Analytical model for bar-end cover separation failure in RC beams strengthened with near-surface mounted FRP

Transcription

1 University o Wollongong Researh Online Faulty o Engineering and Inormation Sienes - apers: art A Faulty o Engineering and Inormation Sienes 212 Analytial model or bar-end over separation ailure in RC beams strengthened with near-surae mounted FR S S. Zhang Hong Kong olytehni University, shishun@uow.edu.au J G. Teng Hong Kong olytehni University, ejgteng@polyu.edu.hk J F. Chen University o Edinburgh ubliation Details Zhang, S. S., Teng, J. G. & Chen, J. F. (212). Analytial model or bar-end over separation ailure in RC beams strengthened with near-surae mounted FR. roeedings o the 12th International Symposium on Strutural Engineering, ISSE 212 (pp ). Researh Online is the open aess institutional repository or the University o Wollongong. For urther inormation ontat the UOW Library: researh-pubs@uow.edu.au

2 Analytial model or bar-end over separation ailure in RC beams strengthened with near-surae mounted FR Abstrat The lexural perormane o RC beams an be improved using the near-surae mounted (NSM) FR strengthening tehnique. A likely ailure mode o suh FR-strengthened RC beams is bar-end over separation whih involves the detahment o the NSM FR reinorement together with the onrete over along the level o the steel tension reinorement. This paper presents a new analytial strength model or this ailure mode. The proposed strength model and two existing strength models or this ailure mode are ompared with test results to demonstrate the superior perormane o the new analytial model. Disiplines Engineering Siene and Tehnology Studies ubliation Details Zhang, S. S., Teng, J. G. & Chen, J. F. (212). Analytial model or bar-end over separation ailure in RC beams strengthened with near-surae mounted FR. roeedings o the 12th International Symposium on Strutural Engineering, ISSE 212 (pp ). This onerene paper is available at Researh Online:

3 ANALYTICAL MODEL FOR BAR-END COVER SEARATION FAILURE IN RC BEAMS STRENGTHENED WITH NEAR-SURFACE MOUNTED FR S.S. Zhang and J.G. Teng* Department o Civil and Strutural Engineering, The Hong Kong olytehni University, Hong Kong, China ejgteng@polyu.edu.hk J.F. Chen Institute or Inrastruture and Environment, Shool o Engineering, The University o Edinburgh, The King s Buildings, Edinburgh EH9 3JL, Sotland, UK Abstrat: The lexural perormane o RC beams an be improved using the near-surae mounted (NSM) FR strengthening tehnique. A likely ailure mode o suh FR-strengthened RC beams is bar-end over separation whih involves the detahment o the NSM FR reinorement together with the onrete over along the level o the steel tension reinorement. This paper presents a new analytial strength model or this ailure mode. The proposed strength model and two existing strength models or this ailure mode are ompared with test results to demonstrate the superior perormane o the new analytial model. Keywords: RC beams, FR strengthening, near-surae mounted (NSM) FR, separation, strength model, inite element analysis bar-end over 1 INTRODUCTION In reent years, the near-surae mounted (NSM) FR strengthening method has attrated signiiant attention worldwide as one o the promising new tehniques or strutural strengthening and as an eetive alternative to the externally bonded (EB) FR strengthening method. The NSM tehnique involves the utting o grooves in the over onrete and the embedding o FR bars in the grooves using an adhesive (normally an epoxy adhesive). In RC beams lexurally-strengthened using NSM FR, several debonding ailure modes have been observed in laboratory tests (De Lorenzis and Teng 27; Zhang 212). Among these ailure modes, a likely ailure mode involves the detahment o the NSM FR reinorement together with the onrete over along the level o steel tension reinorement and is herein reerred to as the bar-end over separation ailure mode. The ailure proess is initiated by the ormation o a rak near the bar-end, ollowed by the propagation o a major rak at the level o the steel tension reinorement towards the middle o the strengthened region (Figure 1). This ailure mode has been observed in laboratory tests onduted by many researhers (e.g. Barros and Fortes 25; Teng et al. 26; Barros et al. 27; Thoreneldt 27) and is similar to the over separation ailure mode observed in RC beams strengthened with EB FR. This paper presents a new analytial strength model or over separation ailure in RC beams with NSM FR based on insight and numerial results rom inite element (FE) modelling. For ease o disussion, only simplysupported beams are expliitly onsidered in the paper although the strength model is appliable to ontinuous beams by treating a segment between two inletion points as a simplysupported beam. age 1 o 6

