Calculation of maximum crack width for practical design of reinforced concrete

Abstract

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.

Crack width verification and minimum reinforcement according to EC 2: Current model with specifications in Germany and Austria vs proposal for revision

“…Further information on the development and different characteristics of these crack stages are given in the literature. 21 From a practical point of view, the distinction made between single crack and stabilized crack stage is particularly important for the consideration of crack formation in prestressed concrete members because here, generally, crack formation in the serviceability limit state does not exceed the single crack. Likewise, by definition, a condition with single cracks is often the case for flat beams and thin slabs under flexure as well as for a large proportion of all members with predominant restraint stresses.…”

“…And yet, if the equations for pure flexure and centric tension regarding the tensile force used as a basis for the reinforcement calculation are analyzed, it becomes apparent that the tensile force due to the cracking force (right term on the right-hand side) exceeds the cracking force of the effective area (left term) with increasing member thickness many times over. However, the crack width is only limited for the cracking force of the effective area with the result that the design using Equation (21) and Equation (22) for the minimum reinforcement may lead to results on the unsafe side. As previously indicated, the design of minimum reinforcement based on the cracking force of the effective area requires explicit consideration of the deformation compatibility or, as a minimum, consideration of the increase in cracking force of the effective area with increasing member thickness.…”

“…The following applies: At this, is the width of the cross section or partial cross section and is the height of the effective area with The background of Equation (1) is explained in detail in the References 3,4. Moreover, Reference 21 shows that the assumption of a constant bond stress (independent of the slip) results in an underprediction of the crack width for small crack widths.…”

“…Overall, the equations specified in References 1,2 can, thus, basically be regarded as a mechanical model although the determination for the mean bond stress and the effective concrete tensile area are partly simplifications and partly empirical in nature. Finally, it is important to point out that the crack width determined in this way can be interpreted as crack width at the surface for ordinary reinforcement configurations and concrete covers, see also Reference 21.…”

Rissbreitennachweis und Mindestbewehrung nach EC 2 – aktuelles Modell versus Vorschlag für die Revision

“…Erstens wird bei einer solchen Extrapolation davon ausgegangen, dass sich die über die Einleitung der Verbundkraft berechnete Rissbreite auf die Bewehrungslage bezieht und sich von dort aus infolge der Krümmung am Querschnitt über die gesamte Betondeckung hinweg linear vergrößert. Wie in[21] und in Abschn. 4.1.3 näher ausgeführt wird, bezieht sich die berechnete Rissbreite aber nicht auf die Schwerelage der Bewehrung, sondern auf eine globale Größe infolge zentrischer Einleitung der Verbundkraft in die effektive Betonzugfläche.…”