, António Pinho Ramos, Aurelio Muttoni Design for punching of prestressed concrete slabs

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