APFIS-001

Copyright Note
Preface	III
Message from the President of IIFC	V
Organising Committee and International Scientific Committee Members	VI
Institutional Sponsors	VII
Industrial Sponsors, Exhibitors and Media Partner	VIII

VOLUME I

Keynote Papers

Building Confidence in the use of Fibre Reinforced Polymers in Construction S. Denton	3
Assessment of Numerical Models for FRP-strengthened Concrete Structures K.W. Neale	13
Fundamental Issues that Govern the Rotation of FRP Retrofitted Columns and Beams: The Intractable Plastic Hinge Ductility Problem D.J. Oehlers, M.S. Mohamed Ali, M.C. Griffith and T. Ozbakkaloglu	23
Debonding Failures of RC Beams Strengthened with Externally Bonded FRP Reinforcement: Behaviour and Modelling J.G. Teng and J.F. Chen	33
Integrated Strengthening of Structures with Bonded Prestressed FRP Reinforcements Z.S. Wu	43
Unified Definition of Safety Factors for Traditional RC Members and Members Incorporating FRP L.P. Ye and P. Feng	53

Strengthening of Concrete Beams and Slabs

Effect of Loading Configurations on the Structural Behavior of FRP Strengthened Concrete Beams J.L. Pan, T. Chung and C.K.Y. Leung	65
The Effect of Initial Strain on Resistance Moment of RC Beams Flexural Strengthened with FRP J.X. Ma and P. Wang	73
Retrofitting Reinforced Concrete Bridge Frames using Externally Bonded FRP Sheets G.R. Pandey, H. Mutsuyoshi and T. Aravinthan	79
Ultimate Load Modeling of RC Flats Elements Strengthened by CFRP L. Michel, E. Ferrier and P. Hamelin	87
Experimental Study on the Effects of Cyclic Loading during Repairing Period on the Effectiveness of Bonded CFRP M. Quiertant, L. Siegert, C. Boulay, P. Fakhri, C. Tourneur and J.-L. Clément	93
Fatigue Damage Model of RC Beams Strengthened with CFL based on Stiffness Degradation C. Zhao and P.Y. Huang	99
Influence of the Concrete Mechanical Properties on the Efficacy of the Shear Strengthening Intervention on RC Beams by NSM Technique V. Bianco, J.A.O. Barros and G. Monti	105
Behavioural Model of FRP Strengthened Reinforced Concrete Beams under Torsion C.E. Chalioris	111

Confinement of Concrete in Compression and Seismic Retrofit

Concrete-Filled Square FRP Tubes under Axial Compression T. Ozbakkaloglu, J.C. Lim and D.J. Oehlers	119
Analytical Study on Efficiency Evaluation of FRP Confinement on Square RC Columns A. Zarafshan and S. Zarafshan	125
FRP Strengthening of RC Columns - Parametric Finite Element Analyses of Bar Quality Effect T.C. Rousakis, G.E. Manolitsi and A.I. Karabinis	131
Square Concrete Section Confined by FRP: Ultimate Strength Prediction G. Monti and N. Nisticò	137
Principles of a Design Method for RC Columns Reinforced by CFRP under Eccentric Compression Loading K. Veròk, M. Quiertant and J.-L. Clément	143
Stress-Strain Model for FRP-confined Concrete Rectangular Columns Y. Ouyang and N.K. Liu	149
Stress-Strain Model for FRP-confined Rectangular RC Sections via an Incremental Procedure K.G. Megalooikonomou, K.D. Kim and G. Monti	155
Assessment of Drucker-Prager Type Plasticity Models for Predicting the Behaviour of FRP-Confined Concrete T. Yu, J.G. Teng, Y.L. Wong and S.L. Dong	161
A Simplified Model for FRP-confined Hollow Circular Concrete Columns under Axial Compression G.P. Lignola, A. Prota, G. Manfredi and E. Cosenza	167
Compressive Strength Models of FRP-Confined Concrete Y.A. Al-Salloum	175
Effects of Pre-damage and Cyclic Compression on Axial Behavior of FRP Jacketed Concrete A. Ilki, C. Demir and N. Kumbasar	181
Anchorage System for External Bonded CFRP Seismic Reinforcement E. Ferrier and P. Hamelin	187
Seismic Retrofitting of Reinforced Concrete Columns using Carbon Fiber Reinforced Polymer (CFRP) O. Ozcan, B. Binici and G. Özcebe	193
Comparative Study on Seismic Performance of Circular Concrete Columns Strengthened with BFRP and CFRP Composites G. Wu, D.S. Gu, Z.S. Wu, J.B. Jiang and X.Q. Hu	199
FRP Tubular Poles with Partial Concrete Filling J. Mitchell and A. Fam	205

