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mkThis page intentionally left blank Actuarial Mathematics for Life Contingent Risks How can actuaries best equip themselves for the products and risk structures of the future? In this new textbook, three leaders in actuarial science give a modern perspective on life contingencies. The book begins traditionally, covering actuarial models and theory, and emphasizing practical applications using computational techniques. The authors then develop a more contemporary outlook, introducing multiple state models, emerging cash ? ws and embedded options. Using spreadsheet-style software, the book presents large-scale, realistic examples. Over 150 exercises and solutions teach skills in simulation and projection through computational practice. Balancing rigour with intuition, and emphasizing applications, this textbook is ideal not only for university courses, but also for individuals preparing for professional actuarial examinations and quali? ed actuaries wishing to renew and update their skills.International Series on Actuarial Science Christopher Daykin, Independent Consultant and Actuary Angus Macdonald, Heriot-Watt University The International Series on Actuarial Science, published by Cambridge University Press in conjunction with the Institute of Actuaries and the Faculty of Actuaries, contains textbooks for students taking courses in or related to actuarial science, as well as more advanced works designed for continuing professional development or for describing and synthesizing research.The series is a vehicle for publishing books that re? ect changes and developments in the curriculum, that encourage the introduction of courses on actuarial science in universities, and that show how actuarial science can be used in all areas where there is long-term ? nancial risk. ACTUARIAL MATHEMATICS FOR LIFE CONTINGENT RISKS D AV I D C . M . D I C K S O N University of Melbourne M A RY R . H A R D Y University of Waterloo, Ontario H O WA R D R . WAT E R S Heriot-Watt Univ ersity, Edinburgh CAMBRIDGE UNIVERSITY PRESSCambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo, Delhi, Dubai, Tokyo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www. cambridge. org Information on this title: www. cambridge. org/9780521118255  © D. C. M. Dickson, M. R. Hardy and H. R. Waters 2009 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press.First published in print format 2009 ISBN-13 ISBN-13 978-0-511-65169-4 978-0-521-11825-5 eBook (NetLibrary) Hardback Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. To Carolann, Vivien and Phelim Contents Preface page xiv 1 Introduction to life insurance 1 1. 1 Summary 1 1. 2 Background 1 1. 3 Life insurance and annuity contracts 3 1. 3. 1 Introduction 3 1. 3. Traditional insurance contracts 4 1. 3. 3 Modern insurance contracts 6 1. 3. 4 Distribution methods 8 1. 3. 5 Underwriting 8 1. 3. 6 Premiums 10 1. 3. 7 Life annuities 11 1. 4 Other insurance contracts 12 1. 5 Pension bene? ts 12 1. 5. 1 De? ned bene? t and de? ned contribution pensions 13 1. 5. 2 De? ned bene? t pension design 13 1. 6 Mutual and proprietary insurers 14 1. 7 Typical problems 14 1. 8 Notes and further reading 15 1. 9 Exercises 15 2 Survival models 17 2. 1 Summary 17 2. 2 The future lifetime random variable 17 2. 3 The force of mortality 21 2. 4 Actuarial notation 26 2. Mean and standard deviation of Tx 29 2. 6 Curtate future lifetime 32 2. 6. 1 Kx and ex 32 vii viii 2. 6. 2 Contents The complete and curtate expected fu ture ? lifetimes, ex and ex 2. 7 Notes and further reading 2. 8 Exercises Life tables and selection 3. 1 Summary 3. 2 Life tables 3. 3 Fractional age assumptions 3. 3. 1 Uniform distribution of deaths 3. 3. 2 Constant force of mortality 3. 4 National life tables 3. 5 Survival models for life insurance policyholders 3. 6 Life insurance underwriting 3. 7 Select and ultimate survival models 3. 8 Notation and formulae for select survival models 3. Select life tables 3. 10 Notes and further reading 3. 11 Exercises Insurance bene? ts 4. 1 Summary 4. 2 Introduction 4. 3 Assumptions 4. 4 Valuation of insurance bene? ts ? 4. 4. 1 Whole life insurance: the continuous case, Ax 4. 4. 2 Whole life insurance: the annual case, Ax (m) 4. 4. 3 Whole life insurance: the 1/mthly case, Ax 4. 4. 4 Recursions 4. 4. 5 Term insurance 4. 4. 6 Pure endowment 4. 4. 7 Endowment insurance 4. 4. 8 Deferred insurance bene? ts (m) ? 4. 5 Relating Ax , Ax and Ax 4. 5. 1 Using the uniform distribution of deaths assu mption 4. 5. 2 Using the claims acceleration approach 4. Variable insurance bene? ts 4. 7 Functions for select lives 4. 8 Notes and further reading 4. 9 Exercises Annuities 5. 1 Summary 5. 2 Introduction 3 4 34 35 36 41 41 41 44 44 48 49 52 54 56 58 59 67 67 73 73 73 74 75 75 78 79 81 86 88 89 91 93 93 95 96 101 101 102 107 107 107 5 Contents 5. 3 5. 4 Review of annuities-certain Annual life annuities 5. 4. 1 Whole life annuity-due 5. 4. 2 Term annuity-due 5. 4. 3 Whole life immediate annuity 5. 4. 4 Term immediate annuity 5. 5 Annuities payable continuously 5. 5. 1 Whole life continuous annuity 5. 5. 2 Term continuous annuity 5. 6 Annuities payable m times per year 5. . 1 Introduction 5. 6. 2 Life annuities payable m times a year 5. 6. 3 Term annuities payable m times a year 5. 7 Comparison of annuities by payment frequency 5. 8 Deferred annuities 5. 9 Guaranteed annuities 5. 10 Increasing annuities 5. 10. 1 Arithmetically increasing annuities 5. 10. 2 Geometrically increasing annu ities 5. 11 Evaluating annuity functions 5. 11. 1 Recursions 5. 11. 2 Applying the UDD assumption 5. 11. 3 Woolhouse’s formula 5. 12 Numerical illustrations 5. 13 Functions for select lives 5. 14 Notes and further reading 5. 15 Exercises Premium calculation 6. 1 Summary 6. 2 Preliminaries 6. Assumptions 6. 4 The present value of future loss random variable 6. 5 The equivalence principle 6. 5. 1 Net premiums 6. 6 Gross premium calculation 6. 7 Pro? t 6. 8 The portfolio percentile premium principle 6. 9 Extra risks 6. 9. 1 Age rating 6. 9. 2 Constant addition to  µx 6. 9. 3 Constant multiple of mortality rates ix 108 108 109 112 113 114 115 115 117 118 118 119 120 121 123 125 127 127 129 130 130 131 132 135 136 137 137 142 142 142 143 145 146 146 150 154 162 165 165 165 167 6 x Contents 6. 10 Notes and further reading 6. 11 Exercises Policy values 7. 1 Summary 7. 2 Assumptions 7. Policies with annual cash ? ows 7. 3. 1 The future loss random variable 7. 3. 2 Policy values for policies with annual cash ? ows 7. 3. 3 Recursive formulae for policy values 7. 3. 4 Annual pro? t 7. 3. 5 Asset shares 7. 4 Policy values for policies with cash ? ows at discrete intervals other than annually 7. 4. 1 Recursions 7. 4. 2 Valuation between premium dates 7. 5 Policy values with continuous cash ? ows 7. 5. 1 Thiele’s differential equation 7. 5. 2 Numerical solution of Thiele’s differential equation 7. 6 Policy alterations 7. 7 Retrospective policy value 7. 8 Negative policy values 7. Notes and further reading 7. 10 Exercises Multiple state models 8. 1 Summary 8. 2 Examples of multiple state models 8. 2. 1 The alive–dead model 8. 2. 2 Term insurance with increased bene? t on accidental death 8. 2. 3 The permanent disability model 8. 2. 4 The disability income insurance model 8. 2. 5 The joint life and last survivor model 8. 3 Assumptions and notation 8. 4 Formulae for probabilities 8. 4. 1 Kolmogorov’s forward equations 8. 5 Numerical evaluat ion of probabilities 8. 6 Premiums 8. 7 Policy values and Thiele’s differential equation 8. 7. 1 The disability income model 8. 7. Thiele’s differential equation – the general case 169 170 176 176 176 176 176 182 191 196 200 203 204 205 207 207 211 213 219 220 220 220 230 230 230 230 232 232 233 234 235 239 242 243 247 250 251 255 7 8 Contents 8. 8 8. 9 Multiple decrement models Joint life and last survivor bene? ts 8. 9. 1 The model and assumptions 8. 9. 2 Joint life and last survivor probabilities 8. 9. 3 Joint life and last survivor annuity and insurance functions 8. 9. 4 An important special case: independent survival models 8. 10 Transitions at speci? ed ages 8. 11 Notes and further reading 8. 12 Exercises Pension mathematics 9. Summary 9. 2 Introduction 9. 3 The salary scale function 9. 4 Setting the DC contribution 9. 5 The service table 9. 6 Valuation of bene? ts 9. 6. 1 Final salary plans 9. 6. 2 Career average earnings plans 9. 7 Funding plans 9. 8 Not es and further reading 9. 9 Exercises Interest rate risk 10. 1 Summary 10. 2 The yield curve 10. 3 Valuation of insurances and life annuities 10. 3. 1 Replicating the cash ? ows of a traditional non-participating product 10. 4 Diversi? able and non-diversi? able risk 10. 4. 1 Diversi? able mortality risk 10. 4. 2 Non-diversi? able risk 10. 5 Monte Carlo simulation 10. Notes and further reading 10. 7 Exercises Emerging costs for traditional life insurance 11. 1 Summary 11. 2 Pro? t testing for traditional life insurance 11. 2. 1 The net cash ? ows for a policy 11. 2. 2 Reserves 11. 3 Pro? t measures 11. 4 A further example of a pro? t test xi 256 261 261 262 264 270 274 278 279 290 290 290 291 294 297 306 306 312 314 319 319 326 326 326 330 332 334 335 336 342 348 348 353 353 353 353 355 358 360 9 10 11 xii Contents 11. 5 Notes and further reading 11. 6 Exercises Emerging costs for equity-linked insurance 12. 1 Summary 12. 2 Equity-linked insurance 12. 3 Deterministic pro? testing fo r equity-linked insurance 12. 4 Stochastic pro? t testing 12. 5 Stochastic pricing 12. 6 Stochastic reserving 12. 6. 1 Reserving for policies with non-diversi? able risk 12. 6. 2 Quantile reserving 12. 6. 3 CTE reserving 12. 6. 4 Comments on reserving 12. 7 Notes and further reading 12. 8 Exercises Option pricing 13. 1 Summary 13. 2 Introduction 13. 3 The ‘no arbitrage’ assumption 13. 4 Options 13. 5 The binomial option pricing model 13. 5. 1 Assumptions 13. 5. 2 Pricing over a single time period 13. 5. 3 Pricing over two time periods 13. 5. 4 Summary of the binomial model option pricing technique 13. The Black–Scholes–Merton model 13. 6. 1 The model 13. 6. 2 The Black–Scholes–Merton option pricing formula 13. 7 Notes and further reading 13. 8 Exercises Embedded options 14. 1 Summary 14. 2 Introduction 14. 3 Guaranteed minimum maturity bene? t 14. 3. 1 Pricing 14. 3. 2 Reserving 14. 4 Guaranteed minimum death bene? t 14. 4. 1 Pricing 14. 4. 2 Reserving 369 369 374 374 374 375 384 388 390 390 391 393 394 395 395 401 401 401 402 403 405 405 405 410 413 414 414 416 427 428 431 431 431 433 433 436 438 438 440 12 13 14 Contents 14. 5 Pricing methods for embedded options 14. 6 Risk management 14. 7 Emerging costs 14. Notes and further reading 14. 9 Exercises A Probability theory A. 1 Probability distributions A. 1. 1 Binomial distribution A. 1. 2 Uniform distribution A. 1. 3 Normal distribution A. 1. 4 Lognormal distribution A. 2 The central limit theorem A. 3 Functions of a random variable A. 3. 1 Discrete random variables A. 3. 2 Continuous random variables A. 3. 3 Mixed random variables A. 4 Conditional expectation and conditional variance A. 5 Notes and further reading B Numerical techniques B. 1 Numerical integration B. 1. 1 The trapezium rule B. 1. 2 Repeated Simpson’s rule B. 1. 3 Integrals over an in? nite interval B. Woolhouse’s formula B. 3 Notes and further reading C Simulation C. 1 The inverse transf orm method C. 2 Simulation from a normal distribution C. 2. 1 The Box–Muller method C. 2. 2 The polar method C. 3 Notes and further reading References Author index Index xiii 444 447 449 457 458 464 464 464 464 465 466 469 469 470 470 471 472 473 474 474 474 476 477 478 479 480 480 481 482 482 482 483 487 488 Preface Life insurance has undergone enormous change in the last two to three decades. New and innovative products have been developed at the same time as we have seen vast increases in computational power.In addition, the ? eld of ? nance has experienced a revolution in the development of a mathematical theory of options and ? nancial guarantees, ? rst pioneered in the work of Black, Scholes and Merton, and actuaries have come to realize the importance of that work to risk management in actuarial contexts. Given the changes occurring in the interconnected worlds of ? nance and life insurance, we believe that this is a good time to recast the mathematics of life continge nt risk to be better adapted to the products, science and technology that are relevant to current and future actuaries.In this book we have developed the theory to measure and manage risks that are contingent on demographic experience as well as on ? nancial variables. The material is presented with a certain level of mathematical rigour; we intend for readers to understand the principles involved, rather than to memorize methods or formulae. The reason is that a rigorous approach will prove more useful in the long run than a short-term utilitarian outlook, as theory can be adapted to changing products and technology in ways that techniques, without scienti? c support, cannot.We start from a traditional approach, and then develop a more contemporary perspective. The ? rst seven chapters set the context for the material, and cover traditional actuarial models and theory of life contingencies, with modern computational techniques integrated throughout, and with an emphasis on the prac tical context for the survival models and valuation methods presented. Through the focus on realistic contracts and assumptions, we aim to foster a general business awareness in the life insurance context, at the same time as we develop the mathematical tools for risk management in that context. iv Preface xv In Chapter 8 we introduce multiple state models, which generalize the life– death contingency structure of previous chapters. Using multiple state models allows a single framework for a wide range of insurance, including bene? ts which depend on health status, on cause of death bene? ts, or on two or more lives. In Chapter 9 we apply the theory developed in the earlier chapters to problems involving pension bene? ts. Pension mathematics has some specialized concepts, particularly in funding principles, but in general this chapter is an application of the theory in the preceding chapters.In Chapter 10 we move to a more sophisticated view of interest rate models and intere st rate risk. In this chapter we explore the crucially important difference between diversi? able and non-diversi? able risk. Investment risk represents a source of non-diversi? able risk, and in this chapter we show how we can reduce the risk by matching cash ? ows from assets and liabilities. In Chapter 11 we continue the cash ? ow approach, developing the emerging cash ? ows for traditional insurance products. One of the liberating aspects of the computer revolution for actuaries is that we are no longer required to summarize complex bene? s in a single actuarial value; we can go much further in projecting the cash ? ows to see how and when surplus will emerge. This is much richer information that the actuary can use to assess pro? tability and to better manage portfolio assets and liabilities. In Chapter 12 we repeat the emerging cash ? ow approach, but here we look at equity-linked contracts, where a ? nancial guarantee is commonly part of the contingent bene? t. The real risks for such products can only be assessed taking the random variation in potential outcomes into consideration, and we demonstrate this with Monte Carlo simulation of the emerging cash ? ws. The products that are explored in Chapter 12 contain ? nancial guarantees embedded in the life contingent bene? ts. Option theory is the mathematics of valuation and risk management of ? nancial guarantees. In Chapter 13 we introduce the fundamental assumptions and results of option theory. In Chapter 14 we apply option theory to the embedded options of ? nancial guarantees in insurance products. The theory can be used for pricing and for determining appropriate reserves, as well as for assessing pro? tability.The material in this book is designed for undergraduate and graduate programmes in actuarial science, and for those self-studying for professional actuarial exams. Students should have suf? cient background in probability to be able to calculate moments of functions of one or two random vari ables, and to handle conditional expectations and variances. We also assume familiarity with the binomial, uniform, exponential, normal and lognormal distributions. Some of the more important results are reviewed in Appendix A. We also assume xvi Preface that readers have completed an introductory level course in the mathematics of ? ance, and are aware of the actuarial notation for annuities-certain. Throughout, we have opted to use examples that liberally call on spreadsheetstyle software. Spreadsheets are ubiquitous tools in actuarial practice, and it is natural to use them throughout, allowing us to use more realistic examples, rather than having to simplify for the sake of mathematical tractability. Other software could be used equally effectively, but spreadsheets represent a fairly universal language that is easily accessible. To keep the computation requirements reasonable, we have ensured hat every example and exercise can be completed in Microsoft Excel, without needing an y VBA code or macros. Readers who have suf? cient familiarity to write their own code may ? nd more ef? cient solutions than those that we have presented, but our principle was that no reader should need to know more than the basic Excel functions and applications. It will be very useful for anyone working through the material of this book to construct their own spreadsheet tables as they work through the ? rst seven chapters, to generate mortality and actuarial functions for a range of mortality models and interest rates.In the worked examples in the text, we have worked with greater accuracy than we record, so there will be some differences from rounding when working with intermediate ? gures. One of the advantages of spreadsheets is the ease of implementation of numerical integration algorithms. We assume that students are aware of the principles of numerical integration, and we give some of the most useful algorithms in Appendix B. The material in this book is appropriate for tw o one-semester courses. The ? rst seven chapters form a fairly traditional basis, and would reasonably constitute a ? st course. Chapters 8–14 introduce more contemporary material. Chapter 13 may be omitted by readers who have studied an introductory course covering pricing and delta hedging in a Black–Scholes–Merton model. Chapter 9, on pension mathematics, is not required for subsequent chapters, and could be omitted if a single focus on life insurance is preferred. Acknowledgements Many of our students and colleagues have made valuable comments on earlier drafts of parts of the book. Particular thanks go to Carole Bernard, Phelim Boyle, Johnny Li, Ana Maria Mera, Kok Keng Siaw and Matthew Till.The authors gratefully acknowledge the contribution of the Departments of Statistics and Actuarial Science, University of Waterloo, and Actuarial Mathematics and Statistics, Heriot-Watt University, in welcoming the non-resident Preface xvii authors for short visits to w ork on this book. These visits signi? cantly shortened the time it has taken to write the book (to only one year beyond the original deadline). David Dickson University of Melbourne Mary Hardy University of Waterloo Howard Waters Heriot-Watt University 1 Introduction to life insurance 1. Summary Actuaries apply scienti? c principles and techniques from a range of other disciplines to problems involving risk, uncertainty and ? nance. In this chapter we set the context for the mathematics of later chapters, by describing some of the background to modern actuarial practice in life insurance, followed by a brief description of the major types of life insurance products that are sold in developed insurance markets. Because pension liabilities are similar in many ways to life insurance liabilities, we also describe some common pension bene? ts.We give examples of the actuarial questions arising from the risk management of these contracts. How to answer such questions, and solve the result ing problems, is the subject of the following chapters. 1. 