tru

re fed ped mandresod

y an

FE model of pultruded composite proles with orthotropic behavior. The same structures were subjected

lymerars, evic ap] introdvior ane been

analytical and experimental approach of Turvey et al. [15,16] isadopted to determine the dynamic behavior of square and circularpultruded GRP (glass reinforced plastic) plates with centralcutouts. A preliminary study of some results analyzed in thisresearch is included in Boscato and Russo [17] and in Boscato[18]. A further research on a free vibration response of a large PFRPcross section is investigated in Boscato et al. [19]. Some authorshave investigated dynamic response through micromechanics

previously analyzed in their healthy state. The literature related todamage detection in different structure typologies of traditionalmaterials and historic structures [24,25] is funded on the assump-tion that damage can produce changes in mode shapes [26,27]; thistheory is assumed as a non-destructive method for identifying andquantifying the present damage and imperfections. However, somestudies on the identication through modal parameters have beenshown that the variations in frequency and in some mode shapesare unaffected by the presence of damage, but particularly inu-enced by the temperature and environmental condition [2830].

Composite Structures 96 (2013) 661669

Contents lists available at

S

sevE-mail address: russo@iuav.itthe check of the stiffness parameters, particularly the damage andimperfection detection on GFRP materials through dynamic tests.

In fact, concerning the study of dynamic response of GFRPelements from experimental and analytical point of view, severalresearches and results have been elaborated [1013]. In particular,Qiao et al. [14] proposed a study on a pultruded composite cantile-ver I-beam to characterize the dynamic response. The combined

literature gives prominence to Timoshenkos shear-deformablebeamtheory [22] for isotropic beams, rather than to EulerBernoullisbeam theory, since the latter neglects the effects of transverse sheardeformations and torsional stiffness. Starting from Timoshenkosbeam model, further research was developed by Huang [23].

The present study shows the dynamic characteristics such asfrequency response and modal parameters of the damaged prolesthe assessment eld, this is the reason why this research deals with

behaviour of the proles [79]; while more deepening is needed in elements in seismic engineering. As regards models for natural fre-

quency analysis of pultruded FRP elements, the currently available1. Introduction

The use of glass ber reinforced pohas increased by now in the last ye[15]. Besides, the adoption of specconstruction of all-FRP structures [6new techniques of mechanical behaand structures. Many researchers hav0263-8223/$ - see front matter 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.compstruct.2012.09.014to damage and their identication is based on dynamic response through the curvature mode shapes.This approach allows to know the location and size of damage, the change in dynamic characteristicsand thus the decrease in strength and stiffness. The damage identication was carried out also with FEanalysis by updating the undamaged beam model.

2012 Elsevier Ltd. All rights reserved.

materials, namedGFRP,en in civil engineeringproaches to design anduces the application ofalysis of new materialsaddressed on the static

analysis, with particular reference to basic materials such as thematrix, the ber reinforcement and the ber/matrix interface[20]. Gibson and Plunkett [21] have studied the dependence ofthe mechanical characteristics on the variation of the vibrationfrequency on a unidirectional composite laminate.

In the authors opinion, the issue here proposed is particularlyinteresting to complete the matter of reliability of this material, alsowith reference to the potential application of GFRP structuralModal analysis ical characteristics and damage assessment of different GFRP members frommodal parameters. The accu-racy analysis, that relies upon the relative condence between the results (exp. and analytical) features aDamage assessment of GFRP pultruded s

Salvatore RussoStructural Engineering, IUAV University of Venice, Dorsoduro 2206, 30123 Venice, Italy

a r t i c l e i n f o

Article history:Available online 2 October 2012

Keywords:GFRP prolesFinite element updatingAssessmentDamage identication

a b s t r a c t

This study shows a procedueters of glass ber-reinforcand experimentally acquirmaterials (resin and bers)ent cross sections, also in pthen the model must be mwork depicts the sensitivit

Composite

journal homepage: www.elll rights reserved.ctural elements

or the identication of the mechanical characteristics and dynamic param-olymer (FRP) pultruded elements. The matching between analytical modelodal and natural frequency data is used to investigate the homogeneity ofthe mechanical characteristics variation for pultruded prole with differ-

ence of induced damage. The experimental results are given primacy, andied by trial and error methodologies of model updating approach. Thisalysis based FE model updating procedure and its application to mechan-