Strengthening of Beam-Column and Slab-Column Connections

An Experimental Investigation on the Strengthening of RC Beam-column Connections with FRP Composites R. Shrestha and S.T. Smith	213
Seismic Upgrading of Existing RC Ordinary Moment Resisting Frames using FRPs S.S. Mahini and H.R. Ronagh	221
A Study on the Application of FRP Laminates to RC Knee Joints M. Safari Gorji and K. Bargi	227
A New CFRP Strengthening Technique to Enhance Punching Shear Strength of RC Slab-Column Connections H. Erdogan, G. Özcebe and B. Binici	233

Strengthening of Masonry Members

Flexure and Shear Strengthening of Masonry Walls with Composite Materials: State-of-the-Art M. Derias and R. El-Hacha	241
Experimental Behavior and Design Criteria for FRP In-plane Strengthening of Tuff Walls G. Marcari and G. Fabbrocino	249
Numerical Simulations of In-plane Behavior of Tuff Masonry Strengthened with Cementitious Matrix-Grid Composites G.P. Lignola, A. Prota and G. Manfredi	255
Strengthening and Retrofitting Unreinforced Masonry Walls with Various FRPs Systems G.A. Parsekian, R. El-Hacha and N.G. Shrive	263
Novelty FRP and TRM Strengthening Systems Applied to Stone Masonry Walls: Experimental Programme Presentation (I) J.T. San-José, D. García, T. El Hadid, R. San-Mateos, A. Al Far and I. Marcos	271
Behaviour of FRP Strengthened Masonry Walls under Out-of-plane Seismic Loading Y.A. Al-Salloum, T.H. Almusallam and S.H. Alsayed	277
Finite Element and Limit Analysis of the Large Scale Model of Mustafa Pasha Mosque in Skopje Strengthened with FRP R. Landolfo, F. Portioli, O. Mammana and F.M. Mazzolani	283

Strengthening of Timber and Glass Members

Strengthening Glulam Beams with Steel or Composite Plates R. Kliger, M. Al-Emrani, M. Johansson and R. Crocetti	291
Strengthening of Wooden Beams with FRP Materials C. Bernardini, L. Credali and G. Pistone	297
Evaluation of Timber Beams Reinforced with FRP Fabrics J. Vanerek and P. Hradil	305
On the Bending of GFRP Reinforced Glass Element E. Speranzini and P. Neri	311

Concrete and Masonry Members Reinforced with Internal FRP

Prefabricated FRP Reinforcement for Concrete Bridge Deck and Railing: Design, Laboratory, Validation, and Field Implementation F. Matta, A. Nanni and L.C. Bank	319
Reliability Assessment on the Serviceability of Concrete Beams Reinforced with Glass Fiber Reinforced Polymer Rods Z. He and F. Qiu	325
Mechanical Performance of Curved FRP Rebars: Part I - Experimental Study T. Imjai, M. Guadagnini and K. Pilakoutas	333
Mechanical Performance of Curved FRP Rebars: Part II - Analytical Study T. Imjai, M. Guadagnini and K. Pilakoutas	339
Experimental Research of Concrete Beams and Masonry Walls Reinforced with GFRP Reinforcement Z. Soric, T. Kisicek and J. Galic	345
Concrete and Masonry Elements Reinforced with Newly Developed FRP Reinforcement D. Horak, M. Zlamal and P. Stepanek	353

Concrete Members Prestressed with Internal or External FRP

Behavior and Ductility of Ultra High Performance Beams Prestressed with CFRP Tendons J. Yang and Z. Fang	361
Elastic Moment Capacity and Prestress Loss of Steel-concrete Composite Beams Strengthened with a Prestressed CFRP Plate J. Deng, M.M.K. Lee and P.Y. Huang	367
Study on Effective Prestress of RC Beam Strengthening with Prestressed FRP X.Y. Guo, P.Y. Huang and G.M. Pan	373
Pretension of Externally Bonded FRP Sheets for Flexural Reinforcement of RC Beams: Methods and Design Equations G. Monti and M.A. Liotta	379
Strengthening of Structures with the CarboStress® System F. Fischli, R. Clénin, A. De Silva and P. Chaemmangkang	387

