promoting aess to White Rose researh papers Universities of Leeds, Sheffield and York http://eprints.whiterose.a.uk/ This is an author produed version of a paper published in Journal of Composites for Constrution. White Rose Researh Online URL for this paper: http://eprints.whiterose.a.uk/42813 Published paper Pilakoutas, K., Neoleous, K., Guadagnini, M. (2002) Design philosophy issues of fiber reinfored polymer reinfored onrete strutures, Journal of Composites for Constrution, 6 (3), pp. 154-161 http://dx.doi.org/10.1061/(asce)1090-0268(2002)6:3(154) White Rose Researh Online eprints@whiterose.a.uk
Design Philosophy Issues of FRP RC Strutures Kypros Pilakoutas 1, Kyriaos Neoleous 2 and Maurizio Guadagnini 3 Abstrat: The onventional design philosophy for reinfored onrete (RC) relies heavily on the dutile properties of steel. These dutile properties are used as a fuse and oneal the large unertainty in the determination of modes of failure aused by onrete. Current design guidelines for FRP RC strutures have inappropriately adopted the same design philosophy used for steel RC, leading either to the adoption of large safety fators or redued strutural reliability. A reliability-based analysis of FRP RC beams shows that the partial safety fators for FRP reinforement on their own do not influene the strutural safety of over-reinfored onrete elements. Proposals are made for the modifiation of the material partial safety fators to ahieve target safety levels. 1 Reader, Centre for Cement and Conrete, Department of Civil and Strutural Engineering, University of Sheffield, UK, k.pilakoutas@sheffield.a.uk 2 Post-Dotorate Researher, Centre for Cement and Conrete, Department of Civil and Strutural Engineering, University of Sheffield, UK, kneoleous@yahoo.o.uk 3 Post-Dotorate Researher, Centre for Cement and Conrete, Department of Civil and Strutural Engineering, University of Sheffield, UK, m.guadagnini@sheffield.a.uk Key words: design philosophy, design guidelines, fibre reinfored polymers, safety, strutural reliability
Introdution The widespread adoption of any new type of reinforement, suh as fiber reinfored polymers (FRP), requires the development of produt speifiation, testing standards and odes of design pratie, a proess that an take many years to be ompleted. Though researh in this field is very reent, the first generation of design guidelines has already been developed in Japan, Canada, Ameria and Europe (JSCE 1997, CHBDC 1996, ACI 440 2001, IGDRCS 1999). All of these guidelines are based on modifiations of existing odes of pratie for steel reinfored onrete (RC) strutures, whih, though they have the lear objetive of ahieving flexural failures through steel yielding, do not have an identifiable design safety philosophy (DSP). It should be pointed out, that the odes have different DSP, with the ACI ode relying on material redution fators, whilst the other odes using partial material safety fators. In addition, even when these guidelines are used for the design of onventional RC strutures: 1. the atual safety, or reliability, levels of the strutures are unknown, (even though standards suh as the Euroode 1 require reliability levels of 10-6 ) 2. the atual reliability levels vary for different strutural elements (depending on the ations and resistane mehanisms), and 3. the apaity margin between eah failure mode is unknown (for example the apaity margin between flexure and shear, making seismi design odes suh as Euroode 8 to adopt radial solutions in order to avoid shear failures). 2
The above problems are worse when dealing with FRP RC elements, sine the predominant mode of failure is likely to be dependent on the onrete rather than on the reinforement. The first generation design guidelines for FRP RC strutures are mainly provided in the form of modifiations to existing steel RC odes of pratie, whih are predominantly using the limit state design approah. The modifiations onsist of basi priniples, whih are heavily influened by the unonventional mehanial properties of FRP reinforement and empirial equations that are based on insuffiient experimental work on FRP RC elements. Though the brittle linearelasti behavior of FRP reinforement is an influening fator behind all of the existing design guidelines, the impat of the hange of failure mode is not addressed in detail. When dealing with FRP reinforement, the amount of reinforement to be used has to be determined by a different approah due to the lower stiffness and the high strength of omposite materials. In fat, for FRP reinforement, the strength to stiffness ratio is an order of magnitude greater than that of steel and this affets the distribution of stresses along the setion. Hene, when onsidering a balaned setion, a ondition desired for steel RC design, the neutral axis depth for FRP RC setions would be very lose to the ompressive end as shown in Fig. 1. This implies that for suh a setion a larger amount of the ross-setion is subjeted to tensile stresses and the ompressive zone is subjeted to a greater strain gradient. Hene, for similar ross setions to that of steel, muh larger defletions and less shear strength are expeted (Fig. 2). 3
