10
–5, can be calculated as follows:Euro-SiBRAM’2002 Prague, June 24 to 26, 2002, Czech Republic
Session 7
Assoc. Prof. Szczepan Wolinski, DrSc.
Rzeszow
University of Technology, Al. Pow. Warszawy 6, 35-959 Rzeszow,
Poland
szwolkkb@prz.rzeszow.pl
This paper examines the advantages of using simulation techniques to teach reliability of structures to civil engineering students and practicing engineers. In this connection four main questions are discussed: What should be the scope and content of courses in the area of structural reliability useful for students and civil engineers? How to bring the understanding of the structural reliability to civil engineers and students? How to introduce simulation techniques into civil engineering education and practice? Which innovations in teaching and learning in civil engineering education can be used for efficient implementation of the simulation-based design?
Key Words: Teaching reliability, civil engineering education, simulation-based design.
Most present day building codes are based on the limit states approach and the semi-probabilistic Partial Factors Method. The Eurocode system of design codes introduces the concept of reliability management freely exert the knowledge and expertise of the designer to select the appropriate models and procedures for probability based design and assessment of a structure. Although the fully probabilistic design methods may be considered as more rational and consistent than the partial factors design, usual way to achieve probabilistic solutions by means of analytical and numerical methods are too sophisticated and difficult for effective practical applications. Simulation techniques enable to solve, at least approximately, complex problems for which closed form solutions are either not possible or very difficult.
Success of the implementation of the probabilistic design methods into engineering practice depends to a large extent on education of students and design engineers. They should be taught well in mathematics, structural mechanics and engineering. On the other hand, traditional methods of learning and the structure of academic course of the structural reliability bring about them a reputation of being difficult, boring and of little importance. Majority of designers and students are using codes without the meaning of safety measures in codes. These state thesis that there is a need for significant changes in the teaching of the probability theory and statistics as well as the structural reliability for students of civil engineering faculties and civil engineers. Simulation techniques and computers can assist teaching and implementation of probabilistic concepts in design and evaluation of many practical problems in civil engineering.
The paper attempts to begin the discussion about the following questions:
- What should be the scope and content of courses in the area of structural reliability
useful for students and civil engineers?
- How to bring understanding of structural reliability concepts to civil engineering
designers and students?
- How to introduce simulation techniques into civil engineering education and practice?
- Which innovations in teaching and learning in civil engineering education can be used
for efficient implementation of the simulation-based structural design and assessment?
2 Scope and content of courses in the area of structural reliability
All components of the building process including planning, design, construction, use and demolition, involve various uncertainties. Because of these uncertainties, majority of the state variables needed to formulate a performance function for the considered mode of failure of a structure, are random variables. Thus, absolute safety of structural elements and structures cannot be achieved, and consequently structures should be designed to serve their function with an assumed finite probability of failure. These facts are included in the present day structural codes and they should be accepted and taken into consideration in the educational process.
Civil engineering faculties and schools worldwide have introduced courses on probability and statistics. The focus of these courses is usually on the rigorous explanations of basic axioms, theorems, proofs and procedures. In structural design courses, the application and interpretation of the current semi-probabilistic approach to design are emphasized. However, students and sometimes lecturers usually don’t understand the probabilistic basis of the specifications. Consequently, many students and engineers are using codes and specifications without understanding of the meanings of measures used to express safety, serviceability and durability of structures. Therefore, in many countries special courses covering the topic of “reliability of structures” have been developed and incorporated in the academic curricula as well as in the curricula of continuing engineering education or lifelong learning for professional engineers.
In my opinion, the course of Reliability of Structures within
faculties (departments) of civil engineering should be obligatory for
undergraduate, graduate and doctoral students. The objective of this
course is to provide the background needed to understand
probability-based design criteria recommended in design codes and to
provide tools for engineers interested in applying probabilistic
methods to other situations. Programs of an introductory course
(30-45 hours) should include the following issues:
a) Short review of the basics of probability and statistics,
b) Simulation techniques (Monte Carlo method),
c) Uncertainties in the building process,
d) Probabilistic models of resistance,
e) Probabilistic models of loads,
f) Safety measures and methods of structural safety analysis,
g) Semi-probabilistic approach to the Limit States Method,
h) Simplified and fully probabilistic methods of reliability assessment and design.
More specific courses should be dedicated to graduate and doctoral students as well as practicing engineers, according with their interests. Objective of these courses is to give students information about: structural risk assessment, risk engineering, statistical quality control, system reliability, design codes, human errors, etc.