4 Figure 1 Bar-end over separation 2 FE MODELLING Zhang and Teng (212) reently developed a novel 2-D nonlinear FE model (herein reerred to as the ull FE model) apable o aurate preditions o over separation in RC beams lexurally strengthened with NSM and EB FR reinorement. In their study, ators important to the aurate predition o over separation ailure were exaed. One o these ators is the radial stresses exerted by the steel tension bars onto the surrounding onrete, whih was identiied and introdued into a theoretial or over separation ailure in RC beams strengthened with either EB FR or NSM FR or the irst time by them. Although the ull FE model o Zhang and Teng (212) an provide aurate preditions o over separation o RC beams strengthened with FR in lexure, it is a rather involved model. Zhang and Teng (212) showed that a simpliied 2-D nonlinear FE model (i.e. the simpliied FE model), in whih only the segment o the RC beam between two adjaent raks nearest to the FR end is inluded, an predit bar-end over separation ailure with good auray. This paper presents an analytial strength model or the bar-end over separation ailure mode in RC beams strengthened with NSM FR or use in pratial design based on numerial results o a parametri study onduted using this eiient, simpliied 2-D FE model. 3 SIMLIFIED FE MODEL In a bar-end over separation ailure, an inlined rak usually ours near the end o the NSM FR bar, and another rak usually appears in the bonded region o FR at a ertain distane (i.e. the rak spaing) away rom the bar end, as illustrated in Figure 2. Obviously, i the strain in the FR near the latter rak at bar-end over separation is known, the moment ating on the orresponding setion an be easily ound through setion analysis i the plane setion assumption is still adopted; the ultimate load an then be easily alulated. Thereore, the part o the RC beam between the two raks near the FR bar end an be isolated to orm a simple model or FE analysis, with the moments on the two raked setions being realized through external loads as shown in Figure 2. A rigid plate is attahed to eah raked setion to impose the plane setion assumption. The plane setion assumption may not be exatly valid here, but it an simpliy the modelling proess and may not introdue substantial errors. The onrete is modelled using 4-node plane stress elements, and some onrete near the bottom part o the rigid plate on eah side is removed to represent the two adjaent raks. As the loading inreases, the initial raks may propagate vertially or along an inlined diretion, depending on the moment ratio between the two raked setions. The steel reinorement is simulated using 2-node beam elements, and both end o the steel reinorement are onneted to the rigid plates. The thikness o the onrete at the steel reinorement level is adjusted to remove the area oupied by the steel reinorement. The ohesive-element-pair (CE) presented in Zhang and Teng (212) and initially proposed or the ull FE model is also used in the simpliied 2-D FE model. As shown in Figure 3, the CE onsists o two 4-node ohesive elements eah o whih onnets two nodes o the plane stress element representing the adjaent onrete to the two nodes o the beam element representing the steel reinorement loated at the mid-height o the onrete element. The upper ohesive element is employed to simulate the shear bond behaviour between the steel tension reinorement and the surrounding onrete, while the lower ohesive element simulates the interation between the steel tension reinorement and the onrete in the normal (vertial) diretion. Beore any deormation ours, the CE overlaps with the adjaent onrete element whose height is equal to the diameter o the steel tension bars. When slips between the steel reinorement and the surrounding onrete our, the upper ohesive element will deorm in shear to represent the shear bond-slip behaviour and does not age 2 o 6

