Design Optimization of GFRP Pole Structures Using Finite Element Analysis

Transcription

1 Aerican Coposites Manufacturers Association January 15-17, 2009 Tapa, FL USA Design Optiization of GFRP Pole Structures Using Finite Eleent Analysis by Hady Mohaed, Departent of Civil Engineering, University of Sherbrooke Radhouane Masoudi, Departent of Civil Engineering, University of Sherbrooke Abstract The applications of the tapered glass fiber-reinforced polyer (GFRP) poles are started as an alternative for traditional aterials such as wood, steel, and concrete, in overhead power line and distribution aerial network. This paper presents a finite eleent (FE) analysis of the nonlinear behavior of laterally loaded, full scale tapered GFRP pole structures. The FE odel was used to detect the perforance of GFRP poles having service opening (holes). Several FE siulations with different cobinations of paraeters such as fiber orientation, nuber of layers and thickness of layers were eployed. Evaluation of the deflection and bending strength characteristics of GFRP Poles [20 and 33 ft] height are presented. Optiu new designs for three zones along the height of the GFRP poles are proposed, under equivalent wind load. The ultiate load carrying capacity and flexural stiffness are iproved with a significant saving in the weight. The new designs are satisfied according to the allowable axiu deflection and the iniu ultiate oent capacity as specified in the ASTM, AASHTO LT S and ANSI standards. Introduction In recent years, FRP coposites, which are ade of reinforcing fibers and a therosetting resin, have been widely used as advanced construction aterials. FRP provide several advantages over traditional construction aterials (steel, concrete, wood): high strength to weight ratio, high stiffness, resistance to corrosion, ease of installation and high durability [1]. Therefore, the tapered FRP poles are currently considered attractive in the application of the light poles and electrical transission tower eleent. There is a lack to study the behavior of the hollow tapered FRP pole structures. These due to the liited nuber of experiental and theoretical studies, which have been conducted on the behavior of the tapered GFRP poles structure under lateral load [2, 3, 4, 5 and 6]. Most of these studies were related to the behavior of the FRP poles without service opening. The existence of service opening in the FRP poles, reduce the strength at the location of this opening, due to sall thickness-to-radius ratio, ovalization and local buckling behavior of the FRP poles [7, 8, 9 and 10]. Therefore the part which includes this hole ust be addressed and finding the optiu geoetrical details for it to be copatible with the upper and lower zones over the of the pole, to attain the required total capacity under lateral loads. The finite eleent analysis is a good way that can be used to siulate and predict the actual behavior of FRP poles. A theoretical analysis by finite eleent ethod were developed for the analysis of FRP hollow tapered poles, to perfor a linear static analysis, linear buckling analysis, linear P- analysis, a geoetrical nonlinear analysis of bea-colun-type bending and an ovalization analysis [2]. Extensive nuerical results were presented showing the effect of different laination and geoetric paraeters of the ultilayered coposite cylinder on the accuracy of the static and vibrational responses [11]. In this paper, the finite eleent progra is used to perfor a nonlinear nuerical analysis for 20 and 33 ft tapered GFRP poles with service opening, under lateral load to present the wind load on the structure. A paraetric study is carried out to study the effect of longitudinal and circuferential angle orientation of the fiber and wall thickness of three zones along the height of the pole. The ultiate capacity, top deflection and the ultiate oent capacity are presented to find the best optiu designs for the GFRP poles. Optiu new designs for three zones along the height of the GFRP poles are proposed, under equivalent wind load. Geoetrical Diension of GFRP Poles The first part in this study is the odeling by the finite eleent (FE) progra of the GFRP poles [20 and 33ft] which were tested by [10]. Coparison between the FE and experiental results are presented. The second part is the optiization of the design of these two poles to eet the requireent for deflection and failure load. The speciens were tapered hollow sections, with different. The inner diaeters of the GFRP poles 20 ft at the base and at the top were and 76.00, respectively. The inner diaeters of the GFRP poles 33 ft at the base and at the top were and , respectively. Each prototype is divided through the height into three zones, I, II and III as shown in Figure 1. The x (width x ) service opening was located at the center of the iddle zone II and was in