SciVerse ScienceDirect

tructures

ier .com/locate /compstruct

In detail, the study of natural frequencies and the procedure ofthe curvatures of mode shapes were used to investigate the imper-fections and the damage in GFRP pultruded elements [31]. First,the undamaged proles have been studied in order to evaluatethe presence and magnitude of imperfections that a compositematerial may present; subsequently damage of different depthswere induced. Then, the results obtained from each damaged pro-le were compared to the respective undamaged. To control modalanalysis of the proles, the results were also nally compared tothe homogeneous and uniform modal shapes derived by the FEAas already done in other publications [32]. For this type of proles,it is important to set the problem of localizing a crack, because itsposition affects the entire dynamics of the structure. The experi-mental results were used also to update the FE model and, in thisway, to detect the reduction of the cross-sectional area and thusthe local stiffness decrease compared to the original one.

2. Damage identication procedures

The work is focused on the modal analysis of the various typesof GFRP proles in order to identify the mechanical properties var-iation of the material along their entire length. The results allow,

an approximation of the actual situation as it is evident in the pas-sage from the continuous structure to the discrete model (thusfrom an innite to a nite number of degrees of freedom).

For a system with n degrees of freedom, we have the knownrelationship:

Mxt C _xt Kxt f t 1

where M, C, K are the mass (1a), damping (1b), and stiffness (1c)matrices, f(t) is the force vector acting on the structure (1d), andx1, x2, x3 are the displacement vectors (1e).

M

m1m2

. ..

mn

266664

377775 1a

C

c1 c2 c2 0c2 c2 c3 0 0 0 cn

26664

37775 1b

662 S. Russo / Composite Structures 96 (2013) 661669rst of all, to observe the heterogeneity this material can exhibit,due to the production process of pultrusion. In the owchart inFig. 1, we can see the proposed process to localize and quantifythe imperfections and induced damage.

At the same time, a FE model that features homogeneous mate-rial along its entire length has been created for each examined pro-le. On the grounds of experimental results, an updating of themodel with a known mass (M) is carried out. Subsequently, thecomparison with Modal Scale Factor (MSF) [33] between exper-imental (EXP) and nite element model (FEM) analysis is carriedout. The correspondence of results allows to evaluate the variationof stiffness (DK) between undamaged (UP) and damaged (DP) pro-les. On the other hand, if the results do not converge it is neces-sary to proceed with the updating of the model and change thestiffness matrix. In detail, the different results in the undamagedbeam is due to non-homogeneous material.

In the most general case, the dynamic model of a structure is gi-ven by a multi-degrees of freedom system: this model representsFig. 1. Flowchart oK

k1 k2 k2 0k2 k2 k3 0 0 0 kn

26664

37775 1c

f t

f1tf2t

..

.

f3t

8>>>>>>>:

9>>>>=>>>>;

1d

xt

x1tx2t

..

.

x3t

8>>>>>>>:

9>>>>=>>>>;

1ef the process.

The model dened by (1) is indicated as a model space and itconsists of the matrices M, C, K normally constructed with anumerical procedure, based on the nite element method. From

properties of composite component materials are shown in Tables1 and 2.

The pultruded FRP shapes can be simulated as a laminated con-

S. Russo / Composite Structures 96 (2013) 661669 663the study of free vibration the eigenvalues and eigenvectors ofthe system (1) can be obtained by numerical approach.

From the experimental point of view, only a limited number offundamental modes and thus modal shapes can be measured. Fi-nally, the determination of frequency response functions is deter-mined by the model of frequency response. This last model canbe obtained directly with the experimental approach.

Assuming harmonic excitation, the force acting on the structurecan be expressed in terms of its angular frequency x, and a com-plex forcing amplitude vector, f , as:

f t f eixt 2In addition, the steady-state response of the structure can be

expressed as:

xt xeixt 3where x is the frequency component of the displacement. Substitut-ing Eqs. (2) and (3) into Eq. (1) yields

x Hxf 4where

Hx K x2M ixC1 5H(x) is called the frequency response function (FRF) matrix of thesystem or, more specically, the receptance matrix.