Ductility

Ductility Behavior of Compression-yielding Reinforced Concrete Beams Y.W. Zhou, Y.F. Wu and J.G. Teng	395
A New Ductility Model for RC/PC Sections Strengthened with or without Bonded FRP Z.G. Guan and J.Z. Li	403
Compression Yielding by SIFCON Block for FRP-reinforced Concrete Beams K. Liu and Y.F. Wu	411
Mechanical Behavior of Mild Steel Compressive Yielding Blocks X.C. Liu, Y.F. Wu, A.Y.T. Leung and J.G. Hou	417

Hybrid Members

The Effect of Core Architecture on the Behaviour of Sandwich Columns under Edgewise Compression Loading T. Omar, T. Aravinthan and G. Van Erp	425
Applications of FRP in Cladding Panels of Buildings T. Sharaf, A. Fam, W. Shawkat and B. Taylor	431
Thermoplastic Composite Structural Insulated Panels (CSIPs) for Building Construction A.S. Vaidya, N. Uddin and U.K. Vaidya	437
Pilot Study on the Horizontal Shear Behaviour of FRP Rubber Isolators T.B. Peng, J.Z. Li and L.C. Fan	443

All FRP Members

On Design and Experimental Verification of Actual Behaviour of Selected All-FRP Structural Components for Civil Engineering J.J. Melcher, M. Karmazinova and M. Filip	453
Shear Deformation Characteristics and Web Crippling of New Hybrid Composite Girders H. Nakamura, K. Maeda, H. Mutsuyoshi and K. Suzukawa	459
Buckling and Reduced Stiffness Criteria for FRP Cylindrical Shells under Compression K. Matsumoto, S. Yamada, H.T. Wang and J.G.A. Croll	465
Radio Frequency Transparent Barriers for Airport Structures: The SAS Project D. Asprone, A. Prota, R. Parretti and A. Nanni	471
Innovative all Composite Multi-Pultrusion Truss Systems – FE Modelling & Behavioural Issues T. Omar, G. Van Erp, T Aravinthan and P. Key	477
Design and Experimental Investigation of Energy Dissipating FRP Box Infill System W.Y. Jung and A.J. Aref	483
Limit Analysis for Orthotropic Composite Laminates A.A. Pisano and P. Fuschi	491
Geometrically Nonlinear Theory of Thin-walled Composite Box Beams T.P. Vo and J. Lee	497
A Study on the Application of Advanced Thermoplastic Composites for use in Building Construction Industry H.K.K. Yeung and R.P Kamineni	503

Field Applications and Case Studies

Long-term Behaviour of a FRP-strengthened Structure: The Case of the Sainte-Émélie-de-l’Énergie Bridge P. Labossière, K.W. Neale, P. Rochette, M. Demers, M. Savard and G. Desgagné	513
Strengthening an Early 20^th Century RC Bridge with FRP (Unidirectional Carbon Fibres) G. Pistone	519
Reinstatement of the Flexural Fatigue Strength of Precast Concrete Link Slabs using CFRP D.L. Beneke and R.J. Feller	527
TFC - FRP Strengthening Solution from FREYSSINET D. Deschamps and T. Wong	533
FRP Application to Remedy As-built Construction Defects D. Choudhuri, A. Bouadi and E. Green	541
CFRP Strengthening of Splice Deficiency A. Bouadi, E. Green and D. Choudhuri	547
Structural Strengthening and Extending Concrete Structure Service Life using FRP and Corrosion Inhibiting Technologies – A Case Study K.Y. Lo, T.H. Yeung, G. Lee, J.S. Wang and S.H. Giam	553
Application and Practice of GFRP Bars in the TBM Launching Shaft of Metro in China M. Li, Y. Cao and H.G. Tang	559
Seismic Rehabilitation of Historical Masonry Vaults using FRPs – A Case Study S.S. Mahini, H.R. Ronagh and A. Eslami	565
Function-integrated GFRP Sandwich Roof Structure T. Keller, Ch. Haas and T. Vallée	571