2 the copression side, when loaded. The stacking sequences at the three zones for [20 and 33 ft] GFRP poles are presented in Table 1. Finite Eleent Model In this study, an appropriate three-diensional odel is developed to accurately siulate the flexural behavior of GFRP pole structures; it is based on the finite-eleent software ADINA 8.4 [12]. Large deflection is included in the analysis and appropriate aterials failure criteria (Tsai-Wu failure criterion) are used to deterine the failure load. The results of the finite eleent analysis are verified through coparison with the available experiental data obtained fro the static testing of full-scale prototypes [10], according to the recoendations described in ASTM and ANSI standards. The following sections present the ajor features of the finite eleent ethod used in this study: Geoetrical Modeling The 20 ft pole was odeled with total nuber of eleents 1648 (16 and 103 in the circuference and longitudinal direction, respectively). In addition, the 33 ft pole was odeled with total nuber of eleents 2224 (16 and 139 in the circuference and longitudinal direction, respectively). The esh layout were fine in the botto area of the axiu stress and expected failure zone, and gradually becoes coarse at the top, this was ade by the autoatic esh density option of the progra. The general layout of the esh distribution and the used finite eleent odels are shown in Figure 2. The underground of the GFRP poles were restraint along two opposite half circuference area, the first area at the end of the base and the second area at the ground line. Each node along the supported area was restrained against the vertical (in z-direction), the horizontal (in x and y directions) oveents. This Configuration of restraints was to siulate the support condition described in standards [13, 14 and 15] for testing the Load- deflection behavior of FRP poles, see Figure 3. Coposite Shell Eleents An eight-node quadrilateral ultilayered shell eleent was used in the odel. Each node has six degrees of freedo, three translations (Ux, Uy, and Uz) and three rotations (Rx, Ry, and Rz). The coposite shell eleents are kineatically forulated in the sae way as the single layer shell eleents, but an arbitrary N nuber of layers can be used to ake up the total thickness of the shell. The interfacial behavior between layers was considered full bonded. Layers are nubered in sequential order starting fro 1 at the botto of the shell [12]. Newton-Cotes with high order of 5 5 nuerical integration was used for the evaluation of the eleent atrices in the r-s plane of the shell eleent, to avoid spurious zero energy. 3-point Newton-Cotes nuerical integration was used through the shell thickness to obtain an accurate profile of the transverse shear stress. The aterial odel be used with the shell eleent is elastic-orthotropic with large displaceent /sall strain. In the large displaceent forulation/sall strain forulation, the displaceent and rotation can be large, but the strains were assued to be sall. Orthotropic aterial properties in the fiber and transverse to the fiber direction were defined. Fiber orientation for each layer was specified by defining the fiber angle with respect to the eleent axes. Loading The FRP pole was subjected to a horizontal pressure load (W) below the top of the pole edge by 300 according to the ANS C The value of (W) was varied fro zero to the ultiate load capacity corresponding to each pole. The pole was increentally loaded using tie steps. This variation is autoatically done by the ADINA User Interface (AUI) according to the condition of convergence. To avoid local failure under the applied load, the load had been distributed over circuferences area to siulate the sae effect of the experiental load. Material Properties The aterial properties for both the fiber and the resin are presented in Table 2. The echanical properties of the FRP lainate were obtained fro the aterial properties of the E-glass fiber and the epoxy resin. They were used to calculate the effective odules of elasticity of the orthotropic aterial based on icroechanical odels. The Rule of Mixture was used to evaluate the odulus of elasticity in the fiber direction (E l ), and the ajor Poisson's ratio (υ l2 ) as follows [16]: Where, E µ υ 1 = Efµ f + E 12 =υfµ f +υµ µ f and µ are the fiber and the atrix volue ratios, respectively; E f and E are the fiber and the atrix Young's odules, respectively; and υ f and υ are the fiber and the atrix Poisson's ratios respectively. 2

