# Mechanics of Composite Materials (v.44, #3)

Stability analysis of CFRP-wrapped concrete columns strengthened with external longitudinal CFRP sheets by V. Tamuzs; V. Valdmanis; R. Tepfers; K. Gylltoft

*(199-208)*. The external confinement by CFRP wrappings is a very efficient method to increase the load-carrying capacity of round concrete columns. Nevertheless, the serviceability of such columns under loads exceeding the strength of unconfined concrete is limited by different factors. One of them is the reduced stability of the columns due to the significantly reduced tangent elastic modulus inactive loading. To increase the critical load of buckling instability of concrete columns, an additional longitudinal composite reinforcement can be used. In this paper, the stability and strength of concrete columns confined by circumferential wrappings and strengthened with a longitudinal external CFRP reinforcement are studied. Plain and confined columns of length 300 and 1500 mm were tested. Theoretical predictions show that the additional longitudinal reinforcement is efficient in improving the stability of confined columns in the region of moderate slenderness. The prediction for the ultimate strength and stability of the columns coincides rather well with experimental results.

**Keywords:**concrete; CFRP wrapping; longitudinal FRP reinforcement; slenderness; stability

Finite-element modeling of the interaction of reinforcement with concrete matrix by Yu. M. Pleskachevskii; A. O. Shimanovskii; G. M. Kuzemkina

*(209-214)*. A finite-element model of a reinforced concrete beam with rebars modeled by a 3-D deformable body has been developed. An analysis of the stress-strain state of the beam allowed us to determine the stress distribution on cross sections of the rebars and the location of zones with cracks in concrete. It is found that the break of bond between the reinforcement and concrete goes outside the areas of intensely cracked concrete matrix.

**Keywords:**concrete matrix; reinforcement; bond; finite-element modeling; stress-strain state

Composite materials for building heated coverings of roads and runways of airdromes by V. Piskunov; O. Volod’ko; A. Porhunov

*(215-220)*. The paper is dedicated to the development of new compositions of electroconductive concretes reinforced with chemical electroconductive fibers. The compositions are designed for building heated coverings of roads and runways of airdromes. A classification of electroconductive concretes is given, and the results of comparative experimental investigations of the compositions developed are presented.

**Keywords:**concrete; electric conductivity; chemical fibers; abrasion resistance; heated covering; road; runway

Braided reinforced composite rods for the internal reinforcement of concrete by C. Gonilho Pereira; R. Fangueiro; S. Jalali; M. Araujo; P. Marques

*(221-230)*. This paper reports on the development of braided reinforced composite rods as a substitute for the steel reinforcement in concrete. The research work aims at understanding the mechanical behaviour of core-reinforced braided fabrics and braided reinforced composite rods, namely concerning the influence of the braiding angle, the type of core reinforcement fibre, and preloading and postloading conditions. The core-reinforced braided fabrics were made from polyester fibres for producing braided structures, and E-glass, carbon, HT polyethylene, and sisal fibres were used for the core reinforcement. The braided reinforced composite rods were obtained by impregnating the core-reinforced braided fabric with a vinyl ester resin. The preloading of the core-reinforced braided fabrics and the postloading of the braided reinforced composite rods were performed in three and two stages, respectively. The results of tensile tests carried out on different samples of core-reinforced braided fabrics are presented and discussed. The tensile and bending properties of the braided reinforced composite rods have been evaluated, and the results obtained are presented, discussed, and compared with those of conventional materials, such as steel.

**Keywords:**concrete; fibre-reinforced composite material; core-reinforced braided fabric; braided reinforced composite rod

An experimentally based analytical model for the shear capacity of FRP-strengthened reinforced concrete beams by C. Pellegrino; C. Modena

*(231-244)*. This paper deals with the shear strengthening of Reinforced Concrete (RC) flexural members with externally bonded Fiber-Reinforced Polymers (FRPs). The interaction between an external FRP and an internal transverse steel reinforcement is not considered in actual code recommendations, but it strongly influences the efficiency of the shear strengthening rehabilitation technique and, as a consequence, the computation of interacting contributions to the nominal shear strength of beams. This circumstance is also discussed on the basis of the results of an experimental investigation of rectangular RC beams strengthened in shear with “U-jacketed” carbon FRP sheets. Based on experimental results of the present and other investigations, a new analytical model for describing the shear capacity of RC beams strengthened according to the most common schemes (side-bonded and “U-jacketed”), taking into account the interaction between steel and FRP shear strength contributions, is proposed.

**Keywords:**concrete beams; steel reinforcement; external strengthening; side bonding; U jacketing

A model for predicting the shear bearing capacity of FRP-strengthened beams by G. Sas; A. Carolin; B. Täljsten

*(245-256)*. The shear failure of reinforced concrete beams needs more attention than the bending failure since no or only small warning precedes the failure. For this reason, it is of utmost importance to understand the shear bearing capacity and also to be able to undertake significant rehabilitation work if necessary. In this paper, a design model for the shear strengthening of concrete beams by using fiber-reinforced polymers (FRP) is presented, and the limitations of the truss model analogy are highlighted. The fracture mechanics approach is used in analyzing the bond behavior between the FRP composites and concrete. The fracture energy of concrete and the axial rigidity of the FRP are considered to be the most important parameters. The effective strain in the FRP when the debonding occurs is determined. The limitations of the anchorage length over the cross section are analyzed. A simple iterative design method for the shear debonding is finally proposed.