3 Simulation techniques in understanding and teaching the structural reliability
According to the present day psychological knowledge people memorize about one quarter of matter heard, nearly one-half of heard and seen and about three-quarters of the matter in which they have actively participated. A traditional approach to structural reliability based on analytical and numerical solutions does not allow for clear and fast analysis of practical problems when performance functions are usually nonlinear and dependant on many random variables. Using simulation techniques and personal computers students can solve a lot of complicated problems in a short time and in transparent way.
Simulation techniques may be used to solve problems of probabilistic assessment and dimensioning of structural elements and structures with reference values of the probability of failure. The Monte Carlo method is a special technique that can be used to obtain a set of results numerically without doing any physical testing. These results can be used to establish the probability distributions of the resultant parameters and their fractiles as well as the probability of failure of an analyzed element or structure. The procedure of Monte Carlo simulation is based on the following factors [1, 2, 4 – see SBRA Method documented in 4, editors comment):
- The important parameters in a considered problem are random variables with known in advance or established probability distributions. Several different modes of representation of random variables may be used, e.g. they can be expressed by bounded histograms,
- The resultant random variable or the reliability (performance) function is analyzed using a simulation technique,
- Safety, serviceability, durability (or generally reliability) is expressed by the probability of failure.
Using Monte Carlo method students can familiarize themselves with generation of different random variables including multidimensional and correlated variables. They can be able to watch changes of the shape of distributions and values of distribution parameters with the width of the intervals for sampling, numbers of simulation steps, etc. Then students can investigate validity of the Central Limit Theorem, analyze linear and nonlinear functions of random variables. They can investigate examples of load effect combinations and resistance of different structural elements and at last to calculate the failure probability of structures. The application of the simulation computer programs such as M-Star and AntHill [4] are very helpful and efficient for this purpose.
For example, the assignment is to calculate the area of tension
reinforcing steel As required in the critical
cross-section of a simply supported reinforced concrete beam, exposed
to the uniformly distributed dead and live loads g + p. The
As–value required with the probability of
failure Pf = 7.210
–5, can be calculated as follows:
,
Geometrical
variables: span L = 5.0 m, effective depth d = 0.35 m,
and width of the cross-section b = 0.25 m are deterministic.
Random uncertainties are expressed by statistical properties of
random variables. The probability distributions are summarized as
follows: yield strength of reinforcing steel fy
LN
(400 MPa, 0.075), modulus of elasticity of steel Es
N
(200 GPa, 0.075), compressive strength of concrete fc
LN
(28 MPa, 0.173), live load p
(4.95
kN/m, 0.374) and dead load p
N
(10.5 kN/m, 0.048). Symbols LN, N and
are
probability density functions: lognormal, normal and gamma,
respectively, and numbers in parenthesis are mean values and
coefficients of variation. All random variables are uncorrelated with
each other. The calculations are performed using the Monte Carlo
simulation technique. Using the above equations and the M-Star
computer program, the resultant histogram of required area of tension
reinforcement was calculated and shown in Figure 1. A total number of
500 000 simulation steps have been applied.
Fig. 1. The histogram of required area of tension reinforcing steel As (M-Star program output)
The Monte Carlo method is powerful and useful technique for performing probabilistic as well as deterministic analyses. However, in some instances, the time needed to evaluate a problem for a single trial may be very long or/and the total number of random variables which have to be taken into consideration, is very large (e.g. when the finite elements model of a structure is considered). The calculation of reliability of such a structure using standard Monte Carlo method may be very time consuming. The importance sampling, the directional sampling and the stratified sampling methods are examples of techniques for reducing the number of simulations needed to obtain reasonable results in these cases [3].
4 Innovations in teaching and learning of reliability of structures
The traditional, passive lecturing approach seems to lack of efficiency in today’s competitive environment. In connection with the traditional approach to structural reliability based on analytical and numerical solutions it brings about academic courses on the probabilistic methods in civil engineering, a reputation of being difficult and uninteresting. Higher engagement and active participation of students in education processes result in greater interest in the subject and higher level of knowledge retention.
With fast advances in information technology, new methods and tools for teaching and learning are being developed. The first, relatively simple but very promising new medium are computer networks which make possible to bring together teachers, students and learning material in different location. Two main teaching/learning modes are usually applied using computer networks:
a) Teaching on-campus at fixed hours with the lecturer present as a mentor, but access to learning material is possible at any time and from any computer (offer for full-time students),
b) Self-learning activities in systematic contact with a teacher, and special teaching on campus offer before examination (proposal for lifelong learning or/and continuing education).
