Finite Element Modeling Of Reinforced Concrete Structures Strengthened .
FINITE ELEMENT MODELING OFREINFORCED CONCRETE STRUCTURESSTRENGTHENED WITH FRP LAMINATESFinal ReportSPR 316Oregon Department of Transportation
FINITE ELEMENT MODELINGOF REINFORCED CONCRETE STRUCTURESSTRENGTHENED WITH FRP LAMINATESFinal ReportSPR 316byDamian Kachlakev, PhDCivil and Environmental Engineering Department,California Polytechnic State University, San Luis Obispo, CA 93407andThomas Miller, PhD, PE; Solomon Yim, PhD, PE;Kasidit Chansawat; Tanarat PotisukCivil, Construction and Environmental Engineering Department,Oregon State University, Corvallis, OR 97331forOregon Department of TransportationResearch Group200 Hawthorne SE, Suite B-240Salem, OR 97301-5192andFederal Highway Administration400 Seventh Street SWWashington, DC 20590May 2001
Technical Report Documentation Page1. Report No.2. Government Accession No.3. Recipient’s Catalog No.FHWA-OR-RD-01-XX4. Title and Subtitle5. Report DateFinite Element Modeling of Reinforced Concrete Structures Strengthened withFRP Laminates – Final ReportMay 20016. Performing Organization Code7.Author(s)8. Performing Organization Report No.Damian Kachlakev, PhD, Civil and Environmental Engineering Department,California Polytechnic State University, San Luis Obispo, CA 93407andThomas Miller, PhD, PE; Solomon Yim, PhD, PE; Kasidit Chansawat; TanaratPotisuk, Civil, Construction and Environmental Engineering Department,Oregon State University, Corvallis, OR 973319. Performing Organization Name and Address10. Work Unit No. (TRAIS)Oregon Department of TransportationResearch Group200 Hawthorne Ave. SE, Suite B-240Salem, OR 97301-519211. Contract or Grant No.SPR 31612. Sponsoring Agency Name and Address13. Type of Report and Period CoveredOregon Department of TransportationResearch Groupand200 Hawthorne Ave. SE, Suite B-240Salem, OR 97301-5192Final ReportFederal Highway Administration400 Seventh Street SWWashington, DC 2059014. Sponsoring Agency Code15. Supplementary Notes16. AbstractLinear and non-linear finite element method models were developed for a reinforced concrete bridge that hadbeen strengthened with fiber reinforced polymer composites. ANSYS and SAP2000 modeling software wereused; however, most of the development effort used ANSYS. The model results agreed well with measurementsfrom full-size laboratory beams and the actual bridge. As expected, a comparison using model results showedthat the structural behavior of the bridge before and after strengthening was nearly the same for legal loads.Guidelines for developing finite element models for reinforced concrete bridges were discussed.17. Key Words18. Distribution Statementfinite element method, FEM, model, ANSYS, SAP2000,bridge, reinforced concrete, fiber reinforced, FRP,composite, strengthening, strain19. Security Classification (of this report)UnclassifiedTechnical Report Form DOT F 1700.7 (8-72)Available from NTIS20. Security Classification (of this page)21. No. of PagesUnclassified22. Price111 appendicesReproduction of completed page authorizediÅ Printed on recycled paper
