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Download this complete Project material titled; Prediction Of Moment Capacity Of Concrete Slabs Singly Reinforced With Carbon Fiber Reinforced Plastics (Cfrp) Using Simulated Annealing with abstract, chapters 1-5, references, and questionnaire. Preview Abstract or chapter one below

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ABSTRACT

Prediction of moment capacity of concrete slabs singly reinforced with carbon fiber reinforced plastics (CFRP) using simulated annealing is looked into. Equations for resistance moment are obtained based on the flexural requirements presented in ACI 440. 1R-06 (2006). These equations are then optimized using the Simulated Annealing (SA) algorithm. The developed algorithm is implemented using Visual Basic for Application (VBA). In addition, identification of design variables, objective function and constraints are also presented. The most important factors which influence the ultimate load carrying capacity of CFRP reinforced concrete structures are- effective depth (d) and breadth (b) of the member, concrete strength () and the material properties of the CFRP reinforcement. Thus, the ultimate moment of resistance based on concrete failure obtained for a CFRP singly reinforced concrete section is , this is 22.4% lower than the predicted in the code formulation.

 

 

TABLE OF CONTENTS

Title Page – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – i Declaration – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – ii
Certification – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – iii Acknowledgement- – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – iv Abstract – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – -v Table of Content – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – — – – – – – – – – – vi
List of Tables – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – x
List of Figures – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – xi Notations – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – -xii 1.0 INTRODUCTION – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 1
1.1 Background – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – — 1
– – – – – – – – – – – – – – –
viii
1.2 Statement of the Problem- – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 3
1.3 Justification of Study – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 4 1.4 Aim and Objectives – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 4
1.5 Scope and limitations – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 5
2.0 LITERATURE REVIEW- – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 7
2.1 Introduction – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 7 2.2 History of FRP Composites – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 8
2.3 FRP Bars – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 10
2.3.1 Mechanical and Physical Properties of FRP Bars (Lofgren, 2005)- – – – – – – – – – – 11 2.4 Use of FRP in Reinforced Concrete – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 13
2.4.1 Analytical Studies- – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 13 2.4.2 Experimental Studies- – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 19 2.5 Optimization of Reinforced Concrete Structures by Simulated Annealing – – – 20 2.5.1 Work Done on Optimization of CFRP Reinforced Concrete Structures- – – – – – – – 22
2.5.2 Simulated Annealing Background- – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 23
– – – – – – – – – – – – – – –
ix
2.6 Flexural Analysis of CFRP RC Slabs to Obtain Resistance Moment Equations – – 23 2.6.1 Simplified Expressions Recommended by ACI 440.1R-06- – – – – – – – – – – – – – – – – 23 2.6.2 Failure Categories of CFRP Reinforced Concrete Slabs- – – – – – – – – – – – – – – – – – – – 26
3.0 METHODOLOGY – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 34
3.1 Simulated Annealing Background- – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 34 3.2 Basic Elements of the Optimization- – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 35 3.3 Advantages and Reasons for Using SA- – – – – – – – – – – – – – 38 3.4 Visual Basic for Application (VAB)- – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 39 3.4.1 Reasons for Using VBA- – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 39 3.4.2 Disadvantages of Visual Basic- – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 40 3.5 Formulation of Objective Function – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 40 3.5.1 Transformation of Constrained Optimization to an Unconstrained Optimization- – 40 3.6 Formulation of Constraints – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 42 3.6.1 Strength of CFRP Reinforced Concrete in Uni-axial Tension- – – – – – – – – – – – – – 42
– – – – – – – – – – – – – – –
x
3.6.2 Constraints on Critical Volume- – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 44 3.6.3 Constraints on Aspect Ratio- – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 45 3.6.4 Constraints on Ultimate Moment- – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 46 3.6.5 Constraints on Tension CFRP – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 46 3.6.6 Constraints on Shear Strength – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 47 3.6.7 Constraints on Area and Spacing of Stirrups- – – – – – – – – – – – – – – – – – – – – – – – – – – – 48 3.6.8 Constraint for Limiting Span/Depth Ratio for Deflection Control- – – – – – – – – – – 49 3.6.9 Constraints on Design Variables- – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 50 3.7 Stress in the CFRP – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 51 3.8 Working Procedure of the Algorithm – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 52 3.9 Stopping Conditions – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 53 4.0 RESULTS AND DISCUSION – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – -55 4.1 Input Parameters (Assumed Values) – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 55 4.2 Simulated Annealing Input Parameters – – – – – – – – – – – – – – – – – – – – – – – – – – 57
– – – – – – – – – – – – – – –
xi
5.0 SUMMARY, CONCLUSIONS AND RECOMMENDATIONS – – – – – – – – – 64 5.1 Summary – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 64 5.2 Conclusions – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 64 5.3 Recommendation and Suggestions – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 66 REFERENCES – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 68 APPENDIX – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 76 Compressed Simulated Annealing VBA Code. – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 85 LIST OF TABLES Table 2.1: Advantages and Disadvantages of FRP – – – – – – – – – – – – – – – 9 Table 2.2: Physical Properties of Fiber – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 11 Table 2.3: Coefficients of Thermal Expansion for Reinforcing Bars – – – – – – – – – – – – – – – 12 Table 2.4: Typical Tensile Properties of Reinforcing FRP Bars – – – – – – – – – – – – – – – 12 Table 2.5: Chronological Development of Documents for FRP – – – – – – – – – – – – – – – 19 Table 2.6: Environmental Reduction Factors for Various FRP Bars – – – – – – – – – – – – – – 27
Table 2.7: Experimental Moment Capacity by Other Researchers Compare with
– – – – – – – – – – – – – – –
xii
Models – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 33 Table 4.1: Limiting Values of Assumed Variables – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 58 Table 4.2: Optimal Moment Capacity Results Using Simulated Annealing – – – – – – – 60