5 experiene any deormation in the normal diretion. In the meantime, rom the shear bond ore developed in the upper ohesive element, the assoiated normal (vertial) bond ore in the lower ohesive element an be dedued; the lower ohesive element does not possess any shear stiness or strength. The FR is also modelled using 2-node beam elements. Load Bar-end over separation FR R Tension steel 3 Cohesive element pair Steel element Rigid plate Initial rak oint A Figure 2 Simpliied FE model Figure 3. Cohesive-element-pair (CE) Only one end (the let end in Figure 2) o the FR bar is onneted to the adjaent rigid plate, while the other end (the right side) representing the atual bar end is let ree. Both horizontal and vertial restraints are imposed on the top end o the let rigid plate, and a vertial restraint is 1 2 Conrete element applied on the top end o the right rigid plate. The load 1 in the horizontal diretion ats on the top end o the right rigid plate, the load 2 ( 2 = - 1 ) ats at the bottom end o the right rigid plate, and the load 3 ats at the bottom end o the let rigid plate. Aording to equilibrium, the reation ore R at the top end o the let rigid plate is always equal to 3 in magnitude but opposite in diretion. The ratio between the moments on the two raked setions an be ahieved by speiying appropriate load ratios (i.e. 1 / 3 or 2 / 3 ). 4 ANALYTICAL STRENGTH MODEL As shown in Figure 2, i the ailure strain in the FR at the let raked setion (oint A) an be obtained, a setion analysis an be onduted to ind the moment ating on the let raked setion based on the plane setion assumption, and the ailure shear ore an be easily ound rom the bending moment and the distane between the let raked setion and the nearest support or a given load distribution. 4.1 FR strain at bar-end over separation A parametri study was onduted with the simpliied FE model desribed above to develop a general expression or the FR strain at the let raked setion at bar-end over separation ailure (Zhang et al. 212). The parameters exaed in the parametri study inlude the moment o inertia o FR bar I, the beam height h, the moment ratio β (between the right raked setion and the let raked setion, i.e. 1 / 3 or 2 / 3 ), the axial rigidity o the FR bar A E ( A and E are the rosssetional area and the elasti modulus o the FR bar respetively), the onrete strength, the rak spaing s, the distane between d the steel reinorement and the FR reinorement, the beam width b and the total diameter o steel bars D (i.e. the sum o the t diameters o the steel bars). Based on a regression analysis o the results o a total o 168 numerial speimens exaed in the parametri study, Eq. 1 is proposed as an analytial model or prediting the FR strain at the let raked setion at onrete over separation ailure: e = 3. b b b b (1) separation 6 R s AE b / Db l ear age 3 o 6

6 β i β.6 β = (2) R β i.6 β 1 ( 4.5 d s β = 1.5 )(.8) (3) s s 23 s (4) β AE +.19 A E = b /. 85 lear b = b D Dt.94 (5) where β relets the eet o moment ratio R between the right and the let raked setions; β relets the ombined eet o s d and s ; β relets the eet o axial rigidity o the AE FR bar A E ; and b relets the eet o b / D the ratio between the beam lear width bl ear = b - D t and the total diameter o the steel tension bars D. 4.2 Crak spaing t To alulate the FR strain at bar-end over separation as well the distane between the let raked setion and the nearest support, the rak spaing needs to be known irst. In the present study, the equation proposed by Zhang et al. (1995) or the imum stabilized rak spaing s is adopted: s Ae t = us Os + u C (6) ailure where A is the area o onrete in tension e whih is taken as twie o the distane rom the entroid o the steel tension reinorement to the bottom surae o the beam multiplied by the beam width; t =. 36 u where is the u onrete ube ompressive strength; us = u =. 28 ; u O is the total s perimeter o the steel tension reinorement; and C is the perimeter length o the ailure ailure plane whih is taken to be the total length o the three groove sides or an NSM FR bar. Later in this paper, the imum stabilized rak spaing s, the maximum stabilized rak spaing s, and an intermediate value.5s are 2 1 onsidered to investigate the eet o rak spaing 4.3 Setion analysis In the setion analysis onduted in present study, the BS 811 (1997) ompressive stressstrain urve o onrete was used. The maximum ompressive strain in the onrete was assumed to be.35. The yield strength o steel and the ultimate strength o FR were either rom material tests or provided by the manuaturer. All partial saety ators were set to unity. Further details o the parametri study are available in Zhang et al. (212). 5 COMARISONS WITH TEST DATA For the proposed design model or bar-end over separation (Eq. 1) to be used with onidene in pratial design, its auray needs to be assessed using laboratory test data. The test data o 11 RC beams strengthened with NSM FR were olleted rom the open literature or this purpose. Only these 11 beams were available or omparison beause they ailed by bar-end over separation and were reported with suiient inormation or use in the strength models. Details o these test beams an be ound in Zhang et al. (212). The existing models proposed by Hassan and Rizkalla (23) and Al- Mahmoud et al. (21) as well as the present design model are all assessed using these test data. The preditions o the present strength model with the rak spaing s = s, 1.5s and 2s are ompared in Figure 4 with the olleted test results. Comparisons or the two existing models are shown in Figures 5 and 6. The preditions o the proposed strength model with rak spaings o 1.5s and 2s lead to average predition-to-test ratios o.927 and.989 respetively; their standard deviations (STDs) are.193 and.2 and their oeiients o variation (CoVs) are.29 and.22 respetively. These statistis are muh better than preditions o the proposed strength model obtained with a rak spaing o s whose average predition-to-test ratio, STD and CoV are.734,.187 and.255 respetively. Nevertheless, the proposed design model with any o the three rak spaing values oers muh loser preditions o the test results than the two existing models proposed by Hassan and age 4 o 6

