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CONTENTS
Volume 2, Number 3, June 2005
 

Abstract
This paper presents a numerical model developed to evaluate the load-deflection and moment curvature relationship for concrete beams strengthened externally with four different Fiber Reinforced Polymer (FRP) composite systems. The developed model considers the inelastic behavior of concrete section subjected to a combined axial force and bending moment. The model accounts for tensile strength of concrete as defined by the modulus of rupture of concrete. Based on the adopted material constitutivernrelations, the model evaluates the sectional curvature as a function of the applied axial load and bending moment. Deflections along the beam are evaluated using a finite difference technique taking into account support conditions. The developed numerical technique has been tested on a cantilever beam with a transverse load applied at its end. A study of the behavior of the beam with tension reinforcement compared to that with FRP areas giving an equivalent ultimate moment has been carried out. Moreover, cracking of the section in the tensile region at ultimate load has also been considered. The results indicated that beams reinforced with FRP systems possess more ductility than those reinforced with steel. This ductility, however, can be tuned by increasing the area of FRP or by combining different FRP layers.

Key Words
concrete; fiber reinforcement; flexure; finite difference; nonlinear behavior.

Address
M. J. Terro; Civil Engineering Department, Kuwait University, KuwaitrnM. M. El-Hawary; Kuwait Institute for Scientific Research, KuwaitrnS. A. Hamoush; Architectural Engineering, Department, A & T State University, Greensboro, NC, USA

Abstract
This paper presents an analysis of some experimental results concerning micro-structural tests,rnpermeability measurements and strain-stress tests of four types of High-Performance Concrete, exposed tornelevated temperatures (up to 700oC). These experimental results, obtained within the ?ITECO?research programme are discussed and interpreted in the context of a recently developed mathematical model of hygro-thermal behaviour and degradation of concrete at high temperature, which is briefly presented in the Part 2 paper (Gawin, et al. 2005). Correlations between concrete permeability and porosity microstructure, as well as between damage and cracks?volume, are found. An approximate decomposition of the thermally induced material damage into two parts, a chemical one related to cement dehydration process, and a thermal one due to micro-cracks?development caused by thermal strains at micro- and meso-scale, is performed. Constitutive relationships describing influence of temperature and material damage upon its intrinsic permeability at high temperature for 4 types of HPC are deduced. In the Part II of this paper (Gawin, et al. 2005) effect of two different damage-permeability coupling formulations on the results of computer simulations concerning hygro-thermo-mechanical performance of concrete wall during standard fire, is numerically analysed.

Key Words
high-performance concrete; permeability; micro-structure; elevated temperature; micro-cracking.

Address
D. Gawin; Department of Building Physics and Building Materials, Technical University of Lodz,rnAl. Politechniki 6, 90-924 Lodz, PolandrnC. Alonso and C. Andrade; Istituto de Ciencias de la Construccion Eduardo Torroja, CSIC, c/Serrano Galvache, s/n, 28033 Madrid, SpainrnC. E. Majorana and F. Pesavento; Department of Constructions and Transportation Engineering, University of Padua, via Marzolo 9, 35131 Padua, Italy

Abstract
In the Part 1 paper (Gawin, et al. 2005) some experimental results concerning micro-structuralrntests, permeability measurements and stress-strain tests of four types of High Performance Concrete, exposed to elevated temperatures (up to 700oC) are presented and discussed. On the basis of these experimental results parameters of the constitutive relationships describing influence of damage and temperature upon material intrinsic permeability at high temperature were determined. In this paper the effects of various formulations of damage-permeability coupling on results of computer simulations are analysed and compared with the results obtained by means of the previously proposed approach, that does not take into account thernthermo-chemical concrete damage directly. Numerical solutions are obtained using the recently developedrnfully coupled model of hygro-thermal and damage phenomena in concrete at elevated temperatures. Highrntemperature effects are considered by means of temperature and pressure dependence of several material parameters. Based on the mathematical model, the computer code HITECOSP was developed. Materialrnparameters of the model were measured by several European laboratories, which participated in thern?ITECO?research project. A model problem, concerning hygro-thermal behaviour and degradation of a HPC structure during fire, is solved. The influence of two different constitutive descriptions of the concrete permeability changes at high temperature, including thermo-chemical and mechanical damage effects, upon the results of computer simulations is analysed and discussed.

Key Words
high-performance concrete; temperature; permeability; thermo-chemical degradation; finite element analysis.

Address
D. Gawin; Department of Building Physics and Building Materials, Technical University of Lodz, Al. Politechniki 6, 90-924 Lodz, PolandrnC. E. Majorana, F. Pesavento and B. A. Schrelfer; Department of Constructions and Transportation Engineering, University of Padua, via Marzolo 9, 35131 Padua, Italy

Abstract
This work is based on a nonlinear finite-element model with proven capacity for yieldingrnrealistic predictions of the response of reinforced-concrete structures under static monotonically-increasing loading. In it, the material description relies essentially on the two key properties of triaxiality and brittleness and, thus, is simpler than those of most other material models in use. In this article, the finiteelement program is successfully used in investigating the behaviour of a series of RC walls under static cyclic loading. This type of loading offers a more strenuous test of the validity of the proposed program since cracks continuously form and close during each load cycle. Such a test is considered to be essentialrnbefore attempting to use the program for the analysis of concrete structures under seismic excitation inrnorder to ensure that the solution procedure adopted is numerically stable and can accurately predict thernbehaviour of RC structures under such earthquake-loading conditions. This is achieved through arncomparative study between the numerical predictions obtained presently from the program and availablernexperimental data.

Key Words
concrete; nonlinear analysis; RC walls; finite elements; cyclic loading.

Address
D. M. Cotsovos; Concept Engineering Consultants, London W3 0RF, UKrnM. N. Pavlovic? Department of Civil & Environmental Engineering, Imperial College, London SW7 2AZ, UK

Abstract
The article presents the results of examination of the fractal dimension D of concrete specimenrnfracture surfaces obtained in fracture toughness tests. The concretes were made from three different types of coarse aggregate: gravel, dolomite and basalt aggregate. Ordinary concretes (C40) and highperformance concretes (HPC) were subjected to testing after 7, 14, 28 and 90 days of curing, respectively. In fracture toughness and compressive tests, different behaviours of concretes were found, depending on the type of aggregate and class of concrete (C40, HPC). A significant increase in the strength parameters tested occurred also after a period of 28 days (up to the 90th day of curing) and was particularly large for concretes C40. Fractal examinations performed on fracture replicas showed that the fractal dimension D was diverse, depending on the coarse aggregate type and concrete class being, however, statistically constant after 7 and 14 days for respective concretes during curing. The fractal dimension D was the greater, the worse strength properties were possessed by the concrete. A cross-grain crack propagation occurred in that case, due to weak cohesion forces at the coarse aggregate/mortar interface. A similar effect was observed for C40 and HPC made from the same aggregate. A greater dimension D was exhibited by concretes C40, in which case the fracture was easier to form compared with highperformance concretes, where, as a result of high aggregate/mortar cohesion forces, the crack propagation was of inter-granular type, and the resulted fracture was flatter.

Key Words
concrete curing; interfacial transition zone; mechanical properties; silica fume; concrete.

Address
Rzeszow University of Technology, Powstan\' cow Warszawy 6, 35-959 Rzeszow, Poland


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