Contents
Executive Summary
Acknowledgements
Chapter 1 Introduction and summary
1.1 Overview of structure reliability
1.2 General steps of a structural reliability analysis
1.3 Overview of uncertainties of marine structure
1.3.1 Uncertainties
1.3.2 Types of uncertainties of marine structures
1.4 General typical failure modes
1.5 Concepts, definitions and notations
1.5.1 Concepts and definitions
1.5.2 Notations and Concepts
1.6 Benefits and drawbacks of using probability-based design method
1.7 Role of reliability analysis in a general probability design procedure
1.8 Conclusions
Chapter 2 Theoretical methods of structural reliability222.1
Introduction
2.2 Overview of reliability calculation
2.3 Analytical methods (Approximate Methods)
2.3.1 Mean-Value First-Order Second-Moment (MVFOSM) method
2.3.2 Advanced First-Order Second-Moment (MVFORM) method
2.3.2.1 The Hasofer-Lind Index
2.3.2.2 Inclusion of distribution information
2.3.3 Second-Order methods
2.4 Direct integration method
2.4.1 Standardized integral region
2.4.2 Joint probability density function
2.4.3 Multivariate integration
2.4.4 Advanced method of integration
2.5 Simulation methods
2.5.1 Basic principle and method
2.5.2 Generation of random numbers for a random variable with a prescribed
continuous probability distribution
2.5.2.1 Random numbers with uniform distributions
2.5.2.2 Random numbers with prescribed distributions
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2.5.3 Sample size and variance reduction techniques
2.5.3.1 Number of samples required
2.5.3.2 Variance reduction techniques
2.5.4 Importance sampling simulation method
2.5.4.1 Theory of importance sampling
2.5.4.2 Choice of importance sampling functions
2.5.4.3 Observations about importance sampling functions
2.5.5 Adaptive sampling simulation
2.6 Response surface methods
2.6.1 Basic theory
2.6.2 Simplifications for large systems
2.6.3 Iterative solution scheme
2.6.4 Response surface and finite analysis
2.6.5 Applications and basic idea of directional simulation method
2.7 Choice of reliability methods
2.8 Conclusions
Chapter 3 Structural probability modelling and sensitivity analysis
methods
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3.1 General
3.2 Identification of problem
3.3 Establishment of limit state function
3.4 Sensitivity analysis and selections of random variables
3.4.1 Introduction
3.4.2 Deterministic sensitivity factor
3.4.3 Overview of probabilistic sensitivity factor
3.4.4 Adaptive probabilistic sensitivity factor
3.4.5 Calculation of practical methods
3.5 Uncertainties and probability distributions
3.6 System reliability
3.6.1 Introduction
3.6.2 General calculation methods
3.6.3 Bounds on the probability of failure of a series system
3.6.3.1 First order bounds
3.6.3.2 Second order bounds
3.6.4 Bounds on the probability of failure of a parallel system
3.6.5 General System
3.6.6 Summaries of the other calculation methods
3.7 Target reliability
3.7.1 General
3.7.2 Definitions of target values
II
3.7.3 Methods of selecting target values
3.7.4 Recommended target reliabilities
3.8 Time dependent models
3.8.1 General
3.8.2 Time dependent models in marine structures
3.9 Conclusions
Chapter 4 Loads on marine structures
80
4.1 General
4.2 Review of computational methods of loads on marine structures
4.2.1 Environmental Loads on Ships
4.2.2 Environmental Loads on Offshore Structure
4.2.3 Hydrodynamic Impact Loads
4.2.4 Probabilistic Methods
4.2.5 Experimental Uncertainty, Verification and Validation of Numerical Codes
4.3 Loads
4.3.1 Return periods and encounter probabilities
4.3.1.1 Encounter probability:
4.3.1.2 Ship routes and the associated encounter probabilities:
4.3.2 Wave loads and load combinations
4.3.3 Slamming loads
4.4 Probabilistic methods
4.5 Conclusions
Chapter 5 Reliability calculation and analysis of ship structure
