Limit State Probabilities Research Articles

Structural Response Variability III

The response variability of statically indeterminate linear structures due to spatial variation of material or geometry properties, or both, is investigated. Utilizing a Green's function formulation or the more general flexibility method, the mean square response of statically indeterminate beams and frames (multistory/multibay) is determined without recourse to a finite element analysis. The response variability is expressed in terms of random variables even though the material or the geometric property, or both, (in this case the fiexibility) are considered to constitute stochastic fields. This makes it easier to estimate not only the response statistics but also the limit state probability, if the limit state conditions are given. The response variability can be estimated by various methods, including the first‐order second moment method and Monte Carlo simulation techniques. Finally, the safety index for the beam midspan deflection and end moment are evaluated using standard methods.

Seismic reliability analysis of plane frame structures

This paper presents a practical and simplified reliability analysis method for plane frame structures subject to in-plane earthquake ground accelerations. The frame modelling is based on the approach used in the computer program TABS77. A condensation technique is used in TABS77 to transform the frame structure into a stick model with lumped mass at each floor level. Dynamic characteristics of the structure such as natural frequencies and mode shapes are also obtained using TABS77. The earthquake ground acceleration is represented by a segment of stationary Gaussian random process with mean zero and a Kanai-Tajimi power spectrum. The power spectrum together with the dynamic characteristics of the structure are utilized in the random vibration analysis to derive the covariance matrices of the structural response. A simplified limit analysis procedure is utilized to determine the failure mechanism and the corresponding storey shear capacity of the frame structure. For this failure mechanism, the limit state probability of each storey, i.e. the storey limit state probability, can be evaluated. Then, the limit state probability of the structure is measured in terms of the largest storey limit state probability. The fragility curve for the frame structure is generated by evaluating the limit state probabilities at different levels of peak ground acceleration. From the hazard curve for a site and the fragility curve for a structure, the annual limit state probability of the structure can also be evaluated. A five-storey building assumed to be located in New York City is used for numerical illustration.

SAFETY ANALYSIS OF STOCHASTIC FINITE ELEMENT SYSTEMS BY MONTE CARLO SIMULATION

Probabilistic safety analysis methods for structural systems involving spatially variable material properties are studied. For the cases to which the first-order second-moment methods cannot be applied well, two different Monte Carlo methods are employed in conjunction with the finite element technique. “Monte Carlo simulation”, which is based on the stochastic field simulation technique and the safety judgment for each trial, is recommended because its accuracy is guaranteed irrespective of the number of random variables. On the contrary, the accuracy of “Monte Carlo integration”, where a numerical integration of the joint density function of the random variables is carried out by means of sample-mean Monte Carlo method, goes down dramatically as the number of random variables getting large. Numerical examples verify the above argument and reveal the effects of correlation parameters on the local and system limit state probabilities.

Discussion of “ Limit State Probabilities for Wood Structural Members ” by Erik M. Hendrickson, Bruce Ellingwood, and Joseph Murphy (January, 1987, Vol. 113, No. 1)

Discussion of “ <i>Limit State Probabilities for Wood Structural Members</i> ” by Erik M. Hendrickson, Bruce Ellingwood, and Joseph Murphy (January, 1987, Vol. 113, No. 1)

Discussion of “ Limit State Probabilities for Wood Structural Members ” by Erik M. Hendrickson, Bruce Ellingwood, and Joseph Murphy (January, 1987, Vol. 113, No. 1)

Discussion of “ <i>Limit State Probabilities for Wood Structural Members</i> ” by Erik M. Hendrickson, Bruce Ellingwood, and Joseph Murphy (January, 1987, Vol. 113, No. 1)

Closure to “ Limit State Probabilities for Wood Structural Members ” by Erik M. Hendrickson, Bruce Ellingwood, and Joseph Murphy (January, 1987, Vol. 113, No. 1)

Closure to “ <i>Limit State Probabilities for Wood Structural Members</i> ” by Erik M. Hendrickson, Bruce Ellingwood, and Joseph Murphy (January, 1987, Vol. 113, No. 1)

DETERMINATION OF DESIGN LOAD COMBINATION AND LOAD FACTORS ON THE BASIS OF LIMIT STATE PROBABILITIES

A rational procedure for determining design load combination and safety format is proposed, in which reliability-based structural design is developed on the basis of limit state probabilities. Load factors or safety factors associated with each design load combination in a safety format are optimized numerically through the objective function so that uniform level of structural reliabilities evaluated by limit state probability can be realized to the target, regardless of structural types and dimensions. Conceptual diagram of limit state probabilities is introduced to interpret the structural reliability, and the methodology to estimate the factors is showed with numerical examples using structural models and load combinations.