2 Background The ? rst actuaries were employed by life insurance companies in the early eighteenth century to provide a scienti? c basis for managing the companies’ assets and liabilities. The liabilities depended on the number of deaths occurring amongst the insured lives each year. The modelling of mortality became a topic of both commercial and general scienti? interest, and it attracted many signi? cant scientists and mathematicians to actuarial problems, with the result that much of the early work in the ? eld of probability was closely connected with the development of solutions to actuarial problems. The earliest life insurance policies provided that the policyholder would pay an amount, called the premium, to the insurer. If the named life insured died during the year that the contract was in force, the insurer would pay a predetermined lump sum, the sum insured, to the policyholder or his or her estate. So, t he ? st life insurance contracts were annual contracts. Each year the premium would increase as the probability of death increased. If the insured life became very ill at the renewal date, the insurance might not be renewed, in which case 1 2 Introduction to life insurance no bene? t would be paid on the life’s subsequent death. Over a large number of contracts, the premium income each year should approximately match the claims outgo. This method of matching income and outgo annually, with no attempt to smooth or balance the premiums over the years, is called assessmentism.This method is still used for group life insurance, where an employer purchases life insurance cover for its employees on a year-to-year basis. The radical development in the later eighteenth century was the level premium contract. The problem with assessmentism was that the annual increases in premiums discouraged policyholders from renewing their contracts. The level premium policy offered the policyholde r the option to lock-in a regular premium, payable perhaps weekly, monthly, quarterly or annually, for a number of years.This was much more popular with policyholders, as they would not be priced out of the insurance contract just when it might be most needed. For the insurer, the attraction of the longer contract was a greater likelihood of the policyholder paying premiums for a longer period. However, a problem for the insurer was that the longer contracts were more complex to model, and offered more ? nancial risk. For these contracts then, actuarial techniques had to develop beyond the year-to-year modelling of mortality probabilities. In particular, it became necessary to incorporate ? nancial considerations into the modelling of income and outgo.Over a one-year contract, the time value of money is not a critical aspect. Over, say, a 30-year contract, it becomes a very important part of the modelling and management of risk. Another development in life insurance in the nineteent h century was the concept of insurable interest. This was a requirement in law that the person contracting to pay the life insurance premiums should face a ? nancial loss on the death of the insured life that was no less than the sum insured under the policy. The insurable interest requirement disallowed the use of insurance as a form of gambling on the lives of public ? ures, but more importantly, removed the incentive for a policyholder to hasten the death of the named insured life. Subsequently, insurance policies tended to be purchased by the insured life, and in the rest of this book we use the convention that the policyholder who pays the premiums is also the life insured, whose survival or death triggers the payment of the sum insured under the conditions of the contract. The earliest studies of mortality include life tables constructed by John Graunt and Edmund Halley. A life table summarizes a survival model by specifying the proportion of lives that are expected to survive to each age.Using London mortality data from the early seventeenth century, Graunt proposed, for example, that each new life had a probability of 40% of surviving to age 16, and a probability of 1% of surviving to age 76. Edmund Halley, famous for his astronomical calculations, used mortality data from the city of Breslau in the late seventeenth century as the basis for his life table, which, like Graunt’s, was constructed by 1. 3 Life insurance and annuity contracts 3 proposing the average (‘medium’ in Halley’s phrase) proportion of survivors to each age from an arbitrary number of births.Halley took the work two steps further. First, he used the table to draw inference about the conditional survival probabilities at intermediate ages. That is, given the probability that a newborn life survives to each subsequent age, it is possible to infer the probability that a life aged, say, 20, will survive to each subsequent age, using the condition that a life ag ed zero survives to age 20. The second major innovation was that Halley combined the mortality data with an assumption about interest rates to ? nd the value of a whole life annuity at different ages.A whole life annuity is a contract paying a level sum at regular intervals while the named life (the annuitant) is still alive. The calculations in Halley’s paper bear a remarkable similarity to some of the work still used by actuaries in pensions and life insurance. This book continues in the tradition of combining models of mortality with models in ? nance to develop a framework for pricing and risk management of long-term policies in life insurance. Many of the same techniques are relevant also in pensions mathematics. However, there have been many changes since the ? st long-term policies of the late eighteenth century. 1. 3 Life insurance and annuity contracts 1. 3. 1 Introduction The life insurance and annuity contracts that were the object of study of the early actuaries w ere very similar to the contracts written up to the 1980s in all the developed insurance markets. Recently, however, the design of life insurance products has radically changed, and the techniques needed to manage these more modern contracts are more complex than ever. The reasons for the changes include: †¢ Increased interest by the insurers in offering combined savings and insurance †¢ †¢ †¢ products. The original life insurance products offered a payment to indemnify (or offset) the hardship caused by the death of the policyholder. Many modern contracts combine the indemnity concept with an opportunity to invest. More powerful computational facilities allow more complex products to be modelled. Policyholders have become more sophisticated investors, and require more options in their contracts, allowing them to vary premiums or sums insured, for example. More competition has led to insurers creating increasingly complex products in order to attract more busines s.The risk management techniques in ? nancial products have also become increasingly complex, and insurers have offered some bene? ts, particularly 4 Introduction to life insurance ? nancial guarantees, that require sophisticated techniques from ? nancial engineering to measure and manage the risk. In the remainder of this section we describe some of the most important modern insurance contracts, which will later be used as examples in the book. Different countries have different names and types of contracts; we have tried to cover the major contract types in North America, the United Kingdom and Australia.The basic transaction of life insurance is an exchange; the policyholder pays premiums in return for a later payment from the insurer which is life contingent, by which we mean that it depends on the death or survival or possibly the state of health of the policyholder. We usually use the term ‘insurance’ when the bene? t is paid as a single lump sum, either on the de ath of the policyholder or on survival to a predetermined maturity date. (In the UK it is common to use the term ‘assurance’ for insurance contracts involving lives, and insurance for contracts involving property. ) An annuity is a bene? in the form of a regular series of payments, usually conditional on the survival of the policyholder. 1. 3. 2 Traditional insurance contracts Term, whole life and endowment insurance are the traditional products, providing cash bene? ts on death or maturity, usually with predetermined premium and bene? t amounts. We describe each in a little more detail here. Term insurance pays a lump sum bene? t on the death of the policyholder, provided death occurs before the end of a speci? ed term. Term insurance allows a policyholder to provide a ? xed sum for his or her dependents in the event of the policyholder’s death.Level term insurance indicates a level sum insured and regular, level premiums. Decreasing term insurance indicates tha t the sum insured and (usually) premiums decrease over the term of the contract. Decreasing term insurance is popular in the UK where it is used in conjunction with a home mortgage; if the policyholder dies, the remaining mortgage is paid from the term insurance proceeds. Renewable term insurance offers the policyholder the option of renewing the policy at the end of the original term, without further evidence of the policyholder’s health status.In North America, Yearly Renewable Term (YRT) insurance is common, under which insurability is guaranteed for some ? xed period, though the contract is written only for one year at a time. 1. 3 Life insurance and annuity contracts 5 Convertible term insurance offers the policyholder the option to convert to a whole life or endowment insurance at the end of the original term, without further evidence of the policyholder’s health status. Whole life insurance pays a lump sum bene? t on the death of the policyholder whenever it occ urs.For regular premium contracts, the premium is often payable only up to some maximum age, such as 80. This avoids the problem that older lives may be less able to pay the premiums. Endowment insurance offers a lump sum bene? t paid either on the death of the policyholder or at the end of a speci? ed term, whichever occurs ? rst. This is a mixture of a term insurance bene? t and a savings element. If the policyholder dies, the sum insured is paid just as under term insurance; if the policyholder survives, the sum insured is treated as a maturing investment. Endowment insurance is obsolete in many jurisdictions.Traditional endowment insurance policies are not currently sold in the UK, but there are large portfolios of policies on the books of UK insurers, because until the late 1990s, endowment insurance policies were often used to repay home mortgages. The policyholder (who is the home owner) paid interest on the mortgage loan, and the principal was paid from the proceeds on the e ndowment insurance, either on the death of the policyholder or at the ? nal mortgage repayment date. Endowment insurance policies are becoming popular in developing nations, particularly for ‘micro-insurance’ where the amounts involved are small.It is hard for small investors to achieve good rates of return on investments, because of heavy expense charges. By pooling the death and survival bene? ts under the endowment contract, the policyholder gains on the investment side from the resulting economies of scale, and from the investment expertise of the insurer. With-pro? t insurance Also part of the traditional design of insurance is the division of business into ‘with-pro? t’ (also known, especially in North America, as ‘participating’, or ‘par’ business), and ‘without pro? t’ (also known as ‘non-participating’ or ‘non-par’). Under with-pro? t arrangements, the pro? s earned on the invested pr emiums are shared with the policyholders. In North America, the with-pro? t arrangement often takes the form of cash dividends or reduced premiums. In the UK and in Australia the traditional approach is to use the pro? ts to increase the sum insured, through bonuses called ‘reversionary bonuses’and ‘terminal bonuses’. Reversionary bonuses are awarded during the term of the contract; once a reversionary bonus is awarded it is guaranteed. Terminal bonuses are awarded when the policy matures, either through the death of the insured, or when an endowment policy reaches the end of the term.Reversionary bonuses 6 Introduction to life insurance Table 1. 1. Year 1 2 3 . . . Bonus on original sum insured 2% 2. 5% 2. 5% . . . Bonus on bonus 5% 6% 6% . . . Total bonus 2000. 00 4620. 00 7397. 20 . . . may be expressed as a percentage of the total of the previous sum insured plus bonus, or as a percentage of the original sum insured plus a different percentage of the pr eviously declared bonuses. Reversionary and terminal bonuses are determined by the insurer based on the investment performance of the invested premiums. For example, suppose an insurance is issued with sum insured $100 000.At the end of the ? rst year of the contract a bonus of 2% on the sum insured and 5% on previous bonuses is declared; in the following two years, the rates are 2. 5% and 6%. Then the total guaranteed sum insured increases each year as shown in Table 1. 1. If the policyholder dies, the total death bene? t payable would be the original sum insured plus reversionary bonuses already declared, increased by a terminal bonus if the investment returns earned on the premiums have been suf? cient. With-pro? ts contracts may be used to offer policyholders a savings element with their life insurance.However, the traditional with-pro? t contract is designed primarily for the life insurance cover, with the savings aspect a secondary feature. 1. 3. 3 Modern insurance contracts I n recent years insurers have provided more ? exible products that combine the death bene? t coverage with a signi? cant investment element, as a way of competing for policyholders’savings with other institutions, for example, banks or open-ended investment companies (e. g. mutual funds in North America, or unit trusts in the UK). Additional ?exibility also allows policyholders to purchase less insurance when their ? ances are tight, and then increase the insurance coverage when they have more money available. In this section we describe some examples of modern, ? exible insurance contracts. Universal life insurance combines investment and life insurance. The policyholder determines a premium and a level of life insurance cover. Some 1. 3 Life insurance and annuity contracts 7 of the premium is used to fund the life insurance; the remainder is paid into an investment fund. Premiums are ? exible, as long as they are suf? cient to pay for the designated sum insured under the ter m insurance part of the contract.Under variable universal life, there is a range of funds available for the policyholder to select from. Universal life is a common insurance contract in North America. Unitized with-pro? t is a UK insurance contract; it is an evolution from the conventional with-pro? t policy, designed to be more transparent than the original. Premiums are used to purchase units (shares) of an investment fund, called the with-pro? t fund. As the fund earns investment return, the shares increase in value (or more shares are issued), increasing the bene? t entitlement as reversionary bonus.The shares will not decrease in value. On death or maturity, a further terminal bonus may be payable depending on the performance of the with-pro? t fund. After some poor publicity surrounding with-pro? t business, and, by association, unitized with-pro? t business, these product designs were withdrawn from the UK and Australian markets by the early 2000s. However, they will remain i mportant for many years as many companies carry very large portfolios of with-pro? t (traditional and unitized) policies issued during the second half of the twentieth century.Equity-linked insurance has a bene? t linked to the performance of an investment fund. There are two different forms. The ? rst is where the policyholder’s premiums are invested in an open-ended investment company style account; at maturity, the bene? t is the accumulated value of the premiums. There is a guaranteed minimum death bene? t payable if the policyholder dies before the contract matures. In some cases, there is also a guaranteed minimum maturity bene? t payable. In the UK and most of Europe, these are called unit-linked policies, and they rarely carry a guaranteed maturity bene? . In Canada they are known as segregated fund policies and always carry a maturity guarantee. In the USA these contracts are called variable annuity contracts; maturity guarantees are increasingly common for these pol icies. (The use of the term ‘annuity’ for these contracts is very misleading. The bene? ts are designed with a single lump sum payout, though there may be an option to convert the lump sum to an annuity. ) The second form of equity-linked insurance is the Equity-Indexed Annuity (EIA) in the USA.Under an EIA the policyholder is guaranteed a minimum return on their premium (minus an initial expense charge). At maturity, the policyholder receives a proportion of the return on a speci? ed stock index, if that is greater than the guaranteed minimum return. EIAs are generally rather shorter in term than unit-linked products, with seven-year policies being typical; variable annuity contracts commonly 8 Introduction to life insurance have terms of twenty years or more. EIAs are much less popular with consumers than variable annuities. 1. 3. 4 Distribution methods Most people ? d insurance dauntingly complex. Brokers who connect individuals to an appropriate insurance product ha ve, since the earliest times, played an important role in the market. There is an old saying amongst actuaries that ‘insurance is sold, not bought’, which means that the role of an intermediary in persuading potential policyholders to take out an insurance policy is crucial in maintaining an adequate volume of new business. Brokers, or other ? nancial advisors, are often remunerated through a commission system. The commission would be speci? ed as a percentage of the premium paid.Typically, there is a higher percentage paid on the ? rst premium than on subsequent premiums. This is referred to as a front-end load. Some advisors may be remunerated on a ? xed fee basis, or may be employed by one or more insurance companies on a salary basis. An alternative to the broker method of selling insurance is direct marketing. Insurers may use television advertising or other telemarketing methods to sell direct to the public. The nature of the business sold by direct marketing meth ods tends to differ from the broker sold business. For example, often the sum insured is smaller.The policy may be aimed at a niche market, such as older lives concerned with insurance to cover their own funeral expenses (called pre-need insurance in the USA). Another mass marketed insurance contract is loan or credit insurance, where an insurer might cover loan or credit card payments in the event of the borrower’s death, disability or unemployment. 1. 3. 5 Underwriting It is important in modelling life insurance liabilities to consider what happens when a life insurance policy is purchased. Selling life insurance policies is a competitive business and life insurance companies (also known as life of? es) are constantly considering ways in which to change their procedures so that they can improve the service to their customers and gain a commercial advantage over their competitors. The account given below of how policies are sold covers some essential points but is necessaril y a simpli? ed version of what actually happens. For a given type of policy, say a 10-year term insurance, the life of? ce will have a schedule of premium rates. These rates will depend on the size of the policy and some other factors known as rating factors.An applicant’s risk level is assessed by asking them to complete a proposal form giving information on 1. 