No abstract
Wegen des Problems möglicher Inhomogenitäten der Faserverteilung/‐ orientierung ist der Einsatz von Fasern als alleinige Bewehrung im konstruktiven Ingenieurbau auf wenige Anwendungsgebiete beschränkt (z. B. Aufnahme von Zwangbeanspruchungen). Unter Zugbeanspruchung lässt sich zudem mit den in der Praxis für normalfeste Betone gebräuchlichen Fasergehalten nach der Erstrissbildung kaum ein verfestigendes Verhalten erzielen. Kombiniert man jedoch Stabstahlbewehrung und Faserbewehrung zu einem stahlfaserverstärkten Stahlbeton, so addieren sich die Vorteile beider Verbundwerkstoffe gleichermaßen. Besonders bei erhöhten Anforderungen an die Rissbreite (Größenordnung: unter 0, 1 mm) kann durch gemischte Bewehrung aus Stabstahl und Fasern eine wesentliche Verbesserung gegenüber Stahlbeton erzielt werden. Im Teil 1 dieses Beitrags wurden die für das Verständnis der unterschiedlichen Wirkungsweisen der beiden Bewehrungselemente “Stabstahl” und “Fasern” erforderlichen mechanischen Zusammenhänge dargestellt. Im Teil 2 erfolgt eine Überprüfung der abgeleiteten Beziehungen anhand experimenteller Untersuchungen an gemischt bewehrten Zugelementen aus ultrahochfestem Beton (UHPC). Für UHPC erreicht die Thematik besondere Aktualität, da aus Gründen der Duktilität der Einsatz von Fasen bei diesen Betonen die Regel ist. Der Nachweis der Begrenzung der Rissbreite bei kombinierter Bewehrung wird zudem an zwei Rechenbeispielen veranschaulicht. Crack Formation and Tensile Behaviour of Concrete Members Reinforced with Rebars and Fibres exemplified by Ultra‐High‐Performance Concrete. Part 2: Experimental Investigations and Examples of Application Due to the problem of possible inhomogeneities of fibre distribution/orientation the use of fibres as sole reinforcement is limited in engineering practice to few applications (e. g. coverage of stresses due to constraints). In addition, it is hardly possible to obtain strain hardening after first crack formation with fibre contents commonly used for normal strength concretes. However, if steel fibre reinforcement is used in combination with bar reinforcement, the advantages of both components are additive in the composite material. Especially for enhanced requirements concerning the crack width (order of magnitude: 0.1 mm), with combined reinforcement of rebars and fibres an essential improvement compared to reinforced concrete can be achieved. In part 1 of this contribution the mechanical relationships required for the understanding of the different behaviours of the two reinforcing elements “rebars” and “fibres” have been presented. In part 2 the derived relationships are validated on the basis of experimental investigations on tensile members with combined reinforcement made of ultra‐high‐performance concrete (UHPC). For UHPC the topic is of special interest, because fibres are added to these concretes generally to improve ductility. The crack width control with combined reinforcement is furthermore illustrated by means of two examples.
This paper provides an overview of serviceability specifications given by the fib Model Code for Concrete Structures 2010 (fib MC2010 [1]). First, the reasons behind crack control and deflection control are discussed, then specific design rules are provided. Simple rules as well as detailed models are also presented. Numerical examples are provided in order to assist in the application of the design recommendations for crack control and deflection control (reinforced and prestressed concrete elements).Simple rules mean indirect control of cracking or deflections without calculations. Indirect crack control may include limitation of stresses and selection of maximum bar diameter or maximum bar spacing. Indirect deflection control normally means limiting the span‐to‐depth ratio.Detailed models are based on physical and mathematical approaches to cracking and deflections. The design crack width is expressed as the maximum bond transfer length multiplied by the mean strain between cracks. Deflection analysis can be provided by integrating curvatures or by using a simplified or refined method. Vibrations and numerical modelling of cracking are also briefly discussed.
Cracks are an essential characteristic of reinforced concrete (RC) construction. Serviceability and durability, however, require a reasonable limitation of the maximum crack width. The prediction of the maximum crack width of RC, however, is not trivial and has been much debated over the past decades. This article starts with a fundamental comparison of basic procedures for determining the crack width, namely using a mechanical or calibrated model. Following, the behavior of reinforced concrete during crack formation is thoroughly discussed with a focus on the bond stress‐slip relation at the reinforcement‐concrete interface and with regard to the particular crack stage. Based on these fundamentals, a mechanical calculation model is then proposed for practical calculation of maximum crack width in RC members. The suitability of the proposed model is demonstrated by the comparison of predicted and experimentally obtained maximum crack widths for a database including 460 crack width measurements. It is shown that the current state of knowledge enables a mechanically plausible calculation of the maximum crack width. Although the formulation based on the bond law is not trivial, the calculation model can be prepared with appropriate simplifications in a practical way.
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