If all of the other modes of failure are avoided, flexural failure an be reahed either by rushing of the onrete in ompression or by rupture of the FRP reinforement in tension. Both modes are brittle and undesirable. Whihever is the desired mode of flexural failure, this is attained primarily by the appliation of speifi material partial safety fators for FRP reinforement (γ FRP ) or member strength redution fators. The appliation of γ FRP implies that there is a target strutural reliability level (P ft ). Reent investigations, however, have shown that the appliation of speifi γ FRP would neither lead to the desired mode of flexural failure nor would attain the target P ft (Neoleous et al.1999). This paper initially presents and disusses the variety of safety fators urrently adopted by the urrent first generation design guidelines and then goes on to examine the above issues further for over-reinfored beams designed to resist uniformly distributed loads in aordane to the preliminary design guidelines developed in Europe (IGDRCS 1999). The work has been arried out as part of the European Union sponsored TMR network ConFibreCrete and task group 9.3 of the International Federation of Conrete (fib), whose aim is the development of design guidelines for onrete strutures reinfored, prestressed or strengthened with advaned omposites. The probability of flexural failure ourring due to onrete rushing (P f ) and the flexural notional strutural reliability level (P f ) of 48 retangular beam onfigurations, reinfored with Eurorete FRP reinforement (Eurorete Projet 1997), are determined for a number of γ FRP. The investigation is arried out for two ases: a) simply supported beams reinfored with arbon FRP 4
(CFRP) reinforement and b) simply supported beams reinfored with glass FRP (GFRP) reinforement. From the results of the above researh the paper goes on to identify the DSP problems that need to be addressed before the emergene of a new generation of design guidelines for FRP RC strutures. Current Safety fators The most reent Japanese design guidelines for FRP RC (JSCE 1997), whih are based on modifiations of the Japanese steel RC ode of pratie, provide a set of material partial safety fators for the FRP reinforement as indiated in Table 1. These guidelines, however, do not provide any information regarding the predominant mode of failure that would result from the appliation of the proposed partial safety fators, nor do they over produt speifiation. Hene the small safety margins given may not adequately over reinforement materials whih have large variability in their properties. The Canadian design guidelines (CHBDC 1996) provide only general information about FRP reinforement. The Amerian design guidelines (ACI 440 2001) are based on modifiations of the ACI 318-99 (ACI 318 1999) RC ode of pratie. These guidelines propose that the predominant mode of failure is flexural onrete rushing rather than flexural re-bar frature. Thus, a minimum limit is 5
imposed on the amount of FRP reinforement in order to attain the desired predominant failure mode. The guidelines also adopt a onservative approah for the derivation of strength redution fators, φ. This is due to the fat that there is very little data regarding the servie and long-term behavior of FRP RC strutures. Thus, a φ of 0.7 is reommended for flexure, whereas for shear, it is reommended that the value of φ be the same as the value adopted by ACI 318-99. Though the impat of a strength redution fator is easier to understand than the impat of partial safety fators, its use an lead to very different levels of safety, depending on the onrete strength and reinforement ratio. Furthermore, the use of a member redution fator does not help the engineer understand the overall stress levels in the onstituent materials, whih means that the level of stress in onrete may be higher than for onventional reinforement. Sine strength redution fators are not supposed to be derived on the basis of reliability, they will not be addressed further in this paper. In the ase of the