3 The equations given by [17] were used to calculate the effective Young's odulus in the transverse direction (E 2 ) and the shear odulus (G 12 ), by using the fiber and atrix properties, (E 2 ) and (G 12 ) were derived as follow: Where, E G 2 12 = µ E f f 1 µ + E 1 = µ f µ + G G G f and G are the fiber and the atrix shear odules, respectively. Finite Eleent Results The ain objective of this section is to discuss the results of the finite eleent analysis. The nuerical results in the current section are copared with the experiental results of [10] to assess the validity of the finite eleent analysis. Once the finite eleent was verified, it is extended to perfor a ore coprehensive paraetric study. First we need to investigate what is the ost convenient odel with respect to esh layout to siulate the FRP pole structure subjected to the top lateral load. The coparison was in ters of the load-deflection relationship and the ultiate load carrying capacity of the GFRP poles. Figure 4 represents the load deflection relationship for the experiental and finite eleent analysis for 20 and 33 ft height GFRP poles. It is evident fro this figure that there is a strong correlation between the results obtained fro the finite eleent analysis and the experiental results. The Proposed Design of GFRP Poles In this section, the objective is to obtain the best optiization with iniu weight for the coplete details of the configuration for [20 and 33 ft] GFRP poles. This is to satisfy the requireent strength criteria for FRP poles which are given in ASTM, AASHTO and the general standard specification of the ANSI C for the axiu deflection, ultiate load capacity and iniu ebedent depth. The finite eleent ethod is eployed to analyze the different proposed odels for 20 and 33 ft GFRP poles. These odels were proposed according to the survey in the literature review of experiental data fro several sources [5, 6, 7, 8, 9 and 10] for different cobination of paraeters such as fiber orientation, nuber of longitudinal and circuferential layers, layer thickness and type of fiber. The details of f the new proposed design are given in Tables 3 and 4 for 20 and 33 ft GFRP poles. It was assued the nuber of layers is varied fro 8 to 12, placed in two-layerincreent layers. All of these layers assued that to be with longitudinal orientation except two circuferential layers for all zones I, II and III. The existence of service opining in zone II akes it weaker than the other zones. It is proposed to increase the ain layers by three additional layers internally and externally in zone II, to ake the total layers of this zone varied fro 14 to 18. The fiber angles assued to be +10 /-10 for longitudinal layers and 90 for circuferential layers, and 90, +45 /-45 are used for the additional layers in zone II. The thickness of each layer varied fro 0.28 to 0.50 and for the additional layers fro 0.56 to 1.0. Finally, a new fibers type of Linear ass (1100 g / k ) and noinal yield (450 Yards / lb) are assued as a reinforceent for the odeled GFRP poles. Evaluation of Deflection and Bending Strength Characteristics for the New Proposed Design Al1 GFRP poles were analyzed using the developed finite eleent odels; the thickness of each pole is coputed using different load liit for each pole applied laterally at 12 inches below the top edge of the pole to attain the required strength criteria. This approach required that for each pole several trial sections were analyzed until the right thickness is achieved. Failure was defined either by aterial failure or by local buckling. The results indicate that a iniu thickness of a GFRP pole is achieved when using two circuferential layers with longitudinal layers fro the total nuber of layers. The results of the finite eleent analysis for the new proposed configurations of the GFRP poles (20 and 33 ft) are given in Table 5. The coparison between the axiu allowable deflection and the deflection of the new proposed design under an equivalent axiu wind loads is given in Table 6. Coparison between the ultiate oent capacity of GFRP poles of the new proposed design and the required ultiate oent capacity due to wind loads are given in Table 7. For all GFRP poles (20 and 33 ft), it is clear that the deflection did not exceed the liit of axiu deflection under the equivalent wind load. The deflection is 25 % lower than the required deflection liit. The poles fail after reaching the specified iniu ultiate bending strength with factor of ty varied fro 2.06 to It eans that an econoic design for these GFRP pole is achieved with the new proposed design. Fro Table 8, it is clear that a significant saving in the weight is achieved with the new designs. All the details between the new and old designs for these GFRP poles, are the sae except optiizing the nuber, thickness, fiber orientations and stacking sequence of layers. 3

