Transaction A: Civil EngineeringVol. 17, No. 5, pp. 407{414c Sharif University of Technology, October 2010

Research Note

Numerical Study on Reinforcingof Thin Walled Cracked Metal

Cylindrical Columns Using FRP Patch

M.Z. Kabir1;� and A.R. Nazari1

Abstract. In this paper a new technique was proposed for the repair of defected metal columns. The�nite element method was chosen to �nd out the adequacy of the proposed method, regarding, the loadcarrying capacity of two types of thin walled cylindrical columns with L=D = 10 and 20 along withcircumferential and longitudinal cracks. The study considers the non linearity behavior in both materialas well as geometrical characteristics. Various con�gurations of the composite patches made from carbon-epoxy were assumed on the cracked region and the in uence of a patch on the load carrying capacity of thecolumns was examined. The obtained results indicate that composite material can not only compensatethe e�ect of damage on column buckling load, but also increase buckling strength to a level even greaterthan in an intact one.

Keywords: Repair; Cracked metal column; Buckling load; FRP patch; Compression loading.

INTRODUCTION

Nowadays, composite materials are utilized in various�elds of industry and building construction due totheir valuable properties such as the high value ofstrength to weight ratio and easy installation. From theprominent usage of these materials in civil engineering,it was addressed to the reinforcement and repair ofconcrete members [1]. Generally this application hasbeen utilized more for concrete rather than metallicstructures, while metallic structural members can beexposed to various damages and defects in their ser-vice lives, one of which being crack may stem fromdi�erent factors such as sudden damage, corrosionenvironment or fatigue loading. Thus, demand for ane�cient repair against these phenomena is a majorconcern of design engineers. On the other hand,using metallic patches and sti�eners requires heavyequipment. Even then welding of these structures,considering their small thicknesses, can be followed

1. Department of Civil and Environmental Engineering, Amirk-abir University of Technology, Tehran, P.O. Box 158754413,Iran.

*. Corresponding author. E-mail: mzkabir@aut.ac.ir

Received 1 February 2010; received in revised form 15 June 2010;accepted 21 August 2010

by temperature defects, extra residual stresses andunexpected deformation.

The presented technique was previously exploredfor repairing defected metallic structures, especiallyunder tension loading rather than compression. Asa literature review, Baker and Jones [2,3] studied arepair technique using adhesively bonded boron/epoxycomposite patches, which is widely considered as a re-liable method for repairing cracked plates under tensileloading. The authors of the present paper investigatedthe in uence of patched FRP pultruded sheets on metalplates in the buckling phenomenon [4]. Teng andHu [5] covered steel tubes and cylindrical shells undercompression loading by FRP jackets during experi-mental and �nite element studies and they displayedthis technique as a useful method for ductility increaseand collapse hindering of these structures. Silvestreet al. [6] investigated the non-linear behavior andload carrying capacity of the CFRP-strengthed open-section columns from cold-formed steel using pultrudedcomposite sheets, and they observed a considerableincrease in the buckling load and improvement of thepost buckling behavior for these members. Shaat andFam [7-9], using FRP sheets on hollow square columns,investigated the in uence of these patches on the load-bearing capacity of the columns. They developed an

408 M.Z. Kabir and A.R. Nazari

analytical model for their experimental specimens andveri�ed the analytical manipulation by experimentalresults. They also extended their theory for variouscharacteristics of the columns, such as slenderness andinitial out-of-straightness.

The main contribution of the current study is thestability of a repaired metal cylinder using an FRPpatch. The in uence of the crack in both longitudinaland circumferential directions was considered on theload carrying capacity of the cylinder. The methodol-ogy is based on numerical study. All the assumptionshere are based on experimental observations by authorspresented in other studies. The columns were made ofsteel alloy in those tests and here they are assumedfrom an aluminum alloy [10]. The obtained resultswould establish the presented retro�tting technique asa unique method for repairing and reinforcing thinwalled tubular sections.