European design guidelines (Clarke et al. 1996, Eurorete report 1997), the reommendations are based on modifiations to British and other European RC odes of pratie suh as Euroode 2 (ENV 1991-1 1994, ENV 1992-1-1 1992). These guidelines were published in the UK as an interim guidane on the design of FRP RC strutures by the Institution of Strutural Engineers (IGDRCS 1999). These guidelines inlude a set of partial safety fators for the material strength and stiffness (Table 2) that take into onsideration both the short and longterm strutural behavior. They do not, however, provide lear indiations about the predominant failure mode that would result from the appliation of these partial safety fators. The omposite 6
ation of the redution fators on the strength and stiffness leads to very onservative results, in partiular when using shear reinforement. The initial approah of developing design guidelines suh as those desribed above may seem reasonable, but it is not entirely appropriate. The onventional steel RC odes of pratie assume that the predominant failure mode is always dutile due to yielding of the flexural reinforement. This is not the ase, however, for the above FRP RC design guidelines, whih seem to aept a brittle flexural failure due to onrete rushing. Furthermore, the steel RC odes of pratie, whih form the basis of these guidelines, have fundamental strutural safety unertainties. These inlude the derivation of the partial safety fators, the atual strutural reliability levels and the resistane apaity margins (RCMs) between the various failure modes. In order to determine the atual strutural reliability levels, it is neessary to have aurate preditive resistane apaity models, a good understanding of the variability of materials and an aurate assessment proedure. With these onerns in mind, both steel and FRP RC elements were analyzed in a omprehensive researh program at the University of Sheffield (Neoleous, 1999) and some of the results are given below. Resistane-apaity predition models Strutural reliability assessment requires the formulation of a model (limit state funtion) that represents the strutural behavior for the limit state for whih the assessment is performed. The limit state funtion, G(R, S), is represented in terms of a strutural resistane omponent, R, and 7
an ation-effet omponent, S. Both R and S are modelled by mathematial relationships of random basi variables, R i and S i, whih represent strutural material properties and ations, respetively. Due to the omplexity of the problem, this paper will try and deal only with the issue of flexural failures, even though work has also been ompleted on shear and bond failures. The strutural reliability of steel RC beams is assessed in terms of the BS8110 (1997) and Euroode 2 (ENV1992-1-1, 1992) odes. Hene, the G(R, S) is formulated using the resistaneapaity predition models adopted for the above failure modes by the two odes of pratie. The Euroode 2 models are elaborated in the appendix and sine the BS8110 models are very similar, they are not given in this paper. In the ase of the FPR RC beams, the strutural reliability assessment is performed in terms of the European design guidelines for FRP RC strutures (Clarke et al, 1996). These guidelines onform to existing European RC odes of pratie and thus, the proposed models are based on the models adopted by these RC odes of pratie. The model for the flexural failure mode, elaborated in Appendix II, is based on the ontrol of strain of the FRP reinforement and utilizes the priniples of the orresponding Euroode 2 model. Statistial data for basi variables The statistial data used in earlier investigations by the authors are utilized for the statistial modeling of all random variables (Neoleous et al. 1999, Neoleous 1999). Tables 3 and 4 summarize the statistial data used for the geometri and loading variables. In the ase of the 8
material strength of onrete and FRP reinforement, the adopted statistial data are derived from the analysis of experimental results provided by manufaturers. A onstant standard deviation of 6 N/mm 2 is used for the onrete ompressive strength and the probability distribution is trunated at 3.16 standard deviations from the mean value. In the ase of CFRP and GFRP (Eurorete) reinforement (Table 5), the strength obtained experimentally in RC beams was adopted, sine existing diret tensile tests fail to simulate the in-servie load-transfer mehanisms for FRP reinforing bars. Assessment Proedure A numerial simulation approah is adopted to determine the P f and flexural P f ; the simulations are performed using MATLAB (MATLAB 1999). The proedure followed in the assessment is illustrated in Fig. 3, and is further elaborated in Neoleous (1999). It is noted that the resistaneapaity models adopted by the European design guidelines, are modified aordingly to aount for flexural failure ourring either due to onrete rushing or reinforement frature. The flexural P f and P f are evaluated by equations 1 and 3, respetively. P f N P = i f i = 1 N (1) P fi = P Q > R G ) = 1 F ( R G ) (2) ( i i Q i i ε 0.0035 = 1 P = i f (3) N 9
