Deflection of reinforced concrete beams simultaneously subjected to sustained load and reinforcement corrosion

Transcription

1 Deflection of reinforced concrete beam imultaneouly ubjected to utained load and reinforcement corroion Davor Grandić 1 ; Dubravka Bjegović 2 ; Ivana Štimac Grandić 3 Summary The bearing capacity and erviceability of reinforced concrete tructure can be evere deteriorated by teel reinforcement corroion. Recent reearch reult how that deterioration of erviceability of tructure due to increaing of deflection begin much earlier than tructural collape. The reult preented in thi paper are a part of a comprehenive experimental reearch. In thi experiment, chloride induced corroion of reinforcement embedded in reinforced concrete beam pecimen i accelerated with alternation of dry and wet period with alt water in an environmental chamber. Such alternation of wet and dry period imulate natural proce of reinforcement corroion in chloride environment. Beam pecimen were imultaneouly ubjected to utained load and reinforcement corroion. In thi paper the method for computing the long-term deflection of beam expoed to reinforcement corroion i propoed. The erviceability parameter which conider effect of localized reinforcement chloride corroion on tenion tiffening and reduced tiffne of corroded reinforcement were introduced. Mentioned erviceability parameter are expreed a a function of corroion tate of reinforcement and evaluated by reult of experimental reearch. Corroion tate of reinforcement can be determined by meauring of reinforcement corroion rate during the time of expoure of reinforced concrete member to corroive environment. The relationhip between corroion tate of reinforcement and deflection i etablihed and evaluated by tet reult. Keyword reinforcement corroion, beam deflection, erviceability parameter, experimental reearch. Theme tructural deign/tet - durability - reinforced concrete 1 Introduction The conequence of reinforcement corroion, except for reduction of the bearing capacity, i deterioration of erviceability of concrete tructure. The two mot important criteria for evaluating tructure erviceability are the magnitude of deflection and width of crack. The reult of conducted reearch up to now [1-3] a well a the reult of experiment conducted a part of the cientific reearch [4] how that reinforcement corroion influence deformation and cracking of reinforcement element ubjected to bending. When the reinforcement i induced by chloride, trace of reinforcement corroion on the urface of tructural element, a are, for example, longitudinal crack in concrete above the reinforcement and corroion mear, appear in place or are not even viible, but till damaging effect of pitting corroion of reinforcement can ignificantly influence the ret of the bearing capacity and erviceability of reinforced concrete tructure. Tranvere crack upright to axi of reinforced concrete element appear in element trained by the moment of bending with or without longitudinal force if the tre in concrete overtep the tenile trength of concrete [4]. 1 Dr.Eng., Aitant Profeor, Univerity of Rijeka, Faculty of Civil Engineering, Croatia davor.grandic@gradri.hr 2 Dr.Eng., Profeor, Univerity of Zagreb, Faculty of Civil Engineering, Croatia dubravka@grad.hr 3 Dr.Eng., Aitant Profeor, Univerity of Rijeka, Faculty of Civil Engineering, Croatia ivana.timac@gradri.hr

