The origin and development of the SBRA method
In the field of the standards for the design of building structures the end of the 80s of the last century was marked by the culmination of the transition from simple deterministic concepts of the reliability assessment to the methods corresponding with the limit states philosophy and based on the so-called partial coefficients method. Without any doubt the transition to the partial coefficients method, representing the random variability of input quantities of the safety and serviceability assessment, was a remarkable improvement of the reliability presentation. However, it should also be mentioned also that the qualitative improvement of the reliability assessment connected with the application of the new fast improving instruments of the computer age was not given adequate attention then.

In that decade, also the fast development of personal computers was launched. After the numerous different incompatible 8bit types, the 16bit computers brought about the first standardisation which permitted the wide spread and the fast development of software and programming tools.

The first personal computers (PC XT) were imported to the then Czechoslovakia from Canada at the beginning of the year 1987. And over one of them Pavel Marek, a civil Engineer, and Milan Guštar, an electrical engineer - representatives of two engineering generations - asked themselves a question how this "little wonder" would influence the design of structures and particularly their reliability assessment in the near future. This was the start of a many-years´ co-operation of an expert on the theory and reliability of structures and a specialist interested in the potential of the fast developing computer hardware and software. At the beginning of their cooperation the M+G team had no idea where their attempt to find the answer to the above mentioned question would lead them.

1987 - 1989
At the beginning the M+G team concentrated on application of the available personal computer to the analysis of the simultaneity of various mutually independent loads applied to building structures (the load effects combination). The known methods of the solution of load effects combinations used in the then standards and codes were based on simplifying assumptions and on the methods corresponding with the application of primitive computation aids and tools - a state which infact has persevered until the present day. Contrary to the previous representation of the individual loads by their “characteristic value“ and the “load coefficient“ (see the present Eurocode, the ASCE, and other codes) the M+G team proposed and developed the load representation by “LDC“ (Load Duration Curves) which enabled an effective application of the well known Monte Carlo simulation methods to the analysis of the load effects combination.

The configuration of the then used PC XT computer (Intel 8088 processor operating at frequency 4.77 MHz, 640 kB operational memory and a 10 MB hard disk) enabled the development of the first practically applicable simulation programs using the Monte Carlo method. The size of the operational memory permitted the solution of models with numerous random input variables, the computational power was sufficient for the computation of tens of thousands simulations in reasonable time and the graphical capabilities allowed the presentation of results in easy-to-understand forms.

The numerical solution of the combination of the load effects was enabled by the new ResCom (KOMOD) computer program. The original method of the solution of the load effects combination proposed by the M+G team was first reported at the conference on steel structures in Hustopeče (Czech Republic) in 1988 and described in detail with explanatory examples in No. 2/1989 of the Czech professional Journal “Pozemní stavby“ (Building Construction). In the years to follow the proposed unconventional analysis of the load effects, the denominated LDC (Load Duration Curves), was extended to the solution of the combinations of the multi-component load effects, documented by the authors in dozens of publications both at home and abroad, and the frequently applied Load Duration Curves were stored in a database.

1989 - 1991
In this period the M+G team piad particular attention to the examination and definition of resistance of the structural members and components using the Monte Carlo simulation technique. The authors introduced the expression of random mechanical characteristics of materials, variability of geometric characteristics (similarly with load variability in the analysis of load effects combinations) and other random variable quantities by a non-parametric distribution (“bounded or cut-off“ histograms). In this way they deviated substantially from the conventional method (characterised by the expression of random variable quantities by parametric analytical distribution) applied in the development of the methods of reliability assessment of structures.

The pilot problems included the study of structural members consisting of components made of different materials. For the numerical solution by the Monte Carlo method the MatCom (KOMAT) simulation program was elaborated. The results published in the French journal Construction Metalique met with a good response which stimulated the M+G team to supplement the previous studies with the first simple examples of the defect probability computations and to start preparation of a corresponding program. The original M-Star program was drafted enabling the dimensioning of simple members in accordance with the given permissible defect probability, determining the defect probability for the given structural member and the given load, etc. The successive improvement of the program resulted in the generation of a highly effective computation instrument.

The applications of the proposed method resulted in the generation of a continuously increasing number of examples illustrating the great potential of the proposed method based on the Monte Carlo simulation technique. Since 1989 the authors have been introducing the methodology and examples of the simulation-based solution of the basic cases of reliability assessment of building components and structural members into the teaching of the students at the Faculty of Civil Engineering, SJSU University in California (U.S.A.).