Probability‐Based Design Criteria for Nuclear Plant Structures

This paper summarizes the results of a research program conducted during 1980–1985 to develop probability‐based analysis and design procedures for structures in nuclear plants. Limit states of concrete containments and shear walls are formulated. Probabilistic models for static and dynamic loads and structural resistance variables are established. Reliability analysis methods are established for estimating limit state probabilities for nuclear plant structures subjected to combinations of static and dynamic loads. Practical probability‐based design criteria are developed for concrete containments and shear walls in a load and resistance factor design format. The load and resistance factors are illustrated for several limit states and target limit state probabilities.

Limit State Probabilities for Wood Structural Members

Estimates of the limit state probability for wood members, where the limit state is failure by creep rupture, must be based on analyses that take into account the temporal characteristics of the applied loads. These estimates require: (1) construction of appropriate load process models; (2) a probabilistic description of wood member strength; and (3) a cumulative damage analysis. Reliability analyses of beams subjected to dead, snow, and live loads were performed to evaluate the effects of using different load duration models and different parameters in the snow and live load process models. It was found that the most important factor determining failure is the duration and magnitude of the extreme load pulses. The choice of load duration model, in contrast, was relatively unimportant. Reliabilities associated with existing design criteria were evaluated, and resistance factors for use in a proposed load and resistance factor design format were determined, using glulam beams in bending as an example.

Probability-based design criteria for shear walls in nuclear power plants

The development of probability-based criteria for the design of reinforced concrete shear walls subjected to dead load, live load and in-plane earthquake forces in nuclear plants is described. These criteria are determined for flexure and shear limit states in a load and resistance factor design (LRFD) format. The flexure limit state is defined according to traditional principles of ultimate strength analysis, while the shear limit state is established from experimental results. Resistance factors for shear and flexure, load factors for dead and live load, and a load factor for effect of Safe-Shutdown Earthquake are determined for target limit state probabilities of 1.0 × 10 −6 and 1.0 × 10 −5 over a a period of 40 years. Comparisons among the proposed design criteria, ACI 349 and US NRC Standard Review Plan 3.8.4 are included.

Probability-based load combinations for the design of concrete containments

This paper describes a procedure for developing probability-based load combinations for the design of concrete containments. The proposed criteria are in a load and resistance factor design (LRFD) format. The load factors and resistance factors are, in general, derived for use in limit states design and are based on a target limit state probability. In this paper, the load factors for accident pressure due to the design basis accident and safe shutdown earthquake are derived for three target limit state probabilities. Other load factors are recommended on the basis of prior experience with probability-based design criteria for ordinary building construction.

Basic Analysis of Structural Safety

The present study reviews some of the more significant recent developments in the area of structural reliability analysis, proposes new interpretations for and emphasis in some of these crucial theoretical developments, and introduces additional useful quantities. To be specific, the first‐order second‐moment methods are reviewed. It is then shown that the Lagrange multiplier formulation (and thus any algorithm associated with it) can be used to evaluate the safety index and the location of the design point. Monte Carlo techniques are recommended for use in estimating limit state probabilities as a practical alternative to other methods. The use of the Stokes and Gauss divergence theorem in two‐ and three‐dimensional integral expressions of a limit state probability is suggested in order to reduce the dimensionality of the integrations by one. Finally, it is recommended that the point of maximum likelihood be used as an alternative to the design point based on the advanced firstorder second‐moment method.

The GI/Geom/N Queue In Discrete Time

AbstractThe paper is concerned with the investigation of the GI/Geom/N queue in discrete time using the method of the imbedded Markov chain. The queueing system under consideration has a general independent input, of which the interarrival times are assumed to be identically distributed positive independent random variables with a general probability distribution {an}, first-come first-served queue discipline, geometric service-time distribution and iVservers. The limiting state probability distribution, the waiting-time probability distribution and the delay probability are determined analytically. The problem is also solved for the case when the queue length is bounded by the number of servers. Of special importance is the probability oi customer loss. Erlang's delay and loss formulae are obtained using a limiting process.

The bearing capacity of joints between walls and floor slabs in multistorey buildings

The paper deals with determination, by traditional and probabilistic methods, of the bearing capacity of joints between walls and floor slabs. All principals factors affecting the probability of limit states being attained are taken into account. The probability analysis is based on specific statistical data.

An automaton in the nonstationary random environment

The purpose of this paper is to consider the behavior of a finite automaton in a nonstationary random environment. The behavior of finite deterministic automata in stationary random environments was considered by Tsetlin. In this paper, the probabilistic automaton is introduced as a random environment in order to generalize the stationary random environment. The interaction between the probabilistic automaton and the two-state deterministic automaton is considered in the case where the probabilistic automaton has two inputs and two states and, besides, is completely isolated by the 0th approximation. And the limiting state probability distribution of this finite automaton is also obtained. Moreover, it is shown that, if the probabilistic automaton is completely isolated by the (0, k)th approximation and satisfies some conditions, then the finite automaton can behave expediently against the probabilistic automaton.