3 Life insurance and annuity contracts 9 relevant rating factors, generally including their age, gender, smoking habits, occupation, any dangerous hobbies, and personal and family health history. The life insurer may ask for permission to contact the applicant’s doctor to enquire about their medical history. In some cases, particularly for very large sums insured, the life insurer may require that the applicant’s health be checked by a doctor employed by the insurer.The process of collecting and evaluating this information is called underwriting. The purpose of underwriting is, ? rst, to classify potenti al policyholders into broadly homogeneous risk categories, and secondly to assess what additional premium would be appropriate for applicants whose risk factors indicate that standard premium rates would be too low. On the basis of the application and supporting medical information, potential life insurance policyholders will generally be categorized into one of the following groups: †¢ Preferred lives have very low mortality risk based on the standard infor- mation.The preferred applicant would have no recent record of smoking; no evidence of drug or alcohol abuse; no high-risk hobbies or occupations; no family history of disease known to have a strong genetic component; no adverse medical indicators such as high blood pressure or cholesterol level or body mass index. The preferred life category is common in North America, but has not yet caught on elsewhere. In other areas there is no separation of preferred and normal lives. †¢ Normal lives may have some higher rated ri sk factors than preferred lives (where this category exists), but are still insurable at standard rates.Most applicants fall into this category. †¢ Rated lives have one or more risk factors at raised levels and so are not acceptable at standard premium rates. However, they can be insured for a higher premium. An example might be someone having a family history of heart disease. These lives might be individually assessed for the appropriate additional premium to be charged. This category would also include lives with hazardous jobs or hobbies which put them at increased risk. †¢ Uninsurable lives have such signi? ant risk that the insurer will not enter an insurance contract at any price. Within the ? rst three groups, applicants would be further categorized according to the relative values of the various risk factors, with the most fundamental being age, gender and smoking status. Most applicants (around 95% for traditional life insurance) will be accepted at preferred or standard rates for the relevant risk category. Another 2–3% may be accepted at non-standard rates 10 Introduction to life insurance because of an impairment, or a dangerous occupation, leaving around 2–3% who ill be refused insurance. The rigour of the underwriting process will depend on the type of insurance being purchased, on the sum insured and on the distribution process of the insurance company. Term insurance is generally more strictly underwritten than whole life insurance, as the risk taken by the insurer is greater. Under whole life insurance, the payment of the sum insured is certain, the uncertainty is in the timing. Under, say, 10-year term insurance, it is assumed that the majority of contracts will expire with no death bene? t paid.If the underwriting is not strict there is a risk of adverse selection by policyholders – that is, that very high-risk individuals will buy insurance in disproportionate numbers, leading to excessive losses. Since high sum insured contracts carry more risk than low sum insured, high sums insured would generally trigger more rigorous underwriting. The marketing method also affects the level of underwriting. Often, direct marketed contracts are sold with relatively low bene? t levels, and with the attraction that no medical evidence will be sought beyond a standard questionnaire.The insurer may assume relatively heavy mortality for these lives to compensate for potential adverse selection. By keeping the underwriting relatively light, the expenses of writing new business can be kept low, which is an attraction for high-volume, low sum insured contracts. It is interesting to note that with no third party medical evidence the insurer is placing a lot of weight on the veracity of the policyholder. Insurers have a phrase for this – that both insurer and policyholder may assume ‘utmost good faith’ or ‘uberrima ? es’ on the part of the other side of the contract. In practi ce, in the event of the death of the insured life, the insurer may investigate whether any pertinent information was withheld from the application. If it appears that the policyholder held back information, or submitted false or misleading information, the insurer may not pay the full sum insured. 1. 3. 6 Premiums A life insurance policy may involve a single premium, payable at the outset of the contract, or a regular series of premiums payable provided the policyholder survives, perhaps with a ? ed end date. In traditional contracts the regular premium is generally a level amount throughout the term of the contract; in more modern contracts the premium might be variable, at the policyholder’s discretion for investment products such as equity-linked insurance, or at the insurer’s discretion for certain types of term insurance. Regular premiums may be paid annually, semi-annually, quarterly, monthly or weekly. Monthly premiums are common as it is convenient for policyho lders to have their outgoings payable with approximately the same frequency as their income. . 3 Life insurance and annuity contracts 11 An important feature of all premiums is that they are paid at the start of each period. Suppose a policyholder contracts to pay annual premiums for a 10-year insurance contract. The premiums will be paid at the start of the contract, and then at the start of each subsequent year provided the policyholder is alive. So, if we count time in years from t = 0 at the start of the contract, the ? rst premium is paid at t = 0, the second is paid at t = 1, and so on, to the tenth premium paid at t = 9.Similarly, if the premiums are monthly, then the ? rst monthly instalment will be paid at t = 0, and the ? nal premium will be paid at the start 11 of the ? nal month at t = 9 12 years. (Throughout this book we assume that all 1 months are equal in length, at 12 years. ) 1. 3. 7 Life annuities Annuity contracts offer a regular series of payments. When an annui ty depends on the survival of the recipient, it is called a ‘life annuity’. The recipient is called an annuitant. If the annuity continues until the death of the annuitant, it is called a whole life annuity.If the annuity is paid for some maximum period, provided the annuitant survives that period, it is called a term life annuity. Annuities are often purchased by older lives to provide income in retirement. Buying a whole life annuity guarantees that the income will not run out before the annuitant dies. Single Premium Deferred Annuity (SPDA) Under an SPDA contract, the policyholder pays a single premium in return for an annuity which commences payment at some future, speci? ed date. The annuity is ‘life contingent’, by which we mean the annuity is paid only if the policyholder survives to the payment dates.If the policyholder dies before the annuity commences, there may be a death bene? t due. If the policyholder dies soon after the annuity commences, the re may be some minimum payment period, called the guarantee period, and the balance would be paid to the policyholder’s estate. Single Premium Immediate Annuity (SPIA) This contract is the same as the SPDA, except that the annuity commences as soon as the contract is effected. This might, for example, be used to convert a lump sum retirement bene? t into a life annuity to supplement a pension.As with the SPDA, there may be a guarantee period applying in the event of the early death of the annuitant. Regular Premium Deferred Annuity (RPDA) The RPDA offers a deferred life annuity with premiums paid through the deferred period. It is otherwise the same as the SPDA. Joint life annuity A joint life annuity is issued on two lives, typically a married couple. The annuity (which may be single premium or regular 12 Introduction to life insurance premium, immediate or deferred) continues while both lives survive, and ceases on the ? rst death of the couple.Last survivor annuity A last survivor annuity is similar to the joint life annuity, except that payment continues while at least one of the lives survives, and ceases on the second death of the couple. Reversionary annuity A reversionary annuity is contingent on two lives, usually a couple. One is designated as the annuitant, and one the insured. No annuity bene? t is paid while the insured life survives. On the death of the insured life, if the annuitant is still alive, the annuitant receives an annuity for the remainder of his or her life. 1. Other insurance contracts The insurance and annuity contracts described above are all contingent on death or survival. There are other life contingent risks, in particular involving shortterm or long-term disability. These are known as morbidity risks. Income protection insurance When a person becomes sick and cannot work, their income will, eventually, be affected. For someone in regular employment, the employer may cover salary for a period, but if the sickness continu es the salary will be decreased, and ultimately will stop being paid at all. For someone who is elf-employed, the effects of sickness on income will be immediate. Income protection policies replace at least some income during periods of sickness. They usually cease at retirement age. Critical illness insurance Some serious illnesses can cause signi? cant expense at the onset of the illness. The patient may have to leave employment, or alter their home, or incur severe medical expenses. Critical illness insurance pays a bene? t on diagnosis of one of a number of severe conditions, such as certain cancers or heart disease. The bene? t is usually in the form of a lump sum.Long-term care insurance This is purchased to cover the costs of care in old age, when the insured life is unable to continue living independently. The bene? t would be in the form of the long-term care costs, so is an annuity bene? t. 1. 5 Pension bene? ts Many actuaries work in the area of pension plan design, valua tion and risk management. The pension plan is usually sponsored by an employer. Pension plans typically offer employees (also called pension plan members) either lump 1. 5 Pension bene? ts 13 sums or annuity bene? ts or both on retirement, or deferred lump sum or annuity bene? s (or both) on earlier withdrawal. Some offer a lump sum bene? t if the employee dies while still employed. The bene? ts therefore depend on the survival and employment status of the member, and are quite similar in nature to life insurance bene? ts – that is, they involve investment of contributions long into the future to pay for future life contingent bene? ts. 1. 5. 1 De? ned bene? t and de? ned contribution pensions De? ned Bene? t (DB) pensions offer retirement income based on service and salary with an employer, using a de? ned formula to determine the pension.For example, suppose an employee reaches retirement age with n years of service (i. e. membership of the pension plan), and with pensionab le salary averaging S in, say, the ? nal three years of employment. A typical ? nal salary plan might offer an annual pension at retirement of B = Sn? , where ? is called the accrual rate, and is usually around 1%–2%. The formula may be interpreted as a pension bene? t of, say, 2% of the ? nal average salary for each year of service. The de? ned bene? t is funded by contributions paid by the employer and (usually) the employee over the working lifetime of the employee.The contributions are invested, and the accumulated contributions must be enough, on average, to pay the pensions when they become due. De? ned Contribution (DC) pensions work more like a bank account. The employee and employer pay a predetermined contribution (usually a ? xed percentage of salary) into a fund, and the fund earns interest. When the employee leaves or retires, the proceeds are available to provide income throughout retirement. In the UK most of the proceeds must be converted to an annuity.In the USA and Canada there are more options – the pensioner may draw funds to live on without necessarily purchasing an annuity from an insurance company. 1. 5. 2 De? ned bene? t pension design The age retirement pension described in the section above de? nes the pension payable from retirement in a standard ? nal salary plan. Career average salary plans are also common in some jurisdictions, where the bene? t formula is the same as the ? nal salary formula above, except that the average salary over the employee’s entire career is used in place of the ? nal salary. Many employees leave their jobs before they retire.A typical withdrawal bene? t would be a pension based on the same formula as the age retirement bene? t, but with the start date deferred until the employee reaches the normal retirement age. Employees may have the option of taking a lump sum with the 14 Introduction to life insurance same value as the deferred pension, which can be invested in the pension plan of the new employer. Some pension plans also offer death-in-service bene? ts, for employees who die during their period of employment. Such bene? ts might include a lump sum, often based on salary and sometimes service, as well as a pension for the employee’s spouse. . 6 Mutual and proprietary insurers A mutual insurance company is one that has no shareholders. The insurer is owned by the with-pro? t policyholders. All pro? ts are distributed to the with-pro? t policyholders through dividends or bonuses. A proprietary insurance company has shareholders, and usually has withpro? t policyholders as well. The participating policyholders are not owners, but have a speci? ed right to some of the pro? ts. Thus, in a proprietary insurer, the pro? ts must be shared in some predetermined proportion, between the shareholders and the with-pro? t policyholders.Many early life insurance companies were formed as mutual companies. More recently, in the UK, Canada and the USA, there has been a trend towards demutualization, which means the transition of a mutual company to a proprietary company, through issuing shares (or cash) to the with-pro? t policyholders. Although it would appear that a mutual insurer would have marketing advantages, as participating policyholders receive all the pro? ts and other bene? ts of ownership, the advantages cited by companies who have demutualized include increased ability to raise capital, clearer corporate structure and improved ef? iency. 1. 7 Typical problems We are concerned in this book with developing the mathematical models and techniques used by actuaries working in life insurance and pensions. The primary responsibility of the life insurance actuary is to maintain the solvency and pro? tability of the insurer. Premiums must be suf? cient to pay bene? ts; the assets held must be suf? cient to pay the contingent liabilities; bonuses to policyholders should be fair. Consider, for example, a whole life insurance contract issued to a life aged 50. The sum insured may not be paid for 30 years or more.The premiums paid over the period will be invested by the insurer to earn signi? cant interest; the accumulated premiums must be suf? cient to pay the bene? ts, on average. To ensure this, the actuary needs to model the survival probabilities of the policyholder, the investment returns likely to be earned and the expenses likely 1. 9 Exercises 15 to be incurred in maintaining the policy. The actuary may take into consideration the probability that the policyholder decides to terminate the contract early. The actuary may also consider the pro? tability requirements for the contract.Then, when all of these factors have been modelled, they must be combined to set a premium. Each year or so, the actuary must determine how much money the insurer or pension plan should hold to ensure that future liabilities will be covered with adequately high probability. This is called the valuation process. For with-pro? t insurance, the actuary must determine a suitable level of bonus. The problems are rather more complex if the insurance also covers morbidity risk, or involves several lives. All of these topics are covered in the following chapters.The actuary may also be involved in decisions about how the premiums are invested. It is vitally important that the insurer remains solvent, as the contracts are very long-term and insurers are responsible for protecting the ? nancial security of the general public. The way the underlying investments are selected can increase or mitigate the risk of insolvency. The precise selection of investments to manage the risk is particularly important where the contracts involve ? nancial guarantees. The pensions actuary working with de? ned bene? t pensions must determine appropriate contribution rates to meet the bene? s promised, using models that allow for the working patterns of the employees. Sometimes, the employer may want to change the bene? t structure, and the actu ary is responsible for assessing the cost and impact. When one company with a pension plan takes over another, the actuary must assist with determining the best way to allocate the assets from the two plans, and perhaps how to merge the bene? ts. 1. 8 Notes and further reading A number of essays describing actuarial practice can be found in Renn (ed. ) (1998). This book also provides both historical and more contemporary contexts for life contingencies.The original papers of Graunt and Halley are available online (and any search engine will ? nd them). Anyone interested in the history of probability and actuarial science will ? nd these interesting, and remarkably modern. 1. 9 Exercises Exercise 1. 1 Why do insurers generally require evidence of health from a person applying for life insurance but not for an annuity? 16 Introduction to life insurance Exercise 1. 2 Explain why an insurer might demand more rigorous evidence of a prospective policyholder’s health status for a te rm insurance than for a whole life insurance. Exercise 1. Explain why premiums are payable in advance, so that the ? rst premium is due now rather than in one year’s time. Exercise 1. 4 Lenders offering mortgages to home owners may require the borrower to purchase life insurance to cover the outstanding loan on the death of the borrower, even though the mortgaged property is the loan collateral. (a) Explain why the lender might require term insurance in this circumstance. (b) Describe how this term insurance might differ from the standard term insurance described in Section 1. 3. 2. (c) Can you see any problems with lenders demanding term insurance from borrowers?Exercise 1. 5 Describe the difference between a cash bonus and a reversionary bonus for with-pro? t whole life insurance. What are the advantages and disadvantages of each for (a) the insurer and (b) the policyholder? Exercise 1. 6 It is common for insurers to design whole life contracts with premiums payable only up to age 80. Why? Exercise 1. 7 Andrew is retired. He has no pension, but has capital of $500 000. He is considering the following options for using the money: (a) Purchase an annuity from an insurance company that will pay a level amount for the rest of his life. b) Purchase an annuity from an insurance company that will pay an amount that increases with the cost of living for the rest of his life. (c) Purchase a 20-year annuity certain. (d) Invest the capital and live on the interest income. (e) Invest the capital and draw $40 000 per year to live on. What are the advantages and disadvantages of each option? 2 Survival models 2. 1 Summary In this chapter we represent the future lifetime of an individual as a random variable, and show how probabilities of death or survival can be calculated under this framework.We then de? ne an important quantity known as the force of mortality, introduce some actuarial notation, and discuss some properties of the distribution of future lifetime. W e introduce the curtate future lifetime random variable. This is a function of the future lifetime random variable which represents the number of complete years of future life. We explain why this function is useful and derive its probability function. 2. 2 The future lifetime random variable In Chapter 1 we saw that many insurance policies provide a bene? t on the death of the policyholder.When an insurance company issues such a policy, the policyholder’s date of death is unknown, so the insurer does not know exactly when the death bene? t will be payable. In order to estimate the time at which a death bene? t is payable, the insurer needs a model of human mortality, from which probabilities of death at particular ages can be calculated, and this is the topic of this chapter. We start with some notation. Let (x) denote a life aged x, where x ? 0. The death of (x) can occur at any age greater than x, and we model the future lifetime of (x) by a continuous random variable whic h we denote by Tx .This means that x + Tx represents the age-at-death random variable for (x). Let Fx be the distribution function of Tx , so that Fx (t) = Pr[Tx ? t]. Then Fx (t) represents the probability that (x) does not survive beyond age x + t, and we refer to Fx as the lifetime distribution from age x. In many life 17 18 Survival models insurance problems we are interested in the probability of survival rather than death, and so we de? ne Sx as Sx (t) = 1 ? Fx (t) = Pr[Tx > t]. Thus, Sx (t) represents the probability that (x) survives for at least t years, and Sx is known as the survival function. Given our interpretation of the ollection of random variables {Tx }x? 0 as the future lifetimes of individuals, we need a connection between any pair of them. To see this, consider T0 and Tx for a particular individual who is now aged