VOLUME II

Fibre Optic Sensors, Measurement and Nondestructive Evaluation

Smart Composites for Civil Infrastructure Applications K.T. Lau, S.T. Smith, H.Y. Tam and S.L. Ho	579
Fibre Optic Sensing for the Delamination Behaviour of FRP Reinforced Steel Girders S. Yamada, Y. Yoshida, S. Saito, S. Yamada and I. Komiya	587
Stress Analysis of Composite Material Embedded with Optical Fiber Sensor Subjected to Anti-Plane Shear S.C. Her and B.R. Yao	593
Quantifying Strain Variation in FRP Confined Concrete using Digital Image Correlation: Proof-of-concept and Initial Results L. Bisby, W.A. Take and A. Caspary	599
Quantifying Defects and Progression of Damage in FRP Rehabilitation of Concrete through IR Thermography A. Shirazi and V.M. Karbhari	605
Application Properties of Hybrid FRP Reinforcing Rods for Self Diagnosing of Concrete Fracture S.K. Park	611

Durability, Fire and Impact

Durability of FRP Strengthening Systems P. Wilcox, Q. Yang and V.M. Karbhar	619
Experimental Investigation on Durability of FRP Strips Confined Concrete Cylinders under Freeze-thaw Cycles D.Y. Gao, C.C. Li and G.T. Zhao	625
Bonded Fibre Reinforced Polymer Strengthening in a Real Fire T.J. Stratford, M. Gillie and J.F. Chen	631
Flame Retardant Fibre Reinforced Polyester Formulation for Roofing Application R. Vasanthakumari	637
Modeling of Thermo-physical Properties and Thermal Responses for FRP Composites in Fire Y. Bai, T. Keller and T. Vallée	645
The Stress Relaxation of Glass Fibre Composites with Low Velocity Impact Damage Y.J. Tong, L.H. Xu and C.Q. Li	651

Product Development and Testing

Study on the Fabricating and Reshaping Process of a New Kind of FRTP Bar

C. Wang and J.P. Ou

659

Braided Reinforced FRP Rods

C.G. Pereira, R. Fangueiro, S. Jalali, M. Araújo and P.P. Marques

665

Crack Development in CFRP Reinforced Mortar – An Experimental Study

B. Täljsten, K. Orosz and G. Fischer

671

IIFC Working Group: Bond Behaviour of FRP in Structures

Message from the Chairmen of the IIFC Working Group on the

Bond Behaviour of FRP in Structures

J.F. Chen and J.G. Teng

679

Basic Bond Mechanisms: Externally Bonded Sheets/Plates

Behaviour of FRP-to-concrete Interfaces between Two Adjacent Cracks in FRP-Plated Concrete Members: A Numerical Investigation G.M. Chen, J.F. Chen and J.G. Teng	683
Bonding CFRP and SRP to Ultra-High Performance Concrete A. Elmahdy, R. El-Hacha and N.G. Shrive	689
Direct versus Indirect Identification of FRP-to-concrete Interface Relationships C. Faella, E. Martinelli and E. Nigro	697
New Three-parameter Bond Strength Model for Externally Bonded FRP-concrete Interface S.M. Shahidul Islam and Z.S. Wu	703
Bond Stress versus Slip Model for CFRP Plates Bonded to Concrete M.K.Y. Loo, S.J. Foster and S.T. Smith	709
A Quantitative Study on Bond Behavior between Fiber-Reinforced Polymer (FRP) and Concrete Interface using Infra-red Thermography (IRT) C.S. Poon, W.L. Lai, S.C. Kou, W.F. Tsang and C.C. Lai	717
Behaviour of CFRP Sheets Bonded to Historical Masonry R. Capozucca	723

Basic Bond Mechanisms: Internally Embedded Bars, Tendons and Anchors

Comparison of the Interfacial Bond and Slip Behaviour of Steel and FRP Reinforcement M. Hasket, D.J. Oehlers and C. Wu	731
Bond Behaviour and Modeling of Fiber Reinforced Polymer Bars to Concrete under Direct Pullout H.X. Zhang and J. Li	739
Pullout and Bond of Glass Fibre Reinforced Polymer/Steel Wire Composite Rebars in Concrete Q.D. Hao, Y.L. Wang and J.P. Ou	745
Flexural Bonding Characteristics of Newly-developed GFRP Rebar H.S. Oh, J.S. Sim, M.K. Ju and T.S. Kang	753
Mechanical and Bonding Performances of Steel Cable-GFRP Composite Rebar Z.C. Zhang and J.P. Ou	761
Investigation on Bond Performance of the Bond-type Anchorage for CFRP Tendon T.Y. Jiang, Z. Fang and D. Liang	767
Pull-out Tests on FRP Anchors S.J. Kim and S.T. Smith	775