PROPOSED MODELS

To follow up the subject of the paper, the selectedmodels are of two various diameters and of identicallength and thickness as L = 1000 mm and t = 1 mm.The diameters were determined as D = 50 mm andD = 100 mm denoting the cylinder aspect ratio forexploring two distinct buckling mode shapes. Theconsidered cracks on the columns were chosen in longi-tudinal and circumferential directions to investigate thein uence of crack in two major orientations. The lengthof the longitudinal crack was assumed 0.2 of the columnlength (C=L = 0:2) and similarly the circumferentialcrack length was 0.2 of the column section perimeter(C=2�r = 0:2).

The column was made of an aluminum alloy (T-6061) with elastic modulus, yield stress and Poissonratio equal to 71.7e3 MPa, 240 MPa and 0.33, respec-tively. It should be emphasized that due to the almost attening out of stress strain in the plastic domain forthe selected aluminum, T-6061, the material behavesin an elastic-fully plastic manner. By placing tworigid plates at both ends, the end conditions of thecolumns were considered as clamped. The criterion ofthe cylinder shortening provided movement betweenthe two rigid plates. The reinforced material waschosen as carbon �ber and epoxy resin with mechanicalproperties as listed in Table 1. In this table, E1 isthe module of the composite in the �bers direction,

E2 is the composite module in the matrix direction,�12 is the major Poisson ratio in the 1-2 plane, G12is the major shear module in the 1-2 plane, XT

denotes the tensile strength in the �bers direction,XC indicates the compressive strength in the �bersdirection, Y T denotes the tensile strength in the matrixdirection, Y C represents the compressive strength inthe matrix direction and, �nally, SL and ST denotethe shear strength in the �bers and matrix directions,respectively.

Figure 1 shows the schematic view of the re-paired cylinder. Here, the important problem is theinteraction between the cylinder and the FRP patch.To determine this relation regarding that observedin the experimental study about contact between theFRP patch and cylinder in [10], in the present study,any debonding between the patch and cylinder wasignored and the movement of the patch elements de-pended on the movement of adjacent cylinder elements.The assumption was validated in the experimentalobservations carried out by the authors in previouswork [5]. Of course, the mentioned hypothesis ignoresany debonding between a composite patch and a metalcylinder.

FE MODELING

Cracked Cylinder

The common commercial program, ABAQUS [11],was utilized for the FE modeling and analysis ofthe assumed columns. For modeling of the columns,nonlinear behavior in both material and geometry

Figure 1. Schematic view of the repaired cylinder bycomposite patch.

Table 1. Mechanical properties of the used FRP.

Material E1

(MPa)E2

(MPa)�12

(MPa)G12

(MPa)XT

(MPa)XC

(MPa)Y T

(MPa)Y C

(MPa)SL

(MPa)ST

(MPa)

t(mm per

layer)

Carbon/epoxy 140421 8982 0.3 3387 800 1100 150 231 520 280 0.2

Reinforcement of Cracked Metal Columns Using FRP 409

domains was considered for the models. Loading on thestructures was carried out considering a low velocity(V = 5 mm/s) on the top rigid plate. In order toconsider the nonlinearity in geometry, at the beginning,the buckling analysis was performed and then byimposing the combination of obtained mode shapes,considering them as an initial imperfection, the nonlinear analysis was conducted. The amplitude of thesmall deformations was considered about 1 �m. Theassumed boundary conditions, both for the top andbottom plates, were implemented as three rotationaland two translational movements. The contact betweenthe rigid plates and the cylinder edges was de�nedboth in normal and tangential directions. The normalcontact was designated as \hard contact" and thetangential contact was introduced with a friction ratioto prevent sliding between the plate and cylinder. Thepresented results are the axial load-end shorteningcurves, which were compared for the intact, crackedand repaired columns. Both cylinders and rigid plateswere modeled using \shell" elements, and for thispurpose, \S4R" element with 4 nodes and 6 degreesof freedom (three translational and three rotational)per node was chosen from the element library of the\ABAQUS.CAE". A mesh convergence study for anintact cylinder with L=D = 10 was carried out tochoose the appropriate size for mesh dimensions (seeTable 2). The buckling process is explained as follows:The plastic buckling takes place at two ends andthe diameter of the cylinder increases in this region.Considering the yield stress, �y, equal to 240 MPa, theyield load, Py, is then estimated as = 75.4 KN, whichis similar to numerical FEM results. Thus, startingwith a 30�30 mm2 �nite element mesh, using non-linearanalysis, a convergence study was conducted for anintact cylinder with L=D = 10. The result from eachre�nement of the mesh is compared with that of theclassical buckling equation (Py) and is summarized inTable 2. Accepting an error margin of 1% for the non-linear buckling load, a mesh consisting of 4000 elementsand 10 mm�10 mm element size was adopted in the

Table 2. Mesh convergence study of the cylinder withL=D = 10.