2 In element ubjected to utained load and at the ame time expoed to reinforcement corroion, the increae of tranveral crack width and deflection due to reinforcement corroion are oberved. In thi paper a part of comprehenive experimental reearch [4] i preented. The calculation method for determination of deflection of beam with corroded reinforcement i propoed. 2 Experimental reearch program 2.1 Tet pecimen and material propertie The beam pecimen elected for the experiment had a cro-ection of 8 12 mm and length of 2 mm. They were reinforced with two bar having a diameter of 8 mm in the tenile zone, two bar of 6-mm diameter in the compreive zone of cro-ection, and with tirrup of 6 mm in diameter paced at interval of 8 mm. The protective concrete cover to the depth of the reinforcement (tirrup) i 1 mm (figure 1). The bar of 6-mm nominal diameter were cold worked ribbed reinforcing teel bar, while thoe of 8-mm nominal diameter were hot rolled ribbed reinforcing teel bar. Figure 1: Beam pecimen Material propertie (concrete and reinforcing teel) were determined from tet performed on at leat three pecimen. Mechanical propertie of hardened concrete were teted according to method [5-8] given in table 1. In table 2, mechanical propertie of reinforcing teel were teted according to ISO [9]. Table 1: Mechanical propertie of hardened concrete Property Tet method Shape and dimenion of tet pecimen Compreive trength (28 Cube EN [5] day), MPa 15x15x15 mm Modulu of elaticity HRN U.M1.25 [6] Prim (28 day), MPa (Croatian tandard) 12x12x36 mm Flexural tenile trength Prim EN [7] (28 day), MPa 1x1x4 mm The pecific fracture energy Prim RILEM method [8] by bending pecimen, J/m 2 1x1x4 mm Mean value

3 Table 2: Mechanical propertie of reinforcing teel (mean value) Reinforcing teel Yield trength*, MPa Tenile trength* MPa Total elongation at maximum force Agt, % Hot rolled ribbed bar Cold worked ribbed bar * Value determined according to real cro ection of bar Tet method ISO [9] The program of the experiment included three level of reinforcement corroion. After each of corroion level of reinforcement had been approximately reached, the beam pecimen were teted until they failed (table 3), and the actual corroion tate of reinforcement determined on the pecimen with corroded reinforcement extracted from the beam. Value P corr in table 3 i a depth of corroion to the reinforcement relative to the original urface of uncorroded reinforcement. Thi value i determined from the reult obtained by meauring the corroion rate. Table 3: Number of beam pecimen and level of corroion with propoed depth of reinforcement corroion Level of corroion I II III Depth of corroion Number of pecimen Control pecimen (not expoed to corroion): Pcorr = mm 1 pecimen at an age of 28 day teted to failure Pcorr.5 mm.1 mm Pcorr <.2 mm Pcorr >.2 mm 1 each of beam pecimen under utained tatic load in environmental chamber for teting corroion tate of reinforcement and chloride penetration 3 pecimen under utained tatic load in laboratory condition (2±2 C, RH 48%) teted to failure at the end of experiment 3 each of the pecimen under utained tatic load in environmental chamber teted to failure after the pecimen had reached a particular corroion level (I, II, III) 2.2 Initiation and acceleration of the proce of reinforcement corroion Reinforcement corroion in the reinforced concrete beam pecimen wa initiated and accelerated, after it had tarted, by repeating the wetting and drying cycle in environmental chamber. The wetting cycle conited of alt water praying while the drying cycle included chamber heating to the temperature about 5 C and ue of a fan to remove exce moiture from the chamber. One cycle took three day. Firt, pecimen were prayed with alt water (3.8% of odium chloride to water ma). 2.3 Meaurement of reinforced concrete pecimen deflection and reinforcement corroion During the expoure to reinforcement corroion, utained load wa applied to beam pecimen in teel frame, which caued the occurrence of crack in the concrete. The level of load wa equivalent to 6% of the deign flexural capacity according to Eurocode 2 [1]. The econd criterion for the utained load magnitude