Flexurally-Strengthened Concrete Beams

Hybrid Bonding System for Optimizing Structural Performance of FRP Flexurally Strengthened Concrete Beams J.G. Dai, H. Yokota and T. Ueda	785
Study on Bond Behaviors between CFRP and Concrete in CFRP-strengthened RC Beams X.Y. Lin and S.Y. Cao	793
Numerical Simulation of Debonding Failure of Reinforced Concrete Beams Strengthened with Externally Bonded FRP K. Farah and Y. Sato	799
Investigation of Stress Concentration in Cut-off Zones of Beam Strengthened by Near Surface Mounted FRPs V.H. Nguyen, M. Guadagnini, K. Pilakoutas and V.N. Le	805
Interlaminar Peeling in Concrete Beams Strengthened with CFRP Plates - Experimental Study P. Rusinowski and B. Täljsten	811

Interfacial Stresses

Debonding Shear Stress of Steel Plates with a Fiber Sheet Inserted under a CFRP Strip I. Okura and T. Ishikawa	819
Influence of End Locations of Inserted Glass Fiber Sheet on Debonding Load of CFRP Bonded to Steel Plates T. Ishikawa, K. Komura, I. Okura, S. Yokota and M. Saito	825
Three-Parameter Elastic Foundation Model of FRP Strengthened Concrete Beams J.L. Wang	831
Influence of Local Imperfections on Interface Stresses of RC Beams Strengthened with Hybrid Fiber Sheets L.J. Li, Y.C. Guo, F. Liu, Y. Yang and Z.J. He	837
Numerical Analysis of Interface Stresses of RC Beams Strengthened with Pre-stressed Hybrid CFS-GFS Y.C. Guo, P.Y. Huang, L.J. Li and J. Deng	843
Analytical and Finite Element Study of Cracking and Interfacial Stress Distribution at the Cracked Zone in a Retrofitted RC Beam M.Z. Kabir and A. Hojatkashani	849

Intermediate Crack Induced Debonding

Displacement Induced and Intermediate Crack Debonding in FRP Strengthened One-way Masonry Beams C.R. Willis, C. Wu, R. Seracino and M.C. Griffith	859
Improved IC Debonding Resistance of Embedded NSM FRP Plates M. Haskett, D.J. Oehlers and C. Wu	865
Nonlinear Fracture Mechanics of Flexural-shear Crack Induced Debonding of FRP Strengthened Concrete Beams J.L. Wang and C. Zhang	871
Intermediate Debonding of FRP Strengthened Beams C. Mazzotti and M. Savoia	877
Prediction of Load Carrying Capacity due to Intermediate Crack-induced Debonding in FRP-strengthened Flexural Members H. Said and Z.S. Wu	885
Debonding Failure in FRP-strengthened RC Beams: A Model-based Approach C. Faella, E. Martinelli and E. Nigro	893

Durability, Fatigue and Cyclic Loading

Durability of the Bonding Performance of FRP-concrete Interface Externally Bonded with FRP Composite Sheet L.L. Zhang, L. Zhang and J.X. Ma	901
Analytical Solution of Bond Behavior in Moist Environments for FRP-concrete Joints under Peel Load Z. Ouyang and B. Wan	907
Theoretical Solution for Fatigue Debonding Growth and Fatigue Life Prediction of FRP-concrete Interface H.M. Diab, Z.S. Wu and K. Iwashita	913
FRP-Concrete Bond Behaviour under Cyclic Delamination Force C. Mazzotti and M. Savoia	923

