The article presents a review of the theory of reliability and its use for design code making procedures based on the probabilistic approach. Principles of structural safety in design code making are considered. To do so, the basic principles of the limit state methods in the form of partial factors and ways of their development are analyzed. The problem of manufactured structures or specimen reliability evaluation is discussed according to the control test results. Classification of loads and actions, which were adopted during the code making, is presented. Descriptions of the load combinations are considered. Evaluation of the risk in civil engineering is observed and estimations of the acceptable and optimal risk are discussed. Development of reliability based design principles is also presented. Based on review of preceding work, general requirements for probabilistic codes are described and the critical observations of the modern methods of the analysis of the failure probability are presented. This review article cites 125 references.

Issue Section:
Review Articles
Keywords:
structural engineering, probability, civil engineering computing, reliability theory
Topics:
Design, Failure, Probability, Reliability, Stress, Risk, Structural design
1.
Commicon Standard ST 384-76, Building structures and foundation base, General principles for design, Moscow (in Russian).
2.
Joint Committee on Structural Safety (JCSS) (1981), General principles on quality assurance for structures, General principles on reliability for structural design, Report, Lisbon.
3.
Eurocode 1 ENV 1991-1 (1994), Basis of design and actions on structures, Part1-Basis on design, CEN.
4.
Raizer VD (1986), Reliability Method of the of Problems Design Code Making in Building Structures, Stroyizdat Publ House, Moscow (in Russian).
5.
ST 2394 (1994), General Principles on Reliability for Structures, ISO TK98.
6.
Pugslev A (1966), The Safety of Structures, Arnold, London.
7.
Randel FA (1977), Historical note on structural safety, Proc Amer Concrete Inst, Vol 70, 669–679.
8.
Mayer M (1926), Die Sicherheit der Bauten und ihre Berechnung nach Granzekra¨ften statt nach zula¨ssigen Spannungen, Springer Verlag, Berlin, 111–126 (in German).
9.
Khozialov
NF
(
1929
),
Safety factor in strength (in Russian
),
J Build Indust
10
,
840
–
844
.
10.
Cornell
CA
(
1967
),
Bounds on the reliability of structural systems
,
J. Struct. Div. ASCE
93
,
171
–
200
.
11.
Freudenthal
AM
(
1947
),
Safety of structures
,
Trans. Am. Soc. Civ. Eng.
112
,
125
–
180
.
12.
Freudenthal
AM
(
1956
),
Safety and probability in structural failure
,
Trans. Am. Soc. Civ. Eng.
121
,
1337
–
1375
.
13.
Hald A (1952), Statistical Theory With Engineering Applications, Wiley, New York.
14.
Jonson AJ (1953), Strength, safety and economical dimension of structures, Bull No 12, Royal Inst of Tech, Stockholm.
15.
Rzhanitsyn AR (1949), Statistic Basis of Design Coefficients: To the theory of structural design on limit state method, Part II, Stroyizdat Publ House, Moscow (in Russian), 18–52.
16.
Snarskis BI (1962), Statistically-economical basis to safety in current capacity of structures, Proc Academy of Science of Litva, B No 2, 1962, No 3, 1963.
17.
Shinozuka
M
(
1964
),
Probability of structural failure under random loading
,
Proc. Am. Soc. Civ. Eng.
EM-5
,
147
–
170
.
18.
Streletsky NS (1947), Statistical Basis of the Safety Factor of Structures (in Russian), Stroyizdat Publ House, Moscow.
19.
Streletsky NS (1961), Limit State Method Used in USSR and General Direction of Applications (in Russian), Stroyizdat Publ House, Moscow.
20.
Baldin VA, Goldenblat II, Kochanov VI, Pildish MA, and Tal KE (1951), Limit State Design Method, Stroyizdat Publ House, Moscow (in Russian).
21.
Augusti G, Baratta A, and Casciati F (1984), Probabilistic Methods in Structural Engineering, Chapman and Hale, London, 1984.
22.
Benjamin IR and Cornell CA (1970), Probability, Statistics, and Decision for Civil Engineers, McGraw-Hill, New York.
23.
Bolotin VV (1969), Statistical Methods in Structural Mechanics, Holden-Day, San Francisco.
24.
