Consistent crack width calculation methods for reinforced concrete elements subjected to 1D and 2D stress states A mixed experimental, numerical and analytical approach

ISBN 978-82-326-3892-5 (printed ver.) ISBN 978-82-326-3893-2 (electronic ver.) ISSN 1503-8181

Doctoral theses at NTNU, 2019:147

Reignard Tan

Consistent crack width calculation methods for

reinforced concrete elements subjected to 1D and 2D stress states

A mixed experimental, numerical and analytical approach

Doct or al thesis

Doctoral theses at NTNU, 2019:147Reignard Tan NTNU Norwegian University of Science and Technology Thesis for the Degree of Philosophiae Doctor Faculty of Engineering Department of Structural Engineering

Reignard Tan

Consistent crack width calculation methods for reinforced concrete elements subjected to 1D and 2D stress states

A mixed experimental, numerical and analytical approach

Thesis for the Degree of Philosophiae Doctor Trondheim, May 2019

Norwegian University of Science and Technology Faculty of Engineering

Department of Structural Engineering

Norwegian University of Science and Technology Thesis for the Degree of Philosophiae Doctor Faculty of Engineering

Department of Structural Engineering

© Reignard Tan

ISBN 978-82-326-3892-5 (printed ver.) ISBN 978-82-326-3893-2 (electronic ver.) ISSN 1503-8181

Doctoral theses at NTNU, 2019:147 Printed by NTNU Grafisk senter

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Figure 1: (a) Shell member subjected to the eight force resultants. (b) Typical section in large-scale concrete structures.

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Table 1 – Crack spacing of investigated specimens

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Figure 6 – Development of crack widths for some of the investigated specimens in Table 1.

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T E C H N I C A L P A P E R

Experimental and theoretical investigation of crack width calculation methods for RC ties

Reignard Tan¹ | Kristoffer Eileraas¹ | Ola Opkvitne¹ | GiedriusŽirgulis¹ | Max A. N. Hendriks^1,2 | Mette Geiker¹ | Dan-Evert Brekke³ | Terje Kanstad¹

1Department of Structural Engineering, NTNU, Norwegian University of Science and Technology, Trondheim, Norway

2Faculty of Civil Engineering and Geosciences, Delft University of Technology, Delft, The Netherlands

3Multiconsult ASA, Oslo, Norway Correspondence

Reignard Tan, Multiconsult ASA, att. Reignard Tan, Postboks 265 Skøyen, 0213 Oslo, Norway.

Email: reignard.tan@multiconsult.no

This paper theoretically and experimentally investigates the semi-empirical formu- las recommended by Eurocode 2 (EC2), fibModel Code 2010 (MC2010), and Eurocode 2 with the German National Annex (DIN) for calculating crack widths in reinforced concrete. It is shown that the formulas can be derived from the princi- ples for the idealized behavior of RC ties. However, instead of explicitly solving the resulting differential equations, the use of simplifications leads to inconsistent formulas. An experimental study was carried out involving the testing of eight RC ties to discover the modeling uncertainty of the formulas. It was found that EC2 substantially overestimated the crack widths for the RC ties. MC2010 and DIN seemed to predict the crack widths better, but gave rather a large number of non- conservative crack width predictions. These experimental results, combined with the theoretical study, suggest that a more consistent calculation model should be formulated by explicitly solving the resulting differential equation.

K E Y W O R D S

calculation methods, cover, crack widths, experiments, large-scale concrete structures, modeling uncertainty, RC ties, semi-empirical formulas, tension stiffening

1 | I N T R O D U C T I O N

There are several methods for calculating crack widths, and a comprehensive summary of them is provided in Borosnyói and Balász.¹This study focuses on the semi-empirical for- mulas for calculating crack widths in cases with relatively large bar diameters and covers, recommended by Eurocode 2 (EC2),²fibModel Code (MC2010),³and Eurocode 2 with the German National Annex (DIN).⁴

This study is a part of an ongoing research project with the overall objective of improving crack width calculation methods for large-scale concrete structures, that is, for large cross sections and thick concrete members. New revisions of EC2 and MC2010 are also currently under way, and this study seeks to contribute by enhancing the crack width

calculation methods currently recommended by these codes.

The main reason for including DIN in this study is that, unlike EC2 and MC2010, it excludes the cover term in cal- culating crack distance. The significance of the cover term has been the subject of major discussion in the development of the semi-empirical formulas. Some investigators argue that it should be abandoned,⁵ while others claim that it should be dominant.^6–8

The aim of this study is to investigate how well the for- mulas comply with the behavior of RC ties, from both a the- oretical and an experimental point of view. First, the idealized behavior of RC ties is discussed, after which the background theory and the main assumptions used when deriving the semi-empirical formulas is revisited. Then, an experimental study of some relatively large RC ties is pre- sented, which are assumed to be representative of the tensile zones of large cross sections exposed to bending. Finally,

Discussion on this paper must be submitted within two months of the print publication. The discussion will then be published in print, along with the authors' closure, if any, approximately nine months after the print publication.

DOI: 10.1002/suco.201700237

1436 © 2018fib. International Federation for Structural Concrete wileyonlinelibrary.com/journal/suco Structural Concrete.2018;19:1436–1447.