1991 - 1993
The M+G team extended the application of the proposed methodology to various criteria of safety and serviceability assessment of metal, concrete, timber and composite structures. They were assisted by a grant provided by the Grant Agency of the Czech Republic which enabled the authors to invite also other specialists to the team. Also the support from Dr. Jerry Haaijer, Vice-President of AISC Chicago, confirmed the interest of some professional institutions in the developed methodology. For the AISC the team prepared the LoadCom program, permitting a comparison of the combinations of one-parametric load effects according to the DIN, LRFD-ASCE, Eurocode and Canadian standards, as well as a study assessing the reliability of structures designed according to the AISC-LRFD standards.

The supplements extending the application of the proposed method also included the examination of the damage accumulation in timber structures and the corresponding DamAc program.

The previously elaborated programs (particularly the M-Star program, intended primarily for the solution of one-component problems) formed the basis of the Anthill program enabling a general analysis of multi-component problems. The founders of the M+G team called the program and the related numerical technique the “Anthill“ to express the set of points representing the random character of the multi-component distribution function. This name, for which the M+G team was granted the trade mark Anthill TM, is being introduced as a technical term in papers dealing with the reliability assessment of structures and similar problems.

By the end of this period the founders of the M+G team came to the conclusion that the achieved results of the development of reliability assessment concept based on the limit states philosophy and applying the Monte Carlo simulation method as an instrument for the analysis of functions containing numerous random variables made it possible to elaborate and present an original probabilistic method of reliability assessment of structures allowing the computation of the defect probability of components, members, and simple structures by the Monte Carlo simulation on the basis of random variable input data expressed by non-parametric distribution. The authors called the proposed method by the acronym SBRA (Simulation-Based Reliability Assessment) and offered the CRC Press, Inc., Boca Raton, Florida, the presentation of the proposed method in a book form.

1994 - 1996
This period was marked by the preparation of the manuscript of the book “Simulation-Based Reliability Assessment for Structural Engineers“ (Marek, Guštar and Anagnos) which the publisher introduced to the market in the Autumn of 1995. At the end of 1996 the book reached the interested specialists in about 20 countries. The first seminar on the SBRA method based on the book and supporting programs took place only a few months later and was attended by more than 25 professors and designers from California. A stimulating assessment of the book was presented by Professor I. Popov from Berkley University.

1997 - 1998
In the autumn of 1996, the main part of the works on the further development of the SBRA method was transferred from the U.S.A. to the Czech Republic, particularly to the three centres:

a) Institute of Theoretical and Applied Mechanics of the Academy of Sciences of the Czech Republic (supported by the Grant Agency of the Czech Republic),

b) ARTech Praha (supported by the Grant Agency of the Czech Republic), and

c) the Faculty of Civil Engineering, Technical University, Ostrava (where the problems of the SBRA expansion and improvement has become the object of the theses of four PhD students and the subject “Reliability of Structures“, based chiefly on the SBRA method, was included into the curriculum of this Faculty).

In cooperation with a growing number of co-workers, the results of the continuing research were published both in the Czech Republic and abroad. The founders of the M+G team summed up the SBRA method and its new achievements (such as its application to the assessment of durability of structures) in a book in German language with the title “Tragwerksbemessung. Von deterministischen zu probabilistischen Verfahren“, which was published by the ACADEMIA publishers in Prague in 1998.

Since this period the website www.sbra-anthill.com has been listing the publications dealing with the development of the SBRA method and further information of general interest.

1999 - 2001
In this period the problem of introducing the SBRA method to universities and to seminars for designers under the professional supervision of the M+G team was solved by an international team supported by the EU program Leonardo da Vinci. From the total number of 33 co-authors of the resulting product (i.e. the book “Probabilistic Assessment of Structures using Monte Carlo Simulation. Basics, Exercises, Software“ published in English), 18 were from the Czech Republic, 1 from France, 1 from Portugal, 1 from Poland, 2 from Hungary, 5 from Lithuania, 1 from Slovakia, 1 from FRG and 3 from the U.S.A. The book was distributed by the publisher, the Academy of Sciences of the Czech Republic, Prague.

In 2000 also the program Anthill for Windows was completed.

In 2000 preparations started for the extension of the SBRA method, previously elaborated for the assessment of components, members, and simple structural systems, to structural systems in general, with reference to both the overall probabilistic concept of reliability and the “rules of the game“ of the assessment of complex structures and the corresponding software. Co-operation with a mathematician, Professor Dr. Z. Dostál, CSc. was established for this purpose.