The solution of Eq. (4) is computationally expensive for largesystems. A more efcient approach is to use the spectral decompo-sition of the receptance matrix H(x) to compute the frequency re-sponse at selected DOF. The spectral decomposition of thereceptance matrix for a proportionally damped viscous dynamicsystem can be expressed as:

Hx Udiag 1x2j x2

!UT 6

It is usually assumed that damage appears as a change in thestiffness of the structure. Considering one damage parameter perstructural element, the updated local stiffness matrix of an elementcan be described as:

Keel 1 alKeeol 7where Keeol is the undamaged stiffness matrix of element l, al is thedamage ratio or index, and Keel is the updated element stiffness ma-trix. The global stiffness matrix is assembled from individual ele-ment contributions as:

Ka X

elements

Kee 8

So, as already explained, the problem of damage identicationbecomes simply the updating of the model parameters to minimizethe difference between a mathematical model and the real behav-ior of the actual structure.

3. Material and experimental setup

Pultruded GFRP elements feature a volume percentage for ma-trix and ber of 60% and 40% respectively. The average mechanical

Table 1Mechanical characteristics of ber, mean values.Fiber Diameter (lm) Density (g/cm3) Elastic modulus (MPa) Tensile

E-glass 10 2.54 72,400 4350guration [34] with the layup components, external mat (triaxiallayers 45 and 0) and internal unidirectional roving (0) layer.All the elements, i.e. one-dimensional proles, have standard fea-tures. Fibers run along the global Z axis of each element Fig. 3;the one-direction ber reinforced composite exhibits orthotropicbehavior, i.e., anisotropic in the Z direction and isotropic in the Xand Y directions. The condition of transversal isotropy is denedby the relationships EX = EY, ZX = ZY, and GZX = GZY, referred tothe coordinate system of Fig. 3, as shown in Table 3 where theaverage mechanical properties for I shape prole are highlighted.

The one-dimensional elements are the most frequently used, asbeams, in the structural engineering eld. These proles, with dif-ferent geometrical sections (Fig. 3), with simply supported bound-ary condition are experimentally investigated.

As regards the test setup, the prole geometry was consideredto dene the excitation points and accelerometer positions(Fig. 2); the simply supported condition was achieved by position-ing the beam on cylindrical elements. The characteristics of theanalyzed composite pultruded elements are reported in Table 4.

The excitation pulse of the structural element was generated bya Dytran 5850A instrumented hammer with specic properties inorder to obtain complete broad oscillation periods. The structuralresponses were recorded by BBN accelerometers, model 507Lf,with a mass of 10 g and a frequency eld of between 0.1 and12 kHz, compatible with the mechanical characteristics ofelements. Both the hammer and sensors are piezoelectric sensingelements featuring a cylindrical shear stress conguration withintegral charge preamplier; they are connected to a data acquisi-tion system through high stability coaxial cables that minimize theenvironmental inuence on the test results.

4. Experimental results and analysis

Modal analysis was carried out for each structural element; thefundamental frequency spectra, due to excitation in the middlepoint of their length, are reported in Fig. 4. It is evident that theprole I and Q have a frequency very similar (respectively30.47 Hz and 30.51 Hz), while that of H which has a length muchhigher than the previous is almost half (16.47 Hz). For the rstmode of vibration, the comparison among all the experimental re-sults highlights the inuence of the length (L) to height (h) ratio ofcross sections, i.e. for I prole L/h = 30, for Q prole L/h = 24while for H is equal to 25.

The most remarkable data of the proles were collected inFig. 5, each graph shows the dynamic response corresponding toall the excitation positions, by representing the modal shapes withthe position of each accelerometer. As regards the acceleration out-comes, a normalization process was applied in order to minimizethe difculties in comparison and thus to avoid the differencescaused by the variation of the impact forces. The rst mode ofthe exural vibrations corresponds to the fundamental mode.Fig. 5 report also the geometrical characteristics.

