Local buckling of steel and carbon fibre reinforced plastic plates restrained by concrete

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1 Local buckling of steel and carbon fibre reinforced plastic plates restrained by concrete B. Uy', C.S. A d and T.Yang' 'Schoolof Civil and Environmental Engineering, The University of New South Wales, Australia Abstract External steel plate bonding by both gluing and bolting has been applied to the retrofitting of reinforced concrete slabs and beams extensively throughout the last decade. More recently the benefits of carbon fibre reinforced plastic (CFRP) plates have also been applied to similar applications due to their higher strength to weight ratio and the improved durability characteristics, which are important in exposed environments. In the study of steel plate bonding, consideration of the effects of local and post-local buckling has been addressed, in cases where the steel plate extends into the compressive zones of the member. To enable the use of side plating using CFRP plates one must consider the local and post-local buckling behaviour of these plates, which have completely different material characteristics to steel. Firstly the plates are anisotropic and they also exhibit elastic brittle behaviour. This paper will discuss the augmentation of an existing elastic finite strip method (FSM). The research will then allow design rules to be developed for applying CFRP plates to existing concrete structures. This paper also considers the local buckling behaviour of CFRP plates restrained by concrete using idealised support conditions using the finite element method (FEM). Furthermore, the effects of discrete supports are also considered which are used to model the effects of bolting in plate-bonded structures. 1 Introduction The aim of this paper is to study the local buckling behaviour of carbon fibre reinforced plastic (CFRP) plates, which are restrained against a rigid medium such as reinforced concrete structural beams and columns as shown in Figure 1. The solution of the local and post-local buckling behaviour of CFRP plates

2 The 2002 WIT Press, Ashurst Lodge, Southampton, SO40 7AA, UK. All rights reserved. 26 High ISBN Performance Strwtwrs and Composites against a rigid medium will allow their use as a rehabilitation material for reinforced concrete structures, which can be stiffened and strengthened. The stiffening and strengthening of existing reinforced concrete structures is of major importance as existing structures are ageing andeteriorating. Furthermore, current buildings in seismically active areas may be able to be stiffened and strengthened economically using such an approach. rmnforced concrete beam local buckllng made /' Representative straln flexure In beam "4 j.. Figure 1: Application of CFRP plates to reinforced concrete elements 2 Fibre reinforced plastic materials Carbon fibre reinforced plastic plate, which is manufactured in a unidirectional manner, exhibits highly anisotropic behaviour. This level of anisotropy is illustrated in Table 1, which summarises the pertinent mechanical properties of CFRP plate manufactured by SIKA and also tested at The University of New South Wales, [l]. ' value of in-plane shear modulus is derived from suggestions by Daniel and Ishai,[2] In addition to the level of anisotropy CFRF' plates also behave significantly differently when subjected to tensile or compressive stresses. This is illustrated in Figure 2 and reflected in Table 1, which shows the results of a uniaxial test of a CFRP plate subjected to tensile and compressive stresses. Plates subjected to tensile stresses are shown to illustrate a greater stiffness and strength than plates in compression. This is of particular importance in the buckling analysis of CFFW plates and is thus reflected in the analysis of this paper.

3 25 20 m 5 l 5 m 2 10 F J 0.5 High Per-formancr 3rwtwesand Composites It Strain.~ -!- -Long!tudinal Termon -Longltudmal Compresslon Le-.- Figure 2: Representative stress-strain curve for CFRP plates, [l] Longitudinal tensile strength, Ftt 1 MPa Transverse tensile strength, Fzt MPa Augmentation of the finite strip method for CFRP The first analysis conducted in this paper involves the augmentation of the finite strip method developed by Uy and Bradford, [3]. The model was originally developed to consider mild steel and cold formed steel plates restrained from buckling by concrete. The augmentation involves modifying the constitutive constants from the property matrix in order to reflect the level of anisotropy associated with CFRP plates. CFRP plates are highly anisotropic and such problems in analysis can be overcome by aligning the principal fibre directions parallel to the chosen coordinate axes. In this case, it can be analysed as an orthotropic material as shown in Figure 3.

4 28 High ISBN Perjormance Structures and Composites 2 l Figure 3: Orthotropic Material Showing Principal Axes 1 8~2, [2] Assuming that the lamina is homogeneous and is under a state of plane stress; the stress-strain relationship can be written as described by Daniel and Ishai, PI: where o and E are components of stress and strain respectively. [D] is the constitutive matrix. Therefore, relationships of the in-plane stress-strain components along the principal material axes are: O12 D22 0 Thus this is characterized by four independent constants: E,, E2, G12 and v12. The minor Poisson's ratio, v21is not independent and also is a tinction of the symmetrical matrix of