Jim’s Nobility in Huck Finn

Houlihan 1 Mike Houlihan Ms. Fledderman English H April 15, 2013 Nobility at the Bottom of Society Someone who is noble is defined as a distinguished person noted for feats of courage and heroism. The character of Jim in  Huckleberry Finn  by Mark Twain certainly fits that description. He risked his life in order to free himself from slavery, and in doing so, helps Huck to realize that he has worth. Huck becomes aware of Jim's sense of love and humanity, his basic goodness, and his desire to help others.Jim faces discrimination based on the color of his skin and is faced with the challenges of racist stereotypes. Twain characterizes Jim as a sincere yet naive character, representing the runaway slave as a fatherly figure who maintains his integrity as being one of the sole characters of the novel who wouldn't be described as hypocritical, despite the fact that Jim also retains a childlike mentality. Throughout the novel Jim expresses nobility through his selfless nature, his stre ngth to good while resisting evil, and his ability to bear with any misfortune that may befall on him or his loved ones.Mark Twain allows Jim to break racist stereotypes by showing more human qualities of him when he expresses his selfless nature. by assuming a role as a father figure to Huck, who he watches over throughout the bulk of the novel. Jim protects Huck by shielding his view from the dead body that turned out to be Huck's father Pap. â€Å"I went in en unkivered him and didn't let you Houlihan 2 come in? Well, den, you kn git yo money when you wants it kase dat wuz him† (320).This show of consideration and paternal care for Huck makes Jim out to be more humane. Jim demonstrates his humanity by not only caring for Huck physically, but also mentally and emotionally in shielding him from a sight that could have been mentally or emotionally strenuous on someone like Huck. Jim’s actions are partly a result of his inability to distance himself from the society whi ch he has been conditioned. There are countless opportunities for Jim to leave Huck during the story, yet he remains by Huck’s side.When Huck and Jim are separated in the fog, Jim says â€Å"When I got all tired out wid work, en wid de callin you, en went to sleep, my heart wuz most broke because I was los, en I didn’t kyer no mo what became er me or der raf† (85). Jim’s freedom is then not worth the price of Huck’s life, and let’s people know that he would readily risk his life for Huck. Twain represents Jim as a paternal figure who maintains his integrity as being one of the only sincere characters of the novel, while contrasting this quality with the typical stereotypes of an uneducated slave during the American slave era.Jim is one of the sole characters of the novel who wouldn't be described as hypocritical, for he has the integrity to do what’s right when everyone around him choose not to. After Jim and Huck decide to travel tog ether on the Mississippi river; the pair has to depend on each other for survival as they encounter  people who cause obstacles and jeopardize Jim’s freedom. For example when Jim is forced to accompany the king and the duke during their scams he says â€Å"But Huck dese kings o ourn is jus reglar rapscallions; dats what dey is deys reglar rapscallions† (153).Although Huck is simply putting on an act and appeasing them in order to prevent turmoil. Jim thinks that it is ridiculous for someone to be entitled to a servant and recognizes that this is wrong by calling them â€Å"rapscallions†. This could also be twain making a jab at slavery, which is Houlihan 3 ironic because Jim has been a slave all his life without asking questions. When Jim talks about his family, he mentions his daughter whom he had hurt due to the misunderstanding that she was deaf and dumb; this proves to be pivotal point in the novel to see what kind of man Jim truly is. Oh, she was plumb de af en dumb, Huck, Plumb deaf en dumb en I’d ben a treatn her so† (156). Jim, like most fathers wanted his child to have manners and due to his ignorance of his daughter’s condition hurt her, for he believed she was just being rude. After coming to the realization of her condition, he begins to feel guilt for being unintentionally cruel. By being simple minded and at the very bottom of the social order, Jim is able to see right wrong, while others who claim to be above him cannot see this. Jim continues to show his nobility by enduring the hardships that he is faced with throughout the novel.He talks about how he feels to Huck to the extent where he forces Huck to stop and think over how he treated Jim. After talking down to Huck after playing a trick on him, Jim tells Huck how he feels and Huck even thinks that â€Å"I wouldn't done that one if I'd a knowed it would make him feel that way† (142). After thinking this, Huck himself subverts the racist stereo type by humanizing Jim and acknowledging that the black man has the capacity to feel, and Huck allows his mood to be negatively influenced by the thought that he hurt the feelings of a man he considered his friend.Jim's condition as a human being is improved even more when Huck considers Jim as his friend, making him equal to a white boy. By making Jim equal to himself, Huck is able to humanize Jim and break the cultural perception that Jim is bound to. Another example of how the book illustrates this theme is when Tom kept Jim locked up as a slave when he clearly could have been set free at any moment. Tom was aware Jim was freed from being a slave but decided to keep it a secret. This caused Jim unnecessary poor treatment. Houlihan 4He was forced by Tom to do things he didn’t want to do. This is shown when Tom forces Jim to have rats, spiders, and snakes in his room. Tom says to Jim â€Å"But Jim, you got to have ‘em- they all do. So don’t make any more fuss a bout it† (263). This was cruel because Jim was forced to live with the creatures that traumatized him in his past. Though Mark Twain breaks some racist barriers with Jim, other stereotypes about blacks in the era are reinforced throughout the novel and Jim still maintains the strength to endure.Throughout the novel, Mark Twain both reinforces and disputes racist stereotypes of the time period through the portrayal of Jim as a noble character. Jim is depicted as a genuine yet unsophisticated character. Twain represents Jim as a selfless, paternal figure that is able to see right from wrong and maintains his integrity as being one of the only sincere characters of the novel. Twain contrasts this quality with stereotypes typical of an uneducated slave during the American slave era.Though he is a stoic character, Jim is able to span the entire novel as a father figure who protects Huck both physically and emotionally and, even after Huck plays tricks on him, forgives Huck and cont inues to protect him. Nobility is reinforced when Jim's simple nature is revealed in various parts throughout the novel. Jim's gullibility and his language relay the stereotypes of the antebellum south that blacks were somehow not people and were much lower than whites. These ideas become relinquished in the end, for readers are able to see the distinguished human being that Jim characterized.

Literature review Essay

A reasonable risk assessment of sex offenders, when combined with good parole supervision and a community-based treatment program aimed at relapse prevention, effectively reduces recidivism. This was the finding of a study conducted by Wilson, Stewart, Stirpe, Barrett, and Cripps in Canada. Published in 2000, the study covered 107 sex offenders who were released to the custody of the Central Ontario District during a period of eight years starting in 1990. According to the authors, their study outlined the general principles laid down by Motiuk, Belcourt, and Bonta in 1995, namely: careful and continuous evaluation of offender risk which ensures that highly dangerous offenders were not allowed to return to the community by sentencing them to life in prison; focusing on criminal behavior when conducting intervention programs with the help of qualified psychologists; effective monitoring of the returning offenders’ activities in the community by employing only competent parole personnel trained in the principles of relapse prevention; and an honest exchange of information among the relatives of sex offenders, the parole personnel, and the treatment staff in order to achieve the right mix of treatment intervention and parole supervision. Wilson et al (2000) found that the strategy resulted to a low 3. 7% recidivism compared to the 5. 4% cited by the study of Motiuk and Brown, and the 6.3% recidivism rate which came out of the study conducted by Barbaree, Seto, and Maric. Both studies were completed in 1996 (Wilson, Stewart, Stirpe, Barrett, and Cripps, 2000). In West Virginia, Gordon and Weldon (2003). Examined the effect of educational programs on recidivism. Studying the records of inmates who attended the General Educational Development (GED) and the Vocational training programs conducted from 1999-2000 at Huttonsville Correctional Center, they found that a recidivism rate of 8. 75% was recorded for those who completed the vocational training program. Inmates who went through both the vocational training program and the GED, on the other hand, reported a lower 6. 71% recidivism rate. Both figures were way below the recidivism rate of 26% which was observed on inmates who did not participate in either educational program. These results were comparative to the findings of a study made by Mace in 1978 of 320 inmates who were discharged from correctional institutions in West Virginia in 1973. Out of the 320, 76 were rearrested after four years, 21 (or 6. 56%) of whom were products of educational programs behind bars while 55 (or 17. 19%) did not attend any educational program while being incarcerated (Gordon and Weldon, 2003). Meanwhile, two cost-effective programs were the subject of an article authored by Harvey Shrum in 2004. Published in the Journal of Correctional Education, the article discussed two additional practices called logotherapy and intensive journal which, according to him, were better at reducing â€Å"future criminality† of both offenders and potential offenders than punishment and surveillance-based programs. Logotherapy, which means â€Å"health through meaning,† was developed by Dr. Viktor Frankl as an effective substitute to the 12-step program of rehabilitation for drug and alcohol abusers generally accepted by most parole boards. The program aims to provide inmates with a â€Å"purpose and direction in life. † Introduced forty years ago to inmates of a California Rehabilitation Center, program participants reported a recidivism rate of 5. 5%. When it was re-introduced to nineteen inmates of Folsom State Prison in 1998, the three participants who were released on parole reported a zero percent recidivism by year 2004. Intensive journal, on the other hand, was first introduced at Folsom State Prison in 1992. Created by Dr. Ira Progoff, it is a â€Å"method of self-development† that makes use of writing exercises. Inmates were made to write about their experiences, relationships with their families, their jobs and health, and the meaning that they give to their lives in a journal. These journals were reviewed and feedbacks were provided. By 2002, ten years after the program was introduced, no participant was ever rearrested (Shrum, 2004). The debate on the value of using recidivism to measure the effectiveness and efficiency of correctional programs continues and, in fact, polarized justice scholars. A dissenting opinion was voiced by Thomas in 2005 when he said that prison facilities and programs have no influence over the behavior of inmates once they return to their communities. He argued that communities are influenced by certain social, cultural, and economic factors which are beyond the control of prison facilities. Policymakers and academics, however, refuse to budge. They insist that there is no other, better measure than the rate of recidivism. According to these academics and policymakers, effective rehabilitation measures should be able to provide inmates with coping mechanisms necessary for them to deal with the â€Å"economic, social, and cultural stresses of post-release life. † In the same vein, they argue that effective deterrence programs should produce inmates who should have learned enough lessons during incarceration to dissuade them from returning to a life of crime. In both cases, they maintain that low recidivism should be the direct result. Although inclined towards the use of recidivism, Maxwell, in an article entitled: â€Å"Rethinking the Broad Sweep of Recidivism: A Task for Evaluators,† suggested that academics should not stop looking for less familiar methods of approaching the problem while policymakers should maintain an open mind so that like policy questions could be considered more objectively (Maxwell, 2005). References Gordon, H. R. D., and Weldon, B. (2003). The Impact of Career and Technical Education Programs on Adult Offenders: Learning Behind Bars. Journal of Correctional Education, 54, 4, 200-209. Maxwell, S. R. (2005). RETHINKING THE BROAD SWEEP OF RECIDIVISM: A TASK FOR EVALUATORS. Criminology & Public Policy, 4, 3, 519-526. Shrum, H. (2004). No Longer Theory: Correctional Practices That Work. Journal of Correctional Education, 55, 3, 225-235. Wilson, R. J. , Stewart, L. , Stirpe, T. , Barrett, M. , and Cripps, J. E. (2000). Community-based sex offender management: Combining parole supervision and treatment to reduce recidivism. Canadian Journal of Criminology, 42, 2, 177-188.