IIFC Working Group: FRP-Strengthened Metallic Structures

Message from the Chairman of the IIFC Working Group on

FRP-Strengthened Metallic Structures

X.L. Zhao

933

Strengthening of Metal Flexural Members

Performance of CFRP Strengthened Lightseel Beams Subjected to End Bearing Forces X.L. Zhao and R. Al-Mahaidi	937
Finite Element Modelling of CFRP-Strengthened Rectangular Steel Tubes Subjected to End Bearing Loads N.D. Fernando, J.G. Teng, T. Yu and X.L. Zhao	943
Strengthening of Steel-Concrete Composite Girders using FRPs: State-of-the-Art N. Ragab, R. El-Hacha and M. Aly	951
Bond Behavior of a CFRP Strengthening System for Steel Structures M. Dawood, M. Guddati and S. Rizkalla	959
Effect of CFRP Reinforcement on CHS Beams in Pure Bending J. Haedir, M.R. Bambach, X.L. Zhao and R.H. Grzebieta	967
Upgrading of Steel Beams using Composite Materials D. Linghoff and M. Al-Emrani	973
An Assessment of the Suitability of Wrought Iron for Strengthening using FRP Composites S.S.J. Moy and H.W.J. Clarke	979

Strengthening of Metal Compression Members and Shells

FRP-stabilised Steel Compression Members K.A. Harries, E. Abraham and A. Peck	987
Control of Overall Buckling of HSS Slender Columns using CFRP Plates A. Shaat and A. Fam	993
Steel Square Hollow Section Short Columns Strengthened with CFRP M.R. Bambach and M. Elchalakani	999
On the use of the EC3 and AISI Specifications to Estimate the Ultimate Load of CFRP-strengthened Cold-formed Steel Lipped Channel Columns N. Silvestre, D. Camotim and B. Young	1005
Elastic Buckling of FRP-strengthened Cylinders with Axisymmetric Imperfections M. Batikha, J.F. Chen and J.M. Rotter	1011

Cyclic Loading and Fatigue

CFRP Reinforcement of Steel Beams Adhesive Cure under Cyclic Load S.S.J. Moy	1019
Environmental Fatigue Test of Bonded Composite Patch Repaired Metallic Structure Y. Okamoto, T. Kamizono, H. Namiki and H. Cai	1025
Strengthening of Old Metallic Structures in Fatigue with CFRP Materials C.S. Hansen, J.W. Schmidt and B. Täljsten	1033
Repair of Fatigue Cracks at Welded Web Gusset Joint using CFRP Strips W. Jiang, H. Nakamura, H. Suzuki, K. Maeda and T. Irube	1039

Analytical and Numerical Modelling

Fracture Mechanics Analysis of Cracked Steel Plates Repaired with Composite Sheets

H.B. Liu, Z.G. Xiao, X.L. Zhao and R. Al-Mahaidi

1047

Control of Interfacial Stresses in Beams Strengthened with Prestressed CFRP Laminates

R. Haghani, M. Al-Emrani and R. Kliger

1053

Numerical and Analytical Investigations on Iron Columns Reinforced by FRP under

Axial Compression

L. Ly, J. Rondal and J.P. Jaspart

1061

IIFC Working Group: FRP Bridge Decks

Message from the Chairman of the IIFC Working Group on

FRP Bridge Decks

T. Keller

1071

Superstructure Behaviour and Development

Dynamic Behavior of an All-FRP Pedestrian Bridge Y. Bai, T. Keller, T. Vallée	1075
Replacing a Composite RC Bridge Deck with an FRP Deck – The Effect on Superstructure Stresses K.A. Harries and J. Moses	1081
Static Behavior of Hybrid FRP-concrete Bridge Superstructure Y.L. Wang, Q.D. Hao and J.P. Ou	1087
Development of a Pedestrian Slab Bridge using GFRP Pultrusion Profiles K. Maeda, H. Nakamura, X. Cui, N. Kitayama and T. Watanabe	1093
A Foam-filled GFRP Bridge Deck G. Zi, J. Jung, B.M. Kim, Y.K. Hwang and Y.H. Lee	1101
Flexural Behavior of Hybrid FRP Girder with Concrete Deck H. Mutsuyoshi, T. Aranvithan, S. Asamoto, A.C. Manalo and K. Suzukawa	1107
Behavioral Characteristics of FRP-Concrete Composite Deck in Negative Moment Zones According to Connection Details S.Y. Park, K. Cho, S.T. Kim, J.R. Cho and B.S. Kim	1113
Flexural Response of Fiber Reinforced Plastic Decks using Higher-order Shear Deformable Plate Theory Y. Kim and J. Lee	1119