4 wa occurrence of crack with width of about.1 mm in tenile zone of beam. The crack accelerated the time until the initiation of corroion and the corroion proce itelf. The econd criterion i uual relation of quai-permanent load for verification erviceability limit tate (dead load and part of live load [11]) and deign bearing capacity for tructure. On the beam pecimen, deflection and reinforcement corroion parameter were periodically meaured. The deflection were oberved at the mid point of pan. In the coure of corroion expoure in the environmental chamber, periodical meaurement taken on reinforced concrete beam pecimen included reinforcement corroion parameter (corroion rate, half-cell potential, and electric reitance) and deflection caued by loading and corroion. The meaurement were made uing a integrated portable equipment whoe operation i baed on a galvanotatic impule method [12, 13]. The beam pecimen in the teting frame, and the arrangement and number of corroion meaurement point on the beam pecimen are illutrated in figure 2. TENSIVE SCREWS HIDRAULIC PRESS AND LOAD CELL 23 g1 g2 1 d1 g1 d2 d3 d4 d5 g2 2 d1 g1 d2 d3 d4 d5 g2 3 d1 d2 d3 d4 d5 g1 g2 4 d1 d2 d3 d4 d5 BEAM SPECIMENS TESTING STEEL FRAME to 4... mark of beam pecimen g1, to g2... corroion meauring point on the top ide of the beam d1 to d5... corroion meauring point on the bottom ide of the beam Figure 2: Beam pecimen in the teting frame and corroion meaurement point To each degree of reinforcement corroion, on whoe ample of corroded reinforcement taken from the beam tenile teting wa conducted, the correponding value of diameter reduction of corroded reinforcement φ(p corr) wa added, defined from the reult of meauring the corroion rate in the elaped period [4, 13, 14] according to thee expreion: P corr = τ ( t) dt = 11.6 icorr ( t) 11.6 i dt corr τ (1) where 2 φ = m. 785( φnompcorr Pcorr )π, (2) ( ) ( φ φ ) 1 φ P corr =, (3) φ P corr - the mean corroion depth in meauring area of enor, i.e. corroion depth calculated on the bai of the reult of meauring the corroion rate of the reinforcement in the period in which the progreion of the

5 reinforcement corroion i monitored (according to expreion (1) in micron, and in the expreion (3) introduced in mm), i corr(t) - corroion rate in µa/cm 2 obtained by periodic meauring on beam ample, t i the lating time of reinforcement corroion in year, τ - time (year) in which the mean depth of corroion i calculated P corr, m - length ma of non-corroded reinforcement (g/mm),.785 i the teal denity (g/mm 3 ), φ nom and φ - the nominal and original diameter of the non-corroded bar (mm) and φ(p corr) i reduction of the diameter of corroded bar in relation to original diameter of the non- corroded bar (%). During the expoure of pecimen to reinforcement corroion which lated 383 day, a total of 18 phae of meaurement of corroion parameter were conducted. Reduction diameter of reinforcement φ(p corr) i alo calculated, for each phae of meauring the corroion rate. 3 Numerical analye Numerical analye are conducted in order to determine parameter which influence the behaviour of reinforcing concrete beam damaged by reinforcement corroion under utained load. 3.1 Contitutive model Contitutive model ued in thee numerical analye decribe the relationhip between tre and train of material. On the bai of failure ratio between uniaxial and patial (3D) tre tate, the program ABAQUS determine the yield urface of concrete according to Lubliner [15], Lee and Fenve [16]. The teting of concrete for planar (2D) and patial tre tate of concrete were not conducted. Suggeted value of the failure ratio which correpond to planar and patial tre tate of concrete according to Kupfer and Bangah [17] were ued. In beam ubjected to bending, the bigget contribution to their behaviour under load ha relationhip between tre and train of concrete and teel in uniaxial tre tate. Stre-train diagram for concrete in compreion and bilinear diagram of reinforcing teel determined on the bai of teting of concrete and reinforcing teel are ued. Further on, the contitutive model of uniaxial treed reinforced concrete i being dicued in more detail Tenile treed concrete in reinforced concrete element Contribution of concrete in tranmitting tenile force between adjacent crack (tenion tiffening) i modeled with help of diagram which define the relation of mean tre and mean train in reinforced concrete element (including the width of the crack). To obtain uch diagram, the CEB-FIP tenion tiffening model are ued [14,18] which are the bai of method for the calculation of deflection and crack according to Eurocode 2 [1]. In elatic range of reinforcement behaviour, the tenion tiffening model according to MC 78 [18] i accepted, which i retained in the calculation for deflection according to Eurocode 2 and for the calculation of curvature (uing the curvature and deflection) according to MC 9 [14]. To determine mean reinforcement train after reaching the yield trength of reinforcement, the tenion tiffening model according to MC 9 i taken. To determine diagram of mean tre and mean tenile train of concrete, the equilibrium condition (N = N cm + N m, in figure 3) i ued which for the elatic range of reinforcement behaviour can be expreed a:

6 = ( σ ε E ) A m 1 σ ctm, (4) Ac, eff where: σ ctm - mean tenile tre of concrete ( between two crack), σ - tenile tre in reinforcement in cro-ection with the crack, ε m - mean train of reinforcement, E - modulu elaticity of reinforcing teel (or tiffne parameter of corroded reinforcement E,corr ), A 1 - cro ectional area of tenion reinforcement, - the effective area of concrete in tenion urrounding the reinforcement. A c,eff σ,σ m σ σ = N A f t f y σ my MC 78 MC 9 σ y ε m ε σ = N A N σ = A cm ε m ε σ r N m σ m = A ε,max ε my ε y ε mu ε u Figure 3: Tenion tiffening model ε m,ε In figure 3 N m and N cm are the mean tenile force in reinforcement and concrete, repectively. Mean train of reinforcement i determined with the help of the expreion (15) according to [18]: ε m ( ζ ) ε + ζ ε = 1 1, (5) where ζ i ditribution coefficient with which the contribution of concrete between the crack (tenile tiffening) i taken in conideration, ε i train of reinforcement in the crack, and ε 1 i train of reinforcement in uncracked condition. The ditribution coefficient ζ i determined according to thi expreion [1, 18]: σ r ζ = 1 β, (6) σ where: σ tenile tre in reinforcement calculated on the bai of cracked cro-ection, σ r tenile tre in reinforcement calculated on the bai of cracked cro-ection under the loading condition cauing firt cracking ( the tenile trength of concrete i reached), β i a coefficient taking account of the influence of the duration of the loading or of repeated loading on the mean train: β = 1. for a ingle hort-term loading, 2

7 β =.5 for utained load or many cycle of repeated loading. "Smeared cracking model i ued, at which the mean train of concrete ε m (including the width of crack) equal to mean train of reinforcement ε m. The effective area of concrete in tenion after tabilizing the cracking A t c,eff i deterimined according to the recommendation of Eurocode 2 [1] and MC 9 [14]: A t c,eff = (h x)/3 b = ( )/3 8 = cm 2, x i the height of compreive zone of cro-ection. To conduct the numerical analye, omewhat bigger effective area of concrete in tenion i taken, which take the behaviour of concrete in conideration, from occurrence of the firt crack, over the phae of occurrence of crack to the tabilization of cracking. On the bai of conducted numerical analye of deflection for hort-term load (without influence of reinforcement corroion), and in comparion to real meaured value of deflection, the effective area of concrete in tenion A c,eff = cm 2 i taken. 3.2 Numerical model for analye The ymmetry of ytem at the modelling wa ued (figure 3). The zone between longitudinal and tranveral plane of ymmetry wa compried in the numerical model, hence the quarter of a beam with introduction of adequate boundary condition. 94 F/2 F/ longitudinal reinforcement: : TRUSS TRUSS hoop: TRUSS TRUSS 94 cm concrete: SOLID SOLID 4 element Figure 4: Scheme of load and numerical model for numerical analye of beam 3.3 Influence of the localized corroion of reinforcement Within the cientific reearch [4], corroion of reinforcement, which wa induced by chloride, wa localized (pitting) corroion. On the bai of conducted obervation, the following can be etablihed: 1. Corroion damage i not evenly ditributed along the reinforcing bar. The conequence i that there i no general reduction of trength and tiffne of bonding between the concrete and reinforcement, but it occur only locally, in zone of greater damage. 2. The zone of pitting corroion generally coincide with the zone of crack in concrete which occurred becaue of bending of ample of beam. Strain of the tenile reinforcement i the greatet in cro-ection with the crack.