Mesh Size(mm)

Number ofElements

BucklingLoad (KN)

Error(%)

30*30 428 77.578 2.90%

20*20 1000 77.059 2.20%

15*15 1745 76.682 1.70%

10*10 4000 76.169 1.02%

7.5*7.5 6951 76.116 0.95%

5*5 15600 76 0.80%

numerical analyses. Regarding the dependence of theaccuracy of the results on the ratio between mesh sizeand cylinder radius, the size of mesh for a cylinderwith L=D = 20 was chosen as half of a cylinder withL=D = 10. This size of mesh was extended for theentire structure except at the vicinity of the crack tips.Observation of the stresses around the crack tip showsthat the mesh size in this region has a dominant e�ecton the stress contour in the region. It was decided tofragment the mesh size at this region to about 1/16 thesize of mesh in other regions through four steps [12].Triangular elements were chosen for meshing of theregions near the crack tips in order to prevent makingnarrow rectangular elements in these areas.

Composite Patch

For modeling of FRP patch con�nement, various meth-ods have been implemented by researchers. In thecurrent study, the composite patch was modeled usingshell elements. The centroid of the patch elements waslocated at an appropriate distance from the centroid ofthe metal cylinder. An o�set was assigned to all con-tributed nodes for contact between cylinder and patchnodes. The continuity between the patch and cylinderduring the loading process was fully established and thedeformation of these two parts was assumed identical.Using \tie" constraint as the direct contact betweenpatch and cylinder nodes, the full bonding will, then,be provided. By de�ning this constraint, the degrees offreedom of the patch elements were introduced as slaveelements and those of the cylinders as master elementswith consideration of no debonding between the patchand cylinder. \S4R" shell elements were adopted tomodel the laminated composite patch with orthotropiccharacteristics and a progressive damage capability.For all proposed models, the �bers were oriented ina circumferential direction in the retro�tting of bothcrack types: longitudinally and circumferentially.

Progressive Damage

The elastic damage modeling was investigated in thesame way as damage initiation and progression inbrittle anisotropic materials such as FRP. In thistheory, the damage is modeled by reducing the sti�nessof materials, based on Hashin and Rotem criteria(1973) [15,16]. In the present modeling, four variousmodes are considered for damage of the composite:

- Fiber rupture in tension.- Fiber buckling and kinking in compression.- Matrix cracking under transverse tension and shear-

ing.- Matrix crushing under transverse compression and

shearing.

410 M.Z. Kabir and A.R. Nazari

On the basis of the four mentioned modes, four damagecriteria are introduced to initiate the damage as follows:

- F tf =��̂11

XT

�2

+ ���̂12

SL

�2

:

- FCf =��̂11

XC

�2

:

- F tm =��̂22

Y T

�2

+��̂12

SL

�2

:

- FCm =��̂22

2ST

�2

+

"�Y C

2ST

�2

� 1

#�̂22

Y C+��̂12

SL

�2

:

In the above equations, �̂11, �̂22, �̂12 are componentsof the e�ective stress tensors which are intended torepresent the stresses acting over the damaged area.� is a coe�cient that determines the contribution ofthe shear stress to the �ber tensile initiation criterionand which varies between 0 and 1, its high value beingassumed here. At the end of each state of analysis,these criteria were checked on each element of theFRP, whether the damage was initiated or not. Havingdamage evolution de�nition for each mode, the sti�nessof the damaged element is replaced by zero in thatmode. For a metal cylinder, the Von-Mises stresscriterion was used and for FRP elements, the Hashindamage criterion was evaluated. These are shown with:HSNFTCRT for maximum value of the �ber tensileinitiation criterion experienced during the analysisor ultimate FTf ; HSNFCCRT for maximum value ofthe �ber compressive initiation criterion experiencedduring the analysis or ultimate FCf ; HSNMTCRT formaximum value of the matrix tensile initiation crite-rion experienced during the analysis or ultimate FTm,and HSNMCCRT for maximum value of the matrixcompressive initiation criterion experienced during theanalysis or ultimate FCm .