ANALYSIS OF SIMULATIONS The flexural design of CFRP RC beams was based on the assumption that a brittle failure would our due to onrete rushing. In the ase of beams with low reinforement ratio (ρ) and high onrete ompressive strength (f ), however, it was assumed that a brittle failure due to frature of the reinforement would be possible. This is a onsequene of the fat that the atual tensile strain developed in the reinforement at the design stage (ε FRP ) exeeds the design limit (ε FRPd ) imposed by the γ FRP. It is noted that this was only observed in six of the examined ases of CFRP RC beams designed using a γ FRP of 1.8 (Fig. 4). In the ase of the GFPR RC beams designed using a γ FRP of 3.6, it was assumed that brittle failure would our due to frature of the longitudinal reinforement, due to the low strength of the reinforement. Whereas, in the ase of GFRP RC beams designed using a γ FRP of 1.3, only three beams had to be designed for frature of the reinforement (Fig. 5). The results obtained for P f indiate that the majority of beams would atually fail due to onrete rushing, as intended at the design stage. In some ases, however, there is a large probability (up to 0.2 for CFRP RC beams and 0.73 for GFRP RC beams) of failure due to frature of the reinforement. This was observed when: a) the design assumed that failure due to frature of the reinforement would our, and b) the value of ε FRP was relatively lose to ε FRPd. In addition, it is observed that the P f dereases as f inreases. This an be attributed to the fat that the tensile strength of FRP reinforement is further utilized. For instane, in the ase of the CFPR RC beams, P f dereases from 0.97 to 0.27 as f inreases from 33 to 50 N/mm 2. 10
Fig. 6 shows that the flexural P f is not affeted by γ FRP, as long as the type of failure assumed at the design stage is onrete rushing. In suh ases, the flexural resistane apaity remains onstant sine the ε FRP does not hange with γ FRP. Thus, if onrete rushing is hosen as the desired mode of flexural failure, it may be seem sensible to disard γ FRP and inorporate the unertainties relevant to flexural reinforement in the partial safety fator adopted for f. As Fig. 7 indiates, the P f is affeted by γ FRP if flexural failure ours due to reinforement frature. In Fig. 6 and 7, it is also observed that the strutural reliability generally satisfies the target value of 10-6 adopted by Euroode 1 (ENV 1991-1 1994), however, the figures indiate that the alulated P f is highly variable. This is due to the effet of various design parameters as illustrated in Fig. 8 and 9 for CFRP and GFRP RC beams, respetively. These figures suggest that the ratio of permanent to variable load greatly influenes the flexural P f. This implies that, for the same γ FRP, the strutural reliability varies for different types of strutures and hene, in order to avoid reliability differentiation, it is reommended to use different γ FRP (or more appropriately, load fators) for different types of strutures. In addition, Fig. 8 and 9 indiate that the ratio of ρ and f influene the P f of both CFRP and GFPR RC beams. The results of the assessment show that the effet of these two parameters is greatly affeted by the type of flexural failure assumed at the design stage. If the flexural design assumes reinforement frature, the P f is influened by both f and ρ (P f inreases with ρ, while it dereases as f inreases) (Fig. 9). If the flexural design assumes onrete rushing, however, the P f is only affeted by f (Fig. 8). It is noted that in this ase the P f is more uniform aross the range of beam onfigurations examined. 11