Bolotin VV (1971), Application of Methods of the Theory of Probability and the Theory of Reliability to Analysis of Structures (in Russian), Stroyizdat Publ House, Moscow.
25.
Elishakoff I (1999), Probabilistic Theory of Structures, Dover, New York.
26.
Ferry-Borges J and Castanheta M (1971), Structural Safety, LNEC, Lisbon.
27.
Haugen EB (1980), Probabilistic Mechanical Design, Wiley Intersience, New York.
28.
Kapur KS and Lamberson LR (1977), Reliability in Engineering Design, Wiley, New York.
29.
Kudsis AP (1985), Reliability Estimation of Reinforced Concrete Structures (in Russian), Moklas Publ House, Vilnius.
30.
Madsen HO, Krenk S, and Lind NC (1977), Methods of Structural Safety, Prentice Hall, Englewood Cliffs.
31.
Melchers RE (1987), Structural Reliability and Predictions, Ellis Horwood, London.
32.
Murzewski J (1989), Niezawodnosc Konstrukcji Inzynierskich, Arkady, Warszawa (in Polish).
33.
Nowak AS and Collins KR (2000), Reliability of Structures, McGraw-Hill, New York.
34.
Pereverzev ES (1987), Stationary Processes in Parametric Models of Reliability (in Russian), Naukova Dumka Publ House, Kiev.
35.
Raizer VD (1995), Analysis of Structural Safety and Design Code Making Procedures (in Russian), Stroyisdat Publ House, Moscow.
36.
Raizer VD (1998), Theory of Reliability in Structural Design, ASU Publ House, Moscow (in Russian).
37.
Rao SS (1992), Reliability-Based Design, McGraw-Hill, New York.
38.
Rzhanitsyn AR (1978), Theory of Reliability Design of Civil Engineering Structures, Stroyizdat Publ House, Moscow (in Russian).
39.
Smith GN (1986), Probability and Statistics in Civil Engineering, Collins Professional and Technical Books. London.
40.
Spaethe G (1987), Die Sicherheit tragender Baukonstruktionen, (in German), VEB, Berlin.
41.
Thoft-Christensen P and Baker MI (1982), Structural Reliability, Theory and Applications, Springer, Verlag, Berlin.
42.
Timashev SA (1982), Reliability of Large Mechanical Systems (in Russian), Nauka Publ House, Moscow.
43.
Tichy M and Rakosnik Y (1976), Design of Reinforced Frame Structures in Plastic Step Distribution of Forces, Stroyizdat Publ House, Moscow (in Russian).
44.
Cornell CA (1969), Structural safety specifications based on second moment reliability analysis, Proc Smp on Concepts of Safety, London, Final Report IABSE, Zurich, 235–246.
45.
Berdichevski
GI
,
Gvozdev
AA
, and
Chistyakov
BA
(
1980
),
Strength control of reinforced concrete structures at factories (in Russian
),
J Concrete and Reinforced Concrete
9
,
17
–
18
.
46.
Gromatskiy
VA
(
1983
),
How to control loads and estimate structural reliability using results of testing (in Russian
),
J. Struct. Mech.
2
,
7
–
10
.
47.
Uzhpolyavichus BB (1982), Non-Damaged Control Methods and Strength Estimation of Concrete and Reinforced Concrete Structures (in Russian), Moklas Publ House, Vilnius.
48.
Gnedenko BV, Belyaev YK, and Soloviev AD (1965), Mathematics Method in the Theory of Reliability (in Russian), Nauka Publ House, Moscow.
49.
Construction Industry Research and Information Association (1977), Rationalization of safety and serviceability factors in structural codes, CIRIA, London.
50.
Reference-Information Book on Climate in USSR (1972), (in Russian), Gidrometeoizdat Publ House, Leningrad.
51.
Bendat JS, and Piersol AG (1971), Random Data Analysis and Measurement Procedures, Wiley Interscience, New York.
52.
Gnedenko BV (1967), Theory of Reliability, Chelsea, New York.
53.
Gumbel EJ (1967), Statistics of Extremes, Columbia Univ Press, New York.
54.
Recommendation for loading and safety regulations for structural design (1987), Nordic Committee on Building Regulations.
55.
Feller WC (1970), An Introduction to Probability Theory and its Applications, Wiley, New York.
56.