DISCUSSION OF THE RESULTS

Repair of Circumferentially Cracked Columnwith L=D = 10

A relatively long cylinder was included in this study inorder to investigate the e�ciency of the proposed tech-nique to repair cylinders which have plastic buckling.The load versus axial shortening in a non-linear manneris depicted in Figure 2, in a non-dimensional graphwhere the vertical axis is the ratio of the applied load(P ) to the ultimate strength (P0) of the intact cylinderand the horizontal axis gives the ratio of the endshortening (�) over the cylinder length (L). Accordingto the �gure, in the presence of a circumferentialcrack with C=2�r = 0:2, the ultimate strength and

Figure 2. The in uence of repair with composite patchon the non-dimensional load-de ection graph of thecircumferentially cracked column with L=D = 10 andC=2�r = 0:2.

absorbed energy of the cylinder were decreased by 37%and 27%, respectively; \C" denotes the length of thecrack. Figure 3 shows the buckling deformations ofthe cylinders in states of being intact and cracked. Itis seen that the buckling of the column deforms fromthe elephant foot mode of an intact cylinder to thelocal crippling mode at the cracked region for a crackedcylinder. In the �rst attempt, only a one-ply compositepatch made of carbon-epoxy with �ber orientationin the circumferential direction and with a length of\200 mm" was used on the cylinder axisymmetricallyrelative to the crack. The maximum buckling load wasconsiderably promoted, as can be seen in Figure 2.The next attempt was speci�ed by strengthening ofthe cracked region using a two-ply composite patch.Figure 2 also shows its in uence on the load bearingbehavior of the repaired column. Figure 3d showsthe buckling deformation of this cylinder, which wasoccurred out of the patch zone. Figure 4 shows theHashin damage criterion about the tensile �bers forboth types of composite patch.

Repair of Longitudinally Cracked Column withL=D = 10

In order to investigate the in uence of the longitudinalcrack on this column, the size of crack was assumedabout 0.2 of the column length at the center. Figure 5shows the non dimensional load de ection curves oflongitudinally cracked cylinders. The repairing patchhas enhanced the cracked cylinder buckling load up tothe intact one. The buckling form of the cylinder isobserved in Figure 6 in the presence of a longitudinalcrack. The cylinder inclines outward from the crackedregion followed by its collapse. To repair this cylinder,a two-ply patch with a length of \300 mm" was

Reinforcement of Cracked Metal Columns Using FRP 411

Figure 3. Buckling deformations of the column with L=D = 10 in states of (a) intact; (b) un-repaired circumferentiallycracked; (c) patched by 1-ply patch; and (d) patched by 2-ply patch.

Figure 4. Hashin damage criterion about the tensile�bers in (a) 1-ply patch and (b) 2-ply patch.

Figure 5. The in uence of repair with composite patchon the non-dimensional load-de ection graph of thelongitudinally cracked column with L=D = 10 andC=L = 0:2.

attached on the crack axisymmetrically relative tothe crack centre. In Figure 6b, the buckling formof the retro�tted column appeared in an elephantfoot mode at one end of the cylinder. Based onthe obtained results, none of the damage criteria was

Figure 6. Buckling deformations of the longitudinallycracked cylinder with L=D = 10 in states of (a)un-repaired longitudinally cracked and (b) repaired bycomposite patch.

referred to FRP failure, which indicates the successfulperformance of an externally bonded composite patchon longitudinally cracked circular columns.

Repair of Circumferentially Cracked Cylinderwith L=D = 20

This section was studied in order to investigate the ap-plicability of the proposed technique for long columnspronouncing Eulerian type buckling mode. The buck-ling form of the intact column is observed in a fullyelastic domain, which is depicted in Figure 7. Similarto the previous model, the assumed circumferentialcrack size for this case is 0.2 of the perimeter of thecylinder. Inserting the circumferential crack decreased

412 M.Z. Kabir and A.R. Nazari

Figure 7. Buckling deformations of the cylinder with L=D = 20 in states of (a) intact; (b) un-repaired circumferentiallycracked; and (c) repaired by composite patch.