5 ifighperjomance Structwes and Composites 29 where E, is the modulus of elasticity in direction I, vy is the Poisson s ratio for the strain in the j-direction when stressed in the i-direction and G12is the in plane shear modulus. 4 Parametric study on anisotropic plates using the FSM The finite strip method (FSM) was used to investigate the effects of boundary conditions, as well as stress gradient. The five boundary conditions considered are given below: e (BCl)- Four edges clamped e (BC2)- One unloaded edge clamped and one simply supported (BC3)- Both unloaded edges simply supported e (BC4)- One unloaded edge free and one clamped (BC5)- One unloaded edge free and one simply supported Furthermore five different stress gradients (a=top fibre stredbottom fibre stress) were also considered in this analysis. 4.1 Comparisons with steel In order to provide a benchmark for the analysis, the finite strip method considering CFRP was compared with the previous results of isotropic steel plates undertaken by Uy and Bradford, [3]. The buckling coefficients expected for CFRP are obviously much lower, since the CFRP has a lower elastic modulus and a high level of anisotropy. Tables 2 to 4 highlight the minimum local buckling coefficients for all five boundary conditions, considering the stress gradients of 1.0, 0.5 and 0.0. In all cases the minimum local buckling coefficient of the CFRP plates is shown to be about 25% of that of the steel plates. Uy and Bradford, [3] did not conduct studies for stress gradients less than 0.0, and thus the effects of plates in tension and bending, as well as pure bending are unable to be compared with steel plates herein. Table 2: Comparison between steel and CFRP plates (a= 1.O) Boundary Buckling Coefficient, kmin Condition Steel CFRP BC BC BC BC BC

6 30 High Perjormance Stmctwes and <'omposifes Table 3: Comparison between steel and CFRP plates (a= 0.5) Boundary Buckling Coefficient, kmin Condition Steel CFRP BC BC BC BC BC Table 4: Comparison between steel and CFRP plates (a= 0) Boundary Buckling Coefficient, kmin Condition Steel CFRP BC BC BC BC BC Parametric study of CFRP In order to consider the effects of plates in combined bending and compression and in pure bending the finite strip model was extended further to analyse other stress gradients. Table 5 shows the results of the minimum local buckling coefficients of plates with stress gradients of a = -0.5 and These results are extremely important when one considers that CFRP plates when applied to beams in bending may have both a tension and compression stress zone. Thus if one applies a uniform compression buckling model to the design, it will result in very thick plates and increased construction costs. Since the analysis in this paper was concerned mainly with plates with unidirectional fibres, it was decided to consider the effects of increasing the transverse modulus. Table 6 summarises the results of the minimum local buckling coefficient when the transverse modulus Ezcwas increased. One can see that a significant increase can be obtained by increasing this value. Furthermore, it is also worth highlighting that the dimensionless buckling half-wavelength increases as the transverse modulus is increased.

7 Iligh Per~fornmnce Structuresand Composites Calibration of the FEM In order to calibrate the plate finite element method used in this study, a comparison with the existing solutions on buckling of anisotropic plates by Bulson [4] has been undertaken. The solution that was used for comparison here had 4 sides simply supported under edge compression. According to Bulson [4], the critical buckling stress is given by equation 5 where is the aspect ratio of the plate Lib. For this particular case, k=3.808/(d Q (7) The minimum k occurs when Q =l.95 and the value of k is 2.65 which is shown in Figure 4. Figure 4 also illustrates the parity between the finite element method and the method developed by Bulson [4] and thus confirms its validity for use in the following parametric study. The finite element method invoked the use of eight node quadrilateral elements. The material properties to consider anisotropy were based on those of Table I, [l].

8 ~ 0 ~ ~ +Bulson [4] ~ ~~~ ~1 i--.~ 1 Llb (Dimensionless half-wavelength) ~.-l Figure 4: Simply supported FRP plate under uniform compression 6 Parametric study on anisotropic plates using the FEM A parametric study was conducted to consider the effects of boundary conditions on anisotropic plates, which are restrained from local buckling by the restraint offered by concrete. The study adopted the material properties as outlined in Table 1 and considered six different boundary conditions which are listed below: (BCI)-Four edges clamped (BC2) - One unloaded edge clamped and one simply supported (BC3)-Both unloaded edges simply supported (BC4)-One unloaded edge free and one clamped (BC5)-One unloaded edge free and one simply supported (BC6)- Intermediate discrete supports 6.1 Pure Compression A parametric study considering the effects of pure compression in CFRP plates was conducted. This study will be useful for analysing and designing CFRP plates in columns subjected to pure compression. Figure 5 illustrates that the minimum buckling coefficient is about 8.4 at a dimensionless half wavelength of 2. This is in comparison with steel, which has a minimum buckling coefficient in the order of 10.3 at a dimensionless half wavelength of unity. Figures 6 to 9 illustrate the results of the finite element analyses using the anisotropic plates, which can be compared with the results of Uy and Bradford [3] for steel plates. In all cases the minimum buckling coefficients have reduced and the dimensionless half-wavelengths have increased which is due to the highly anisotropic nature of the material in comparison with steel. Figure 10 illustrates the effects of number of bolts on the minimum buckling coefficient. The results show that there is no major increase in the buckling