8 3. The hape and intenity of the reinforcement damage occurred becaue of pitting corroion were uneven and irregular. On real tructure it i not poible to do a thorough and detailed topography of corroion damage along the reinforcing bar damaged by pitting corroion. All above lited point (from 1 to 3) objectively repreent the difficultie in cae when one would want to comprie local characteritic of corroion damage with the numerical model, according to intenity and to their allocation. However, the problem can be oberved and a the influence of pitting corroion of reinforcement to contribution of concrete in tenion between crack (tenion tiffening). The effect of pitting corroion of reinforcement to tenion tiffening can be explained with following two mechanim: 1. Local reduction of cro ectional area of tenion reinforcement lead to reduction of it tiffne, and therefore the change contribution of concrete in tenion between crack. 2. Local reduction of bond trength and tiffne alo reduce contribution change contribution of concrete in tenion between crack. Reduction of contribution of concrete in tenion between crack becaue of pitting corroion of reinforcement i conidered uing the modified ditribution coefficient ζ at the calculation of mean train of reinforcement: 2 σ r ζ = 1 k corr, p β, (7) σ where k corr,p i the coefficient which take into account the effect of pitting corroion of reinforcement to contribution of concrete in tenion between crack. Coefficient k corr,p i determined with the help of numerical analye at the model hown in Figure 4. Sutained load in the experiment and in the calculation were two concentrated force F = 4.21 kn. In contitutive model of tenile treed concrete in reinforced concrete element which i decribed in chapter modified mean train of reinforcement according to expreion (11). The change of coefficient k corr,p lead to the change of diagram of mean tre and mean train of tenile treed reinforced concrete ((σ ct,max/σ ctm)-ε m diagram in Figure 5.), which i the contitutive model of tenile trained concrete with corroded reinforcement for the numerical analye. σ ct,max /σ ctm 1, ,.8,8.6,6.4,4.2,2 f ctm = σ ct,max = 3,4 N/mm 2 β =,5 k corr,p = 1, for level of corroion I k corr,p =,788 for level of corroion II k corr,p =,596 for level of corroion III Level of corroon I, 181 day under load Level of corroion II, 336 day under load Level of corroion III, 391 day under load.,,..2,2.4,4.6,6,8.8,1.1 ε m Figure 5: Diagram (σct,max/σctm)-εm of tenile treed concrete at the utained loaded ample of beam expoed to reinforcement corroion in the climate chamber (f ctm i the mean value of tenile trength of concrete)

9 In numerical analye, the meaured data about the propertie of corroded reinforcement for each degree of corroion wa ued. The mechanical propertie of reinforcement were determined by tenile tet of ample of uncorroded and corroded reinforcement. The mechanical propertie are obtained regarding to original cro ectional area of uncoroded bar. For the calculation of deflection (and crack) the tiffne parameter E corr i an important characteritic, i.e. the modulu of elaticity of corroded reinforcement. The numerical model wa firtly calibrated by comparion of calculated and meaured value of deflection of uncorroded ample of beam. The excellent agreement of calculated and meaured value of deflection with mean difference le than 1% wa etablihed. Numerical analye are repeated with different coefficient k corr,p till the deflection obtained with numerical analye wa equalized with the mean meaured value of deflection in oberved moment of time. In thi way, the value of coefficient k corr,p i determined (Figure 5). Shrinkage and creep train of concrete were conidered a function of time according to the expreion given in Eurocode 2 [1]. 4 Calculation of deflection of element with corroded reinforcement For calculation of deflection of element damaged by reinforcement corroion, the modification of the method according to Eurocode 2 [1] can be uggeted. The modification conit of the following: 1. Geometric characteritic of cro-ection for uncracked and cracked condition are calculated with original cro ectional area of uncoroded reinforcing bar (or at practical calculation with nominal cro ectional area), but with the uage of tiffne parameter of corroded reinforcement E,corr intead of the modulu of elaticity of uncorroded teel for reinforcing E,corr. 2. Expreion (5) for the calculation of the ditribution coefficient i ubtituted with the expreion (12), according to which the modified ditribution coefficient i calculated. Corroion parametar of erviceability E,corr and k corr,p are function of tate of corroded reinforcement (Figure 6 and 7), i.e. the corroion reduction of reinforcement diameter φ(p corr) determined from reult of meauring of corroion rate according to the expreion (1) to (3) E,corr = -193,9x (MPa) E,corr (MPa) value obtained by teting regreion line x = φ(p corr) (%) Figure 6: Stiffne parameter of hot rolled reinforcement ample of beam a the function of reinforcement corroion