Figure 8. The in uence of repair with composite patchon the non dimensional load-de ection graph of thecircumferentially cracked column with L=D = 20 andC=2�r = 0:2.

the column ultimate strength about 23% (see Figure 8).According to Figure 7, the buckling shape is outwarddeformation form cracked region. In order to repairof this cylinder a two-ply patch with a length of \200mm" was used on the cracked surface and the bucklingstrength enhanced about 35% in comparison with theintact column (see Figure 8). According to this �gure,the obvious reason for enhancement of the load bearingcapacity of the reinforced column is transformation ofthe buckling phenomenon from the Eulerian mode tothe local plastic buckling mode, which was occurredin the un-patched zone. The main reason for thesephenomena is the interaction of the patch on the lengthof the cylinder. In fact, the patch divides the cylinderinto shorter lengths: patched length and un-patchedlength. So, the local mode would then be governedto the plastic buckling by an un-retro�tted area thatimproves the buckling behavior of the column to a

possibly more favorable mode than the other withhigher strength and more ductility.

Repair of Longitudinally Cracked Cylinderwith L=D = 20

Applying the same size of crack in a longitudinaldirection equal to 0.2 of the cylinder length located atthe mid length of the cylinder the buckling strength ofthis defected column was reduced to about 20% of theintact one with the buckling mode shape at an outwardinclination from the cracked region. The variation ofnon dimensional applied load versus axial shorteningis depicted in Figure 9. The considerable increasein buckling strength of the retro�tted column with atwo-ply patch and length of \200 mm" is observable.The �bers orientation was assumed in a circumferential

Figure 9. The in uence of repair with composite patchon the non dimensional load-de ection graph of thelongitudinally cracked column with L=D = 20 andC=L = 0:2.

Reinforcement of Cracked Metal Columns Using FRP 413

Figure 10. Buckling deformations of the longitudinally cracked cylinder with L=D = 20 in states of (a) crackedun-repaired and (b) repaired by composite patch.

direction. Figures 10a and 10b show the bucklingdeformation of the cracked un-patched and patchedcolumns, respectively. The damage indices show valuesfar from failure, which indicate the high success of theproposed repair scheme for this case as well.

CONCLUSIONS

In the present paper, FRP wrapping of the defectedmetal columns was proposed as an e�ective techniquefor repairing of these members. In this regard, two sizesof column length: L=D = 10 and 20, were studied toinvestigate the adequacy of the proposed technique fortwo prominent buckling shapes. For this purpose withthe assistance of a FE program, the in uences of FRPlocal patches for on the repair of circumferential andlongitudinal cracks were studied on the load carryingcapacity of columns. The following results can bemarked as useful conclusions:

1. The circumferential crack on the relatively longcolumn with L=D = 10 reduced the ultimatestrength about 37% and, by using a partial patchon the cracked region, the ultimate strength of thecracked column was fully recovered.

2. The longitudinal crack on the column with L=D =10 reduced the ultimate strength by 35%; theapplication of the composite patch could return itsload carrying capacity to that of the intact one, andthe buckling failure was moved to the un-patchedregion.

3. The circumferential crack on the column withL=D = 20 reduced the ultimate strength by22%, however, implementing the composite patchnot only recovered the load carrying capacity butalso could enhance the ultimate strength of the

reinforced column by 35%, in comparison with theintact column.

4. The longitudinal crack on the cylinder with L=D =20 reduced the ultimate strength by 20%. Byapplying the FRP patch, the buckling strengthsurpassed the intact column strength and, also thebuckling mode would then transform from elasticEulerian to local plastic mode.

5. The obtained results in this paper not onlyintroduced the proposed technique as an ef-�cient repair method for defected cylinders,but also showed its capability to improvethe load bearing behavior of the columnsin comparison with intact ones. Therefore,the FRP wrapping technique can be appliedas a very unique and promising method forthe repair, retro�t and reinforcement of metalcolumns.

