Damaged RC beams strengthened with GFRP

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XIIV International Conferrence on Bu uilding Pathhology and Constructio C ons Repair – CINPAR 2018 2 XIIV International Conferrence on Bu uilding Pathhology and Constructio C ons Repair – CINPAR 2018 2

Damagged RC beams b sttrengthen ned with h GFRP Damag ged RC beams ba,a *, E. Mag stgagnini trengthen ned with h GFRP a R. Capozucca C , M.V. M Vecchiettia

XV Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal a, a a ofgagnini M Marche, Ancona, Italy R. Capozucca C Polythechnnic *,University E. Mag , M.V. M 60100,Vecch iettia a

Thermo-mechanicalPolythechn modeling ofMarche, a high pressure turbine blade of an nic University of M Ancona, 60100, Italy Absttract airplane gas turbine engine a

Abst tract years onee of the most important duty of civil engineeers is to defin In reecent ne methods of r bboth for historiic and a c rehabilitation , V. m Infanteofbconst , A.M. Deus modeern structures. R Reinforced conncreteP. is aBrandão relativ vely modern material truction and it * iss often damageed both with craacking In reecent yearsorone eorrosion of the most important duty of civil eers is toand defin ne methods ofced rehabilitation r concrete (R bbothbeams for histori and due to t loading co of reinnforcement. In this paperengine undaamaged dam maged reinforc RC) haveeicbeen a DepartmentR of Mechanical ncrete Engineering, Instituto Superior Técnico, Universidade de Lisboa, Rovisco Pais, ed 1, 1049-001 Lisboa, mode structures. a relativ vely m material of constning truction and itAv. is s often damage both with craacking expeern rimentally analReinforced lyzed undercon beendingisloading withmodern and with hout strengthen by near su urface mounted d (NSM) glass fiber Portugal due t loading or co ofrod. reinnforcement. In tive this paper unda and dam reinforcced concrete (R RC) beams durin have e been bto rorrosion (GFRP) method offamaged control based dmaged on vibration tests has been n utilized ng the reinfforced A Engineering, nondestruct IDMEC,polymer Department of Mechanical Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, experiments rimentally under beimental ending loading with hout strengthen ning by near su urface mounted d (NSM) glass fiber expe on anal RClyzed beams: experi vibratio onwith testsand have be een carried out t on RC beams without and w with strengtheni ng by Portugal cforced polymer rg (GFRP) rod. tive method offr control based dofonFrequency vibration been nions utilized durin ng the reinf CeFEMA, Department of Mechanical Engineering, Instituto Técnico, Universidade de Lisboa, Av. has Rovisco Pais, 1, 1049-001 Lisboa, GFR RP rod assuming free-free endss A andnondestruct hinged en nds. In theSuperior paper the envelope Response Rtests functi (FRFs) obt tained Portugal expe riments on exp RCperimental vibratio tests have be een carried outency t on RC beams and with strengtheni beams: experi ng by by th he dynamic testsimental are shown and donthe changes of f natural freque values are without correlated to w thhe damage degree of GFR RP rod assuming g free-free ends s and hinged en nds. In the paper r the envelope of Frequency Response R functi ions (FRFs) obt tained beam m elements. A ccomparison of experimental e an nd theoretical reesults is shown and discussed. by th he dynamic expperimental tests are shown and d the changes off natural frequeency values are correlated to thhe damage degree of Abstract beam m elements. A ccomparison of experimental e an nd theoretical reesults is shown and discussed. Copy yright © 2018 E Elsevier B.V. All A rights reserveed. Copyright 2018operation, Elsevier B.V.modern All rightsaircraft reserved. During ©their engine components are subjected to increasingly demanding operating conditions, Peer-review under r responsibility of CINPAR the(HPT) CINPAR 2018 organizerrs Peer-review under responsibility ofturbine the 2018 organizers especially the high pressure blades. Copy yright © 2018 E Elsevier B.V. All A rights reserve ed. Such conditions cause these parts to undergo different types of time-dependent degradation, one of which is creep. A model using the finite element method (FEM) was developed, in order to be able to predict Peer-review under rresponsibility os; f the CINPAR 2018 FE organizer Keyw words: NSM techn nique; CFRP rods Vibration; Dam mage; Modellirs ing. the creep behaviour of HPT blades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation company, were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model Keyw words: NSM technnique; CFRP rodss; Vibration; Dam mage; FE Modelliing. needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were 1. obtained. In ntroduction The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D rectangular block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The 1. overall In ntroduction expected behaviour in terms of displacement observed, in particular at the trailing edge of the blade. such a Among A the meethods availab ble for repairiing orwas strengt thening reinfo orced concrete e (RC) beams s, the Therefore near su urface model can be useful in the goal of predicting turbine blade life, given a set of FDR data. mou unted (NSM) technique hass been shown n to be a suitaable method in many casees of practice [De Lorenziss and