10 k corr,p = e -.184x k corr,p 1. R 2 =.9629 k corr,p numerical analyi regreion curve x = φ(p corr) (%) Figure 7: Coefficient k corr,p of beam a the function of reinforcement corroion At the utained load, it i neceary to conider the long-term train of concrete becaue of hrinkage of concrete and creep of long-term treed concrete at the calculation of deformation of reinforced concrete element. The value of train of concrete under contant tre i obtained a the um of elatic train and train becaue of creep of concrete [14] according to the expreion: ( t, t ) ( 28) c 1 ϕ ε ( t, t ) = σ ( t ) +, (8) c c E ( ) c t E where σ c(t ) i contant tre in concrete achieved in the moment t, E c(28) i tangent modulu of elaticity of 28 day old concrete, E c(t ) i tangent modulu of elaticity of concrete in time t, ϕ(t,t ) i creep coefficient of concrete aged t which wa loaded in the moment t, t i time of application of load to concrete and t i oberved time. The creep coefficient a the function of time are ued, which were determined according to the method in EN-a [1]. With o calculated creep coefficient, the tangent modulu of elaticity E c(28) 1,5E cm [1] for the calculation of creep train of concrete i ued. If the E c(t ) E c(28) i taken, the following i obtained: 1+ ϕ ( ) ( ) ( t, t ) ( ) ε t, t = σ t c c, (9) Ec 28 where the expreion in bracket can be expreed a effective modulu of elaticity of concrete: E c, eff ( 28) ( t, t ) Ec =. (1) 1+ϕ The influence of hrinkage train of concrete i conidered with the help of total hrinkage train for free hrinkage of concrete according to Eurocode 2 [1]. In Figure 8 the meaured and calculated value of deflection a function of time (t t) in day paed after the application of load to ample of beam (uing the parameter E,corr and k corr,p in Figure 6 and 7) are hown.

11 11 1 meaured deflection v e calculated deflection v c calculated deflection without impact of corroion Deflection (mm) 9 8 Level of corroion I Level of corroion III Time (t-t ) (day) Figure 8: Meaured and calculated magnitude of deflection of ample of beam Meaured and calculated value of deflection are proportional in oberved period. According to Figure 8 it can be expected that oberved proportional trend will be preerved in the following period of time (i.e. for greater reinforcement corroion). Calculated deflection are 2 to 4% greater than the meaured one, which i acceptable deviation. 5 Concluion Calculated value of deflection determined by the preented method are very well coinciding with the meaured value of deflection. A the reduction of diameter of reinforcing bar caued by corroion increae in time, o do the corroion parameter of erviceability, which are ued in the preented method for the calculation of deflection, are function of time. The corroion reduction of diameter of bar (tate of reinforcement corroion) can be determined on the bai of meaured corroion rate in oberved period of time. Therefore, the uggeted method can be ued for predicting the deflection at the evaluation of ervice life in view of the criteria of tructural erviceability. The application of uggeted method on real tructure hould be combined with detailed invetigation and meaurement on the tructure. If the monitoring of the tructure expoed to reinforcement corroion i conducted, within which the periodic meaurement of deflection (and crack) i conducted, and the periodic or continuing meauring of parameter of reinforcement corroion, then the corroion parameter of erviceability can be valued and calibrated according to meaured value of deflection. Thi way, the prediction of the magnitude of deflection in the following period of erviceability of a tructure can be improved. Reference [1] Rodríguez, J.; Ortega, L. M.; Aragoncillo, J.; Izquieredo, D.; Andrade, C.: Structural aement methodology for reidual life calculation of concrete tructure affected by reinforcement corroion, International RILEM Workhop on Life Prediction and Aging Management of Concrete Structure, Cane, France, 2, [2] Zhang, R.; Catel, A.; Françoi, R.: Serviceability Limit State criteria baed on teel-concrete bond lo for corroded reinforced concrete in chloride environment, Material and Structure, 42 (21),