SI* (MODERN METRIC) CONVERSION FACTORSAPPROXIMATE CONVERSIONS TO SI UNITSSymbolWhen You KnowMultiply ByTo FindAPPROXIMATE CONVERSIONS FROM SI UNITSSymbolSymbolWhen You KnowLENGTHMultiply ByTo kilometerskmkmkilometers0.621milesmiin2square inches645.2millimeters squaredmm2mm2millimeters squared0.0016square inchesin2ft2square feet0.093meters squaredm2m2meters squared10.764square feetft2yd2square yards0.836meters hakm2kilometers squared0.386square milesmi2mi2square miles2.59kilometers squaredkm2mLmilliliters0.034fluid ouncesfl ozLAREAAREAVOLUMEVOLUMEfl ozgalft3yd3fluid .264gallonsgal3meters cubed35.315cubic feetft33mmeters cubed1.308cubic bMgmegagrams1.102short tons (2000 lb)Tm3cubic feet0.028meters cubedmcubic yards0.765meters cubedm3MASS3NOTE: Volumes greater than 1000 L shall be shown in m hort tons (2000 lb)0.907megagramsMgTEMPERATURE (exact) CCelsius temperature1.8 32Fahrenheit FTEMPERATURE (exact) FFahrenheittemperature5(F-32)/9Celsius temperature C* SI is the symbol for the International System of Measurement(4-7-94 jbp)ii
ACKNOWLEDGEMENTSThe authors would like to thank Mr. Steven Soltesz, Project Manager, and Dr. Barnie Jones,Research Manager, of the ODOT Research Group for their valuable suggestions and manycontributions to this project.DISCLAIMERThis document is disseminated under the sponsorship of the Oregon Department ofTransportation and the United States Department of Transportation in the interest of informationexchange. The State of Oregon and the United States Government assume no liability of itscontents or use thereof.The contents of this report reflect the views of the author(s) who are solely responsible for thefacts and accuracy of the data presented herein. The contents do not necessarily reflect theofficial policies of the Oregon Department of Transportation or the United States Department ofTransportation.The State of Oregon and the United States Government do not endorse products ofmanufacturers. Trademarks or manufacturers’ names appear herein only because they areconsidered essential to the object of this document.This report does not constitute a standard, specification, or regulation.iii
FINITE ELEMENT MODELINGOF REINFORCED CONCRETE STRUCTURESSTRENGTHENED WITH FRP LAMINATESTABLE OF CONTENTS1.0 INTRODUCTION. 11.1 IMPORTANCE OF FRP RETROFIT FOR REINFORCED CONCRETESTRUCTURES . 11.2 OBJECTIVES . 21.3 SCOPE . 21.4 COMPUTER MODELING OF FRP-STRENGTHENED STRUCTURES . 22.0 MODELING FULL-SIZE REINFORCED CONCRETE BEAMS . 52.1 FULL-SIZE BEAMS . 52.2 ELEMENT TYPES . 62.2.1 Reinforced Concrete. 62.2.2 FRP Composites. 72.2.3 Steel Plates . 72.3 MATERIAL PROPERTIES. 82.3.1 Concrete . 82.3.2 Steel Reinforcement and Steel Plates. 142.3.3 FRP Composites. 152.4 GEOMETRY. 172.5 FINITE ELEMENT DISCRETIZATION. 252.6 LOADING AND BOUNDARY CONDITIONS. 29NONLINEAR SOLUTION. 312.7.1 Load Stepping and Failure Definition for FE Models. 322.8 COMPUTATION RESOURCES. 343.0 RESULTS FROM FINITE ELEMENT ANALYSIS OF FULL-SIZE BEAMS. 353.1 LOAD-STRAIN PLOTS. 353.1.1 Tensile Strain in Main Steel Reinforcing. 353.1.2 Tensile Strain in FRP Composites . 413.1.3 Compressive Strain in Concrete. 433.2 LOAD-DEFLECTION PLOTS. 463.3 FIRST CRACKING LOADS. 513.4 EVOLUTION OF CRACK PATTERNS. 513.5 LOADS AT FAILURE . 573.6 CRACK PATTERNS AT FAILURE. 593.7 MAXIMUM STRESSES IN FRP COMPOSITES . 623.7.1 Comparisons to Parallel Research. 63v
4.0 ANALYSIS OF HORSETAIL CREEK BRIDGE . 654.1 INTRODUCTION. 654.2 BRIDGE DESCRIPTION AND FIELD DATA. 654.2.1 Horsetail Creek Bridge. 654.2.2 Loading conditions. 654.2.3 Field data . 674.3 FEM MODEL . 684.3.1 Materials properties. 684.3.2 Bridge modeling and analysis assumptions . 694.3.3 Finite element discretization . 704.4 COMPARISONS OF ANSYS AND SAP 2000 PREDICTIONS WITH FIELD DATA 764.4.1 Analysis of responses to empty truck load. 874.4.2 Analysis of responses to full truck load . 874.4.3 Analysis of responses in general . 