Among Ag, 2007;the me ethods availabble for repairi strengt thening2007; reinfo orced concrete beams s, theNeverthe near su urface Teng Szab bò and Balazsw w, 2007; El Hacha Hing orand Rizzkalla, De D Lorenzis and ae (RC) Nanni, 20001]. eless, ©unted 2016 The Authors. Published bybeen Elsevier B.V. mou (NSM) technique has s shown n to be a suita able method in many case es of practice [De Lorenzis s and thePeer-review effect e of tensi ile concrete cr racking on the e bond mecha anisms of fibe er reinforced polymer p (FRP P) rods in rod-resin under of 2007; the Scientific of PCF 2016. Teng g, 2007; Szab bòinresponsibility and Balazsw El Hacha Hes Committee 2007; ated. De D Lorenzis and ance Nanni, 20001]. eless, interrfaces and/or resin concw, crete interfac hasand yetRiz toozkalla, be investiga Occurren of damag ge inNeverthe a reinfo orced the effect e of tensiile concrete crracking on thee bond mechaanisms of fibeer reinforced polymer p (FRPP) rods in rod--resin Keywords: High Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation. interrfaces and/or in resin conccrete interfaces has yet too be investigaated. Occurren nce of damagge in a reinfo orced * Corrresponding authoor. Tel.: +39.071..2204570; fax: +3 39.071.2204576. E-mail E address: [email protected] * Corrresponding authoor. Tel.: +39.071..2204570; fax: +3 39.071.2204576. E-mail E-3216 address: 2452Copyrightr.ccapozucca@univ © 2018 Elseviervpm.it B.V. All rights reeserved. Peer-rreview under respponsibility of thee CINPAR 2018 organizers. o 2452--3216 Copyright © 2018 Elsevier B.V. All rights reeserved. Peer-r review under resp ponsibility of thee218419991. CINPAR 2018 organizers. o * Corresponding author. Tel.: +351 E-mail address: [email protected]

2452-3216 © 2016 The Authors. Published by Elsevier B.V.

Peer-review under responsibility of the Scientific Committee of PCF 2016. 2452-3216 Copyright  2018 Elsevier B.V. All rights reserved. Peer-review under responsibility of the CINPAR 2018 organizers 10.1016/j.prostr.2018.11.052

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R. Capozucca et al. / Procedia Structural Integrity 11 (2018) 402–409 R. Capozucca, E. Magagnini, M.V. Vecchietti / Structural Integrity Procedia 00 (2018) 000–000