REFERENCES

1. Teng, J.G., Chen, J.F., Smith, S.T. and Lam, L., FRPStrengthened RC Structures, John Wiley & Sons Ltd(2002).

2. Baker, A.A. and Mallick, P.K., Ed., Composite Engi-neering Handbook, Part 14, Marcel Decker Inc., NewYork (1997).

3. Baker, A.A. and Jones, R., Eds., Bonded Repairof Aircraft Structures, Martinus Nijho� Publishers,Dordrecht (1988).

4. Kabir, M.Z. and Nazari, A.R. \Enhancing of stabilitycapacity of thin metal plates using bonded compositepatches", in Proceedings of the 1st International Con-ference on Composites: Characterization, Fabricationand Application, Kish, Iran, CCFA-643490 (15-18 Dec.2008).

414 M.Z. Kabir and A.R. Nazari

5. Teng, J.G. and Hu, Y.M. \Behaviour of FRP-jacketedcircular steel tubes and cylindrical shells under axialcompression", Construction and Building Materials,21, pp. 827-838 (2007).

6. Silvestre, N., Young, B. and Camotim, D. \Non-linear behavior and load carrying capacity of CFRP-strengthed lipped channel steel columns", EngineeringStructures, 30, pp. 2613-2630 (2008).

7. Shaat, A. and Fam, A. \Axial loading tests on shortand long hollow structural steel columns retro�ttedusing carbon �bre reinforced polymers", CanadianJournal of Civil Engineering, 33(4), pp. 458-70 (2006).

8. Shaat, A. and Fam, A. \Fiber-element model forslender HSS columns retro�tted with bonded high-modulus composites", Journal of Structural Engineer-ing (ASCE), 133(1), pp. 85-95 (2007).

9. Shaat, A. and Fam, A. \Finite element analysis ofslender HSS columns strengthened with high moduluscomposites", Steel & Composite Structures, 7(1), pp.19-34 (2007).

10. Kabir, M.Z. and Nazari, A.R. \Treatment of thecracked metal cylinders subjected to the axial com-pression loading using FRP patch con�nement", Engi-neering Structures, submitted for possible publication(2009).

11. ABAQUS, ABAQUS/Standard User's Manual.ABAQUS Inc (2003).

12. Estekanchi, H.E. and Vafai, A. \On the bucklingof cylindrical shells with through cracks under axialloading", Thin Walled Struct., 35, pp. 255-74 (1999).

13. Vaziri, A. and Estekanchi, H.E. \Buckling of crackedcylindrical thin shells under combined internal pressureand axial compression", Thin-Walled Structures, 44,pp. 141-151 (2006).

14. Paik, J.K., Satish Kumar, Y.V. and Lee, J.M. \Ulti-mate strength of cracked plate elements under axialcompression or tension", Thin-Walled Structures, 43,pp. 237-272 (2005).

15. Hashin, Z. \Analysis of properties of �ber compositeswith anisotropic constituents", ASME J. Appl. Mech.,46, pp. 543-50 (1979).

16. Hashin, Z. \On elastic behaviour of �bers reinforcedmaterials of arbitrary transverse phase geometry", J.Mech. Phys. Solids, 13, pp. 119-34 (1965).

BIOGRAPHY

Mohammad Zaman Kabir is an associate professorin Department of Civil and Environmental Engineer-ing, Amirkabir University of Technology, Tehran, Iran.He received his B.S. and M.S. from Amirkabir Univer-sity of Technology and Ph.D. from Waterloo Universityin Canada. His research interest includes StructuralStability, Structural Analysis using FEM, Experimen-tal Methods in Structural Engineering, CompositeStructures, Structural Optimization, Damage Detec-tion and Rehabilitation of Structures.

Ali Reza Nazari is a Ph.D. candidate in Departmentof Civil and Environmental Engineering, AmirkabirUniversity of Technology. He received his B.S. fromIsfahan University of Technology and M.S. from Amirk-abir University of Technology. His research interestincludes Composite Structures, Structural Analysisusing FEM, Experimental Methods in Structural Engi-neering, Damage Detection especially in the CompositeStructures and Rehabilitation of Structural Membersusing FRP Materials.