In the above graphs, the different mode shapes for each impactalong the proles are presented. The most evident feature is theabsence of uniformity of the modal shapes of each prole, dueprobably by the heterogeneity of the material. The difference foundbetween each impact force is very low, as it can be read in thestrength (MPa) Elongation (%) Thermal expansion coefcient (106 C1)

4.8 5

exur

ctuTable 2Mechanical characteristics of matrix, mean values.

Matrix Tensile strength (MPa) Elastic modulus (MPa) Fl

664 S. Russo / Composite Strupercentages of variation between the accelerations recorded by theaccelerometers (Table 5). In detail, columns 3 and 5 report the min-imum andmaximum difference between the values recorded by allaccelerometers for each impact force; the last column (6) showsthe average of the results of all recorded acceleration in each pro-le (column 1).

Vinilester (98035) 87 3309 3379

Table 3Mechanical characteristics of FRP material, range and mean values.

Longitudinal tensile strength (sampleprole)

rt 200 500 MPa

Tensile elastic modulus (sample prole) Et 20,000 30,000 MPa

Flexural elastic modulus (sample prole) Ef 15,000 20,000 MPa

Longitudinal elastic modulus (prole) EZ 23,000 MPaTransversal elastic modulus (prole) EX = EY 8500 MPaTransversal shear modulus (prole) GXY 3455 MPaShear modulus (prole) GZX = GZY 3000 MPaLongitudinal Poissons ratio mXY 0.23Transversal Poissons ratio mZX = mZY 0.09Material density c 1600 1800 kg/m3

Fiber volume ratio 40%

Fig. 2. Test

Fig. 3. Cross section of GFRP structural elements, cm dimensions.

Table 4Characteristics of GFRP structural elements.

Element J (cm4) L (cm) Area (cm2) Weight (kg)(1) (2) (3) (4) (5)

I 209.22 300 14.72 8.65Q 492 240 36 14.87H 4342.3 500 67 625. Numerical analysis

In the numerical approach, the equations of the bending vibra-tions were used taking into account the different geometrical prop-erties. For the determination of natural frequencies with simplysupported condition (fn-s), the following equation was used:

fns n2 p21L2

EZJagAc

s9

where n is the number of modes of vibration, L is the structural ele-ment length, EZ is the longitudinal elastic modulus, J is the momentof inertia, ag is the acceleration of gravity, A the cross section areaand c the material density.

For an exhaustive analytical approach, it would be necessary toconsider the inuence of transverse shear deformations and rota-tory inertia. Here, a simplied version (12) of the complete Eq.(10) of the natural frequency of a prismatic bar with supportedends has been used, as indicated in Timoshenko [22]:

EZJagAc

s !2p4n4

L4 x2 n

2p2q2

L21 EZ

kGZX;ZY

x2

q2c

kagGZX;ZY

!x4 0 10

where q is the rotatory inertia and GZX,ZY is the shear modulus;while the coefcient k, depending on the form of the cross section,

al elastic modulus (MPa) Flexural tensile strength (MPa) Elongation (%)

149 4.2

setup.

res 96 (2013) 661669is equal to:

k Jb0S0A

11

where b0 is the width of cross section and S0 is the rst moment ofarea.

Thus, restricting the effect of shear for simply supported ele-ments, it gives:

f 1ns p2

EZJagAc

sn2

L21 1

2p2q2 n

2

L2

1 EZ

kGZX;ZY

12

where f 1ns is the natural frequencies with simply supported condi-tion considering the correction due to rotatory inertia and shear.

6. Finite element analysis

A nite element model was created and used to determine themodal shapes and related natural frequencies. The simulated struc-tural element is analyzed in the linear elastic eld and is made of ahomogeneous material with orthotropic elastic properties.

Fig. 4. Free vibration response in frequency domain, rst mode.

Fig. 5. Modal shapes of proles.

Table 5Difference between the eigenvectors.

Element Accelerometer difference min Difference min (%) Accelerometer difference max Difference max (%) Average of differencebetween all accelerations (%)

(1) (2) (3) (4) (5) (6)

I A4 1.2 A8 9.4 4.08Q A7 6.2 A8 17.1 11.69H A7 1.0 A2 9.9 3.88

S. Russo / Composite Structures 96 (2013) 661669 665

A commercial nite-element software was used to perform thenatural frequencies analysis; four-node isoparametric shell ele-ments were employed in the modeling.