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concrete element leads to changes in its dynamic response so that in many cases, experimental vibration monitoring of strengthening through dynamic tests is a convenient, non-destructive method [Capozucca, 2009; Salawu, 1997]. In the last decades, repairing reinforced concrete (RC) structures using composite materials has become a significantly common technique in field practice using different strengthening techniques. The method investigated in this paper is the Near-Surface Mounted (NSM) technique which uses Fiber Reinforced Polymer (FRP) rods inserted into grooves on concrete covers [De Lorentis and Nanni, 2001]. Examples of NSM using steel rods for RC structures go back to the early 1950s. The advantages of NSM FRP rods compared to steel as strengthening is that they are easier and quicker to assemble due to the lightness of the strengthening materials, the slimness of the grooves attributable to the higher traction resistance, and FRPs’ better resistance to corrosion. The NSM technique appears more advisable of externally bonded FRP reinforcements to damage deriving from collision, high temperature and fire [De Lorentis and Teng, 2007]. The availability of strengthening with NSM FRP rods depends on maintaining the bond between rods and concrete although many factors affect bond mechanism: bond length, the diameter of the rods used, the type of FRP material employed, rods’ surface configuration and groove size [Sharaky et al., 2013;De Lorentis and Nanni, 2001; De Lorentis and Nanni, 2002; Hassan and Rizkalla, 2004]. NSM FRP rods are prone to show greater slips than steel reinforcement due to potentially lower bond shear stress of FRP materials [Capozucca, 2013], to the presence of surrounding adhesive layers and local cracking in the cover concrete [De Lorentis et al., 2002; Perera et al., 2009; Focacci et al., 2000]. Investigations and theoretical studies addressing the bond behaviour of FRP rods in RC elements [Capozucca, 2009; Capozucca, 2013] have been developed. On the other hand, a non-destructive method that appears convenient to apply for the analysis of response of beams strengthened with FRP rod [Capozucca, 2013] is the free vibration analysis. The basic concept behind vibration monitoring is that dynamic characteristics are functions of structures’ physical properties, therefore any change caused by damage results in change in dynamic response [Salawu, 1997]. In the NSM of strengthening bond-slip may be influenced by the cracking of concrete and loss of adhesion of rods which can modify frequency values and beams’ modes of vibration [Capozucca, 2013]. Over the years, many studies based on frequency change measures have been developed to detect damage in uniform beams and significant researches have been carried out in the analysis of damage to RC beams. Dynamic tests with frequency change measures have demonstrated that the method is useful to detect damage in the case of RC/PRC elements [Capozucca, 2013]. This paper analyses the effects of damages due to bending cracking of concrete and loss of bond of NSM glassFRP (GFRP) rectangular rods on the static and dynamic responses of strengthened RC beams. An investigation was developed to evaluate the experimental vibration response of two RC beams; one beam was built and examined experimentally by static tests increasing bending moment and by tests of free vibration after strengthening by NSM GFRP rectangular rod. The non-strengthened beam was tested to evaluate frequency value changes due to also a series of notches on concrete cover. The experimental results include both the static bending tests and the dynamic tests measuring the beams’ natural vibration modes and the frequency values. Experimental vibration tests have been carried out on RC beams without and with strengthening by GFRP rod assuming free-free ends and hinged ends. In the paper the envelope of Frequency Response functions (FRFs) obtained by the dynamic experimental tests are shown and the changes of natural frequency values are correlated to the damage degree of beam elements. A comparison of experimental and theoretical results is shown and discussed. Nomenclature f c, f y Es,Ec,Ef λ ω, fi, r Di D*i εc, εs Δfi/fD*i

strength of concrete and steel Young’s modulus of steel, concrete and GFRP eigenvalue circular frequency, frequency value and mode of vibration damage degree for notches damage degree for cracking of concrete strain at compressive concrete and on steel bar difference between frequencies

R. Capozucca et al. / Procedia Structural Integrity 11 (2018) 402–409 R. Capozuccca, E. Magagnini, M.V. Vecchietti ti / Structural Inteegrity Procedia 00 (2018) 000–0000

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3

2. Dynamic D analyysis of undam maged RC beam Two T experimeental RC beaams, B1 and d B2, were bbuilt with fo ollowing mateerials: concreete of streng gth fc =36..80N/mm²; reiinforcement as a four longitu udinal bars off diameter 10m mm and stirru ups of diameteer 6mm with yield stren ngth fy ≅500 N/mm² and Young’s Y mod dulus Es=210∙kkN/mm². In Figure F 1 is sh hown section of RC beam with presence of groovve at intrados of section 20 0mm∙20mm; tthe beam was subjected to static and dyn ynamic tests; in i the nd mechanicall parameters of o beams. The experimentall dynamic testt was Tablle 1 are indicaated the main geometric an carriied out using a specific imppact hammer (Brüel ( & Kjærr, Type 8202) using the com mmon techniqque where a mobile m acceelerometer meeasures the accceleration of the t structural eelement triggeered using a hammer h in a fi fixed point (Fiigs.24).

Fig. 1. Geometric dim mensions of RC beams.

The T accelerom meter used in the t dynamic experiment e waas a Brüel & Kjær K produced d Piezoelectriic CCLD bran nd no 4508 8. The dynam mic test, on all the specimen ns, was carriedd out recordin ng the response of the structture in 9 posittions, impaarted by impaact hammer inn a fixed posiition (Fig. 4), with an averrage of 10 beaats per locatioon. A Fast Fo ourier Tran nsformation (F FFT) two-channnel analyzer, Multichanneel Data Acquiisition Unit 28 816 Type, andd PULSE Lab shop softw ware were useed for the for data d acquisitio on. 2.1. Free vibration of uniform beam b The T natural freequencies of a uniform slen nder beam aree considered below b neglectiing gravity forrces, the effeccts of rotarry inertia, shear deformation and dampin ng. For a beam m in flexure on nly the compo onent of displaacement v(x,t)) is of interrest. The inerttia force of thee element is �𝜌𝜌 𝜌𝜌 ∙𝐴𝐴𝐴 𝐴𝐴𝐴𝐴 � ⁄𝑑𝑑 � 𝑡𝑡� where ρ is density of th he material off the beam and d A is the cross-sectiona c al area. As knoown the follow wing equationn is obtained fo or free vibration of beam:

a

b

Figg. 2. (a) Beam B2 hung to elastic springs; (b) set upp of dynamic testss for B2 with free e-free edge condittion. metric and mechanical parameters of B1 and B2 beams under vibration (undamaged ccondition D0). Table 1. Geom

𝐸𝐸𝐸𝐸 𝐸

�� �

�� �

+ 𝜌𝜌 𝜌 𝜌𝜌 𝜌

Width b [mm]

Thickness T t [mm]

Length L [mm]

Young'ss modulus Ec [kN//mm2]

120

160

22 20

34.50

��� �� �

nsity Den 𝝆𝝆 [N Ns2 /mm4] 2,43 3 x 10-9

Moment of inertia I[m mm4] 3.89 9x107

(1)

=0

The solution of Eqq. (1) must bee an harmonic function of tiime i.e. 𝑣𝑣�𝑥𝑥,, 𝑡𝑡� = 𝑉𝑉�𝑥𝑥� ∙ ss�����𝑡𝑡 + ��

Intro oducing Eq.(22) in Eq.(1), annd assuming 𝜆𝜆� =

(2) �𝐸�𝐸�� ��

wee obtain:

4 ��� �� �

R. Capozucca et al. / Procedia Structural Integrity 11 (2018) 402–409 R. Capozucca, E. Magagnini, M.V. Vecchietti / Structural Integrity Procedia 00 (2018) 000–000

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(3)

+ 𝜆𝜆� ∙ 𝑉𝑉 𝑉 𝑉𝑉

The differential Eq. (3) is of fourth order so the general solution is of the type: 𝑉𝑉�𝑥𝑥� = 𝐵𝐵� sinh 𝜆𝜆𝜆𝜆𝜆𝜆𝜆� cosh 𝜆𝜆𝜆𝜆𝜆𝜆𝜆𝜆� sinh 𝜆𝜆𝜆𝜆𝜆𝜆𝜆� cosh 𝜆𝜆𝜆𝜆𝜆

(4)

𝑉𝑉 �� |��� =0; 𝑉𝑉 ��� |��� =0; 𝑉𝑉 �� |��� =0; 𝑉𝑉 ��� |��� =0

(5)

cos 𝜆𝜆𝜆𝜆𝜆𝜆𝜆𝜆𝜆𝜆 𝜆𝜆𝜆𝜆 𝜆 𝜆 𝜆𝜆

(6)

Eq. (4) has five unknown parameters 𝐵𝐵� (i=1,2,3,4), and an eigenvalue λ. To reduce the errors of experimental measures, the boundary conditions used in the vibration tests were free-free ends; so that in the case of free ends for beam, applying the following boundary conditions: an algebraic linear system in the unknown constants 𝐵𝐵� may be obtained. A non-trivial solution exists when the determinant becomes: � 𝜆𝜆�

The eigenvalue for a free end beam at the r mode may be correlated to the value 𝜆𝜆� = 𝑟𝑟 𝑟 𝑟𝑟𝑟𝑟𝑟 for a simply � supported beam in the following way: 𝜆𝜆� = ξ ∙ 𝜆𝜆� with ξ=coefficient that depends on the different r mode of vibration, equal to 1.506, 1.25, 1.167 and 1.125, respectively, for the first four modes. In the case of a simply supported, the expression of a circular natural frequency is the following: 𝜔𝜔� =