Lew
M
and
Mart
GC
(
1979
),
Microzonation in wind engineering
,
J Struct Eng
105
, Proc. ASCE
ST6
ST6
, June.
57.
Observations of meteorology laboratory of Moscow State Univ (MGU) (1966–1985), MGU Publ House, Moscow (in Russian).
58.
Zavarina MV (1976), Climatology for Building Design (in Russian), Gidrometeoizdat Publ House, Leningrad.
59.
Raizer VD (1996), Probabilistic models for snow loads in structural analysis, Proc 3rd Int Conf Snow Eng, Senday, Japan.
60.
Otstavnov VA and Rosenberg LS (1976), Some peculiarities in the problem of collection of initial climatic data on snow loads (in Russian), Design of Structures, Proc TSNIIS No 42, AR Rzhanitsyn (ed) Stroyizdat Publ House, Moscow, 91–98.
61.
Rzhanitsyn
AR
,
Sukhov
YD
, and
Bulychev
AP
(
1975
),
Probabilistic method of structural design on snow load (in Russian
),
J. Struct. Design Mech. Anal. Struct.
1
,
6
–
8
.
62.
Anapolskaya AE, and Gindin LS (1958), Method of design wind speed calculations for definition of wind loads at structures (in Russian), Meteorology and Gidrology Publ House, 10, 9–17.
63.
Klepikov
LV
and
Otstavnov
VA
(
1962
),
Loads definition in structural design (in Russian
),
J. Struct. Mech. Anal. Struct.
5
,
39
–
45
.
64.
Savitskiy GA (1972), Wind Load on Structures (in Russian), Stroyizdat Publ House, Moscow.
65.
Avramenko
PV
(
1988
),
Temporary live loads in multistoried office buildings (in Russian
),
J. Struct. Mech. Anal. Struct.
5
,
67
–
71
.
66.
Doveika VY and Snarskis BF (1972), Some results of researches of live loads (in Russian), Reliability Problems in Structural Design, 45–49, Sverdlovsk.
67.
Mitchell GR and Woodgate RW (1971), Floor loading in office building, The result survey current paper CP3/71, Building Research, Garston, UK.
68.
Bulychev
AP
(
1982
),
Probability-economic method of definition of equivalent loads on elements in buildings (in Russian
),
J. Struct. Mech. Anal. Struct.
1
,
6
–
9
.
69.
Ellingwood
BR
, and
Ellingwood
BR
(
1977
),
Analysis of live load on office buildings
,
J. Struct. Eng, ASCE
103
, No ST8, Paper 13109,
1551
–
1560
.
70.
Bolotin
VV
,
Chirkov
VP
, and
Scherbakov
AN
(
1980
),
Load combination in design of offshore structures (in Russian
),
J. Struct. Mech. Anal. Struct.
5
,
6
–
10
.
71.
Bulychev
AP
and
Suknov
YD
(
1978
),
Application of the theory of reliability for loads code making procedures (in Russian
),
J. Struct. Mech. Anal. Struct.
3
,
15
–
19
.
72.
Ditlevsen O (1977), Note 1—Principles of approximate reliability invariant reduction on problem dimension, Note 2—A code model for combination of actions, Int Workshop Struct Reliability, Mexico, printed in DIALOG-2-76, DIAB, Lyndby, 612–621.
73.
Ditlevsen O and Madsen NO (1981), Probabilistic modeling of man-made load processes and their individual and combined effects, Proc of 3rd Int Conf on Struct Safety and Reliability (ICOSSAR’81), Trondherm, 103–134.
74.
Faravelli
L
(
1982
),
A proposal on load combination for level formats
,
J. Eng. Struct.
4
,
197
–
206
.
75.
Fedorov EI (1976), Structural design when loads are presenting as Markov processes, Design of Structures, Proc TSNIIK, No 42, 132–143 AR Rzhanitsyn (ed.) Design of Building Structures, Stroylzdat Publ House, Moscow (in Russian).
76.
Fedorov
EI
and
Lositskaya
KS
(
1980
),
Selection of loads combination factor (in Russian
),
J. Struct. Mech. Anal. Struct.
No 1
,
18
–
21
.
77.
Ghiocel D and Lungu (1975), Wind, Snow and Temperature Effects in Structures Based on Probability, Abacus Press, Turnbridge, Wells, UK.