Each modeling element is proportioned to the total size of therespective cross-section, each node has ve degrees of freedom,i.e. translation along local x, y and z axes and rotation around localx and y, with z always normal to the shell element. The deformedshape of the rst mode of exural vibration was determined foreach global direction along the weakest and the strongest axis.The mechanical properties for nite element analysis are the onesin Table 3, referred to the axis systems of Fig. 2.

Table 6 compares the natural frequency values obtained fromnumerical approach (Th), nite element analysis (FEA) and exper-imental data (Exp). The experimental data of Table 6 correspond tothe intervals of fundamental frequencies that are the closest to theanalytical results, which highlights the good agreement betweenexperimental and numerical results. As for hollow and open Hproles with low slenderness, it is evident that formula (12) min-imizes the difference between experimental and analytical data.

The modal shapes of experimental and FE analysis were com-pared (Fig. 6). In detail, the worst modal shape of experimental testand the uniform modal shape obtained from the FE model weresuperimposed. It is evident (Fig 6) that the difference betweenthem is very low; the greater variation of 1.57% concerns the resultof the accelerometer 8 (A8) recorded at the impact force number 6(B6). Also in the Q proles the result of the accelerometer 8 (A8)records the most different variation between experimental andFEM tests. The H presents the highest difference in the accelera-tion of sensor A15.

7. Damage identication

7.1. Experimental results and analysis

The same beams, previously analyzed in their healthy state,were subjected to a damaging action in a single point at 20% of to-tal length from the support (Fig. 7). The damage is of different en-tity, to be able to identify with the greatest possible accuracy the

Table 6Natural frequencies, rst mode of vibration.

Structural element FEA (Hz) Th (Hz) by Eq. (9) Th (Hz) by Eq. (12) Exp (Hz)(1) (2) (3) (4) (5)

I 30.26 30.53 28.28 30.47Q 37.66 38.34 34.71 35.09H 18.80 18.39 17.54 16.47

666 S. Russo / Composite Structures 96 (2013) 661669Fig. 6. Modal shapes of proles.

ama

uctuFig. 7. Detailed d

S. Russo / Composite Strmagnitude of degradation in the whole prole. The entities of dam-age were established to 4% (D1), 8% (D2) (Fig. 8) and 50% (D3) ofthe prole height as it can be seen in Fig. 7.

The damage reduces the local stiffness of the beam and thus in-duces a change in frequency and accelerations. This is evident inthe comparison of the modal shape of UP and DP throughout differ-ent entities (Fig. 9), in which accelerations increase in D1 and D2while decrease in D3. The damage in a structure involves a reduc-tion of accelerations, as it is shown by the modal shape of the worstdamage (D3), not only in the damaged area but also in the wholelength; in this case (Fig. 9), the difference between this accelera-tion and that of the undamaged beam at midspan is equal to0.008 g. The known damage is located between sensors 1 and 2, ex-actly in the middle between them. Observing all the curves of thedamaged beam, it is clear that damage (Fig. 9) has been detected bysensor 2, due to its greater distance than sensor 1 from the supportof the beam. Moreover, it can be seen how the whole modal shape

Fig. 8. Detail of secon

Fig. 9. Modal shapes of undamag

Table 7Longitudinal elastic modulus of rst mode of vibration.

Structural element EZ (MPa) ED1Z (MPa) ED1Z (MPa)

Analytical Eq (12) Analytical Eq (12) FEM(1) (2) (3) (4)

I 26390 25379 22080ge region in DP.

res 96 (2013) 661669 667of the structure is changed, in particular the curve of D1 and D2show slightly higher accelerations (respectively 0.001 g and0.017 g) and shape changes in the most part of the length with re-spect to the undamaged beam.

7.2. Dynamic and mechanical characteristics of undamaged anddamaged prole

The longitudinal dynamic elastic modulus EZ (Table 7, column2) was calculated with Eq. (12), on the basis of the experimentalfrequencies of vibration modes of the undamaged structural ele-ments indicated in column 5 of Table 6.