� � �� ��

��

∙ � ��

(7) �

By considering only the first three values of the eigenvalue 𝜆𝜆� and substituting the parameters of the experimental prototype (Tab. 1), the first three theoretical natural frequencies were calculated (Tab. 2). These frequencies were compared with the experimental frequencies recorded in the undamaged condition D0. 2.2. Dynamic analysis of undamaged beam by FEM The linear elastic FE modeling of beam B2, tested with free-free ends condition, was carried out with 3D ANSYS code (Fig. 3). Eight-node solid brick elements - Solid65 - were used to model the concrete. The solid element has eight nodes with three degrees of freedom at each node with capability of plastic deformation, cracking in three orthogonal directions and crushing. Generally, three techniques to model steel reinforcement in concrete by finite element are adopted: the discrete model, the embedded model, and the smeared model. The reinforcement in the discrete model uses beam elements that are connected to concrete mesh nodes. The embedded model overcomes the concrete mesh restrictions although increasing the number of nodes and degrees freedom. The smeared model assumes that reinforcement is spread uniformly throughout the concrete elements in a defined region. This approach is used for large-scale models where reinforcement does not significantly contribute to the overall response of the structure. In this study, the smeared model was used to model steel reinforcement. Furthermore, the Solid185 element was used for epoxy adhesive. Solid185 is used for the three-dimensional modeling of solid structures. The element is defined by eight nodes having three degrees of freedom at each node: translations in the nodal x, y, and z directions. The Beam188 element was assumed to model the CFRP circular rods. Beam188 is a linear beam element in 3D with six degrees of freedom at each node. Element Combin 14 was inserted in the numerical modelling in addition to the aforementioned elements in order to model the beams’ suspension springs simulating the same free beam conditions in vibration. The element is defined by two nodes, a spring constant k and damping coefficients. The first three bending vibration modes for beam B2 are represented in Figure 3. The theoretical and experimental frequency values obtained for undamaged beam are shown and compared in Table 2. The frequency values obtained for damage degree D0 for the hinge-hinge beam, as shown in Figure 4, are contained in the same table.

406

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5

Fig. 3. View of o first three vibraation modes r=1… …3 at D0 – B2.

1. beam b 2. accelerom meter 3. impact hhammer 4. analyzeer FFT 5. PC Fig. 4. Set up for dynnamic tests of beaam B1with hingee-hinge condition and instrumentattion for dynamic tests. T Table 2. Theoreticcal and experimen ntal frequency vaalues of undamag ged RC beam.

Eulerr-Bernoulli uniform beam with freee-free ends

f1 [Hz] 126.20

f2 [Hz] 347.70

f3 [Hz] 681.80

Eulerr-Bernoulli uniform beam with hin nge-hinge ends

64.18

222.51

500.66

Unifo form beam with frree-free ends - FE EM

124.70

334.65

633.15

Expeerimental averagee values with freee-free ends – B2

130.00

350.00

659.00

Expeerimental averagee values with hing ge-hinge ends – B B1

68.00

248.00

679.00

Freq quency values un ndamaged Beam m D0

3. Experimental dynamic testts on damaged RC beam 3.1. Beam damageed by notchess The T beam B2 was also arttificially damaaged at the eextrados with notches of section s equal to 20∙20mm with direcction normal tto the longituddinal developm ment of the beeam; beam B2 2 was subjecteed to dynamicc vibration anaalysis to ev valuate the inffluence of this damage. Th he same beam was reinforceed with a GFR RP rod with a diameter of 9mm inserrted into the ggroove; the GF FRP rod was characterizedd by the follow wing mechaniccal characterisstics: experim mental tensiile strength ffft=1040 N/mm m² and Young g’s modulus E f=33.60kN/m mm². Figure 5 shows the nuumerical mod deling beam m B2 with thee grooves fillled with epox xy resin and th the first three vibrational modes m obtaineed from the modal m analy ysis carried oout for FE beeam model. In n Table 3 thee numerical and a experimen ntal results off frequency values v obtaained by expeerimental testss and numeriical analysis aare shown. Itt is possible to note that tthe numericall and expeerimental resuults are quite similar s and thee influence off strengthening g by resin into o notches has a very small effect e on th he vibration reesponse. 3.2. Beam damageed by bendingg tests The T damage caaused by the cracking c of thee concrete is aabsolutely thee most commo on type of dam mage for the beams b in c..a. During thee static bendinng test (Fig. 6) four damagee degree steps with the inccreasing of loaad P, D*1, ..., D*4, weree obtained for the beam B2..