12 [3] Yoon, S.; Wang, K.; Wei, W. J.; Shah, S. P., Interaction between Loading, Corroion, and Serviceability of Reinforced Concrete, ACI Material Journal, V. 97, No. 6, Nov.-Dec. 2, pp [4] Grandić, D.: Calculation procedure for evaluating remaining load bearing capacity and erviceability of corroded reinforced concrete tructure, Doctoral Thei, Faculty of Civil Engineering, Univerity of Zagreb, Croatia, 28. (in Croatian) [5] EN :21, Teting hardened concrete - Part 3: Compreive trength of tet pecimen, CEN, Bruel, 21., 18 pp. [6] HRN U.M1.25:1982, Concrete, Determination of modulu of elaticity in compreion, 6 pp. (in Croatian) [7] EN :2, Flexural trength of tet pecimen, CEN, Bruel, 21, 12 pp. [8] Bažant, Z. P; Swartzl, S. E. et al., Fracture Mechanic of Concrete: Concept, Model and Determination of Material Propertie, ACI 446.1R-91, Reported by ACI Committee 446, Fracture Mechanic (Chairman: Zdênek P. Bažant), American Concrete Intitute, 1991, (Reapproved 1999), 146 pp. [9] ISO :22, Steel for the reinforcement and pretreing of concrete Tet method Part 1: Reinforcing bar, wire rod and wire, ISO, Geneva, 22, 15 pp. [1] EN , Eurocode 2: Deign of concrete tructure Part 1-1: General rule and rule for building, CEN, Bruele, 24. [11] EN 199, Eurocode: Bai of tructural deign, CEN, Bruele, 22. [12] Brite-Euram III - Smart Structure Project Report, (Contract No. BRPR-CT98-75), Integrated Monitoring Sytem for Durability Aement of Concrete Structure, EU, Sept. 22, 79 pp. [13] Klinghoffer, O., In-Situ Monitoring of Reinforcement Corroion by Mean of Electrochemical Method, Nordic Concrete Reearch, V. 16, No. 1, Olo, Norway, 1995, 13 pp. [14] CEB-FIP Model Code 199 (MC-9), Deign Code, Comité Euro-International du Béton (CEB), Thoma Telford Service Ltd., London, [15] Lubliner, J. J.; Oller, S. O.; Oñate, E.: A Platic-Damage Model for Concrete, International Journal of Solid and Structure, 25 (1989), [16] Lee, J.; Fenve, G. L.: Platic-Damage Model for Cyclic Loading of Concrete Structure, Journal of Engineering Mechanic, 124 (1998) 8, [17] Mihanović, A.; Marović, P.; Dvornik, J.: Non-linear Analyi of Concrete Structure, DHGK, Zagreb, 1993 (in Croatian). [18] CEB Deign Manual on Cracking and Deformation, Bulletin D Information N 158-E, Comité Euro- International du Béton (CEB), Lauanne 1985.