DESIGN RECOMMENDATIONS Based on the findings of the analysis, design reommendations are proposed for the flexural (short-term) design of over-reinfored FRP RC beams, reinfored with (Eurorete) FPR reinforement. Sine the results show that onrete rushing is the most probable type of flexural failure, it is reommended that flexural design be arried out to attain onrete rushing. This an be ahieved by ensuring that minimum amounts of flexural reinforement are provided, whih will also protet the strutural elements from large raks developing as soon as the onrete tensile stress is exeeded. Provided that flexural failure ours due to onrete rushing, it was determined from the analysis that the use of γ FRP to aount for the unertainties in the mehanial harateristis of the FRP reinforement is not vital, sine the flexural P f is not affeted by γ FRP. Based on this finding, it is proposed that the unertainties relevant to mehanial harateristis of the flexural reinforement should be inorporated into the γ m adopted for f, whih would involve the modifiation of onrete γ m used urrently in flexural limit state design. The mehanial behavior of FRP reinforement in flexure is not established thoroughly, sine aepted standards for the determination of the mehanial harateristis that take into aount the behavior of FRP bars in onrete are not yet available. In addition, sine FRP reinforement is primarily intended for use in aggressive environments, its long-term harateristis in onrete should also be taken into aount. It will not be prudent, therefore, to abolish the use of γ FPR based on the existing knowledge. Consequently, it is reommended to adopt the smallest γ FRP 12
examined during the assessment of the CFRP and GFRP RC beams. In the ase of CFRP reinforement, a value of 1.15 is reommended and a γ FRP of 1.3 is seleted for GFRP reinforement. It should be noted that the different γ FRP - reommended for Eurorete CFRP and GFRP reinforement - reflet the different material harateristis of the two reinforements. In addition, it is noted that these γ FRP are reommended for the short-term design of FRP RC beams and hene, they do not take into aount the long-term behavior of FRP reinforement. A limit is also imposed on ρ, as shown in equation 4, in order to diminish the possibility of flexural failure ourring due to reinforement frature. ρ min 0.81(fk + 8) ε = (4) f FRPk f FPR ( + ε ) k E FRP k Finally, the use of safety fators on the stiffness of the FRP only makes sense if that safety fator is used just in the determination of defletions and raking, and not in onjuntion with strength safety fators when determining flexural apaity. It is proposed that the stiffness safety fators be disarded and the effet of stiffness unertainty taken into aount diretly in the equations dealing with deformations. Further researh at Sheffield (Neoleous, 1999) has taken into aount the effet of other modes of failure as well, and it has led to the development of a more omprehensive DSP based on targeted failure mode hierarhy. This approah allows the designer to hoose different failure mode hierarhies, depending on the materials used, by seleting appropriate material safety fators. 13
CONCLUSIONS This study has examined the effet of design parameters and γ FRP, adopted for FRP reinforement, on the flexural behavior of over-reinfored FPR RC beams. One of the main findings of the assessment is that the desired mode of flexural failure is not attained by the appliation of γ FRP alone. Thus, in order to attain the desired mode of failure, it is neessary to apply limits on the design parameters onsidered by the models adopted to predit the resistane-apaity. A minimum amount of reinforement is proposed, whih will ensure flexural failure due to onrete rushing. The flexural strutural reliability is not uniform due to the effet of various design parameters. The ratio of permanent to variable load is one of the most influening parameters and hene, it is reommended to adopt different load fators for different types of strutures. The use of large values for γ FRP for flexural reinforement is not neessary, if the design is devised to ahieve flexural failure due to onrete rushing. Minimum values for γ FRP are proposed and these values should be extended by further researh to take into aount the longterm behavior of FRP reinforement in onrete. 14
The use of safety fators for the stiffness of FRP is not neessary and the effet of stiffness unertainty should be taken into aount by the equations dealing with deformations. A more omprehensive DSP is required that integrates all of the failure modes and takes into aount the properties of different types or reinforing materials. ACKNOWLEDGEMENT The authors wish to aknowledge the European Commission for funding the EU TMR Network "ConFibreCrete". 15