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R. Capozucca et al. / Procedia Structural Integrity 11 (2018) 402–409 R. Capozuccaa, E. Magagnini, M.V. Vecchietti / Structural Integ grity Procedia 00 0 (2018) 000–0000

a

407

b

Fig. F 5. (a) Typicaal mesh for FE annalysis of beam B2; (b) view of firsst three vibration n modes r=1,…,3 for damage beam m B2 by FE analy ysis. Table 3. Experim mental frequency values of damageed RC beam by notches. n Frequency values damaged beam b B2 with no otches

f1 [Hz]

f2 [Hz]

f3 [Hz]

Damaged B2 with free-free ennds FEM

116.90

325.995

620.20

Damaged B2 Exp. average vallues with free-freee ends

120.70

334.000

627.00

Damaged B2 - D0* Exp. averaage values with frree-free ends notcches filled with ep poxy resin

121.00

333.110

631.25

Experimental E diagrams loadd, P, vs deflecction at mid-sppan section arre shown in Figure 7 for evvery damage degree d step p. Static test w was carried ouut until failuree. Main resultss recorded du uring the staticc bending testt are summarizzed in Tab ble 4. The typiical cracking state s at damag ge D*4 with a load value equ ual to P=28kN N is shown in Figure 8.

Fig. 6 (a) Setup of beam m B2 under staticc loading. Load [k kN]

30 25 20

D1*

15

D2*

10

D3*

5

D4*

0

0

5

10

15

20 0

25

m] displacement aat mid-span [mm Fig.7. Exp. diagrram load, P, vs diisplacement at miid span of beam B2. B

R. Capozucca et al. / Procedia Structural Integrity 11 (2018) 402–409 R. Capozuccca, E. Magagnini, M.V. Vecchietti ti / Structural Inteegrity Procedia 00 (2018) 000–0000

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Tablee 4. Exp. results for f strengthened RC R beam B2 at daamage degrees Di. Load L P [kN] 4 4.00 8.00 16.00 2 28.00 3 37.35

Damage degrees D*1 D*2 D*3 D*4 D*5

Defleection at midsp pan [mm]] 0.61 2.83 8.65 17.00 0 62.25 5

Strainn at comppressive concrrete εc 3 (10 0.10 )

Strain at steel (intrados) εs (10-6) -0.08 -0.94 -1.90 -7.37 -

0.31 0.72 1.4 -

Curvature χ [mm-1·10-5] 0.33 1.51 3.31 10.00 -

The T beam was analysed undder vibration at every damagge step in the free-free edgee condition. Thhe FRF envelopes, for the t different ddamage degree, at each poiint of the acceelerometer, arre shown for B1 B in Figure 9. It is possib ble to again n observe thee shift of the diagrams d at vaarious steps D Di with reductiion of the freq quency valuess due to increasing conccrete crackingg damage.

Fig.8. Crackin ng state of beam B B2 at steps of stattic damage D4*. Tablee 5. Exp. average frequency valuess for r = 1,2,3 mo odes of damaged R RC beam B2.

D0 *

f1 [Hz] 121

Δf1 /fDi* (%) -

f2 [[Hz] 3333.14

Δf2 /f Di* (%)) -

f3 [Hz] 631.2 25

Δf3 /f DDi* (%) -

D1 *

121.17

0

3333.67

0

629.2 25

0

D2 *

112

8

3319.33

4

604.88

4

D3 *

106.33

5

2292.33

8

566.2 25

6

D4 *

93,5

12

2280,5

4

524,2 25

7

Damage degree

In n Figure 10 thhe frequency variation v values in referencce to the differrent damage degree d by bendding are comp pared with h the initial vaalue recorded at a the unloadeed condition D D0* for B2. It is possible to notice how thhe load increm ments at th he high damaage levels, D3* and D4*, cause the greaatest frequenccy’s variation,, up to 50%, in the fist naatural vibraation mode. T This result is caused by th he presence oof the strength hening that allows to decrrease the effeect of conccrete crackingg at the loweest load levells. In the casse of unreinfforced beams without FRPP rod, the highest variaations are alsoo recorded at low l load stepss that trigger thhe concrete crracking. 1 0,11

lg

0,011 0,0011

0,00011 0,000011

0

MODE EI D0 *

200

MODE II D0*

400

MODE III D0 *

600 80 00 F Frequency [Hzz]

MO ODE IV D0*

1000

Fiig.9. Envelope off FRFs for differennt damage degreee, D*I, for beam B2. B

8

R. Capozucca et al. / Procedia Structural Integrity 11 (2018) 402–409 R. Capozucca, E. Magagnini, M.V. Vecchietti / Structural Integrity Procedia 00 (2018) 000–000

