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R. Lackner:
"Scale Transition in Steel-Concrete Interaction: From Material Modeling to the Analysis of RC Surface Structures";
Talk: US-Japan-Europe Workshop on Simulation of Collapse of Concrete Structures: from Research to Practice, Makena, Hawai, USA (invited); 2003-11-02 - 2003-11-04.

Cox and Herrmann (1998) distinguish between three different scales of
observation in the steel-concrete interaction in reinforced concrete (RC): the "rib"-scale, the "bar"-scale, and the "member"-scale. For determination of the effect of the steel-concrete interaction at the "member"-scale, the up-scaling of information from the "rib"-scale
over the "bar"-scale to the "member"-scale is required. The scale transition from the "rib"-scale to the "bar"-scale, e.g., provides the bond slip - bond stress relation. Hence, it allows to account for phenomena taking place in the steel-concrete interface (such as, e.g., oxidation of the reinforcement).

In this paper, an up-scaling procedure from the "bar"-scale to the "member"-scale is presented. Hereby, the aforementioned bond slip - bond stress relation, which is taken from CEB-FIP (1990), serves
as input for a one-dimensional composite model, consisting of steel bars and the surrounding concrete. The solution of the underlying differential equation for bond slip (Rehm, 1961) provides the load-carrying characteristics of the composite model at the "bar"-scale. The effect of the latter at the "member"-scale is obtained by extending the fracture energy concept, originally developed for the simulation of cracking of plain concrete, to reinforced concrete. The information gained at the "bar"-scale is used to increase the fracture energy related to the opening of primary cracks, accounting for the additional energy release in consequence of bond slip between steel and concrete.

The performance of the proposed transition of the steel-concrete interaction from the "bar"-scale to the "member"-scale is assessed by means of re-analysis of experiments performed on RC bars (Rostasy, Koch, and Leonhardt, 1976). The applicability to real-life structures, on the other hand, is illustrated by the analysis of two RC surface structures recently investigated numerically at Vienna University of Technology (Lackner and Mang, 2003):

(a) the RC cooling tower III Ptolemais SES (Greece) and
(b) a part of the shotcrete tunnel lining installed at the Lainzer tunnel (Austria).

For the simulation of the latter, the proposed up-scaling technique is extended to early-age fracture of shotcrete. Several analyses characterized by different degrees of consideration of the steel-concrete interaction are performed, giving insight into the influence of the steel-concrete interaction on the load-carrying
behavior of both RC surface structures.

CEB-FIP (1990). Model Code 1990, Bulletin d'Information. CEB, Lausanne, Switzerland.

Cox, J. and Herrmann, L. (1998). Development of a plasticity bond model for steel reinforcement. Mechanics of Cohesive-Frictional Materials, 3:155--180.

Lackner, R. and Mang, H. (2003). Scale transition in steel-concrete interaction I: model. II: applications. Journal of Engineering Mechanics (ASCE), 129(4):393--413.

Rehm, G. (1961). Ueber die Grundlagen des Verbundes zwischen Stahl und Beton. Deutscher Ausschuss fuer Stahlbeton, 138. In German.

Rostasy, F., Koch, R., and Leonhardt, F. (1976). Zur Mindestbewehrung fuer Zwang von Aussenwaenden aus Stahlleichtbeton. Deutscher Ausschuss fuer Stahlbeton, 267. In German.