78.
Rzhanitsyn
AR
and
Sukhov
YD
(
1974
),
Consideration of loads combination in structural design (in Russian
),
J. Struct. Mech. Anal. Struct.
4
,
40
–
43
.
79.
Timashev SA, and Shterenson VA (1979), Practical Methods of Reliability Design for Different Systems Under Combinations of Loads Research Reliability of Engineering Structures (in Russian), LenPromstroiproekt Publ House Leningrad, 36–52.
80.
Turkstra CJ (1970), Probabilistic Design Formats Theory of Structural Design Decisions, Sol Mech Eng, Univ Waterloo, SM Studies, Series, No 2.
81.
Wen
YK
(
1977
),
Statistical combination of extreme loads
,
J. Struct. Div. ASCE
103
,
ST5, 1079
ST5, 1079
.
82.
Wentzel ES, Investigations of operations problems, Methodology (in Russian), Nauka Publ House, Moscow.
83.
Raizer VD (1996), Problem of risk estimation in structural design, Problems of Reliability and Improvement of Structures (in Russian), Yakutsk Univ Publ.
84.
Ditlevsen O (1987). The structural system reliability problem, Qualitative Considerations of Reliability and Risk Analysis in Civil Engineering, NC Lind (ed), Inst for Risk Res Univ Waterloo, 1–11.
85.
Driving
AY
(
1973
),
Economical approach to definition of optimal safety factor (in Russian
),
J. Struct. Mech. Anal. Struct.
5
,
7
–
10
.
86.
Fedorov EI (1976), Probability-optimization design of structures under some loads, research of loads and reliability of structures (in Russian), Proc TSNIISK, 108–124, Rzhanitsyn AR (ed.), Stroyizdat Publ House, Moscow.
87.
Lind
NC
(
1976
),
Approximate analysis and economics of structures
,
Proc. Am. Soc. Civ. Eng.
102
(
ST6
ST6
).
88.
Rzhanitsyn
AR
,
Snarskis
BI
, and
Sukhov
YD
(
1979
),
General principles probability optimization method for structural design (in Russian
),
J. Struct. Mech. Anal. Struct.
3
,
67
–
71
.
89.
Snarskis BI (1972), Optimal design and control values of random parameters as a way for reliability optimization, Reliability Problems in Design (in Russian), 202–206, Sverdlovsk.
90.
Snarskis BI (1972), Connection between methods of optimal design values with limit state method (in Russian), Reliability Problem in Design, 206–211, Sverdlovsk.
91.
Rosenblueth E (1987), What should we do with reliability, Reliability and Risk Analysis in Civil Engineering, NC Lind (ed), Univ Waterloo Press, 24–33.
92.
Ang
AH
and
Amin
(
1969
),
Safety factors and probability in structural design
,
J. Struct. Eng.
95
,
1389
–
1404
.
93.
Driving AY (1972), Recommendations to application economical methods in design of structures with economical responsibility (in Russian), Proc TSNIISK Publ House.
94.
Suknov
YD
(
1975
),
Probability-economic model of exploitation for structures (in Russian
),
J Struct Mech Anal Struct
4
,
13
–
16
.
95.
Lind NC (1979), Optimization, cost benefits analysis specifications, Proc 3rd Int Conf Appl Stat Soil Struct Eng, (ICASP 3), Sydney, Vol 3, 373–384.
96.
Cornell
CA
(
1969
),
Probability-based structural code
,
ACI J.
66
,
974
–
985
.
97.
Cornell CA (1969), Stochastic process models in structural engineering, Dept of Civil Eng, Stanford Univ, Tech Report, No 34, 14–18.
98.
Ang AH and Ma HF (1981), On the reliability of structural system, Proc of ICSSR 3rd Int Conf Struct Safety Reliability, 245–314.
99.
Ditlevsen O (1987), Generalized second moment reliability index, DCAAM, Rep No 144.
100.
Ellingwood BR, Igusa T, and Buonopane SG (2001), Reliability-based simulation for performance-based design, Proc of 1st Int Conf Struct Safety Reliability, ICSSR-01, Balkema Publ.
101.
Esteva L (1975), Second-moment probabilistic analysis of statically loaded nonlinear structures, Proc of 2nd Int Conf Appl Stat Prob Soil Struct Eng (ICASP 2), Aachen, 115–130.