APPENDIX I. Euroode 2 (ENV1992-1-1, 1992) models for steel Design Moment Resistane RC beams The design rules of Euroode 2 utilize the simplified stress blok approah (Fig. A.1) to determine the design moment resistane. The following assumptions are made by the design rules. 1. The strains in the onrete and the reinforement are diretly proportional to their distane from the neutral axis. 2. The strain in bonded reinforement is the same as in the surrounding onrete. 3. The onrete tensile strength is ignored. 4. The onrete ompressive stresses and the reinforement stresses are derived from idealized design stress-strain urves. 5. The onrete ompressive strain is limited to 0.002, if the RC setion is subjeted to pure longitudinal ompression. Otherwise, the strain is limited to 0.0035. The following algorithm is adopted for the evaluation of the design moment resistane. Initially, it is assumed that plasti failure would our and the effetive depth of the RC beam is evaluated from equation A.1. Expressions for the design fore in the tensile reinforement, F Sd, and the design ompressive fore of onrete, F Cd, are afterwards derived (equations A.3 and A.1.1 respetively). 16
F Cd = 0.85 f k γ 0.8 x b 0.68 f k = (A.1.1) γ x b By onsidering the fore equilibrium, F Cd = F Sd, x is alulated: x = A s f 0.68 f yk k γ b γ s (A.1.2) Before proeeding to the alulation of the lever arm, z, of the fore ouple, the same proedure as in setion A.1 is utilized to hek if the above value of x orresponds to plasti failure. Thus, the neutral axis limit and ε y are determined from the setion strain diagram and the stress-strain diagram, respetively. If x/d exeeds the neutral axis limit, x is realulated on the basis that elasti failure ours due to onrete rushing. Then the value of ε s is derived from the strain diagram and is used together with the material safety fator to determine F Sd. By onsidering fore equilibrium and substituting in A.1.1, the following expression is obtained: x = A s d x E s ε u ( ) γ x 0.68 f b γ k s (A.1.3) x is determined by solving the resulting quadrati equation: 0.68 f k b γ s 2 x + x d = 0 (A.1.4) A E ε γ s s u 17
Then, z is alulated by using the appropriate value of x: z = d - 0.4 x (A.1.5) Finally, the design moment of resistane is obtained: M u = 0.68 f k γ b x z (A.1.6) APPENDIX II. Models for Design Moment Resistane of FRP RC beams The model adopted for the design moment resistane of FRP RC beams is based on the design rules of Euroode 2, and hene the same assumptions apply for the urrent model. The ompression strength of FRP reinforement is also ignored due to the anisotropi nature of the reinforement. The use of FRP reinforement in RC onstrution would generally lead to over-reinfored setions sine the high strength of FRP is not fully utilized. Thus, there is a hange in the failure mode (from dutile to brittle). To aommodate this, the model is modified aordingly and the design is based on the ontrol of the strain in the FRP reinforement (ACI 440-98, 1998; JSCE, 1997). The following algorithm is applied for the evaluation of the design moment resistane. 18
Initially the effetive depth of the RC is alulated based on an assumed bar diameter. Then, it is assumed that flexural failure ours due to onrete rushing. Assuming that the onrete ompressive strain at failure, ε, is equal to 0.0035, the design onrete ompressive fore, F Cd, is derived (equation A.2.1). Sine Euroode 2 is the basis for the design rules, a speially derived equation (Neoleous, 1999) is used to determine the mean stress fator, 2 α = 68711ε + 464.79 ε 0.01, whih is used in the simplified stress blok for onrete. + F Cd = αf k γ x b (A.2.1) Sine it is assumed that failure ours due to onrete rushing, the atual stress in the reinforement (equation A.2.2) is deemed to be less than the design stress (equation A.2.3) at whih frature of the reinforement ours. The design fore of the reinforement is derived based on this assumption (equation A.2.4). f FRP = ε FRP E FRP (A.2.2) f f FRPd = γ FRPk FRP (A.2.3) F Sd = A f = A ε E (A.2.4) FRP FRP FRP FRP FRP By onsidering a simple strain diagram, the neutral axis depth, x, is derived: 19
x = ε ε FRP d + ε (A.2.5) Then by onsidering fore equilibrium between F Cd and F Sd, equations A.2.1, A.2.4 and A.2.5 are solved simultaneously to determine the atual tensile strain of the reinforement, ε FRP : α f k ε ε γ FRP d + ε b = A FRP ε FRP E FRP (A.2.6) By solving the following quadrati equation, the atual reinforement strain, ε FRP, is alulated: ε α f k b d ε + ε ε FRP 0 (A.2.7) γ A E 2 FRP = FRP FRP Before proeeding into the alulation of the lever arm, z, and design moment resistane, M u, it is heked if ε FRP has exeeded the design limit, ε FRPd, whih is defined by equation A.2.8. f ε FRPd = E FRPd FRP (A.2.8) If ε FRPd is exeeded by ε FRP, then flexural failure ours due to frature of the FRP reinforement. In this ase, F Sd and x are determined from equation A.2.9 and A.2.10 respetively. F Cd is also rederived (equation A.2.11) by substituting equation A.2.10 to A.2.1. The onrete ompressive 20