Campaign Analysis Essay Example | Topics and Well Written Essays - 1500 words

Campaign Analysis - Essay Example In September 2004, the campaign for real beauty was officially launched for the rise of some consciousness of all issue associate with beauties. The campaign was purposely meant to challenge the stereotypes that had been set by the beauty industry. It had numerous intentions in making as many women as possible feel beautiful every day. The campaign led to the release of the global research that explored the relationship between women and beauty and what beauty links to their happiness all across the world. It was such an effective campaign and was accompanied with much advertising that inspires the society and more especially women to think differently about the definition of beauty. The campaign was also attached with some fundraising initiatives that were aimed at helping young girls who had low self-esteem related to their beauty. The DOVE SELF ESTEEM FUND supported the fund raising initiatives. According to the campaign, every woman was to possess something beautiful and unique. Sixty eight percent of all people believe that unrealistic standards of beauty exist within the advertising world and the media. Forty-seven percent has believed that only attractive women are portrayed in the well-known cultures while eighty-five percent agree that beauty can be achieved through spirit and personal attitude. This was critically analyzed throughout the campaign period that left many individuals convinced about the associated beauty with the dove products. The associated strengths with the company include its broad market equipped with quality products. Their advertising is very much inspiring with much emotional appeal. This has created perfect public relations that give it enormous strengths compared to its competitors. The company has also a positive self-image. This act as a driving factor in motivates every undertaking within the company creates a motivating factor to all the stakeholders. They make broad

Brett Dennen - Ain't No Reason writing about the song and the video Essay

Brett Dennen - Ain't No Reason writing about the song and the video - Essay Example Speakers use what they know to find their attitudes on a subject and their understanding of a reader (Lamb 4). Summary of the text The song â€Å"ain’t no reason† by Brett Dennen talks about how things like ignorance, priviledge, and life’s daily routine get in the way not just of addressing but also recognizing the suffering around us. He talks about how many lives are been irreparably changed and hurt and the way our world has been destroyed and hence the future generation tends to have a bleak outlook. The reasons for this he explains are because of poverty, war, violence, hatred, genocide, environmental degradation, oppression and most importantly because we are unable to see the suffering that surround and end up working against it. This text can trigger the audience to debate about what it really means to be conscious of suffering and the moral obligations we have to make in order to effect change. Bretten stresses that we should passively understand that t he answer to all this is love. He describes it as a practice of kindness, compassion and respect among all the living things our planet included. He is strongly against the idea of living a disconnected life. Aristotle argued that it is possible to connect to your audience logically emotionally and ethically. These three forms what is referred to as the rhetorical triangle (Lutze 1). ETHOS (WRITER) LOGOS (TEXT) PATHOS (READER) (Henggeler 2). These three appeals in the triangle form a balance of what the writer should use to be able to form an effective argument. Each appeal is important to be able to produce a well balanced argument as they directly affect each other. Rhetorical appeals (ethos, pathos, logos) Ethos Ethos refers to character of a writer. This explores the ability to deal with a topic. (Metzeger 7). The writer or singer Brett Dennen is well conversant with the way people are living around him. This is evidenced by the way he refers to the way people are living around him. We are made aware of that by the fact that he says he does not understand or neither explains why they live the way they live yet they do it everyday.’ I can't explain why we live this way. We do it every day (Dennen n. p.)’. The writer is also able to explore the issue of politics of lies and also the deception used by those in power. Pathos Pathos refers to the arguments or rather the appeals to emotions. This can be viewed a show well the writer is able to draw the audience’s emotions and tap in to them. It is the role of the audience in the argument (Henggeler 1). The song artist Brett Dennen is able to draw the listeners emotions in his song ‘Ain’t No Reason’ and thereby has effectively used pathos to connect to his listeners. He is able to draw the emotions of confusion when he points out that he can’t explain why they live that way yet they continue to do it every day. ‘I can't explain why we live this way. We do it e very day (Dennen).’ The song artist’ is also able to explore the emotion of bitterness and also expresses the continuity of their suffering. The writer states, ’I gotta a basket full of lemons and they all taste the same’ shows of the continuous bitterness. This can also suggest that there is recurrence of the same things over and over again till they start getting used to the feeling of being bitter with the occurrences. Brett Dennen

Country feasibility for Burger King in Brazil Research Paper

Country feasibility for Burger King in Brazil - Research Paper Example For instance, it is documented that from China alone, Brazil made as much as US$30.8 billion in the year 2010. The chart below gives a detailed value of trade for the top ten trade partners of Brazil. In terms of trade surplus, China was identified as the strongest with $5.2 billion achievement in 2010 while Argentina gained $4.1 billion with the United States of America recording $7.8 billion. Workman notes that â€Å"it appears that the lower American dollar paid dividends in 2010, driving up Brazilian demand for comparatively lower-priced U.S. goods.† In terms of macroeconomic indicators, Brazil could be classified as an excellent performer in the past few years, counting as one of the world’s major economic competitors. The table below is a summary of figures of some of Brazil’s major macroeconomic indicators for various years. Laws that govern foreign direct investments are very crucial to the economic development of every nation, including companies and corporate bodies who would be seeking for investment in one country or the other. To this, Brazil has a number of foreign ownership laws that are meant to be of great economic cover to both Brazil as a country and foreign investors such as Burger King. Some highlights of the laws include the fact that the percentage of foreign ownership allowed is 30% as of 2002 (Encyclopedia of the Nations, 2012). This is a figure that could be said to be of very good favor to foreign investors, of which King Burger can take advantage. In fact, since 1995, â€Å"the petroleum, telecommunications, mining, power generation, and internal transportation sectors were opened up to foreign investment† (Encyclopedia of the Nations, 2012). Brazil boasts and benefits from a very large consignment of foreign investor profits. However, â€Å"repatriation of foreign capital registered with the Central Bank of Brazil to its country of origin requires no prior

International Business - Overseas Market Entry Actions Essay

International Business - Overseas Market Entry Actions - Essay Example However, the cosmetics industry in Iceland has escaped most of the fallout resulting from financial market collapse in the country, which has opened up internationalization as a viable strategic objective. This paper will focus on Blue Lagoon Cosmetics Company and its potential entry into the Kuwaiti market, including the most viable international business strategy, its marketing actions, and appropriate organizational structure. In order to do this, the paper will use literature studies on international business strategy and apply theoretical models to the entry of Blue Lagoon into Kuwait. Blue Lagoon was started in 1976 as a way to take advantage of a geothermal plant constructed in the Reykjanes-peninsula. The geothermal plant produces water rich in natural minerals that are also integrated into the white silica clay on land, which Blue Lagoon collects and sells as cosmetic products (Icelandnaturally.com, 2013: p1). Blue Lagoon Ltd. was established in 1992 due to the popularity of its warm spa water, after which bathing facilities were opened in 1999, which made it one of the most popular tourist destinations in Iceland with at least 70% of all tourists visiting Iceland also visiting the Blue Lagoon. The company has three state-of-the-art geothermal spa facilities, which host restaurants, conference rooms, an indoor pool, and modern changing and shower rooms. In addition, Silica mud is also part of the company’s assets, in which visitors can bathe. Blue Lagoon has dedicated its activities to developing the health of visitors, building on the presence of geoth ermal water that contains blue-green algae, silica, and salt (Icelandnaturally.com, 2013: p1). The company began producing skincare products as Blue Lagoon Iceland made of unique chemicals, which were first marketed in the late 90s. In the early part of the 2000s, they launched

HSA 535 WK 8 D1 & DB2 Coursework Example | Topics and Well Written Essays - 1000 words

HSA 535 WK 8 D1 & DB2 - Coursework Example For example, the imaging tests include the use of Mammograms and computed tomography scans. Understanding Laboratory tests requires that there is a fact sheet used to keep records for the role of screening and diagnostic laboratory tests. The fact sheets usually contain a list of the common tests done in cancer medicine hence could be used as a reference. Pap and HPV testing are some of the laboratory tests in cancer medicine that patients are likely to get through during their diagnosis and treatment procedures. A fact sheet is used which includes information about cervical cancer screening guidelines which can be used on the patients. There is also the Prostate-Specific Antigen Test that is used as a way of diagnosis of prostate cancer in patients. The fact sheet presents guidelines of the procedure together with the benefits and limitations of the test. These tests are efficient, however, only in the first world countries. Third world countries lack the necessary resources and financing to run cancer screening centers effectively and of a large magnitude. However, the US is a developed country with a well-established means of ensuring affordable health care to all its citizens hence has effective procedures. Prostate cancer is usually more prevalent in patients who are older hence it is advisable that older people go for regular screening. This could reduce the extra costs that would be incurred during treatment because once detected early, there are higher chances of treatment. There are a number of ways to address and communicate to the public about the disease. This can be done by engaging the mass in social media using posts that can target their interests. In this contemporary world, the social media has been very active as a tool of communication. Youths can share ideas and criticize hence gaining more knowledge about the disease. The other way would be through free

Compare and Contrast the theme of Good verse Evil in the two short Essay

Compare and Contrast the theme of Good verse Evil in the two short stories Barn Burning by William Faulkner and good Old Country People by Flannery O'Connor - Essay Example In both these stories, there is a struggle between good and evil but the outcome of the struggles differ from one another. The story Barn Burning is about the youngest son, Sartoris Snopess struggle of trying to do what is right for his family, against the wishes of his own father, Abner Snopes during the post Civil War period. Sartoris or Sartys wish to keep his family together is tested in the beginning of the story itself. When his father Abner was charged for arson, he knows that his father is wrong. But, Abner by constantly reminding him of the importance of family elicits a favorable response from him. He tells Sarty, "You got to learn to stick to your own blood or you aint going to have any blood to stick to you." (Faulkner). That is, Abner instills in Sarty that only if an individual is loyal to the family, even if it is right or wrong, he will in turn get familys help in needy times. But, in the course of the story Sarty feels an aversion towards his father because of his wrongs and violent behavior. Abner exhibits violence towards Sarty and also others who questions his authority. Sarty descri bes his father as: "There was something about his wolf-like independence" (Faulkner). So, the whole family including Sarty and his sisters dislike him. The main theme of Barn Burning is Sartys desire to stand by good and fight the evil which is represented by his wicked father. That is, when his father was bent on burning down Major de Spains barn, Sarty reveals to him about his fathers intentions, thereby leading to his fathers death and victory of good over evil. The theme of good verse evil is depicted in the story through Sarty’s struggle between loyalty for his family and morality. Similarly, the story Good Country People presents the theme of good verse evil. The protagonist of the story, Hulga is a thirty two year old woman. She had lost one leg in an accident

Police pursuits Essay Example | Topics and Well Written Essays - 1500 words

Police pursuits - Essay Example e inability to control pursuits resulting in problems to the public have become a common phenomena and it is high time that clearcut tactics, legislation and policies are formulated and executed in this regard. The question is whether the police pursuits add to public security or public misery. The moral question is whether the benefits derived from a successful chase would compensate for the concomitant risk to public health and safety. Lack of applicable standards to decide whether the police pursuit was for the right cause or to prove that the police officers have not shown any neglect of duty of care is the major drawback related to police pursuits. The policy pursuits very often result in liabilities for accidents, or litigation for injury to personal and property. Viola king in this regard remarks that â€Å"...officer liability in police pursuits arises only when the police vehicle actually impacts the other vehicles.† (King, Viola.) Thus, it is clear that the police do not have to take the liability for any accidents which are not directly caused due to their pursuits. But the officers have to be judicious enough to decide and employ high speed chases only when it is necessary. If the police ask a speeding car to stop and it doesn’t, it is well within the officer’s jurisdiction to pursue it. The high rate of crashes, injuries and deaths during police pursuits has not set a positive note for the department from the public. In a survey conducted by John Hill, it was found that, by and large, the public did not want to be passerby during high speed pursuits. Although 58 % of them felt that it was morally right for the officer to stop a speeding vehicle, and if the vehicle did not stop, it was well within their right to chase it. But when the question came as to whether the officer was justified in hot pursuit if it involved danger to public health and safety, the proportion who justified police pursu it, dropped from over 58 % to just 29%. (Karen, J.

Answer four questions Essay Example | Topics and Well Written Essays - 1500 words

Answer four questions - Essay Example On the other hand, management accounting innovation is the adoption of new ideas or modern forms of management accounting systems. Management accounting innovations are among the central themes driving modern organisations. These modern organisations manage to prosper and retain its success in the aggressive market environments through stable innovations towards organisational prosperity. This paper will outline the contribution of management accounting innovations towards organisational success. 1. Why Management Accounting Innovation is one of the core themes driving modern organisations Innovations are of many types, and research suggests that distinguishing the difference between them is very essential because innovations have different attributes (Schmeisser, 2010). More so, the adoption processes of innovations are not the same and factors affecting them differ. There are different types of innovation that mainly are technical innovation, administrative innovation, process inno vation, product innovation, radical innovation and incremental innovation. To start with, technical innovation relates to the major work activities that are carried out in an organisation, while administrative innovation relates to the organisational structure and administrative processes inclusive of the management. Thirdly, process innovation contains an organisation’s process in new elements. ... Innovations vary differently in different organisations due to the sise and activities of an organisation. However, in management accounting only two innovations are commonly used. These two innovations are administrative and radical innovations. 2. Management accounting is the core theme in driving innovation in modern organisations In the past decades, management accounting strategies included both decision-making and analysis (Emsley, 2005). These past management strategies are claimed to be the predecessor for the emerging innovation and the latest technologies. The modern accounting represents both the operational and the financial planning and control. Managerial accounting is a very essential tool in an organisation because it provides essential data with which the organisation operates. In other words, managerial accounting can be simply referred to as cost accounting. The management accountants have the role of preparing reports that focus on how well or bad managers and the business unit have performed (Lucey, 2003). The management accountants go ahead to measure these performance measures and the results are compared to plans and benchmarks. Most of these reports provide frequent updates on essential indicators and any arising problem is addressed. The main problems that arise in the reporting field are declining in profitability, global market crisis and other emerging problems. These problems are then solved strategically. Therefore, management accounting analyses the past, present and the future of an organisation’s performance through financial transactions. These summarised outputs are essential in planning the current and future stability of an organisation through

Inquiring Minds Want to Know-Now Essay Example for Free

Inquiring Minds Want to Know-Now Essay Penton Media is a publisher of several business trade magazines, and their research department is studying the long-term viability of the reader service card within its publications (Cooper Schindler, 2014). This card is an advertisement card used for readers to request product or service information, and potentially could be generating fewer leads than in the past (Cooper Schindler, 2014). The research division of Penton Media conducted a meticulous research with many diverse readers through various diverse forms of communication. Penton Media is now faced with the challenge on determining if this reader service card will sustain ad be beneficial in the future. The survey is not clear and is perplexing. Questions should be directive and closed ended. In this survey the questions asked are not directive questions, but moderately open ended questions that would discourage a user from completing the survey. When the questions are not specific it would give feedback that is not what key decision makers are seeking. The wording of the questions is equally adequate for the responses needed; but, they could be more designed to yield desired results. This method could motivates users to not only complete the survey, but also provide honest and reliable feedback. There is not enough purpose or direction present to encourage the participant to give revealing answers (Cooper Schindler, 2014). Having a more direct, concise, and structured questionnaire would not only get the feedback that is warranted, increase participation, but more time could be used to reevaluate the response that are received. This survey was not designed properly to accomplish the specified objectives. Coding involves assigning numbers or other symbols to the questionnaire for the purpose of grouping the data (Cooper Schindler, 2014). For each question the researcher must assign numbers to each response available in order to code the data correctly. A code sheet will allow an SPSS system to quickly find the frequency, percent, valid percent, and cumulative percent of each response. The detail of the code sheet will produce detailed SPSS results which will allow the researcher to clearly interpret the data.