 

Project Topics

 

CHAPTER ONE

INTRODUCTION
1.1Background
Since the 1970s, researchers have been motivated to investigate alternative solutions to overcome the problem of corrosion phenomenon of concrete structures reinforced with steel (Nawy et al., 1977). Though many solutions have come into action, the use of non-metallic materials became one of the promising alternative solutions. Fiber reinforced plastic (FRP) materials are lightweight, thermally non-conductive, exhibit high tensile strength, and have been reported (Nawy et al., 1977) to be noncorrosive in nature when compared with conventional steel reinforcement; these composites have been suggested as suitable reinforcement for concrete structures instead of steel. FRP composites are very easy to shape and form, which is always not possible with other high strength materials. FRP composites are anisotropic and possess good strength along the fiber length, but reduced strength across the fiber axis (Benmokrane et al., 2010,). The ACI 440 1R-06, (2006) allows the use of CFRP bars as main reinforcement for concrete structures such as bridge decks, floor slabs and wall type structures (abutments, stems and wing walls). In these members, flexural strength is provided by the longitudinal reinforcement and shear strength is provided by the concrete only.
The tensile properties of CFRP reinforcing bars range from 450 to 3500 /2 and from 38,000 to 300,000 /2 in terms of Young’s modulus and 0.8% to 4.0% in terms of failure strains (Clarke, and O’ Regan, 1995). Tensile strength is also influenced by the diameter of the reinforcement, however similar effects do not exist in the case of conventional steel reinforcement (Achillides, 1997).
The use of CFRP reinforcements, in lieu of conventional steel reinforcements requires better understanding under various loading and performance conditions (Benmokrane et al., 2010,). Considerable researches have been carried out mainly on CFRP reinforced concrete specimens under monotonically increasing load (Sivagamasundari and Kumaran, 2008). Only limited research works have been carried out on CFRP reinforced concrete specimens under pulsating or repeated loading conditions (Sivagamasundari and Kumaran, 2008).
This work presents the Prediction of moment capacity of concrete slabs singly reinforced with carbon fiber reinforced plastics (CFRP) using simulated annealing by way of simulation using a formulated computer application which finds the optimum value of the objective function — the optimal moment capacity (), as modeled using the nominal moment equations in the ACI 440 1R-06, (2006) code. The optimum resistance moment of CFRP reinforced concrete sections is then
2
obtained from .
The parameters that affect the resistance moment of CFRP reinforced concrete slabs include the flexural strength of members, cross sectional properties, geometric and material properties of reinforcing CFRP bars. Among all these properties, the member’s effective depth, d, breadth, b, concrete compressive strength, ′, and CFRP bar diameter, , are dealt with as the random variables that affect the moment resistance of CFRP reinforced concrete slabs while CFRP reinforcement ratio, is treated as a deterministic design variable in the assessment.
Equations based on the ACI 440 1R-06 (2006) are modeled to predict the nominal strength in flexure of CFRP reinforced concrete slabs. Thus, the simulation involves an optimization problem that maximizes the objective function and predicts the resistance moment of CFRP reinforced slabs. Unlike other optimization problems, here the objective function is considered as the maximization of resistance moment rather than the reduction of cost. The algorithm developed for the optimization is adopted from the method of Simulated Annealing and it is executed using Visual