strain is iteratively redued until the fore equilibrium between F Cd (equation A.2.11) and F Sd (equation A.2.9) is satisfied. F Sd = A f (A.2.9) FRP FRPd x = ε ε FRPd d + ε (A.2.10) F Cd = α f k ε ε FRPd γ d + ε b (A.2.11) Using the appropriate value of x, the entroid fator, γ, and the lever arm, z, are then determined from equation A.2.12. 2 z = d γ x where, γ = 1962.6 ε + 17.89 ε 0.33 (A.2.12) + Finally, the design moment resistane, M u, is alulated, depending on the mode of flexural failure. If failure ours due to onrete rushing, equation A.2.13 is applied. It should be noted that F Cd is determined from equation A.2.1. Otherwise, if failure is due to frature of the re-bar, equation A.2.14 is determined by using the appropriate value of F Sd. M u = F Cd z M u = F Sd z (A.2.13) (A.2.14) 21
22
APPENDIX III. REFERENCES ACI Committee 318 (1995). Building Code Requirements for Reinfored Conrete, ACI-318-95, Detroit ACI Committee 440 (2001). Guide for the Design and Constrution of Conrete Reinfored with FRP Bars, ACI 440.1R-01, ACI, Farmington Hills, MI, USA British Standards Institution (1985). BS 8110. Strutural use of Conrete. Part 1: 1985. Code of pratie for design and onstrution, BSI CHBDC - Canadian Highway Bridge Design Code (1996). "Setion 16: Fibre Reinfored Strutures", Final Draft Clarke J. L., O'Regan D. P. and Thirugnanenedran C. (1996). EUROCRETE Projet, Modifiation of Design Rules to Inorporate Non-Ferrous Reinforement, EUROCRETE Projet, Sir William Halrow & Partners, London ENV 1991-1 (1994). Euroode 1 Basis of Design and Ations on Strutures Part 1: Basis of Design, European Prestandard, European Committee for Standardisation, 85 pp ENV 1992-1-1 (1992). Euroode 2. Design of Conrete Strutures, Part 1, General Rules and Rules for Buildings, European Committee for Standardisation 23
Eurorete Projet (1997). The Development of Non-ferrous Reinforement for Conrete Strutures Final Report, Prepared by Euro-Projets (LTTC), 109 pp IGDRCS (1999). Interim Guidane on the Design of Reinfored Conrete Strutures Using Fibre Composite Reinforement, The Institution of Strutural Engineers, 116 pp JSCE (1997). Reommendation for Design and Constrution of Conrete Strutures Using Continuous Fiber Reinforing Materials, Researh Committee on Continuous Fiber Reinforing Materials, Japan Soiety of Civil Engineers, Otober 1997, 325 pp MATLAB (1999). The Language of Tehnial Computing, Version 5.3, Published in the Math Works In. Website: http://www.mathworks.om/produts/matlab, 1999 Neoleous K. (1999). Design and Safety Philosophy for Conrete Strutures Reinfored with Fibre Reinfored Polymers (FRP), Ph.D. Thesis, The University of Sheffield, Department of Civil and Strutural Engineering, Sheffield Neoleous K., Pilakoutas K. and Waldron P. (1999). Strutural Reliability Levels for FRP RC Strutures, ACI SP-188, Proeedings of the Fourth International Symposium on Fiber Reinfored Polymers for Reinfored Conrete Strutures (FRPRCS-4), Baltimore USA, 31 Otober 5 November 1999, pp 65 74 24
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APPENDIX IV. NOTATION E FRPk F i () f f FRPk G i N harateristi value of elasti modulus of FRP reinforement umulative distribution funtion of a variable i onrete ompressive strength harateristi value of tensile strength of FRP reinforement permanent load evaluated at eah simulation yle, i amount of simulation yles performed P f mean probability of failure, whih orresponds to the notional P f P f P f P fi P ft Q R i ε ε FRP notional strutural reliability level probability of flexural failure ourring due to onrete rushing probability of failure evaluated at eah simulation yle target strutural reliability level variable load resistane-apaity evaluated at eah simulation yle onrete strain atual tensile strain developed in the FPR reinforement at the design stage ε FRPd γ FRP design limit imposed on the tensile strain of FRP reinforement by γ FRP material partial safety fator for FRP reinforement 26
Table 1 Partial safety fators proposed by JSCE (1997) (1) Ultimate Limit State Servieability Limit State Fatigue Limit State Conrete γ (2) 1.3* or 1.5 Material Fator γ m FRP γ mf (3) 1.15* * to 1.3 Steel γ s (4) 1.0 or 1.05 Member Fator γ b (5) 1.15 to 1.3 Strutural Analysis Fator γ a (6) 1.0 Load Fator γ f (7) 1.0 to 1.2 Strutural Fator γ i (8) 1.0 to 1.2 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.3* or 1.5 1.15** to 1.3 1.05 1.0 to 1.1 1.0 1.0 Notes: * 1.3 when harateristi strength of onrete is less than 50 N/mm 2 ** 1.15 for FRP with arbon or Aramid fibres 1.0 to 1.1 27