For the undamaged conguration (Table 7, column 2), the vari-ation of EZ against the mean value of static elastic modulus EZ (Ta-ble 3) is relevant for open cross section proles, altogether thedynamic elastic modulus values are very close to the static modu-lus highlighting the robustness of the experimental technique. The

d damage (D2).

ed and damaged I prole.

ED2Z (MPa) ED2Z (MPa) E

D3Z (MPa) E

D3Z (MPa)

Analytical Eq (12) FEM Analytical Eq (12) FEM(5) (6) (7) (8)

24404 21206 22017 19060

enc

F

N((

3332

ctusame operation was carried out also for notched beams (columns 3,5 and 7 of Table 7) in order to calculate the dynamic elastic mod-ulus for different damage congurations (ED1Z ; E

D2Z and E

D3Z , see

Fig. 7).The correlation between the values of fundamental frequencies

obtained by FE analysis and experimental test calculated by

Fig. 10. Decrease of frequ

Table 8Comparison between experimental (EXP) and FEM natural frequency.

Element Undamaged,damage

EXP

Natural frequency(Hz)

Decrease of frequency(%)

(1) (2) (3) (4)

I D0 30.47 /D1 29.88 1.936D2 29.30 3.839D3 27.83 8.664

668 S. Russo / Composite Struchanging the stiffness parameter (DK) in model updating proce-dure (Fig. 1), allows to assess the longitudinal stiffness (ED1Z ; E

D2Z

and ED3Z ) of different notched proles.

7.3. Comparison between experimental and FEA results

To compare the results of the experimental to the nite elementanalysis, formula (13) was used; the complete convergence be-tween the results of the different analysis is supposed equal to 1.This formula is for a quantity sometimes referred to as the ModalScale Factor (MSF) and it represents the slope between experi-mental and FEM results. From Ewins [33] this quantity is denedas:

MSFexp ; FEM Pn

j1w exp jwFEMjPnj1wFEMjwFEMj

13

where n is the number of DOFs and in this case Wexp and WFEM arerespectively the natural frequency of experimental and FEManalysis.

The natural frequency of the experimental and FE analysis de-creases as the damage becomes more severe as it is possible tosee in Fig. 10 and in detail in Table 8. Column 4 lists the valuesof the difference between the natural frequency of the each dam-aged (D1, D2 and D3) and that of the same undamaged (D0) beam(Table 8, column 2). It is evident (Fig. 10) that the decrease in fre-quency, especially in FEM curve, is not constant.

All the entities of the damage were taken as input in the FEmodel of the undamaged prole previously constructed. With thisupdating, the natural frequency of the damaged beam model havebeen found and, subsequently, these results were compared withthe experimental ones. In Table 8 both results (column 3 and 5)and their comparison (column 7) by Formula (13) are shown.Observing column 8, it is clear that the discrepancy between dam-aged and undamaged beam is very low. Reading more carefully theresults of column 4 and 6, it can be seen that the variation of theFEM frequencies in D1 and D2, with respect to the undamagedbeam, do not show a very evident decrease; this is in contrast to

y in damaged I prole.

EM MSF(exp,FEM)

Variation fromperfectequality = 1

atural frequencyHz)

Decrease of frequency(%)

5) (6) (7) (8)

0.26 / 1.007 +0.0070.24 0.066 0.988 0.0120.04 0.727 0.975 0.0257.42 9.385 1.014 +0.014

res 96 (2013) 661669the variation in D3, that is very similar to that obtained in theexperimental analysis.

8. Conclusions

On the basis of experimental results and analysis upon damagecheck in GFRP structural elements, by modal identication andFEA, the following nal considerations can be proposed:

The need to dene a damage identication procedure seems tobe very useful for this kind of structural elements, due to theirproduction technology and the increasing static employment.

The damage identication proposed, that uses the dynamicresponse and the analysis of curvature mode shapes, allows toknow quite well the location and extent of the damage.

The updating of the FE model permits to identify the decrease infrequency and elastic modulus of the proles due to the induceddamage.