884.5 ANALYSIS OF THE UNSTRENGTHENED HORSETAIL CREEK BRIDGE. 895.0 CONCLUSIONS AND RECOMMENDATIONS . 915.1 SUMMARY AND CONCLUSIONS. 915.1.1 Conclusions for finite element models of the full-scale beams . 915.1.2 Conclusions for finite element models of the Horsetail Creek Bridge . 915.2 RECOMMENDATIONS . 925.2.1 Recommended FE modeling and analysis procedure . 925.2.2 Recommended FE modeling procedure for reinforced concrete beams . 935.2.3 Recommended FE modeling procedure for the reinforced concrete bridge . 946.0 REFERENCES . 95APPENDICESAPPENDIX A: STRUCTURAL DETAILS OF THE HORSETAIL CREEK BRIDGEAPPENDIX B: CONFIGURATION OF DUMP TRUCK FOR STATIC TESTS ON THEHORSETAIL CREEK BRIDGEAPPENDIX C: LOCATIONS OF FIBER OPTIC SENSORS ON THE HORSETAIL CREEKBRIDGELIST OF FIGURESFigure 2.1: Solid65 – 3-D reinforced concrete solid (ANSYS 1998) . 6Figure 2.2: Link8 – 3-D spar (ANSYS 1998). 7Figure 2.3: Solid46 – 3-D layered structural solid (ANSYS 1998) . 7Figure 2.4: Solid45 – 3-D solid (ANSYS 1998). 8Figure 2.5: Typical uniaxial compressive and tensile stress-strain curve for concrete (Bangash 1989). 9Figure 2.6: Simplified compressive uniaxial stress-strain curve for concrete. 12Figure 2.7: 3-D failure surface for concrete (ANSYS 1998) . 13Figure 2.8: Stress-strain curve for steel reinforcement . 14Figure 2.9: Schematic of FRP composites (Gibson 1994, Kaw 1997) . 15Figure 2.10: Stress-strain curves for the FRP composites in the direction of the fibers . 16Figure 2.11: Typical beam dimensions (not to scale) . 18vi
Figure 2.12: Use of a quarter beam model (not to scale) . 18Figure 2.13: Typical steel reinforcement locations (not to scale) (McCurry and Kachlakev 2000) . 19Figure 2.14: Typical steel reinforcement for a quarter beam model. Reinforcement at the common faces wasentered into the model as half the actual diameter. (not to scale) . 20Figure 2.15: Element connectivity: (a) concrete solid and link elements; (b) concrete solid and FRP layeredsolid elements . 21Figure 2.16: FRP reinforcing schemes (not to scale): (a) Flexure Beam; (b) Shear Beam; (c) Flexure/ShearBeam (McCurry and Kachlakev 2000). 22Figure 2.17: Modified dimensions of FRP reinforcing for strengthened beam models (not to scale): (a) FlexureBeam; (b) Shear Beam; (c) Flexure/Shear Beam. 24Figure 2.18: Convergence study on plain concrete beams: (a), (b), (c), and (d) show the comparisons betweenANSYS and SAP2000 for the tensile and compressive stresses; and strain and deflection at centermidspan of the beams, respectively. . 26Figure 2.19: Results from convergence study: (a) deflection at midspan; (b) compressive stress in concrete; (c)tensile stress in main steel reinforcement . 27Figure 2.20: FEM discretization for a quarter of Control Beam . 28Figure 2.21: Loading and support locations (not to scale) (McCurry and Kachlakev 2000) . 29Figure 2.22: Steel plate with line support . 30Figure 2.23: Loading and boundary conditions (not to scale). 30Figure 2.24: Displacements of model: (a) without rotation of steel plate (b) with rotation of steel plate. 31Figure 2.25: Newton-Raphson iterative solution (2 load increments) (ANSYS 1998). 32Figure 2.26: Reinforced concrete behavior in Flexure/Shear Beam . 33Figure 3.1: Selected strain gauge locations (not to scale) . 35Figure 3.2: Load-tensile strain plot for #7 steel rebar in Control Beam. 36Figure 3.3: Load-tensile strain plot for #7 steel rebar in Flexure Beam. 37Figure 3.4: Load-tensile strain plot for #7 steel rebar in Shear Beam. 37Figure 3.5: Load-tensile strain plot for #6 steel rebar in Flexure/Shear Beam (Beam did not fail during actualloading.). 