4 Conclusions The ultiate capacity and perforance of the tapered filaent wound GFRP poles (20 and 33 ft) subjected to cantilever bending are evaluated. The finite eleent analysis used in this study gives a good prediction of the flexural behaviours and failure loads. The proposed odels with optiizing nuber, thickness, fiber orientations and stacking sequence of layers give excellent result. The internal and external additional three layers (90, ±45) for the lainate at the iddle zone II with the service opening iproved the flexural behaviour. Optiu cross-section diensions for (20 and 33 ft) GFRP poles were obtained using the finite eleent odels. These GFRP poles are designed to satisfy the requireent strength criteria as specified in the ASTM, AASHTO and ANSI standards for the axiu deflection and ultiate load capacity Acknowledgents: The research reported in this paper was partially sponsored by the Natural Sciences and Engineering Research Council of Canada (NSERC). The authors also acknowledge the contribution of the Canadian Foundation for Innovation (CFI) for the infrastructure used to conduct testing. Special thanks to the anufacturer (FRE Coposites, St-André d Argenteuil, Qc, Canada) for providing FRP tubes. The opinion and analysis presented in this paper are those of the authors. The technician Nicolas Siard participates in the specien preparation and testing. Author(s): Hady Mohaed is a Ph.D. Candidate at the University of Sherbrooke, Sherbrooke, QC, Canada. He received his B.Sc. and M.Sc. degree fro the Faculty of Engineering, Helwan University, Egypt in 1999 and 2005, respectively. His research interest is the use of fiber-reinforced polyers (FRP) in reinforced concrete structures. Mohaed is a eber of several professional associations including the Aerican Concrete Institute (ACI), the Aerican Society of Civil Engineers (ASCE), the Canadian Society of Civil Engineering (CSCE) and the Egyptian Professional Engineers Association. Eail address: Hady.Mohaed@usherbrooke.ca Radhouane Masoudi is a Professor at the University of Sherbrooke, Sherbrooke, QC, Canada. He received his M.Sc. and Ph.D. degree fro University of Sherbrooke. His research interests include the developent, design, testing and use of fiber-reinforced polyers (FRP) in utility and reinforced concrete structures as well as the finite eleent odeling of FRP structures. Masoudi is a eber of several professional associations including the Aerican Concrete Institute (ACI), the Canadian Society of Civil Engineering (CSCE) and the Society for the Advanceent of Material and Process Engineering (SAMPE). Eail address: Rahouane.Masoudi@usherbrooke.ca References: 1. K. Fujikake, S. Mindess, and H. Xu, (2004). Analytical Model for Concrete Confined with Fiber Reinforced Polyer Coposite JOURNAL OF COMPOSITES FOR CONSTRUCTION ASCE, 8(4), ZM. Lin (1995). Analysis of pole-type structures of fiber-reinforced Plastics by finite eleent ethod, Ph.D. Thesis, University of Manitoba, Winnipeg, Manitoba, Canada. 3. W. Crozier, J.P. Dussel, R. Bushey, J. West, (1995). Evaluation of deflection and bending strength characteristics of fiber-reinforced plastic lighting standards. Departent of Transportation, New York, State of California, USA. 4. G.L. Derrick (1996). Fiberglass Coposite Distribution and Transission Poles, Manufactured Distribution and Transission Pole Structures Workshop Proceeding, July 25-26, Eclectic Power Research Institute, S. Ibrahi, D. Polyzois, and S. Hassan (2000). Developent of glass fiber reinforced plastic poles for transission and distribution lines. Can. J. Civ. Eng. 27, S. Ibrahi, and D. Polyzois (1999). Ovalization analysis of fiber reinforced plastic poles. Coposite Structures, 45, R. Masoudi and H. Mohaed (2006). Finite Eleent Modeling of FRP-Filaent Winded Poles Third International Conference on FRP Coposites in Civil Engineering (CICE 2006), Deceber, Miai, Florida, USA, H. Mohaed and R. Masoudi Behavioral Characteristics for FRP Coposites Pole Structures: Nonlinear Finite Eleent Analysis, Proceedings of the Annual Conference of the Can. Soc. of Civ. Eng., Yellowknife, Northwest Territories, Canada.. 9. R. Masoudi, H. Mohaed and S. Metiche. (2008) Finite Eleent Modeling For Deflection and Bending Responses of GFRP Poles, Journal of Reinforced Plastics and Coposites, Vol. 27, No. 6, S. Metiche and R. Masoudi. (2007) Full-Scale Flexural Testing on Fiber-Reinforced Polyer (FRP) 4