Fibre Reinforced Polymer Composites to Strengthen Structures

Fibre Reinforced Polymer Composites to Strengthen Structures Aim The project aim is to identify the use of FRP (Fibre Reinforced Polymers) composites in strengthening of structures. The general process and methodology considered in achieving this objective is by externally bonding Fibre reinforced plastics to the metal structure/plate and thus testing the specimen under 3 point bend as well as 4 point bend tests. The preliminary report will focus on the project introduction, literature review related to the project topic, project plan and further to be carried out. Analysis of Tasks As mentioned the projectà ¢Ã¢â€š ¬Ã¢â€ž ¢s main focus is strengthening of structures. So the question is why is there a need for strengthening of structures? The reason behind the strengthening of structures is that the structure will be able to support greater magnitude of loads than the values for which the structures are originally designed. Strengthening may become necessary in course of time in order to overcome the damage caused due to environmental factors such as corrosion as well as fatigue cracking. The method of bonding reinforcement represents an attractive solution to the problem as it can be achieved with relatively small impact on the structure. The next stage of the preliminary thesis will focus on the literature review. The literature review section is divided in to two sections firstly it will focus on the topics related to the Composite Materials, which will involve the following topics. Definition of Composite Material Classification of Composite Materials Types of Matrix Types of Reinforcement Advantages and Disadvantages of Composite Materials Manufacturing of Composite Materials The next section of the literature review will focus on the topics related to strengthening of structures. For this section following topics will be considered. Different Methods for Structure Strengthening Different Methods for Structure Strengthening using FRP Composites. The preliminary thesis will also look at the comparison between the structural strengthening using FRP Composites and Steel plates. This will help in giving a suitable reason as to why Composites are preferred over Steel plates for structural strengthening. Composites are considered as one of the most promising material for reducing the weight as well as increasing the strength of the material. The theory of hybrid material has been successfully exploited when studying sandwich panel technology. Now the concept of integrated multi materials is extended to a wider variety of structures, components and applications. Fibre reinforced plastics (FRPà ¢Ã¢â€š ¬Ã¢â€ž ¢s) have been successfully used for the post strengthening of structures over a number of years. The design and manufacturing of composites has led to its application in variety of industries such as automotive, aerospace, sporting goods, construction and in the marine as well as oil and gas industries. Moreover the method of bonded reinforcements also comes into account when there have been cases where errors in design or construction of a structure have questioned safety aspect. This can be achieved by externally bonding reinforcements at a cost of very small impact to the structures. Project Time-Line (Gantt chart) Literature Review Composite Materials Composite materials also known as composites are defined as a combination of two or more materials to give a unique combination of properties [1]. This definition is very general and thus includes metals, alloys, plastic co-polymers, minerals and wood. A material is only classified as a composite if the material satisfies the following conditions [2]: The material must be manufactured It should consist of two or more physically and/or chemically distinct, suitably arranged or distributed phases with an interface separating them. The characteristics of the composites are not depicted by any of the components in the isolation. Fibre reinforced composite materials differ slightly from the general definition because in this FRP the constituent materials are different at the molecular level and at mechanically separable. However the final material properties of the composite are better in comparison to that of the constituents. The figure 1 below gives a basic idea of how the structure of composite material looks like. The composites can be classified as fibre reinforced, particle reinforced, dispersion strengthened and laminates composites. Figure Structure of Composite Material [http://resources.edb.gov.hk/~s1sci/R_S1Science/sp/en/syllabus/unit14/new/images/s.gif] The composite material consists of two main elements the matrix and reinforcements (fibre). The classification of Composite materials is as shown in figure 2. Composite Materials Matrix Reinforcements Polymer Metal Ceramic Particle Reinforcement Fibre Reinforcement Structural Reinforcement Laminates Long Fibre Short Fibre Preferred Orientation Random Orientation Bidirectional Unidirectional Preferred Orientation Random Orientation Figure Classification of Composite Material Types of Matrix There are three main types of matrix considered when studying composites materials namely Polymer, Metal and Ceramic. Polymer Matrix composites are the most common types of matrix composites. They are also known as FRP (Fibre reinforced polymers). The resin used in here is polymer based combined with a variety of fibres such as Glass, Carbon and Aramid as reinforcements. Metal Matrix Composites are mainly used in the automotive industry. The materials use a metal for example Aluminium as the matrix which is then reinforced with fibres such as silicon carbide. Ceramic Matrix Composites are used in very high temperature environments. This type of materials uses Ceramic as the matrix and the matrix is then reinforced with short fibres such as Silicon Carbide and Boron Nitride. A matrix plays an important role in a Composite structure. There are several functions of Matrix most of which are very important to the satisfactory performance of the structure. The following points outline the important functions of the matrix. The matrix binds the fibre together and thus transfers the load to the fibres. The matrix provides the rigidity and shape to the structure. The matrix isolates the fibres such that each individual fibre can perform separately, due to this crack propagation process slows down. The surface finish quality of the structure is provided by the matrix. The matrix acts as a protection to the reinforced fibres from chemical attack and mechanical wear and tear. The type of material selected as matrix affects the ductility and failure mode of the structure together with the fibreà ¢Ã¢â€š ¬Ã¢â€ž ¢s compatibility. Types of Reinforcements The other constituent in the composite material is called the Reinforcement. This gives the composite the necessary strength and stiffness. The structure of the reinforcement is thin rod like. The most commonly used reinforcements are Glass, Carbon, Aramid, and Boron fibres. The diameters of these fibres range from 5 µm to 20  µm. [1] Due to the thin diameter of the fibre, the fibres are flexible and can be formed easily into any shapes. Fibres can come into many forms such as continuous fibre, discontinuous fibre, short fibres, long fibres, organic fibres and inorganic fibres. Fibre brings out the high performance of the material; this is due to three important characteristics of the fibres. The orientation of the fibres also has an impact on the performance of the composite. The fibres can be unidirectional, cross ply or random in its arrangement. Small diameter in comparison to the grain size. As a result of this higher fraction of theoretical strength can be attained. High aspect ratio (length/diameter); this allows a larger amount of load to be transferred. High degree of flexibility. The main functions of fibres are as listed below [1]; To carry the load. Hence fibres are made from materials with high tensile strength and high elastic modulus. Provides strength, stiffness, thermal stability and other structural properties in the composites. Provide electrical conductivity or insulation, depending on the type of fibre used. Advantages of Composites Composites are designed to perform in applications which require lighter weight and higher performance. The advantages of using composites are listed below. High resistance to Corrosion; due to this the application in marine, infrastructure and chemical is very good. High specific stiffness and high specific strength; this gives a weight reduction so is used for the application in aerospace, automotive and manufacturing of sporting goods. The impact resistance is high compared to metal. Higher fatigue strength. Unidirectional carbon/epoxy composites have good fatigue strength of almost 90% of its static strength. Composite materials offer increased amount of design of flexibility. For example the coefficient of thermal expansion of composite can be made zero if suitable constituents and lay up sequence is selected. As the coefficient of thermal expansion is relatively low compared to metals, the composite structure thus provides a good dimensional stability. Also due to the design flexibility, composite materials can be formed into any shapes. Process cycle times and costs are also reduced because of the use of composites in production of net shape and near net shape parts. Composite materials dampen the vibrations an order of magnitude better than metals. Glass reinforced and aramid reinforced composite meet the FAA and JAR requirements for low smoke and toxicity and thus are used in interior panels of aircrafts, stow bins and galley walls. Disadvantages of Composites There will always be limitations to the benefits of the composites. The disadvantages are as listed below. Weaker in transverse direction and low in toughness. Material cost is high compared to that of steel and aluminium. The lack of high volume production limits the wide spread use of composite materials. However this is changing as modern production methods such as Pultrusion, Resin transfer Moulding and other methods have been automated to increase the rate of production. The knowledge through books and database is limited when comes to designing parts with composite. Composites absorb moisture, which affects the properties and dimensional stability of the composite. Difficult to join together with other material due to its anisotropic properties and high sensitivity to damage. For example when drilling holes for mechanical fastening. Brittle like behaviour. Difficult to repair as most composites use thermo set matrices that can not be re shaped. On the contrary thermoplastics can be repaired how ever they are rare [4]. Solvent resistance, chemical resistance and environmental stress cracking of composite depend on the properties of polymers. Some polymers have low resistance to the solvents and environmental stress cracking[1]. Manufacturing of Composite Materials Before looking into manufacturing of composite materials; it is important to look at manufacturing of fibre performs briefly. Fibre performs is how fibre are manufactured before being bonded to the matrix to form a composite material. Fibre performs are often manufactured in sheets or filaments in case of spraying applications. The fibre manufacturing process is carried out by adopting the technique used in textile industry. The techniques used are weaving, knitting, braiding and stitching [5]. The manufacturing process of composite material in general can be divided into two main processes. Prepreg Moulding Wet Moulding PrepReg Moulding The process of prepreg moulding can be further categorized as: Bladder Moulding Compression Moulding Autoclave/Vacuum bag Moulding Mandrel Wrapping [6]Bladder Moulding: In this process the sheets of prepreg material are laid up and placed in female style mould along with a balloon like bladder. The mould is then closed and placed in the heated press. Eventually, the bladder is pressurized which then forces the layers of material against mould walls. The part is then cured and removed from the hot mould. The process is ideally suited for complex hollow shapes. Also the process has great cost to performance balance. Typical example of equipment using bladder moulding technique is the manufacturing of tennis racquet. Average cure cycle range is 15-60 minutes. Compression Moulding: A process where a à ¢Ã¢â€š ¬Ã…“performà ¢Ã¢â€š ¬? or à ¢Ã¢â€š ¬Ã…“chargeà ¢Ã¢â€š ¬? of single moulding compound (SMC) or bulk moulding compound (BMC) or sometimes prepreg fabric is placed in the mould cavity. Once the mould is closed, the material is compacted and cured inside by heat and pressure. The process also offers excellent detailing for geometric shapes. The average cure cycle range is 2-20 minutes. The tooling is process is often more expensive. Auto Clave/Vacuum Bag Moulding: The figure below gives an idea of vacuum bagging for prepreg lay-up process. Figure Vacuum bagging for prepreg lay up process [http://www.highcomp.no/design/bilder/vacum/vacum.gif] Once all the prepregs are laid out in the desired sequence, vacuum bagging preparations are set up as per the figure 3 for curing of the part. First step is application of release film on the top of all the prepreg. The release film is a perforated film that allows captured air, excess resin and volatiles to escape. Secondly is the application of bleeder on top of release film; it is a porous fabric that absorbs moisture and excess resin coming from stack of prepregs/laminates. Thirdly is the application of non porous and non-perforated film on top of bleeder. After this a breather layer is applied; this is a porous fabric which creates even pressure around the part and at the same time allowing air and volatiles to escape. Then final layer is of vacuum bag. The vacuum bag is an expendable polyamide film. The film is sealed on all sides of laminate using a seal tape. A nozzle is inserted into the vacuum bag and is then connected to hose vacuum pump for creating vacuum. Mandrel Wrapping: In these process sheets of prepreg material is wrapped around steel or aluminium mandrel. The prepreg material is compacted by nylon or polypropylene cello tape. Parts are cured by hanging in the oven. Once the curing process is completed, the cello and mandrel are removed which results in a hollow carbon tube. Advantages of prepreg lay up process are that it is simple process when manufacturing complex parts. Also strong and stiff parts can be fabricated using this process. Also allows production of high fibre volume fraction. Prepregs usually have more than 60% fibre volume fraction. Limitations of the process being that labour is intensive as a result of which the process is not suitable for high volume production applications. Also parts manufactured by this process are very expensive. Wet Moulding Wet moulding process can be divided into following processes. Wet layup Spray Up process Filament winding Pultrusion Resin transfer Moulding (RTM) Resin transfer moulding under vacuum (VARTM) Wet Lay-up: in this process a fabric is placed in open mould which is then hand saturated with wet resin. The curing occurs normally at room temperature. However it can be cured at higher temperatures based on the heat resistance of the mould. The advantage of this process is that the material cost and tooling cost is low. Because of this the process is considered as low tech process. Spray-up process: The processing steps are similar to that of the wet lay-up process except for the method of creating the laminates. The basic steps are as follows [1]. The mould is waxed and polished for easy de-moulding Gel coat is applied to the mould surface and allowed to harden before building any other layer. The barrier coat is applied to avoid fibre print through the gel coat surface. Oven curing of barrier coat. Mixing of resin with fillers and the mixture is then pumped to a holding tank. Spraying of resin, catalyst and chopped fibres on the mould surface. This is done with the aid of hand held spray gun. The spraying is carried out in typical pattern to create uniform thickness of the laminate. A roller is then used in order to make the fibre and resin material compact as well as create a smooth and even surface. The laminate is then cured in the oven. The part is then de-moulded and sent for finishing work. The process of spray lay-up is very economical, maximizes the use of low cost tooling as well as low cost material systems however it is not suitable for making parts that have high structure requirements, fibre volume fraction can be difficult to control as well as the thickness. The surface finish on both the sides is not same. Also dimensional tolerance is poor. Filament Winding: This is a process in which resin-impregnated fibres are pulled and wound over a rotating mandrel at desired angle. The fibre pulled is from a wet bath of resin. Curing occurs at room temperature or higher temperature. The performance is limited and it is difficult to obtain uniform fibre distribution and resin content through out the thickness of the laminate. The process is very suitable for tubular parts such as pressure vessels. Figure Filament Winding Process [http://www.thaicomposites.com/images/filament-winding.gif] The advantages of this process being its ability to utilize low cost raw material and low cost tooling systems. It can be automated for the production of high volume composite parts. The figure 4 gives an indication of the filament winding process. Pultrusion: As the name suggests, it is a process which will have pulling and extrusion (cutting). In this process resin impregnated fibres are pulled through to make a part. Saturated material is pulled through a heated closed die and cured while continuously moving through the die. The figure 5 gives an indication of the process. Figure Pultrusion process [http://www.ultrafiberglass.com/pultrusion%20process.jpg] The advantage of pultrusion process is that it is a continuous process and can be completely automated to get the finished product. The process is suitable for making high volume composite parts. Utilizes low cost fibre and resin systems thus provide a low production cost of products. The limitations being that the thin wall parts, tapered and complex parts cannot be produced. Resin Transfer Moulding A resin and catalyst are placed in two separate tanks A and B. A release agent such as gel coat is then applied to mould for good surface finish. The preform is placed inside the mould and the mould is then clamped. The mould is then heated to a specified temperature. Mixed Resin is then injected at selected temperature and pressure. Vacuum is also created to remove air bubbles as well as assist in resin flow. The injection continues until the mould is completely filled. The vacuum is turned off. The pressure inside the mould is increased to ensure that remaining porosity is collapsed. After curing for certain period of time depending on resin, the composite part is removed from mould. In this process, fabrics are placed in to a mould and then wet resin is injected. Resin is pressurized and is then forced into the cavity which is under vacuum. In the VARTM process resin is completely pulled in to cavity under vacuum. This moulding process allows precise tolerance and detailed shaping, however this may result in at times failure to fully saturate fabric leading to weak shape in the final product. The figure and steps following the figure describe the process. Figure Resin Transfer Moulding [http://www.ctihuatai.com/index.files/rtmstatic.gif] Strengthening of Structures The next stage of literature review will now focus on the strengthening of structures. As explained earlier the need for strengthening of structures; it is important to look at first the different methods adopted in order to strengthen the structure. The structure strengthening methods include the following. Span Shortening Pre-stressed Concrete Section Enlargement Structure Strengthening using FRP Composites. Span Shortening This is method in which length of a beam is shortening. This is achieved by installing additional supports underneath