Use of the Internet technologies in various types of continuing engineering education introduces promising opportunities in order to improve so-called distance education. Self-directed learning in interactive computer environment (Slice) integrates textual material, animation, simulation and video clips. It is intended to develop and foster self-learning abilities as an essential prerequisite for lifelong learning.
The problem is that nowadays only a few departments of civil engineering make use of computer networks for teaching reliability of structures and Slice-type projects are in the early stage of preparation. In order to set in motion and use of these projects large financial burdens are necessary to keep the hardware and software up to-date and teachers have to spent a lot of time and effort on updating their working skill.
Courses of reliability of structures should concentrate students’ attention on the ability to use mathematical techniques and particularly simulation techniques in practical solutions, but exploration of the theory behind them should be also important. The project oriented programs of courses of the structural reliability should be carefully designed in cooperation with engineers and educators if new approaches are to utilize the full capabilities of information technologies. Practical applications of simulation-based design and reliability assessment for structural elements and systems should be closely connected with courses of reinforced and prestressed concrete, steel, timber and other structures. Complex problems can be explored using simulation-based computer programs.
5 TERECO Project
The problem of the qualitative improvement of the structural reliability assessment concepts with the training of students and designers in this respect, was the reason why international project on “Teaching reliability concepts in civil engineering using simulation techniques” (TERECO Project) – sponsored through the Leonardo da Vinci Agency in Brussels was introduced into practice in 1999-2001. The purpose of the project was propose an innovation methods in education and to develop teaching tools leading to understanding the approaches applied in probabilistic design and reliability assessment of building structures, including the application of simulation techniques (see [4], editors comment].
The final product of the project consists of classes, courses and seminars for students and professional engineers, articles, papers and the textbook: Marek P., Brozzetti J., and Gustar M., editors, “Probabilistic Assessment of Structures using Monte Carlo Simulation. Background, Exercises and Software.” ITAM, Praha, Czech Republic, 2001 [2]. The application of the simulation-based reliability assessment and probabilistic design method is there explain using more than 150 solved examples worked out by 31 authors from eight European countries and from U.S. On the attached CD-ROM it can be found the input files and computational tool enabling the duplication of the examples on a personal computer, and presentations of examples in Microsoft Power Point. The book should serve as an aid introducing designers to the strategy of probabilistic design and reliability assessment of elements, components and systems using Monte Carlo simulation and personal computers. A series of courses for practicing engineers and graduate students have been organized in a few countries using lecture notes and computational tools developed within the confines of the TERECO Project.
6 Concluding remarks
To the questions posed in the Introduction, the following brief answers can be offered:
- Concerning the scope and content of courses in the area of structural reliability, it emerges that they should familiarize students with the basic concepts and tools needed to understand and to intentionally apply reliability-based design criteria included in contemporary structural codes. Courses for advanced learners should give designers and students skills necessary to select the appropriate models and procedures for probability based design and assessment of structures.
- The second question, which needs to be answered, is how to bring understanding of structural reliability concepts to students and practicing engineers. From a negative viewpoint, a certain frustration may be observed in some students and engineers who touch upon problems of probabilistic design and assessment but they do not understand concepts and methods using to solve them. It seems to be connected with the crucial problem of the transition from a deterministic to a probabilistic way of thinking about properties of structural materials, loads and load effects, resistance and safety of structures. Simulation techniques, especially powerful and simple Monte Carlo method, should assist in such a transition.
- Concerning methods of introduction of simulation techniques into civil engineering education and practice, it seems that potential of simulation techniques should be demonstrated to the milieu of student and civil engineers. Dissemination of reliable and user-friendly simulation-based computer programs is most likely to woo the support of students and engineers.
- The last question is about innovations in teaching and learning which can be used for efficient implementation of the simulation-based structural design and assessment. Regarding to this question, promising opportunities are introduced with the use of new methods of knowledge presentation and the use of novel technologies: multimedia, interactivity and the Internet.
Acknowledgment: This work has been party supported by the Polish National Research Committee under the project No. 153/E-363/SPUB-M.
References
[1] Rubinstain R.Y.: Simulation and Monte Carlo Method. Wiley, New York, 1981.
[2] Marek P., Brozzetti J., Gustar M. (editors): Probabilistic Assessment of Structures using Monte Carlo Simulation. background, Exercises and Software. ITAM, Academy of Science of the Czech Republic, Praha, 2001.
[3] Nowak A. S., Collins K. R.: Reliability of Structures. McGraw-Hill Int. Editions, Boston, etc., 2000.
[4] Marek P., Guštar M. and Anagnos, T. (1995). Simulation-based Reliability Assessment for Structural Engineers. CRC Press, Inc., Boca Raton, Florida.