102.
Freudenthal
AM
(
1961
),
Safety and probability in structural design
,
ASCE J. Struct. Div.
78
,
814
–
823
.
103.
Hasofer
AM
and
Lind
NC
(
1974
),
An exact and invariant first order reliability format
,
J. Eng. Mech.
100
,
111
–
121
.
104.
Madsen HO (1977), Some experience with Rackwitz-Fiessler algorithm for calculation of structural reliability under combined loading, DIALOG-77, DIAB, Lyndby, 73–98.
105.
Rackwitz
R
(
1976
),
Practical probabilistic approach to design CEB
,
Bull d’Information
112
,
113
–
189
.
106.
Rackwitz R and Fiessler B (1977), An algorithm for calculation of structural reliability under combined loading, in Berichte zur Sicherheitstheorie der Bauwerke, Lab fu¨r Konstr Ingb, Munich, 489–494.
107.
Sexsmith
RG
(
1999
),
Probability-based safety analysis value and drawbacks
,
ASCE J. Struct. Div.
21
,
301
–
310
.
108.
Shinozuka
M
(
1983
),
Basic analysis of structural safety, ASCE
,
J. Struct. Eng.
59
(
3
),
721
–
740
.
109.
Veneziano D (1974), Contribution on second moment reliability theory, Dept of Civil Engineering, MIT, Struct Publ No 389.
110.
Veneziano D (1978), Random processes for engineering application, Lecture notes, Dept of Civil Engineering, MIT, Cambridge MA.
111.
Perelmuter AV (1999), Selected Problems of Reliability and Structural Safety (in Russian), Ukrainian Inst of Steel Constrictions Publ, Kiev.
112.
Otstavnov
VA
,
Smirnov
AF
,
Raizer
VD
, and
Suknov
YD
(
1981
),
Introduction of importance factor in building code (in Russian
),
J. Struct. Mech. Anal. Struct.
1
,
11
–
14
.
113.
Bolotin VV (1992), Safety of technical objects and structural risk (in Russian), Nonlinear Problems of Dynamics of Machines, Nauka Publ House, Moscow, 117–132.
114.
Elishakoff I (1992), Essay on reliability index, Probabilistic Interpretation of Safety Factor and Convex Models of Uncertainty, Reliability Problems, General Principles and Application, F Casciati and JB Roberts (eds), Springer, Vienna, 237–271.
115.
Weiss GH (1964), A survey of some mathematical models in the theory of reliability ed, M Zelin Univ Wisconsin Press, Madison.
116.
Metropolis
N
and
Ulam
S
(
1949
),
The Monte-Carlo method
,
J. Amer. Stat. Assoc.
44
(
247
247
).
117.
Sauliev VK (1974), Statistic Modeling Monte-Carlo Method (in Russian), Nauka Publ House, Moscow.
118.
Sobol IM (1973), Numerical Methods, Monte-Carlo Procedures (in Russian), Nauka Publ House, Moscow.
119.
Andreev
OO
(
1984
),
Estimation of current capacity of reinforced concrete cross-sections considered probabilistic nature of concrete and steel strength (in Russian
),
J. Struct. Mech. Anal. Struct.
5
,
7
–
9
.
120.
Krakovski
MB
(
1982
),
Statistic simulation method in definition of structural reliability (in Russian
),
J. Struct. Mech. Anal. Struct.
2
,
10
–
13
.
121.
Mitropolski AK (1971), Procedures of Statistic Calculations (in Russian), Nauka Publ House, Moscow.
122.
Pollak YG (1971), Probabilistic Modeling With Computer (in Russian), Soviet Radio Publ House, Moscow.
123.
Tikhonov VI (1970), Intersections of Stochastic Processes (in Russian), Nauka Publ House, Moscow.
124.
Raizer VD, Suknov YD, and Lebedeva J (1998), Reliability analysis of multi-element spatial structures (in Russian), Proc of Int IASS Congress, Moscow.
125.
Hasofer AM (1984), Objective probabilities for unique subjects; Risk, Structural Engineering and Human Error, M Grigoriu (ed), Waterloo Univ Press.
Copyright © 2004
 by ASME
You do not currently have access to this content.