38Figure 3.6: Variation of tensile force in steel for reinforced Concrete Beam: (a) typical cracking; (b) crackedconcrete section; (c) bond stresses acting on reinforcing bar; (d) variation of tensile force in steel (Nilson1997). 39Figure 3.7: Development of tensile force in the steel for finite element models: (a) typical smeared cracking; (b)cracked concrete and steel rebar elements; (c) profile of tensile force in steel elements. 40Figure 3.8: Load versus tensile strain in the CFRP for the Flexure Beam . 41Figure 3.9: Load versus tensile strain in the GFRP for the Shear Beam. 42Figure 3.10: Load versus tensile strain in the CFRP for the Flexure/Shear Beam (Actual beam did not fail). 42Figure 3.11: Load-compressive strain plot for concrete in Control Beam . 43Figure 3.12: Load-compressive strain plot for concrete in Flexure Beam . 44Figure 3.13: Load-compressive strain plot for concrete in Shear Beam . 45Figure 3.14: Load-compressive strain plot for concrete in Flexure/Shear Beam (Actual beam did not fail.). 45Figure 3.15: Load-deflection plot for Control Beam . 46Figure 3.16: Load-deflection plot for Flexure Beam . 47Figure 3.17: Load-deflection plot for Shear Beam. 48Figure 3.18: Load-deflection plot for Flexure/Shear Beam (Actual beam did not fail) . 49Figure 3.19: Load-deflection plots for the four beams based on measurements (Beam No.4 did not fail)(Kachlakev and McCurry 2000) . 50Figure 3.20: Load-deflection plots for the four beams based on ANSYS finite element models . 50Figure 3.21: Integration points in concrete solid element (ANSYS 1998) . 52Figure 3.22: Cracking sign (ANSYS 1998) . 52Figure 3.23: Coordinate system for finite element models . 52Figure 3.24: Typical cracking signs occurring in finite element models: (a) flexural cracks; (b) compressivecracks; (c) diagonal tensile cracks . 53Figure 3.25: Evolution of crack patterns: (a) Control Beam; (b) Flexure Beam. 55Figure 3.26: Evolution of crack patterns (Continued): (a) Shear Beam; (b) Flexure/Shear Beam. 56Figure 3.27: Toughening mechanisms: (a) aggregate bridging; (b) crack-face friction (Shah, et al. 1995) . 57vii
Figure 3.27 (continued): Toughening mechanisms: (c) crack tip blunted by void; (d) crack branching (Shah, etal. 1995) . 58Figure 3.28: Stress-strain curve for reinforcing steel: (a) as determined by tension test; (b) idealized (Spiegeland Limbrunner 1998). 58Figure 3.29: Crack patterns at failure: (a) Control Beam; (b) Flexure Beam. 60Figure 3.30: Crack patterns at failure: (a) Shear Beam; (b) Flexure/Shear Beam. 61Figure 3.31: Locations of maximum stresses in FRP composites: (a) Flexure Beam; (b) Shear Beam . 62Figure 3.31 (continued): Locations of maximum stresses in FRP composites: (c) Flexure/Shear Beam. 63Figure 4.1: Locations of truck on the Horsetail Creek Bridge . 66Figure 4.1 (continued): Locations of truck on the Horsetail Creek Bridge . 67Figure 4.2: Locations of the monitored beams on the Horsetail Creek Bridge . 68Figure 4.3: Truck load simplification: (a) and (b) show configurations of the dump truck and the simplifiedtruck, respectively. 69Figure 4.4: Linear truck load distribution . 70Figure 4.5: Steel reinforcement details: (a) and (b) show typical reinforcement in the transverse and longitudinalbeams at the middle and at the end of the bridge, respectively . 71Figure 4.5 (continued): Steel reinforcement details: (c) and (d) show typical reinforcement in the bridge deck atboth ends of the bridge . 