5.1 General
5.2 Failure modes
5.3 Ultimate strength of ship structure
5.3.1 Overview the calculation methods of ultimate strength of ship structure
5.3.2 Estimation of ultimate strength of global hull
5.3.3 Estimation for a stiffened panel ultimate strength
5.3.4 Estimation for an unstiffened panel ultimate strength
5.4 Limit state equations of ship structure
5.5 Analysis of uncertainties and choice of basic variables and their distributions
5.5.1 Strengths
5.5.2 Loads
5.5.2.1 Stillwater bending moment M sw
5.5.2.2 Extreme wave-induced bending moment M w
5.5.2.3 Dynamic slamming bending moment M d
5.5.3 Load combination factors
5.5.4 Joint probability density function
5.6 Calculation and analysis
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5.6.1 Time-invariant analysis
5.6.2 Time-variant analysis
5.6.2.1 Rectangular wave renewal jump process
5.6.2.2 Time-variant calculations
5.7 Fatigue Reliability
5.7.1 determination of uncertainties
5.7.2 Establishment of failure limit state
5.7.3 Calculation of fatigue reliability
5.7.4 Establishment of target reliability index
5.7.5 Calibration of partial safety factors
5.8 Conclusions
Chapter 6 Reliability-based design and code developments
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6.1 General
6.2 Reliability assessment of structure safety
6.3 Calibration of partial safety coefficients
6.3.1 General method
6.3.2 Characteristic values
6.3.2.1 Characteristic values for strength parameters
6.3.2.2 Characteristic values for loads
6.3.3 Illustration
6.3.3.1 Procedure of structural reliability analysis and assessment
6.3.3.2 Procedure of calibration of partial coefficients
6.4 Calibration procedure of calculating partial safety factors for ship structure
6.5 Conclusion
Chapter 7 Quantitative Risk Assessment with Structure Reliability
Analysis
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7.1 Introduction and concepts
7.1.1 General
7.1.2 Concepts
7.1.3 Objectives of risk analysis
7.2 QRA and SRA
7.3 Integrating QRA and SRA methods
7.3.1 Classical Bayesian approach and integration of SRA methods
7.3.2 Fully Bayesian approach and integration of SRA methods
7.3.3 Conclusions and discussions of the Bayesian approaches
7.4 Risk analysis methodology
7.4.1 Preliminary hazard analysis – PHA
7.4.1.1 Introduction
7.4.1.2 Procedure
7.4.1.3 Probability and consequence classes
IV
7.4.1.3.1 Probability classes
7.4.1.3.2 Consequence classes
7.4.2 Failure mode and effect analysis
7.4.2.1 Approach and methodology
7.4.2.2 FMEA sheets
7.4.3 Event tree analysis methodology
7.4.3.1 Introduction
7.4.3.2 Event tree for escape and evacuation
7.4.3.3 Major hazard scenarios
7.4.3.4 Initiating event frequency and nodes in event trees
7.5 Conclusions
Chapter 8 Conclusions
149
8.1 General
8.2 Theoretical methods of structural reliability
8.3 Structural probability modelling and sensitivity analysis methods
8.4 Loads on marine structures
8.5 Reliability calculation and analysis of ship structure
8.6 Reliability-based design and code developments
8.7 Quantitative Risk Assessment with Structural Reliability Analysis
References
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Acknowledgements
The authors acknowledge the grant kindly given by the Carnegie Trust, without whom
this document would not have been completed. This is a very appropriate time for such
a document, as there has not previously been guidance available to the marine industry
community on structural reliability and its application to design. The authors would also
like to express their appreciation to the following specialists for supporting this
research:
Professor Julian Wolfram (Heriot-Watt University)
Professor Michael J Baker (University of Aberdeen)
Dr Venki Venugopal (Heriot-Watt University)
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