7 Rizkalla (23) and Al-Mahmoud et al. (21). The preditions o Hassan and Rizkalla s (23) model are very onservative with a large satter, with the predition-to-test average ratio, STD and CoV being.55,.258 and.47 respetively. The preditions o Al-Mahmoud et al. s (21) model are very un-onservative with an even larger satter, with the average predition-to-test ratio, STD and CoV being 1.8, and.76 respetively. The superior perormane o the proposed strength model an also be seen in the shear ore omparisons shown in Figures 4 to 6. Test shear ore (kn) redited shear ore (kn) 12 (a) Crak spaing= s Test shear ore (kn) redited shear ore (kn) () Crak spaing= 2s Figure 4. Comparison between tests and preditions o the proposed model Test shear ore (kn) redited shear ore (kn) Test shear ore (kn) 9 6 Figure 5. Comparison between tests and preditions o Hassan and Rizkalla s model redited shear ore (kn) (b) Crak spaing= 1.5s Test shear ore (kn) redited shear ore (kn) Figure 6. Comparison between tests and preditions o Al-Mahmoud et al. s model age 5 o 6

8 6 CONCLUSIONS A new analytial strength model or bar-end over separation ailure mode in RC beams strengthened with NSM FR has been presented in this paper. The proposed strength model, together with two existing strength models, has been ompared with test results available in the published literature. These omparisons have shown that the proposed strength model oers muh more aurate preditions than the existing strength models. In partiular, the version o the proposed strength model based on the assumption o a rak spaing near the bar end equal to twie the imum stabilized rak spaing proposed by Zhang et al. (1995) provides the losest preditions o the test results. ACKNOWLEDGMENT The authors are grateul or the inanial support reeived rom the National Basi Researh Researh rogramme o China (rojet No.: 212CB262) and The Hong Kong olytehni University. REFERENCES Al-Mahmoud, F., Castel, A., Franois, R. and Tourneur, C. (21). "RC beams strengthened with NSM CFR rods and modeling o peeling-o ailure." Composite Strutures, 92(8), BS 811. Strutural Use o Conrete-art 1: Code o ratie or Design and Constrution, London: British Standards Institute; Barros, J. A. O., Dias, S. J. E. and Lima, J. L. T. (27). "Eiay o CFR-based tehniques or the lexural and shear strengthening o onrete beams." Cement & Conrete Composites, 29(3), Barros, J. A. O. and Fortes, A. S. (25). "Flexural strengthening o onrete beams with CFR laates bonded into slits." Cement & Conrete Composites, 27(4), De Lorenzis, L. and Teng, J. G. (27). "Nearsurae mounted FR reinorement: an emerging tehnique or strengthening strutures." Composites: art B, 38(2), Hassan, T. K. and Rizkalla, S. H. (23). "Investigation o bond in onrete strutures strengthened with near surae mounted arbon iber reinored polymer strips." Journal o Composites or Constrution, ASCE, 7(3), Teng, J. G., De Lorenzis, L., Wang, B., Rong, L., Wong, T. N. and Lam, L. (26). "Debonding ailures o RC beams strengthened with near-surae mounted CFR strips." Journal o Composites or Constrution, ASCE, 1(2), Thoreneldt, E. (27). "Bond apaity o CFR strips glued to onrete in sawn slits." roeedings, 8th International Conerene on Fibre Reinored lastis or Reinored Conrete Strutures, atras, Greee, July 16 to 18, 27 (CD-ROM). Zhang, S., Raoo, M. and Wood, L. A. (1995). "redition o peeling ailure o reinored-onrete beams with externally bonded steel plates." roeedings, the Institution o Civil Engineers-Strutures and Buildings, 11(3), Zhang, S. S. (212). Behaviour And Modelling O RC Beams Strengthened In Flexure With Near-Surae Mounted FR Strips. hd thesis, The Hong Kong olytehni University, Hong Kong, China. Zhang, S.S. and Teng, J.G. (212). Finite element model or over separation ailure in FR-strengthened RC beams, in preparation. Zhang, S.S., Teng, J.G. and Chen, J.F. (212). Strength model or over separation ailure in FR-strengthened RC beams, in preparation. age 6 o 6