the existing members. Materials used in this process are mainly structural steel members and cast in place reinforced concrete members. The members are connected mechanically using bolts and adhesive anchors. Span shortening reduces the deflection in the beam. This can be proved by means of simple calculation. P1ÃŽÂ ´1 Let us consider a beam of length à ¢Ã¢â€š ¬Ã…“L (m)à ¢Ã¢â€š ¬? under a load P kN undergoing a 3 point bend test. l1 Where ÃŽÂ ´ is the deflection in the beam. Let us consider a pair of equations in order to calculate deflection in the beam. ; If ratio of the deflection is taken in to account, and doubling the span length meaning l2 = 2l1. Then, Then ÃŽÂ ´2 = 8 x ÃŽÂ ´1; this means that central deflection will become 8 times. So to conclude the method shorter the span, less deflection will occur at the centre. Pre stressed Concrete Pre stressed concrete is a method used for overcoming concreteà ¢Ã¢â€š ¬Ã¢â€ž ¢s natural weakness in tension. Pre-stressing tendons generally made of high tensile steel rods are used to provide clamping load that generates compressive stresses which balances out the tensile stress that would be experienced by the concrete beams due to bending [7]. The process of pre stressing can be achieved in three ways: pre tensioned concrete, bonded or un-bonded post-tensioned concrete. However the method is mainly used for civil engineering and construction projects. The figure below gives an indication of the method. Figure Pre Stressing Method [http://www.fhwa.dot.gov/BRIDGE/pt/images/pt102.gif] Section Enlargement In simple terms, it is when the second moment of area is changed. The method involves placing an additional bonded reinforcement concrete to an existing structure member in the form of an overlay or a jacket. The main advantage of this technique is that it increases the load bearing capacity or stiffness. The technique reduces bending and shear forces on overstressed beams. Structure Strengthening using FRP Composites Fibre reinforced polymers are applied to strengthen structure. There method can be primarily divided in to two categories. One is the strengthening of structure at manufacturing phase and other is after manufacturing. The technique used to strengthen structure at manufacturing phase is known as Near Surface Mounted Reinforcement (NSMR) and the strengthening of structure can be achieved once the manufacturing is completed is by external plate bonding method. Near Surface Mounted Reinforcement Near surface mounted reinforcement is one of the latest and most promising techniques to be considered when strengthening concrete structures. Using FRP instead of steel in this technique has many advantages such as its better resistance to corrosion, quick and easy installation due to light weight. When compared with external bonding method, the NSMR has many advantages such as amount of site installation work is reduced for example removal of plaster, etc. second advantage being that NSMR is less prone to de-bonding from concrete substrate. NSMR bars can be easily anchored into adjacent members to prevent failures due to de-bonding. This feature is very important when considering flexural strengthening. NSMR bars can be easily pre-stressed. As the bars are covered by cover of concrete, so they are less exposed to accidental impact or mechanical damage such as fire or wear and tear. As the NSMR technique is new, the knowledge on this technique is limited than that of externally bonded reinforcement. In recent studies CFRP (carbon fibre reinforced polymer) NSM reinforcements have been widely used to strengthen structures. The following general steps must be performed during the strengthening. Sawing up slots in concrete cover, depth of the structure is dependent on the product used. After sawing of slots, careful cleaning is required. If using an epoxy system, the slots where the bars are to be installed must be dry before bonding. If cement system is used then the surface must be wet. Adhesive is applied in the slot when using epoxy system or cement mortar is used when using cement system. The figure below gives an indication of the technique. Figure Near Surface mounted Reinforcement technique [http://msw.mcmaster.ca/~koranyy/Photos/NSM-vertical.jpg] In the above figure it can be seen that a carbon fibre rope is placed in the centre of the brick wall and an epoxy paste is applied. The figure on the left is for vertical reinforcement and the figure on the right is for horizontal reinforcement. The second part of the images is the finished version of structure once the method is completed. The application of this technique is mainly on flat surfaces and is suitable for strengthening in bending. The process is also helpful in increasing the shear capacity of the beams. The next method considered for structure strengthening using FRP composites is external plate bonding. However it is first important to compare the advantage of using composites over steel plates. These are explained in the next segment of the report. External Plate Bonding The general principle of external plate bonding method is that in this method transfer of stresses takes place from the structural element to the additional plates that are adhered or bolted. Whilst strengthening structure many problems are faced such as. Load Increases: Structure with externally bonded plates has capacity to accept higher live loads for example in factories where heavy machines are installed. External plate bonding also reduces deformation and is also helpful where vibrations are an issue. Damage to Structural Parts: it can be utilized in cases where the building has been damaged due to fire or vehicle collision. Improvement in suitability: This can be achieved by limiting deflection and reducing crack widths and stresses. Modification of Structural System: Plate bonding provides a cost effective solution where structure has been weakened by removal of walls and columns or opening cuts. Errors in planning or construction: Plate bonding provides solution to earlier design errors and calculation errors. In general terms external plate bonding can reduce deflection thus limit cracking as well as increase the load bearing capacity and also increase the flexural strength and finally improve resistance to shear in certain cases. As the method of plate bonding can be achieved by both using Composites as well as steel plates so it is important to understand the advantage of composite over steel plates. This analysis will be carried on three grounds namely technical, practical/application and Economic. The table on the next page summarizes the technical differences between the composite and steel plates Composite Steel Plates High tensile strength of Carbon fibre (5650N/mm2) Tensile strength of steel is (235 N/mm2) No corrosion Highly prone to corrosion Strength to weight ratio is higher Strength to weight ratio is lower Table Technical differences between Composite and Steel Plates When performing practical application on site; installation of steel plates requires an extensive amount of work such as drilling holes in plates, wrapping plates and bolting the plates. Where as the composite plates would require very limited work such as bonding to the metal plate using an epoxy. Table 2 summarizes the economic differences Potential Cost Composite Steel Plates High Low Volume Typically 10-50% of steel Relatively high Adhesive smaller area of plates required so less adhesive Area of plates is high so higher amount of adhesive Preparation Off site On site Limited Limited Extensive Extensive Labour Requirement Low High Equipment Low High Temporary support None Yes Time Fast Slow Table Economic Differences between Composite and steel plates The application of the plates externally can be varying such as if the surface is horizontal than FRP is applied horizontally or in the U shape. If the structure is a circular column then FRP is applied by wrapping around it. Wrapping sheets have fabrics in same direction or bi-directional. One thing to be considered when using FRP is that it needs to be protected from fire. An FRP plate applied to the bottom of structure (tension face) increases the strength of beam and reduces deflection. Where as application of FRP strips attached in U shape around the sides and bottom of beam increases shear resistance. Wrapping of sheets around column results in higher strength and restrains lateral expansion of columns. The figures below give an example of application of FRP composite to structure. (A) (B) (C) Figure Strengthening using FRP Composites [http://sites.google.com/site/frpstrengthening/frpdrawing2-custom-size-398-103.jpg] [http://www.structural.net/Article_Images/Figure%204.JPG] Figure A and B look at plate bonding and figure C gives an indication of wrapping columns. Discussion The project is currently in its research phase. The topics covered in the literature review section of the report are vital as it is important to gain knowledge about the subject and understand its applications in the real engineering world. The future work in the project will involve an additional literature review for structural strengthening and the next stage will be to set up a meeting with the supervisor to discuss the experiment as to what needs to be performed. Once this is completed the project plan will be reviewed to meet the final submission date of the thesis as mentioned earlier in the deliverables section. To conclude the test to be carried out for this purpose will be a 3 point bend test and 4 point bend test and thus the results will be concluded. Bibliography Dag Linghoff (2009), Thin Walled Structures, Carbon-fibre Composites for strengthening steel structures, volume 47 pages 1048-1058. U.Meier (1995), Construction and Building Materials, Strengthening of structures using carbon fibre epoxy composites, volume 9 issue 6 pages 341-351. A.R.Rahai and M.M.Alinia (2008), Construction and Building Materials, Performance Evaluation and Strengthening of concrete structures with composite bracing members, volume 22 issue 10 pages 2100-2110 J.G.Broughton (1997), International Fibre Reinforced Polymer Composites to Strengthen Structures Fibre Reinforced Polymer Composites to Strengthen Structures Aim The project aim is to identify the use of FRP (Fibre Reinforced Polymers) composites in strengthening of structures. The general process and methodology considered in achieving this objective is by externally bonding Fibre reinforced plastics to the metal structure/plate and thus testing the specimen under 3 point bend as well as 4 point bend tests. The preliminary report will focus on the project introduction, literature review related to the project topic, project plan and further to be carried out. Analysis of Tasks As mentioned the projectà ¢Ã¢â€š ¬Ã¢â€ž ¢s main focus is strengthening of structures. So the question is why is there a need for strengthening of structures? The reason behind the strengthening of structures is that the structure will be able to support greater magnitude of loads than the values for which the structures are originally designed. Strengthening may become necessary in course of time in order to overcome the damage caused due to environmental factors such as corrosion as well as fatigue cracking. The method of bonding reinforcement represents an attractive solution to the problem as it can be achieved with relatively small impact on the structure. The next stage of the preliminary thesis will focus on the literature review. The literature review section is divided in to two sections firstly it will focus on the topics related to the Composite Materials, which will involve the following topics. Definition of Composite Material Classification of Composite Materials Types of Matrix Types of Reinforcement Advantages and Disadvantages of Composite Materials Manufacturing of Composite Materials The next section of the literature review will focus on the topics related to strengthening of structures. For this section following topics will be considered. Different Methods for Structure Strengthening Different Methods for Structure Strengthening using FRP Composites. The preliminary thesis will also look at the comparison between the structural strengthening using FRP Composites and Steel plates. This will help in giving a suitable reason as to why Composites are preferred over Steel plates for structural strengthening. Composites are considered as one of the most promising material for reducing the weight as well as increasing the strength of the material. The theory of hybrid material has been successfully exploited when studying sandwich panel technology. Now the concept of integrated multi materials is extended to a wider variety of structures, components and applications. Fibre reinforced plastics (FRPà ¢Ã¢â€š ¬Ã¢â€ž ¢s) have been successfully used for the post strengthening of structures over a number of years. The design and manufacturing of composites has led to its application in variety of industries such as automotive, aerospace, sporting goods, construction and in the marine as well as oil and gas industries. Moreover the method of bonded reinforcements also comes into account when there have been cases where errors in design or construction of a structure have questioned safety aspect. This can be achieved by externally bonding reinforcements at a cost of very small impact to the structures. Project Time-Line (Gantt chart) Literature Review Composite Materials Composite materials also known as composites are defined as a combination of two or more materials to give a unique combination of properties [1]. This definition is very general and thus includes metals, alloys, plastic co-polymers, minerals and wood. A material is only classified as a composite if the material satisfies the following conditions [2]: The material must be manufactured It should consist of two or more physically and/or chemically distinct, suitably arranged or distributed phases with an interface separating them. The characteristics of the composites are not depicted by any of the components in the isolation. Fibre reinforced composite materials differ slightly from the general definition because in this FRP the constituent materials are different at the molecular level and at mechanically separable. However the final material properties of the composite are better in comparison to that of the constituents. The figure 1 below gives a basic idea of how the structure of composite material looks like. The composites can be classified as fibre reinforced, particle reinforced, dispersion strengthened and laminates composites. Figure Structure of Composite Material [http://resources.edb.gov.hk/~s1sci/R_S1Science/sp/en/syllabus/unit14/new/images/s.gif] The composite material consists of two main elements the matrix and reinforcements (fibre). The classification of Composite materials is as shown in figure 2. Composite Materials Matrix Reinforcements Polymer Metal Ceramic Particle Reinforcement Fibre Reinforcement Structural Reinforcement Laminates Long Fibre Short Fibre Preferred Orientation Random Orientation Bidirectional Unidirectional Preferred Orientation Random Orientation Figure Classification of Composite Material Types of Matrix There are three main types of matrix considered when studying composites materials namely Polymer, Metal and Ceramic. Polymer Matrix composites are the most common types of matrix composites. They are also known as FRP (Fibre reinforced polymers). The resin used in here is polymer based combined with a variety of fibres such as Glass, Carbon and Aramid as reinforcements. Metal Matrix Composites are mainly used in the automotive industry. The materials use a metal for example Aluminium as the matrix which is then reinforced with fibres such as silicon carbide. Ceramic Matrix Composites are used in very high temperature environments. This type of materials uses Ceramic as the matrix and the matrix is then reinforced with short fibres such as Silicon Carbide and Boron Nitride. A matrix plays an important role in a Composite structure. There are several functions of Matrix most of which are very important to the satisfactory performance of the structure. The following points outline the important functions of the matrix. The matrix binds the fibre together and thus transfers the load to the fibres. The matrix provides the rigidity and shape to the structure. The matrix isolates the fibres such that each individual fibre can perform separately, due to this crack propagation process slows down. The surface finish quality of the structure is provided by the matrix. The matrix acts as a protection to the reinforced fibres from chemical attack and mechanical wear and tear. The type of material selected as matrix affects the ductility and failure mode of the structure together with the fibreà ¢Ã¢â€š ¬Ã¢â€ž ¢s compatibility. Types of Reinforcements The other constituent in the composite material is called the Reinforcement. This gives the composite the necessary strength and stiffness. The structure of the reinforcement is thin rod like. The most commonly used reinforcements are Glass, Carbon, Aramid, and Boron fibres. The diameters of these fibres range from 5 µm to 20  µm. [1] Due to the thin diameter of the fibre, the fibres are flexible and can be formed easily into any shapes. Fibres can come into many forms such as continuous fibre, discontinuous fibre, short fibres, long fibres, organic fibres and inorganic fibres. Fibre brings out the high performance of the material; this is due to three important characteristics of the fibres. The orientation of the fibres also has an impact on the performance of the composite. The fibres can be unidirectional, cross ply or random in its arrangement. Small diameter in comparison to the grain size. As a result of this higher fraction of theoretical strength can be attained. High aspect ratio (length/diameter); this allows a larger amount of load to be transferred. High degree of flexibility. The main functions of fibres are as listed below [1]; To carry the load. Hence fibres are made from materials with high tensile strength and high elastic modulus. Provides strength, stiffness, thermal stability and other structural properties in the composites. Provide electrical conductivity or insulation, depending on the type of fibre used. Advantages of Composites Composites are designed to perform in applications which require lighter weight and higher performance. The advantages of using composites are listed below. High resistance to Corrosion; due to this the application in marine, infrastructure and chemical is very good. High specific stiffness and high specific strength; this gives a weight reduction so is used for the application in aerospace, automotive and manufacturing of sporting goods. The impact resistance is high compared to metal. Higher fatigue strength. Unidirectional carbon/epoxy composites have good fatigue strength of almost 90% of its static strength. Composite materials offer increased amount of design of flexibility. For example the coefficient of thermal expansion of composite can be made zero if suitable constituents and lay up sequence is selected. As the coefficient of thermal expansion is relatively low compared to metals, the composite structure thus provides a good dimensional stability. Also due to the design flexibility, composite materials can be formed into any shapes. Process cycle times and costs are also reduced because of the use of composites in production of net shape and near net shape parts. Composite materials dampen the vibrations an order of magnitude better than metals. Glass reinforced and aramid reinforced composite meet the FAA and JAR requirements for low smoke and toxicity and thus are used in interior panels of aircrafts, stow bins and galley walls. Disadvantages of Composites There will always be limitations to the benefits of the composites. The disadvantages are as listed below. Weaker in transverse direction and low in toughness. Material cost is high compared to that of steel and aluminium. The lack of high volume production limits the wide spread use of composite materials. However this is changing as modern production methods such as