Table 2 Partial safety fators proposed for FRP RC strutures by Clarke et al (1996) (1) Strength Stiffness Material Partial Safety Fator, γ FRP (Short and Long Term) (2) (3) E-Glass reinfored 3.6 Aramid reinfored 2.2 Carbon reinfored 1.8 E-Glass reinfored 1.8 Aramid reinfored 1.1 Carbon reinfored 1.1 28
Table 3 Statistial data for geometrial basi variables Dimension Desription Mean Value µ i (mm) (2) Standard Deviation σ i (mm) (3) Probability Distribution (4) (1) Width Nominal + 2.4 4.8 Normal Overall Depth Nominal 3.2 6.4 Normal Conrete Cover Nominal + 1.6 11.6 Normal Beam Spaing and Span Nominal 17.5 Normal 29
Table 4 Statistial data for loading Load Desription (1) Coeffiient of variation ov i (2) Charateristi i k (3) Probability Distribution (4) Permanent Load G 0.05 µ G + 0.082 Normal Variable Load Q 0.4 µ. Q 1.98 Gamma 30
Table 5 Statistial data for CFRP and GFRP reinforement Tensile Strength (N/mm 2 ) Young s Modulus (N/mm 2 ) (1) CFRP (2) GFRP (3) CFRP (4) GFRP (5) Mean µ i 1380 810 115000 45000 Standard Deviation σ i 69 40.5 5750 2250 Coeffiient of Variation ov i 0.05 0.05 0.05 0.05 Minimum i min 1235.1 725 105800 41400 Maximum i max 1524.9 895.1 124200 48600 Charateristi i k 1272.2 746.7 106012.8 41483.3 Probability Distribution Normal Normal Normal Normal 31
Figure 1 Strain distribution for a GFRP RC setion 32
Figure 2 Defletion and raking in FRP RC beams 33
DATA INPUT Calulation of of the the flexural design load. Failure ours either due to to onrete rushing or or reinforement frature Determination of of the the harateristi variable and permanent load Determination of of the the mean value and standard deviation for for the the variable and permanent load Generation of of pseudo-random values for for all all basi variables by by using the the Latin Hyperube variane redution tehnique Evaluation of of flexural R ii Calulation of of flexural P ff by by using the the Conditional Expetation variane redution tehnique Determination of of P f f Figure 3. Assessment proedure 34
Figure 4. Atual tensile strain developed in the CFPR reinforement at the design stage 35
Figure 5. Atual tensile strain developed in the GFPR reinforement at the design stage 36
Figure 6. Effet of γ FRP on the flexural P f of CFRP RC beams 37
Figure 7. Effet of γ FRP on the flexural P f of GFRP RC beams 38
Flexural Notional Strutural Reliability Levels 10 11 E-14 10 11 E-12 10 11 E-10 10 11 E-08 10 11 E-06 10 11 E-04 EC1 Annual Target Level 25 30 35 40 45 50 55 60 Mean Conrete Cylinder Compressive Strength, N/mm 2 ρ = 0.75% 0.5 ρ = 1.25% 0.5 ρ = 1.75% 0.5 ρ = 2.5% 0.5 Σεριεσ8 ρ = 0.75% 1 ρ = 1.25% 1 ρ = 1.75% 1 ρ = 2.5% 1 Figure 8. Effet of f, ρ and load ratio on the flexural P f (CFRP RC beams γ FRP = 1.8) 39
Flexural Notional Strutural Reliability Levels 11 E-22 10 11 E-20 10 11 E-18 10 11 E-16 10 11 E-14 10 11 E-12 10 11 E-10 10 11 E-08 10 11 E-06 10 EC1 Annual Target Level = 10-06 25 30 35 40 45 50 55 60 Mean Conrete Cylinder Compressive Strength, N/mm 2 ρ = 0.75% 0.5 ρ = 1.25% 0.5 ρ = 1.75% 0.5 ρ = 2.5% 0.5 Σεριεσ14 ρ = 0.75% 1 ρ = 1.25% 1 ρ = 1.75% 1 ρ = 2.5% Figure 9. Effet of f, ρ and load ratio on the flexural P f (GFRP RC beams γ FRP = 3.6) 40
4% Relative Frequeny 3% 2% 1% Applied Load Bond Shear Flexure 0% 0 50 100 Resistane-Capaity 150 200 250 300 350 Figure 10 Conept of failure mode hierarhy 41
Cross-setion Strain Diagram Stress Blo k Equivalent Stress Blok ε 0.85f k /γ N.A. x 0.8 x F Cd d z A s b ε s F Sd Figure A.1 Simplified stress blok used by Euroode 2 42
List of Captions Table 1 Partial safety fators proposed by JSCE (1997) Table 2 Partial safety fators proposed for FRP RC strutures by Clarke et al (1996) Table 3 Statistial data for geometrial basi variables Table 4 Statistial data for loading Table 5 Statistial data for CFRP and GFRP reinforement Figure 1 Strain distribution for a GFRP RC setion Figure 2 Defletion and raking in FRP RC beams Figure 3. Assessment proedure Figure 4. Atual tensile strain developed in the CFPR reinforement at the design stage Figure 5. Atual tensile strain developed in the GFPR reinforement at the design stage Figure 6. Effet of γ FRP on the flexural P f of CFRP RC beams Figure 7. Effet of γ FRP on the flexural P f of GFRP RC beams Figure 8. Effet of f, ρ and load ratio on the flexural P f (CFRP RC beams γ FRP = 1.8) Figure 9. Effet of f, ρ and load ratio on the flexural P f (GFRP RC beams γ FRP = 3.6) Figure 10 Conept of failure mode hierarhy Figure A.1 Simplified stress blok used by Euroode 2 43