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4. Conclusions

Δfi/fD0* [%]

In this paper the behavior of two RC beams have been analyzed under free vibration; one of RC beams was damaged with notches and cracking by bending tests and strengthened with NSM GFRP rod. The strengthened RC beam has been subjected to free vibration tests at different degrees of damage obtained under bending test with freefree ends. The main results of experimental tests are as follows: 1-the effect of damage due to notches in the concrete cover of RC beam’s intrados surface was non-relevant for variation of dynamic response; 2-free vibration of RC beam damaged by bending with cracking of concrete is influenced by the damage degree although the strengthening of RC beam with NSM GFRP rod reduces the variation of frequency values; 3- the behavior of RC beam strengthened with NSM GFRP rod under static loading until failure allows to verify availability of this technique of strengthening based on the bond of GFRP rod. 25% 20% 15% 10% 5% 0%

D0*-D1* D0*-D2* D0*-D3* D0*-D4* I

II

III

mode

IV

Fig.10. Comparison of variations (%) of frequency values at damage degrees respect undamaged degree D0* for B2 – modes r=1…4.

Acknowledgements The author thanks the technicians who collaborated in the experimental research financed by University Polytechnic of Marche, Italy. References De Lorenzis, L., Teng, J. G., 2007. Near-Surface mounted FRP reinforcement: an emerging technique for strengthening structures. Composites Part B: Eng. 38, 119-143. Szabò, Z.K., Balazsw, G.L., 2007. Near surface mounted FRP reinforcement for strengthening of concrete structures. Civil Eng.51(1), 33-38 El-Hacha, R, Rizkalla, S., 2004. Near-surface mounted fiber reinforced polymer reinforcements for flexural strengthening of concrete structures. ACI Structural Journal 101(5), 717-726. De Lorenzis, L., Nanni, A., 2001, Shear strengthening of reinforced concrete beams with NSM fiber-reinforced polymer rods. ACI Str. J 98(1), 60–68. Sharaky, I.A., Torres, L., Baena, M., Miàs, C., 2013. An experimental study of different factors affecting the bond of NSM FRP bars in concrete. Comp.Struct. 99, 350-365. De Lorenzis, L., Nanni, A., 2001. A bond between near-surface mounted FRP rods and concrete in structural strengthening. ACI Str.J. 99(2), 123-132. De Lorenzis, L., Nanni, A., 2002. Bond between near surface mounted fiber reinforced polymer rods and concrete in structural strengthening. ACI Structural Journal 99, 123-133. Hassan, T., Rizkalla, S. 2004. Bond mechanism of NSM FRP for flexural strengthening of concrete structures. ACI Struct. J. 101(6), 830-839. Capozucca, R., 2013. Analysis of bond-slip effects in RC beams strengthened with NSM CFRP rods. Comp. Struct. 102, 110-123. De Lorenzis, L., Rizzo, A., La Tegola, A. A, 2002. Modified pull-out test for bond of near-surface mounted FRP rods in concrete. Composites Part B: Engineering 33, 589-603. Perera, K., Ibell, T., Darby, A., Denton, S., 2009. Bond mechanisms of various shapes of NSM CFRP bars. 4th Int. Conf. on Advanced Composites in Construction, ACIC 09, Edinburgh, 250-257. Focacci, F., Nanni, A., Bakis, C.E., 2000. Local bond-slip relationship for FRP reinforcement in concrete. ASCE J. of Comp. Constr. 4, 24-31. Cawley, P., Adams, RD., 1979. The location of defects in structures from measurements of natural frequencies. J strain Anal Eng Des 14, 49-57. Baghiee, B., Esfahani, M.R., Moslem, K. 2009. Studies on damage and FRP Strengthening of reinforced concrete beams by vibration monitoring. Engineering Structures 31, 875-893. Salawu, O.S., 1997. Detection of structural damage through changes in frequency: a review. Engineering Structures 19, 718-723. Capozucca, R., 2009. Static and dynamic response of damaged RC beams strengthened with NSM CFRP rods. Comp. Struct.91, 237-248. Capozucca, R., 2013. Assessment of CFRP strengthened RC beams through dynamic tests. Composite: Part B 46, 69-80. ASTM D 3039/D 3039 M - 08. 2008. Standard Test Method for Tensile Properties of Polymer Matrix Composite Materials. Warburton, G.B., 1964. The dynamical behaviour of structures. Pergamon Press, Oxford.