Pultrusion, Resin transfer Moulding and other methods have been automated to increase the rate of production. The knowledge through books and database is limited when comes to designing parts with composite. Composites absorb moisture, which affects the properties and dimensional stability of the composite. Difficult to join together with other material due to its anisotropic properties and high sensitivity to damage. For example when drilling holes for mechanical fastening. Brittle like behaviour. Difficult to repair as most composites use thermo set matrices that can not be re shaped. On the contrary thermoplastics can be repaired how ever they are rare [4]. Solvent resistance, chemical resistance and environmental stress cracking of composite depend on the properties of polymers. Some polymers have low resistance to the solvents and environmental stress cracking[1]. Manufacturing of Composite Materials Before looking into manufacturing of composite materials; it is important to look at manufacturing of fibre performs briefly. Fibre performs is how fibre are manufactured before being bonded to the matrix to form a composite material. Fibre performs are often manufactured in sheets or filaments in case of spraying applications. The fibre manufacturing process is carried out by adopting the technique used in textile industry. The techniques used are weaving, knitting, braiding and stitching [5]. The manufacturing process of composite material in general can be divided into two main processes. Prepreg Moulding Wet Moulding PrepReg Moulding The process of prepreg moulding can be further categorized as: Bladder Moulding Compression Moulding Autoclave/Vacuum bag Moulding Mandrel Wrapping [6]Bladder Moulding: In this process the sheets of prepreg material are laid up and placed in female style mould along with a balloon like bladder. The mould is then closed and placed in the heated press. Eventually, the bladder is pressurized which then forces the layers of material against mould walls. The part is then cured and removed from the hot mould. The process is ideally suited for complex hollow shapes. Also the process has great cost to performance balance. Typical example of equipment using bladder moulding technique is the manufacturing of tennis racquet. Average cure cycle range is 15-60 minutes. Compression Moulding: A process where a à ¢Ã¢â€š ¬Ã…“performà ¢Ã¢â€š ¬? or à ¢Ã¢â€š ¬Ã…“chargeà ¢Ã¢â€š ¬? of single moulding compound (SMC) or bulk moulding compound (BMC) or sometimes prepreg fabric is placed in the mould cavity. Once the mould is closed, the material is compacted and cured inside by heat and pressure. The process also offers excellent detailing for geometric shapes. The average cure cycle range is 2-20 minutes. The tooling is process is often more expensive. Auto Clave/Vacuum Bag Moulding: The figure below gives an idea of vacuum bagging for prepreg lay-up process. Figure Vacuum bagging for prepreg lay up process [http://www.highcomp.no/design/bilder/vacum/vacum.gif] Once all the prepregs are laid out in the desired sequence, vacuum bagging preparations are set up as per the figure 3 for curing of the part. First step is application of release film on the top of all the prepreg. The release film is a perforated film that allows captured air, excess resin and volatiles to escape. Secondly is the application of bleeder on top of release film; it is a porous fabric that absorbs moisture and excess resin coming from stack of prepregs/laminates. Thirdly is the application of non porous and non-perforated film on top of bleeder. After this a breather layer is applied; this is a porous fabric which creates even pressure around the part and at the same time allowing air and volatiles to escape. Then final layer is of vacuum bag. The vacuum bag is an expendable polyamide film. The film is sealed on all sides of laminate using a seal tape. A nozzle is inserted into the vacuum bag and is then connected to hose vacuum pump for creating vacuum. Mandrel Wrapping: In these process sheets of prepreg material is wrapped around steel or aluminium mandrel. The prepreg material is compacted by nylon or polypropylene cello tape. Parts are cured by hanging in the oven. Once the curing process is completed, the cello and mandrel are removed which results in a hollow carbon tube. Advantages of prepreg lay up process are that it is simple process when manufacturing complex parts. Also strong and stiff parts can be fabricated using this process. Also allows production of high fibre volume fraction. Prepregs usually have more than 60% fibre volume fraction. Limitations of the process being that labour is intensive as a result of which the process is not suitable for high volume production applications. Also parts manufactured by this process are very expensive. Wet Moulding Wet moulding process can be divided into following processes. Wet layup Spray Up process Filament winding Pultrusion Resin transfer Moulding (RTM) Resin transfer moulding under vacuum (VARTM) Wet Lay-up: in this process a fabric is placed in open mould which is then hand saturated with wet resin. The curing occurs normally at room temperature. However it can be cured at higher temperatures based on the heat resistance of the mould. The advantage of this process is that the material cost and tooling cost is low. Because of this the process is considered as low tech process. Spray-up process: The processing steps are similar to that of the wet lay-up process except for the method of creating the laminates. The basic steps are as follows [1]. The mould is waxed and polished for easy de-moulding Gel coat is applied to the mould surface and allowed to harden before building any other layer. The barrier coat is applied to avoid fibre print through the gel coat surface. Oven curing of barrier coat. Mixing of resin with fillers and the mixture is then pumped to a holding tank. Spraying of resin, catalyst and chopped fibres on the mould surface. This is done with the aid of hand held spray gun. The spraying is carried out in typical pattern to create uniform thickness of the laminate. A roller is then used in order to make the fibre and resin material compact as well as create a smooth and even surface. The laminate is then cured in the oven. The part is then de-moulded and sent for finishing work. The process of spray lay-up is very economical, maximizes the use of low cost tooling as well as low cost material systems however it is not suitable for making parts that have high structure requirements, fibre volume fraction can be difficult to control as well as the thickness. The surface finish on both the sides is not same. Also dimensional tolerance is poor. Filament Winding: This is a process in which resin-impregnated fibres are pulled and wound over a rotating mandrel at desired angle. The fibre pulled is from a wet bath of resin. Curing occurs at room temperature or higher temperature. The performance is limited and it is difficult to obtain uniform fibre distribution and resin content through out the thickness of the laminate. The process is very suitable for tubular parts such as pressure vessels. Figure Filament Winding Process [http://www.thaicomposites.com/images/filament-winding.gif] The advantages of this process being its ability to utilize low cost raw material and low cost tooling systems. It can be automated for the production of high volume composite parts. The figure 4 gives an indication of the filament winding process. Pultrusion: As the name suggests, it is a process which will have pulling and extrusion (cutting). In this process resin impregnated fibres are pulled through to make a part. Saturated material is pulled through a heated closed die and cured while continuously moving through the die. The figure 5 gives an indication of the process. Figure Pultrusion process [http://www.ultrafiberglass.com/pultrusion%20process.jpg] The advantage of pultrusion process is that it is a continuous process and can be completely automated to get the finished product. The process is suitable for making high volume composite parts. Utilizes low cost fibre and resin systems thus provide a low production cost of products. The limitations being that the thin wall parts, tapered and complex parts cannot be produced. Resin Transfer Moulding A resin and catalyst are placed in two separate tanks A and B. A release agent such as gel coat is then applied to mould for good surface finish. The preform is placed inside the mould and the mould is then clamped. The mould is then heated to a specified temperature. Mixed Resin is then injected at selected temperature and pressure. Vacuum is also created to remove air bubbles as well as assist in resin flow. The injection continues until the mould is completely filled. The vacuum is turned off. The pressure inside the mould is increased to ensure that remaining porosity is collapsed. After curing for certain period of time depending on resin, the composite part is removed from mould. In this process, fabrics are placed in to a mould and then wet resin is injected. Resin is pressurized and is then forced into the cavity which is under vacuum. In the VARTM process resin is completely pulled in to cavity under vacuum. This moulding process allows precise tolerance and detailed shaping, however this may result in at times failure to fully saturate fabric leading to weak shape in the final product. The figure and steps following the figure describe the process. Figure Resin Transfer Moulding [http://www.ctihuatai.com/index.files/rtmstatic.gif] Strengthening of Structures The next stage of literature review will now focus on the strengthening of structures. As explained earlier the need for strengthening of structures; it is important to look at first the different methods adopted in order to strengthen the structure. The structure strengthening methods include the following. Span Shortening Pre-stressed Concrete Section Enlargement Structure Strengthening using FRP Composites. Span Shortening This is method in which length of a beam is shortening. This is achieved by installing additional supports underneath the existing members. Materials used in this process are mainly structural steel members and cast in place reinforced concrete members. The members are connected mechanically using bolts and adhesive anchors. Span shortening reduces the deflection in the beam. This can be proved by means of simple calculation. P1ÃŽÂ ´1 Let us consider a beam of length à ¢Ã¢â€š ¬Ã…“L (m)à ¢Ã¢â€š ¬? under a load P kN undergoing a 3 point bend test. l1 Where ÃŽÂ ´ is the deflection in the beam. Let us consider a pair of equations in order to calculate deflection in the beam. ; If ratio of the deflection is taken in to account, and doubling the span length meaning l2 = 2l1. Then, Then ÃŽÂ ´2 = 8 x ÃŽÂ ´1; this means that central deflection will become 8 times. So to conclude the method shorter the span, less deflection will occur at the centre. Pre stressed Concrete Pre stressed concrete is a method used for overcoming concreteà ¢Ã¢â€š ¬Ã¢â€ž ¢s natural weakness in tension. Pre-stressing tendons generally made of high tensile steel rods are used to provide clamping load that generates compressive stresses which balances out the tensile stress that would be experienced by the concrete beams due to bending [7]. The process of pre stressing can be achieved in three ways: pre tensioned concrete, bonded or un-bonded post-tensioned concrete. However the method is mainly used for civil engineering and construction projects. The figure below gives an indication of the method. Figure Pre Stressing Method [http://www.fhwa.dot.gov/BRIDGE/pt/images/pt102.gif] Section Enlargement In simple terms, it is when the second moment of area is changed. The method involves placing an additional bonded reinforcement concrete to an existing structure member in the form of an overlay or a jacket. The main advantage of this technique is that it increases the load bearing capacity or stiffness. The technique reduces bending and shear forces on overstressed beams. Structure Strengthening using FRP Composites Fibre reinforced polymers are applied to strengthen structure. There method can be primarily divided in to two categories. One is the strengthening of structure at manufacturing phase and other is after manufacturing. The technique used to strengthen structure at manufacturing phase is known as Near Surface Mounted Reinforcement (NSMR) and the strengthening of structure can be achieved once the manufacturing is completed is by external plate bonding method. Near Surface Mounted Reinforcement Near surface mounted reinforcement is one of the latest and most promising techniques to be considered when strengthening concrete structures. Using FRP instead of steel in this technique has many advantages such as its better resistance to corrosion, quick and easy installation due to light weight. When compared with external bonding method, the NSMR has many advantages such as amount of site installation work is reduced for example removal of plaster, etc. second advantage being that NSMR is less prone to de-bonding from concrete substrate. NSMR bars can be easily anchored into adjacent members to prevent failures due to de-bonding. This feature is very important when considering flexural strengthening. NSMR bars can be easily pre-stressed. As the bars are covered by cover of concrete, so they are less exposed to accidental impact or mechanical damage such as fire or wear and tear. As the NSMR technique is new, the knowledge on this technique is limited than that of externally bonded reinforcement. In recent studies CFRP (carbon fibre reinforced polymer) NSM reinforcements have been widely used to strengthen structures. The following general steps must be performed during the strengthening. Sawing up slots in concrete cover, depth of the structure is dependent on the product used. After sawing of slots, careful cleaning is required. If using an epoxy system, the slots where the bars are to be installed must be dry before bonding. If cement system is used then the surface must be wet. Adhesive is applied in the slot when using epoxy system or cement mortar is used when using cement system. The figure below gives an indication of the technique. Figure Near Surface mounted Reinforcement technique [http://msw.mcmaster.ca/~koranyy/Photos/NSM-vertical.jpg] In the above figure it can be seen that a carbon fibre rope is placed in the centre of the brick wall and an epoxy paste is applied. The figure on the left is for vertical reinforcement and the figure on the right is for horizontal reinforcement. The second part of the images is the finished version of structure once the method is completed. The application of this technique is mainly on flat surfaces and is suitable for strengthening in bending. The process is also helpful in increasing the shear capacity of the beams. The next method considered for structure strengthening using FRP composites is external plate bonding. However it is first important to compare the advantage of using composites over steel plates. These are explained in the next segment of the report. External Plate Bonding The general principle of external plate bonding method is that in this method transfer of stresses takes place from the structural element to the additional plates that are adhered or bolted. Whilst strengthening structure many problems are faced such as. Load Increases: Structure with externally bonded plates has capacity to accept higher live loads for example in factories where heavy machines are installed. External plate bonding also reduces deformation and is also helpful where vibrations are an issue. Damage to Structural Parts: it can be utilized in cases where the building has been damaged due to fire or vehicle collision. Improvement in suitability: This can be achieved by limiting deflection and reducing crack widths and stresses. Modification of Structural System: Plate bonding provides a cost effective solution where structure has been weakened by removal of walls and columns or opening cuts. Errors in planning or construction: Plate bonding provides solution to earlier design errors and calculation errors. In general terms external plate bonding can reduce deflection thus limit cracking as well as increase the load bearing capacity and also increase the flexural strength and finally improve resistance to shear in certain cases. As the method of plate bonding can be achieved by both using Composites as well as steel plates so it is important to understand the advantage of composite over steel plates. This analysis will be carried on three grounds namely technical, practical/application and Economic. The table on the next page summarizes the technical differences between the composite and steel plates Composite Steel Plates High tensile strength of Carbon fibre (5650N/mm2) Tensile strength of steel is (235 N/mm2) No corrosion Highly prone to corrosion Strength to weight ratio is higher Strength to weight ratio is lower Table Technical differences between Composite and Steel Plates When performing practical application on site; installation of steel plates requires an extensive amount of work such as drilling holes in plates, wrapping plates and bolting the plates. Where as the composite plates would require very limited work such as bonding to the metal plate using an epoxy. Table 2 summarizes the economic differences Potential Cost Composite Steel Plates High Low Volume Typically 10-50% of steel Relatively high Adhesive smaller area of plates required so less adhesive Area of plates is high so higher amount of adhesive Preparation Off site On site Limited Limited Extensive Extensive Labour Requirement Low High Equipment Low High Temporary support None Yes Time Fast Slow Table Economic Differences between Composite and steel plates The application of the plates externally can be varying such as if the surface is horizontal than FRP is applied horizontally or in the U shape. If the structure is a circular column then FRP is applied by wrapping around it. Wrapping sheets have fabrics in same direction or bi-directional. One thing to be considered when using FRP is that it needs to be protected from fire. An FRP plate applied to the bottom of structure (tension face) increases the strength of beam and reduces deflection. Where as application of FRP strips attached in U shape around the sides and bottom of beam increases shear resistance. Wrapping of sheets around column results in higher strength and restrains lateral expansion of columns. The figures below give an example of application of FRP composite to structure. (A) (B) (C) Figure Strengthening using FRP Composites [http://sites.google.com/site/frpstrengthening/frpdrawing2-custom-size-398-103.jpg] [http://www.structural.net/Article_Images/Figure%204.JPG] Figure A and B look at plate bonding and figure C gives an indication of wrapping columns. Discussion The project is currently in its research phase. The topics covered in the literature review section of the report are vital as it is important to gain knowledge about the subject and understand its applications in the real engineering world. The future work in the project will involve an additional literature review for structural strengthening and the next stage will be to set up a meeting with the supervisor to discuss the experiment as to what needs to be performed. Once this is completed the project plan will be reviewed to meet the final submission date of the thesis as mentioned earlier in the deliverables section. To conclude the test to be carried out for this purpose will be a 3 point bend test and 4 point bend test and thus the results will be concluded. Bibliography Dag Linghoff (2009), Thin Walled Structures, Carbon-fibre Composites for strengthening steel structures, volume 47 pages 1048-1058. U.Meier (1995), Construction and Building Materials, Strengthening of structures using carbon fibre epoxy composites, volume 9 issue 6 pages 341-351. A.R.Rahai and M.M.Alinia (2008), Construction and Building Materials, Performance Evaluation and Strengthening of concrete structures with composite bracing members, volume 22 issue 10 pages 2100-2110 J.G.Broughton (1997), International