72Figure 4.5 (continued): Steel reinforcement details: (e) shows typical reinforcement in the columns . 73Figure 4.6: FE bridge model with FRP laminates: (a), (b), and (c) show the FRP strengthening in differentviews. 74Figure 4.7: Boundary conditions for the bridge . 75Figure 4.8: Fiber optic sensor (plan view) . 77Figure 4.9: Comparison of strains from Field Tests 1 and 2, ANSYS, and SAP2000 for the empty truck at theseven Locations: (a) - (d) show the strains on the transverse beam. 79Figure 4.9 (continued): Comparison of strains from Field Tests 1 and 2, ANSYS, and SAP2000 for the emptytruck at the seven Locations: (e)-(h) show the strains on the longitudinal beam. 80Figure 4.10: Comparison of strains from Field Tests 1 and 2, ANSYS, and SAP2000 for the empty truck at theseven locations: (a) - (d) show the strains on the transverse beam . 81Figure 4.10 (continued): Comparison of strains from Field Tests 1 and 2, ANSYS, and SAP2000 for the emptytruck at the seven locations: (e)-(h) show the strains on the longitudinal beam. . 82Figure 4.11: Comparison of strain versus distance of the single axle from the end of the bridge deck for FieldTests 1 and 2, ANSYS, and SAP2000 based on an empty truck: (a) - (d) show the strains on the transversebeam . 83Figure 4.11 (continued): Comparison of strain versus distance of the single axle from the end of the bridge deckfor Field Tests 1 and 2, ANSYS, and SAP2000 based on an empty truck: (e)-(h) show the strains on thelongitudinal beam . 84Figure 4.12: Comparison of strain versus distance of the single axle from the end of the bridge deck for FieldTests 1 and 2, ANSYS, and SAP2000 based on a full truck: (a) - (d) show the strains on the transversebeam . 85Figure 4.12 (continued): Comparison of strain versus distance of the single axle from the end of the bridge deckfor Field Tests 1 and 2, ANSYS, and SAP2000 based on a full truck: (e)-(h) show the strains on thelongitudinal beam . 86viii
LIST OF TABLESTable 2.1: Summary of material properties for concrete . 10Table 2.2: Summary of material properties for FRP composites (Kachlakev and McCurry 2000) . 17Table 2.3: Numbers of elements used for finite element models . 28Table 2.4: Summary of load step sizes for Flexure/Shear Beam model . 33Table 3.1: Comparisons between experimental and ANSYS first cracking loads. 51Table 3.2: Comparisons between experimental ultimate loads and ANSYS final loads . 57Table 3.3: Maximum stresses developed in the FRP composites and the corresponding ultimate tensilestrengths . 62Table 4.1: Material properties (Kachlakev and McCurry, 2000; Fyfe Corp., 1998). 68Table 4.2: Summary of the number of elements used in the bridge model. 70Table 4.3: Differences between ANSYS and SAP2000 bridge models. 76Table 4.6: Comparison of strains on the transverse beam between FE bridge models with and withoutFRP strengthening. 89Table 4.7: Comparison of strains on the longitudinal beam between FE bridge models with and withoutFRP strengthening. 90ix
1.01.1INTRODUCTIONIMPORTANCE OF FRP RETROFIT FOR REINFORCEDCONCRETE STRUCTURESA large number of reinforced concrete bridges in the U.S. are structurally deficient by today’sstandards. The main contributing factors are changes in their use, an increase in loadrequirements, or corrosion deterioration due to exposure to an aggressive environment. In orderto preserve those bridges, rehabilitation is often considered essential to maintain their capabilityand to increase public safety (Seible, et al. 1995; Kachlakev 1998).In the last decade, fiber reinforced polymer (FRP) composites have been used for strengtheningstructural members of reinforced concrete bridges. Many researchers have found that FRPcomposite strengthening is an efficient, reliable, and cost-effective means of rehabilitation(Marshall and Busel 1996; Steiner 1996; Tedesco, et al. 1996; Kachlakev 1998). Currently inthe U.S.,