Basic for Applications, VBA.
1.2Statement of the Problem
Concrete structures face major problems from the deterioration and corrosion of the reinforcing steel. Retrofitting and rehabilitation, instead of replacement, are needed to increase the ultimate strength for those inadequate concrete structures. One of the innovative technologies to strengthen the concrete structures is to use fiber reinforced polymers (FRP). Recently the interest in the application of FRP in reinforced concrete structures has been increasing (Chen and Chung, 1996).
Most of the work done on CFRP are significantly due to its attractive properties, such as high tensile strength, lightweight, corrosion resistance and are concentrated on the retrofitting of reinforced concrete beams and columns (Chen and Chung, 1996). However, very limited tests have been conducted to study the flexural behavior of reinforced concrete slabs strengthened internally by this composite material (Chen and Chung, 1996).
1.3Justification of Study
This work is considered because, asides the well-recognized advantages that CFRP strengthening systems possess, there are also some important doubts about using it; bearing in mind that CFRPs are new materials and not so widely used, there is a need to determine the optimum resistance moment of CFRP in singly reinforced concrete slab sections though a proposal has been given in ISIS (2011).
3
1.4Aim And Objectives
1.4.1Aim
This work aims at predicting the moment capacity of concrete slabs singly reinforced with carbon fiber reinforced plastics (CFRP) using simulated annealing which can be safely used for their designs.
1.4.2Objectives
The objectives of this work are:
i. To derive an optimum value for the resistance moment of singly
reinforced concrete slab sections reinforced with CFRP.
ii. Study the bending behavior of slabs reinforced with CFRP using relevant a simulation technique for the purpose of predicting the optimum resistance moment of CFRP in singly reinforced concrete slab sections which will satisfy the design requirements of ACI 440 1R-06, (2006).
1.5Scope And Limitations
1.5.1Scope
The scope of this work is limited to improving the understanding of the bending behavior of CFRP singly reinforced concrete slabs, obtaining the optimum resistance moment in accordance with ACI 440 1R-06, (2006), design requirements and for their practical applications when CFRP bars are used as reinforcing bars.
1.5.2Limitations
The limitations of this work are:
4
i. CFRP has not been widely used because of its low ductility as depicted by its elastic modulus.
ii. CFRP bars when loaded in tension, exhibit linear stress-strain behavior up to rupture.
iii. There is no yield point and associated plateau to provide a ductile response when used as tensile reinforcement in concrete, thus they fail abruptly. iv.The absence of plasticity in CFRP materials implies that under-reinforced flexural sections experience a sudden tensile rupture instead of a gradual yielding, as in the case with steel reinforcement. Thus, the concrete crushing failure mode of an over-reinforced member is more desirable, due to enhanced energy absorption and greater deformability leading to a more gradual failure mode. Member recovery is essentially elastic with little or no energy dissipation resulting from large deformations.
v. There have been attempts to improve the ductility of CFRP with little or no success. (Michael, 1997).
vi. The optimum results of a simulated annealing algorithm depends largely on the anneal start temperature and number of iterations.
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