5 Poles, The Open Civil Engineering Journal, ISSN: , 1, 37-50, K. Noor, W. Sctt Butron,. and M. Peters Jeanne. (1991) Assessent of coputational odels for ultilayered coposite cylinders Int. J. solids structures. 27(10), ADINA. (2006). Theory Manual, version 8.4. ADINA R&D, Inc Wastertown, USA. 13. Aerican Association of State Highway and Transportation Officials, AASHTO (2001), Standard Specifications for Structural Supports for Highway Signs, Luinaires and Traffic signals. 14. Aerican National Standard Institute. (2005). Fiber-Reinforced Plastic (FRP) Lighting Poles, Aerican National Standard for Roadway Lighting Equipent, USA, ANSI C Aerican Society for Testing and Materials. (2001). Standard Specification for Reinforced Therosetting Plastic Poles, Annual book of ASTM Standards, D , USA. 16. R.D Adas. (1987). Daping properties analysis of coposites Engineering aterials handbook. Edited by T.J. Reinhart et al. ASM International, Materials Park, Ohio, Vol. 1, Coposites, D. Gay. (1989) Matériaux coposites, Paris, 2e édition, Heres. 485 p. Table 1: Stacking sequences for the GFRP poles (Masoudi et al 2008) Pole 20 ft 33ft Zone I [-60/60/-25/25/±70] [70/-80/±20/70/-80] Zone II [90/-60/60/±15/±60] [90/±15/70/-80] Zone III [±15/-60/70] [±15/90] Table 2: Mechanical and physical properties of fibers and resin Fibers (E-Glass) Linear ass (g / k ) 2000 Noinal Yield (Yards / lb) 250 Tensile odulus(mpa) Shear odulus(mpa) Poisson s ratio 0.25 Epoxy resin Araldite GY 6010 Density (Kg / 3 ) 1200 Tensile odulus(mpa) 3380 Shear odulus(mpa) 1600 Poisson s ratio 0.4 Table 3: New design stacking sequences for the GFRP poles Pole Zone I and III Zone II {A-L, [M-L], A-L} M-L : Main layers A-L : Additional layers 20 [90, (±10) 3, 90] {90, ±45, [90, (±10) 3, 90] ±45, 90} 33 [90, (±10) 4, 90] {90, ±45, [90, (±10) 4, 90] ±45, 90} 5

6 Proto. Table 4: Details of new design Lainate for the GFRP poles N T Zone I, III Thickness of each layer T T N T No. of ain layers No. of additional Layers Zone II Thickness of each layer Thickness of each layer (A-L) () () () () () N T : Total nuber of layers T T : Total thickness T T Proto. Table 5: Results of finite eleent analysis for the new design P F.E (N) Maxiu deflection () Weight (kg) P F.E : Finite eleent failure load Table 6: Coparison between the axiu allowable deflection and the deflection of the new proposed design for the GFRP poles under the equivalent axiu wind loads. Proto. F.E () * () F.E / * Notes Safe Safe F.E : Deflection of finite eleent analysis under the equivalent axiu wind loads. * : The axiu allowable deflection under the axiu wind loads (10 percent of the pole above the grade line). Table 7: Coparison between the ultiate oent capacity for GFRP poles of the new proposed design and required ultiate oent capacity due to wind loads. Proto. P F.E (N) M F.E (N.) M w (N.) Factor of ty M F.E /M w Notes Weight econoic design (kg) M F.E M w econoic design : Ground oent due to finite eleent failure load : Cobined ground oent due to wind loads on luinaire and pole 6

7 Table 8: Factor of ty for oent, deflection and the weight ratio of [10] and proposed GFRP poles. Factor of ty Factor of ty for oent for deflection Pole M test /M w M F.E /M w test / * F.E / * Weight ratio W test /W prop Reduction in weight % Uneconoic un Uneconoic test : Deflection test under the equivalent axiu wind loads Zone II Zone I Zone III Zone II Zone I Zone III ft 20 ft Figure 1: Poles diension Figure 2: Finite eleent esh 7

8 Wood support saddles with Rubber Ground line GFRP Pole Load line W Under ground height Above ground pole height Figure 3: Specified ethods for testing FRP poles Figure: 4.a. Coparison between experiental and FE load-deflection relationship for 20 ft GFRP pole Figure: 4.b. Coparison between experiental and FE load-deflection relationship for 33 ft GFRP pole 8