that the structural behavior of the bridge before and after strengthening was nearly the same for legal loads. Guidelines for developing finite element models for reinforced concrete bridges were discussed. 17. Key Words finite element method, FEM, model, ANSYS, SAP2000, bridge, reinforced concrete, fiber reinforced, FRP,
Finite element analysis DNV GL AS 1.7 Finite element types All calculation methods described in this class guideline are based on linear finite element analysis of three dimensional structural models. The general types of finite elements to be used in the finite element analysis are given in Table 2. Table 2 Types of finite element Type of .
element type. This paper presents a comprehensive study of finite element modeling techniques for solder joint fatigue life prediction. Several guidelines are recommended to obtain consistent and accurate finite element results. Introduction Finite element method has been used for a long time to study the solder joint fatigue life in thermal .
1 Overview of Finite Element Method 3 1.1 Basic Concept 3 1.2 Historical Background 3 1.3 General Applicability of the Method 7 1.4 Engineering Applications of the Finite Element Method 10 1.5 General Description of the Finite Element Method 10 1.6 Comparison of Finite Element Method with Other Methods of Analysis
Finite Element Method Partial Differential Equations arise in the mathematical modelling of many engineering problems Analytical solution or exact solution is very complicated Alternative: Numerical Solution – Finite element method, finite difference method, finite volume method, boundary element method, discrete element method, etc. 9
3.2 Finite Element Equations 23 3.3 Stiffness Matrix of a Triangular Element 26 3.4 Assembly of the Global Equation System 27 3.5 Example of the Global Matrix Assembly 29 Problems 30 4 Finite Element Program 33 4.1 Object-oriented Approach to Finite Element Programming 33 4.2 Requirements for the Finite Element Application 34 4.2.1 Overall .
2.7 The solution of the finite element equation 35 2.8 Time for solution 37 2.9 The finite element software systems 37 2.9.1 Selection of the finite element softwaresystem 38 2.9.2 Training 38 2.9.3 LUSAS finite element system 39 CHAPTER 3: THEORETICAL PREDICTION OF THE DESIGN ANALYSIS OF THE HYDRAULIC PRESS MACHINE 3.1 Introduction 52
Figure 3.5. Baseline finite element mesh for C-141 analysis 3-8 Figure 3.6. Baseline finite element mesh for B-727 analysis 3-9 Figure 3.7. Baseline finite element mesh for F-15 analysis 3-9 Figure 3.8. Uniform bias finite element mesh for C-141 analysis 3-14 Figure 3.9. Uniform bias finite element mesh for B-727 analysis 3-15 Figure 3.10.
Click 500 series – Customizable devices built on our Click 500 platform This user guide covers the Click 500 series. For the Click 100–400 series, please see the Click 100–400 Series User Guide. Using this Manual This manual is divided into two parts: Part I: Introduction to the Click Series – This part contains information common to the Click line, beginning with basic module .
