Palle Thoft-Christensen

Application of structural systems reliability theory

1. Fundamentals of Structural Reliability Theory.- 1.1 Introduction.- 1.2 Modelling of Load and Resistance Variables.- 1.3 The Fundamental Case.- 1.4 Basic Variables and Failure Surfaces.- 1.5 The Hasofer and Lind Reliability Index.- 1.6 Estimate of the Reliability of Single Elements.- 1.7 Non-Normal Basic Variables.- 2. Modelling of Structural Systems.- 2.1 Introduction.- 2.2 Modelling of Structural Elements.- 2.3 Fundamental Systems.- 2.4 Systems Modelling At Level N.- 2.5 Systems Modelling at Mechanism Level.- 2.6 Formal Representation of Systems.- 2.7 Approximations of the Multivariate Normal Distribution Function.- 3. Reliability of Series Systems.- 3.1 Introduction.- 3.2 Probability of Failure of Series Systems.- 3.3 Reliability Bounds for Series Systems.- 3.4 Series Systems with Equally Corelated Elements.- 3.5 Series Systems with Unequally Correlated Elements.- 3.6 The Hohenbichler Approximation.- 4. Reliability of Parallel Systems.- 4.1 Introduction.- 4.2 Probability of Failure of Parallel Systems.- 4.3 Reliability Bounds for Parallel Systems.- 4.4 Equivalent Linear Safety Margins for Parallel Systems.- 4.5 Parallel Systems with Equally Correlated Elements.- 4.6 Parallel Systems with Unequally Correlated Elements.- 5. Automatic Generation of Safety Margins.- 5.1 Introduction.- 5.2 Generation of Safety Margins for Truss Structures.- 5.3 Generation of Safety Margins for Frame Structures Subjected to Single Load Effect.- 5.4 Generation of Safety Margins for Frame Structures Subjected to Combined Load Effects.- 5.5 Generation of Fundamental Mechanisms for Elastoplastic Structures.- 6. Reliability Analysis of Structural Systems by the ?-Unzipping Method.- 6.1 Introduction.- 6.2 Non-Normal Basic Variables.- 6.3 Reliability of Single Elements.- 6.4 Estimate of Systems Reliability at Level 1.- 6.5 Estimate of Systems Reliability at Level 2.- 6.6 Estimate of Systems Reliability at Level N > 2.- 6.7 Estimate of Systems Reliability at Mechanism Level.- 7. The Branch-and-Bound Method.- 7.1 Introduction.- 7.2 Failure Paths and Failure Modes.- 7.3 The Concept of the Branch-and-Bound Method.- 7.4 Identification of Dominant Failure Paths.- 7.5 Evaluation of the Systems Reliability.- 7.6 Application to Offshore Structures.- 7.7 Further Developments and Numerical Examples.- 8. Optimization of Structural Systems.- 8.1 Introduction.- 8.2 Probability-Based Optimum Design Problem.- 8.3 Various Problems of Probability-Based Optimum Design.- 8.4 Optimum Design Based on Element Reliability.- 8.5 Optimal Design by The ?-Unzipping Method.- Appendix the Standard Normal Distribution Function c.

Reliability and Optimization of Structural Systems

For the practica! applications of probabilistic reliability methods it is important to make decisions about the target reliability level. Presently calibration to existing design practice seems to be the only practicable and politically reasonable solution to this decision problem. However, severa! difficulties of ambiguity and definition show up when attempting to make the transition from a given authorized partial safety factor code to a superior probabilistic code. For any chosen probabilistic code format there is a considerable variation of the reliability level over the set of structures defined by the partial safety factor code. Thus there is a problem about which of these levels to choose as target level. Moreover, if two different probabilistic code formats are considered, then a constant reliability Jevel in the one code does not go together with a constant reliability Jevel in the other code. The Jast problem must be accepted as the state of the matter, and it seems that it can only be solved pragmatically by standardizing a specific code format as reference format for constant reliability. By an example this paper illustrates that a presently valid partial safety factor code imposes a quite considerable variation of the reliability measure as defined by a specific probabilistic code format. Decision theoretical principles are applied to get guidance about which of these different reliability levels of existing practice to choose as target reliability level. Moreover it is shown that the chosen probabilistic code format not only has strong influence on the formal reliability measure but also on the formal cost of failure to be associated if a design made to the target reliability Jevel is considered tobe optimal. In fact, the formal cost of failure can be different by severa] orders of size for two different by and large equally justifiable probabilistic code formats. Thus the consequence is that a decision theoretical code format formulated as an extension of a probabilistic code format must specify formal values to be used as costs of failure. A principle of prudency is suggested for guiding the choice of the reference probabilistic code format for constant reliability. To the authors opinion there is an urgent need for establishing a standard probabilistic reliability code. This paper presents some considerations that may be debatable but nevertheless point at a systematic way to choose such a code.