**Keywords:**FRP; shear; concrete; beams; strengthening; strain; anchorage; debonding; fracture mechanics

Anchorage strength models for end-debonding predictions in RC beams strengthened with FRP composites by V. Nardini; M. Guadagnini; M. R. Valluzzi

*(257-268)*. The increase in the flexural capacity of RC beams obtained by externally bonding FRP composites to their tension side is often limited by the premature and brittle debonding of the external reinforcement. An in-depth understanding of this complex failure mechanism, however, has not yet been achieved. With specific regard to end-debonding failure modes, extensive experimental observations reported in the literature highlight the important distinction, often neglected in strength models proposed by researchers, between the peel-off and rip-off end-debonding types of failure. The peel-off failure is generally characterized by a failure plane located within the first few millimetres of the concrete cover, whilst the rip-off failure penetrates deeper into the concrete cover and propagates along the tensile steel reinforcement. A new rip-off strength model is described in this paper. The model proposed is based on the Chen and Teng peel-off model and relies upon additional theoretical considerations. The influence of the amount of the internal tensile steel reinforcement and the effective anchorage length of FRP are considered and discussed. The validity of the new model is analyzed further through comparisons with test results, findings of a numerical investigation, and a parametric study. The new rip-off strength model is assessed against a database comprising results from 62 beams tested by various researchers and is shown to yield less conservative results.

**Keywords:**debonding; FRP; RC beam; composites; strengthening; strength model; anchorage

An analytical study on the bond behaviour between an externally bonded FRP and concrete in the case of continuous beams by L. Vasseur; S. Matthys; L. Taerwe

*(269-278)*. One of the greatest challenges in structural engineering nowadays is the strengthening, upgrading, and retrofitting of existing structures. The use of fibre-reinforced polymers (FRPs) bonded to the tension face of a structural member is an attractive technique in this field of application. The strengthening of reinforced concrete structures by means of an externally bonded reinforcement (EBR) is achieved by gluing a FRP laminate to the concrete substrate. For an efficient utilization of the FRP EBR systems, an effective stress transfer is required between the FRP and concrete. The paper discusses the bond behaviour between a FRP and concrete in the case of flexural strengthening of continuous beams. With respect to this type of beams, only a few studies have been reported, though continuous members often occur in concrete constructions. The structural behaviour of statically indeterminate elements is typically characterized by redistributions of the internal forces. These distributions are related to the nonlinear deformations of the beams and has also a distinct influence on the bond behaviour between the FRP and concrete.

**Keywords:**continuous concrete beam; flexural strengthening; FRP (Fibre-Reinforced Polymer); EBR (Externally Bonded Reinforcement); nonlinear behaviour; moment redistribution; debonding

Strengthening of RC beams with an innovative timber-FRP composite system by N. Mazzon; M. Guadagnini; M. R. Valluzzi

*(279-288)*. The results of a theoretical and experimental research project on the use of an innovative technique for strengthening concrete beams are presented. A spacer element is inserted between the tension side of a beam and the composite material to increase its lever arm and to enhance the over all stiffness of the strengthened beam. The main aim of this exploratory project was to increase the ultimate failure load of strengthened beam specimens, whilst guaranteeing acceptable over all deflections at the serviceability limit states. This resulted into a significant reduction in the amount of FPR required and in a better utilization of the materials employed. A preliminary theoretical study was carried out to investigate the effect of Young’s modulus, failure strain, and thickness of the element to be used as a spacer in order to determine the best possible candidate material. Three tests on 2.5-m-long beams were carried out, and different anchorage techniques were used to try and prevent the debonding of the strengthening system. The results from this pilot study are very promising, as the strengthening system ensures an adequate initial stiffness along with an improved ultimate flexural capacity.

**Keywords:**beam; FRP; timber; strengthening; serviceability limit state; deflection; crack width; flexural behaviour

Square and rectangular concrete columns confined by CFRP: Experimental and numerical investigation by G. Monti; N. Nistico

*(289-308)*. The results of an experimental and theoretical investigation into the deformation behavior of CFRP-confined square and rectangular concrete columns under axial loads are presented. Three types of columns are considered: unwrapped; fully wrapped; and fully wrapped, with L-slaped steel angles placed at the corners. A mechanical deformation model for them is proposed, which is based on a nonuniform distribution of the stresses caused by the confining device. The results given by the model are in a good agreement with the experimental results obtained.

**Keywords:**FRP; confinement; rectangular section; experimental investigation; modeling; failure criterion

Design equations for the assessment and FRP-strengthening of reinforced rectangular concrete columns under combined biaxial bending and axial loads by S. Alessandri; G. Monti

*(309-322)*. A simple procedure is proposed for the assessment of reinforced rectangular concrete columns under combined biaxial bending and axial loads and for the design of a correct amount of FRP-strengthening for underdesigned concrete sections. Approximate closed-form equations are developed based on the load contour method originally proposed by Bresler for reinforced concrete sections. The 3D failure surface is approximated along its contours, at a constant axial load, by means of equations given as the sum of the acting/resisting moment ratio in the directions of principal axes of the sections, raised to a power depending on the axial load, the steel reinforcement ratio, and the section shape. The method is extended to FRP-strengthened sections. Moreover, to make it possible to apply the load contour method in a more practical way, simple closed-form equations are developed for rectangular reinforced concrete sections with a two-way steel reinforcement and FRP strengthenings on each side. A comparison between the approach proposed and the fiber method (which is considered exact) shows that the simplified equations correctly represent the section interaction diagram.

**Keywords:**RC columns; assessment; FRP-strengthening; interaction domain; biaxial bending; closed-form equations; seismic up grade