The comparison between FEM and EXP values actually limitedto I shape gives the possibility of a detailed detection ofimperfections in the beam material properties, also in termsof reduced homogeneity of mechanical characteristics.

For different damage levels, a good agreement between experi-mental and numerical results is reached; for this prole, themodel of notched beam can satisfactorily simulate a damageinvolving the whole shear-resistant area of cross section.

Experimental results show a very similar response, indeed in allproles I Q and H each impact force has generated thesame modal shape. The percentage error among tests is rela-tively low. As a matter of fact the curves are quite uniform.The open cross section of I and H give the best response.

The reliability of the results shows that the modes of vibrationanalysis of GFRP pultruded structural elements can beapproached with currently available theories and computa-tional methods, even if usually employed for isotropicmaterials.

The research work in progress aims to implement the checkdamage procedure with other experimental testing, orientedalso to closed cross section GFRP proles.

Acknowledgements

Particular thanks are given to Dr. Ph.D. Giosu Boscato and Ph.D.student Alessandra Dal Cin, who helped me to carry out the eldtests.

[14] Qiao P, Zou G, Song G. Analytical and experimental study of vibration behaviorof FRP composite I-beams. In: Proc. 15th ASCE engineering mechanics conf.,Reston, VA; 2002

[15] Turvey GJ, Mulcahy N, Widden MB. Experimental and computed naturalfrequencies of square pultruded GRP plates: effects of anisotropy, hole sizeratio and edge support conditions. In: Proc., international workshop onexperimental validation of theoretical predictions for composite structures,Melbourne, Australie, vol. 50(4); 2000. p. 391403.

[16] Turvey GJ, Mulcahy N. Free Vibration of clamped pultruded GRP circular plateswith central circular cut-outs. In: Proc., fourth international conference onthin-walled structures ICTWS, Loughborough University, LoughboroughLeicestershire, UK; 2004. p. 92734.

[17] Boscato G, Russo R. Free vibration of pultruded FRP elements: mechanicalcharacterization, analysis and applications. J Compos Const ASCE2009;13(6):56574.

[18] Boscato G. Dynamic behaviour of GFRP pultruded elements. Nova Gorica,(Slovenia): University of Nova Gorica; 2011.

[19] Boscato G, Mottram JT, Russo S. Dynamic response of a sheet pile of berreinforced polymer for waterfront barriers. J Compos Const ASCE December2011;15(6).

S. Russo / Composite Structures 96 (2013) 661669 669References

[1] Russo R. Experimental and nite element analysis of a very large pultruded FRPstructure subjected to free vibration. Compos Struct J February2012;94(3):1097105.

[2] ASCE. Structural plastic design manual, vols. 12, Reston, Va. 1984[3] Clarke JL. EUROCOMP design code and handbook. Structural design of polymer

composites. London.Clarke: E&FN Spon; 1996.[4] Boscato G, Russo S. On mechanical performance of different type of FRP beams

as reinforcement of pedestrian bridge. In: IABMAS08 The fourth internationalconference on bridge maintenance, safety and management, Seoul, Korea; 1317 July 2008.

[5] Adilardi A, Russo S. Innovative design approach to a GFRP pedestrian bridge:Structural aspects, engineering optimization and maintenance. In: Bridgemaintenance, safety, management and life-cycle optimization - proceedings ofthe 5th international conference on bridge maintenance, safety andmanagement; 2010. p. 245559.

[6] Boscato G, Mottram JT, Russo S. Design and free vibrations of a large temporaryroof FRP structure for the Santa Maria Paganica Church in LAquila, Italy. In: 6thInternational conference on frp composites in civil engineering CICE 2012;Rome, 1315 June 2012.

[7] Russo S. Buckling of GFRP pultruded columns. In: International conferencecomposites in construction, Porto, Portugal; 2001.

[8] Russo S. Creep on GFRP structural shape. In: International conferencecomposites in construction, Porto, Portugal; 2001.

[9] Di Tommaso A, Russo S. Shape inuence in buckling of GFRP pultrudedcolumns. Mech Compos Mater 2003;39(4).