Optimal strategy for inspection and repair of structural systems

Abstract A new strategy for inspection and repair of structural elements and systems is presented. The total cost of inspection and repair is minimized with the constraints that the reliability of elements and/or of the structural system are acceptable. The design variables are the time intervals between inspections and the quality of the inspections. Numerical examples are presented to illustrate the performance of the strategy. The strategy can be used for any engineering system where inspection and repair are required.

Assessment of the Reliability Profiles for Concrete Bridges

In this paper calculation of reliability profiles is discussed. ULS as well as SLS limit states are formulated. Corrosion due to chloride penetration is the considered deterioration mechanism. Three models for corrosion are formulated. A definition of service lifetime for concrete bridges is presented and discussed. The proposed method of calculating reliability profiles is illustrated on an existing U.K. bridge.

An Expert System for Concrete Bridge Management

The importance of bridge repair versus new bridge construction has risen in recent decades due to high deterioration rates that have been observed in these structures. Budgets both for building new bridges and keeping the existing ones are always limited. To help rational decision-making, bridge management systems are presently being implemented by bridge authorities in several countries. The prototype of an expert system for concrete bridge management is presented in this paper, with its functionality relying on two modules. The inspection module relies on a periodic acquisition of field information complemented by a knowledge-based interactive system, BRIDGE-1. To optimize management strategies at the headquarters, the BRIDGE-2 module was implemented, including three submodules: inspection strategy, maintenance and repair.

RELIABILITY OF STRUCTURAL SYSTEMS WITH CORRELATED ELEMENTS

Abstract Calculation of the probability of failure of a system with correlation members is usually a difficult and time-consuming numerical problem. However, for some types of systems with equally correlated elements this calculation can be performed in a simple way. This has suggested two new methods based on so-called average and equivalent correlation coefficients. By using these methods approximate values for the probability of failure can easily be calculated. The accuracy of these methods is illustrated with examples.

Life-cycle cost-benefit (LCCB) analysis of bridges from a user and social point of view

During the last two decades, important progress has been made in the life-cycle cost-benefit (LCCB) analysis of structures, especially offshore platforms, bridges and nuclear installations. Due to the large uncertainties related to the deterioration, maintenance, and benefits of such structures, analysis based on stochastic modelling of all significant parameters seems to be the only relevant analysis. However, a great number of difficulties are involved, not only in the modelling, but also in the practical implementation of the models developed at present. The main purpose of this paper is to present and discuss some of these problems from a user and social point of view. A brief presentation of a preliminary study of the importance of including benefits in life-cycle cost-benefit analysis in management systems for bridges is shown. Benefits may be positive as well as negative from the user point of view. In the paper, negative benefits (user costs) are discussed in relation to the maintenance of concrete bridges. A limited number of excerpts from published reports that are related to the importance of estimating user costs when repairs of bridges are planned, and when optimized strategies are formulated, are shown. These excerpts clearly show that user costs in several cases completely dominate the total costs. In some cases, the user costs are more than ten times higher than the repair costs. A simple example of how to relate and estimate user costs to the repair of a single bridge is shown. Finally, how the total maintenance costs (including user costs) may be estimated for a large bridge stock is discussed. This paper is based primarily on two previous International Association for Bridge Maintenance and Safety (IABMAS) conference papers by Thoft-Christensen (2004b, 2006).

Dynamic response of non-linear systems to poisson-distributed pulse trains: Markov approach

Abstract The dynamic response of non-linear systems with algebraic non-linearities to Poisson-distributed trains of impulses and general pulses is considered. The displacement and velocity response of the system form in that case a Poisson-driven Markov vector process. The differential equations governing the joint response moments are obtained by making use of a generalized Itos differential rule which is valid for this kind of problems. Two closure techniques are used to truncate the hierarchy of moment equations: an ordinary and a modified cumulant-neglect closure technique. Transient response statistics such as the mean value and the variance are evaluated numerically. Verification of the obtained approximate analytical results against Monte Carlo simulations shows that the ordinary cumulant-neglect closure technique is appropriate in the case of non-linear systems subject to Poisson-distributed impulses and general pulses if the mean arrival rate of impulses is not very low, i.e. if the departure of the excitation from the Gaussian process is not very large. Otherwise, i.e. in the case of a low mean arrival rate of impulses, the modified cumulant-neglect closure scheme provides better results.

Reliability Bounds for Structural Systems

In chapter 7, the concept of modelling of structural systems by series and parallel systems was introduced. It was shown that in general the exact determination of the probability of failure of such systems is not possible and that a numerical calculation is often rather time-consuming. However, upper and lower bounds for the exact probability of failure can often be formulated, but the practical value of such bounds depends on how narrow they are. In this chapter two sets of bounds will be derived, namely the so-called simple bounds and Ditlevsen bounds.

On Reliability-Based Structural Optimization

In this paper a brief presentation of the state-of-the-art of reliability-based structural optimization (RBSO) is given. Special emphasis is put on problems related to application of RBSO on real (large) structures. Shape optimization, knowledge-based optimization and optimal inspection strategies are briefly discussed. A list of 125 references is included in the appendix.