[10] Russo S. Strutture in composito: Sperimentazione, teoria e applicazioni, U.Hoepli, ed., Milano, Italy; 2007

[11] Russo S, Silvestri M. Perspectives of employment of pultruded FRP structuralelements in seismic engineering eld. Seismic engineering conferencecommemorating the 1908 Messina and reggio Calabria earthquake,MERCEA08, Reggio Calabria; 81 July 2008. p. 110312.

[12] Boscato G, Russo S. GFRP Structures subjected to dynamic action. In: CICE2010Conference, department of civil engineering tsinghua university Beijing, China;2729 September 2010.

[13] Boscato G, Russo S. GFRP Members in free vibrations eld, dynamicparameters of proles and 3D structure. In: CICE2010 Conference,department of civil engineering tsinghua university Beijing, China; 2729September 2010.[20] Hashin Z, Rosen BW. The elastic moduli of ber reinforced materials. J. Appl.Mech. 1964;31:22332.

[21] Gibson RF, Plunkett R. Dynamic mechanical behavior of ber-reinforcedcomposites: measurement and analysis. J Compos Mater 1976;10:32541.

[22] Timoshenko SP. On the correction for shear of the differential equation fortransverse vibrations of prismatic bars. Philos Mag 1921;41245:7446.

[23] Huang TC. The effect of rotatory inertia and shear deformation on thefrequency and normal mode equations of uniform beams with simple endconditions. ASME J Appl Mech 1961;28:57984.

[24] Boscato G, Rocchi D, Russo S. Anime Sante Churchs Dome after 2009 LAquilaearthquake, monitoring and strengthening approaches. Advanced MaterialsResearch 2012;446449:346785. Available from: 2012/Jan/24 atwww.scientic.net (2012) Trans Tech Publications, Switzerland. http://dx.doi.org/10.4028/www.scientic.net/AMR.446-449.3467.

[25] Russo S. Testing and modelling of dynamic out-of-plane behaviour of thehistoric masonry faade of Palazzo Ducale in Venice, Italy. EngineeringStructures 2013;46:1309. http://dx.doi.org/10.1016/j.engstruct.2012.07.032.

[26] Myung-Keun Y, Dirk H, John WG, Colin PR, Roger MC. Local damage detectionwith the global tting method using operating deection shape data. JNondestruct Eval 2010;29:2537.

[27] Beskhyroun Sherif, Wegner Leon D, Sparling Bruce F. Newmethodology for theapplication of vibration-based damage detection techniques. Struct ControlHealth monitor 2011.

[28] Askergaard V, Mossing P. Long term observations of RC-bridge using changesin natural frequency. Nordic Concr Res 1988;7:207.

[29] Farrar CR, Doebling SW, Cornwell PJ, Strase EG. Variability of modalparameters measured on the Alamosa Canyon Bridge. In: Proceeding of the202 IMAC 15 conference, Orlando, FL; February 1997. pp. 25763.

[30] Peeters B, Maeck J, Roeck GD. Vibration-based damage detection in civilengineering: excitation sources and temperature effects. J Smart Mater Struct2001;19:51827.

[31] Pandey A, Biswas M, Samman M. Damage detection from changes in curvaturemode shapes. J Sound Vib 1991;145(2):32132.

[32] Myung-Keun Y, Dirk H, John WG, Colin PR, Roger MC. Local damage detectionwith the global tting method using mode shape data in notched beams. JNondestruct Eval 2009;28(2):6374.

[33] Ewins DJ. Modal testing, theory, practice and application. Research StudiesPress Ltd.; 2000.

[34] Davalos JF, Salim HA, Qiao PZ, Lopez-Anido R, Barbero EJ. Analysis and designof pultruded FRP shake under bending. Compos Part B Eng J 1996;27(3-4):295305.

Damage assessment of GFRP pultruded structural elements1 Introduction2 Damage identification procedures3 Material and experimental setup4 Experimental results and analysis5 Numerical analysis6 Finite element analysis7 Damage identification7.1 Experimental results and analysis7.2 Dynamic and mechanical characteristics of undamaged and damaged profile7.3 Comparison between experimental and FEA results

8 ConclusionsAcknowledgementsReferences