Paul H. Wirsching

Considerations of probability-based fatigue design for marine structures

Abstract Fatigue is a major failure modelin marine structures which respond dynamically to random wave and wind loading. Oscillatory stresses produce fatigue at points of stress concentration, typically the welded joints. Because all fatigue design factors are subject to significant uncertainty, a reliability approach to management of such uncertainty seems appropriate. This article summarizes some studies in fatigue reliability research and demonstrates how reliability methods can be effectively utilized by designers to avoid fatigue in marine structural components. Included are (1) a description of fatigue damage under variable amplitude stresses employing the characteristics S-N and fracture mechanics models, (2) models for reliability assessment relative to fatigue and the use of these models to derive design criteria, and (3) an elementary application of system fatigue reliability analysis to establish component design criteria.

Reliability with respect to ultimate strength of a corroding ship hull

A reliability assessment relative to the ultimate strength failure of a ship hull experiencing structural degradation due to corrosion is presented. The midship section modulus is considered a random process with a monotonically decreasing mean value. ‘Failure’ occurs when the maximum wave-induced bending moment associated with the extreme loading condition plus the stillwater bending moment exceeds the ultimate strength of the hull. Effects of uncertainties in the design variables (including wave and stillwater bending moments, yield strength, and section modulus) on structural performance can be quantified using statistical methods. A reliability analysis method for ultimate strength is developed and, as an example, the reliability assessment of a corroding tanker is illustrated. Reliability as a function of time (as predicted prior to service) is estimated. Also, conditional reliability, given that the ship has survived up to time τs, is computed as a function of t. The purpose of these reliability analyses is to provide information to ship designers and/or owners to be used for general risk assessment relative to decisions on corrosion margins and corrosion protection during construction, as well as decisions on steel replacement during the ships life.

Sensitivity factors and their application to marine structures

Abstract Sensitivity measures suitable for application to marine structures are provided in this paper. Interpretations of these sensitivity and importance factors are made for two modes of failure: ultimate strength under extreme loading conditions and fatigue strength. Four ships of different types have been selected, and the corresponding sensitivity measures have been computed. The results were compared to show the impact of ship type on the relative importance of the design variables. These reliability-based sensitivity factors provide quantitative measures of the importance of the design variables and their impact on structural safety. The paper illustrates the potential for using such sensitivity factors in design decisions and tradeoff studies.

Fatigue realibility and maintainability of marine structures

Abstract The integrity of structural systems relative to fatigue under variable amplitude loading and fracture under extreme loading can be ensured by a rational program which coordinates a design, inspection and repair process to minimize life-cycle costs. A Monte Carlo simulation is employed for performing fatigue and fracture reliability analysis, given a program of periodic inspection and repair. Fatigue crack growth is described by a fracture mechanics mode. Model parameters and other design factors are considered as random variables. Probability of failure estimates are used for an economic value analysis to establish optimal strategies for design and for a maintenace schedule. Application of the method to a marine structure is presented.

Safety design concepts for seismic structures

Abstract A nonstationary stochastic process, having statistical characteristics similar to actual earthquakes, was developed using a random signal generator and an analog computer. Dynamic models of multistory structures were also programmed on analog computer circuits to obtain many simulations in a relatively short period of time. The dynamic behavior of multistory seismic structures, with the addition of low-cost passive motion reduction devices, was studied using the analog simulation. It was demonstrated that such devices as (a) an absorber attached to the roof (b) a nonlinear spring between the foundation and structure, and (c) a damping mechanism at the first floor can be extremely effective in reducing the seismic response and thus the probability of failure of a multistory structure.

Optimal economic strategies with considerations of reliability of fatigue-sensitive structural systems☆

Abstract The integrity of structural systems relative to fatigue and fracture can be ensured by a rational program which coordinates a design, inspection, and repair process to minimize life-cycle costs in the context of a reliability analysis which treats uncertainties in fatigue design factors and inspection performance. The features of the process are summarized, and a simple illustration is provided. Research needs relative to this problem, delineated herein, are principally those of developing reliability models of material behavior, obtaining the data to compute parameter values, and developing efficient computational methods for fatigue reliability and maintainability analysis of “large”-scale series and redundant structures.

Low Cycle Fatigue Analysis of Marine Structures

There are situations where a marine structure is subjected to stress cycles of such large magnitude that small, but significant, parts of the structural component in question experiences cyclic plasticity. Welded joints are particularly vulnerable because of high local stress concentrations. Fatigue caused by oscillating strain in the plastic range is called “low cycle fatigue”. Cycles to failure are typically below 104 . Traditional welded joint S-N curves do not describe the fatigue strength in the low cycle region (< 104 number of cycles). Typical Class Society Rules do not directly address the low cycle fatigue problem. It is therefore the objective of this paper to present a credible fatigue damage prediction method of welded joints in the low cycle fatigue regime.Copyright

Creep-Rupture Reliability Analysis

A probabilistic approach to the correlation and extrapolation of creep-rupture data is presented. Time temperature parameters (TTP) are used to correlate the data, and an analytical expression for the master curve is developed. The expression provides a simple model for the statistical distribution of strength and fits neatly into a probabilistic design format. The analysis focuses on the Larson-Miller and on the Manson-Haferd parameters, but it can be applied to any of the TTPs. A method is developed for evaluating material dependent constants for TTPs. It is shown that optimized constants can provide a significant improvement in the correlation of the data, thereby reducing modelling error. Attempts were made to quantify the performance of the proposed method in predicting long term behavior. Uncertainty in predicting long term behavior from short term tests was derived for several sets of data. Examples are presented which illustrate the theory and demonstrate the application of state of the art reliability methods to the design of components under creep.

Code Development for Ship Structures—A Demonstration

A demonstration summary of a reliability-based structural design code for ships is presented for two ship types: a cruiser and a tanker. One reason for the development of such a code is to provide specifications which produce ship structure having a weight savings and/or improvement in reliability relative to structure designed by traditional methods. Another reason is to provide uniform safety margin for ships within each type. For both ship types, code requirements cover four failure modes: hull girder bulkling, unstiffened plate yielding and buckling, stiffened plate buckling, and fatigue of critical detail. Both serviceability and ultimate limit states are considered. Because of limitation on the length, only hull girder modes are presented in this paper. Code requirements for other modes will be presented in future publication. A specific provision of the code will be safety check expression, which, for example, for three bending moments (still water Ms , wave Mw , and dynamic Md ), and strength Mu , might have the form, following the partial safety factor format: γsMs + γwMw + γdMd ≤ φMu γs , γw , γd , and φ are the partial safety factors. The design variables (M ’s) are to be taken at their nominal values, typically values in the safe side of the respective distributions. Other safety check expressions for hull girder failure that include load combination factors, as well as consequence of failure factors, are considered. This paper provides a summary of safety check expressions for the hull girder modes.

Fatigue reliability: a review of recent advances

Fatigue is generally considered the most important failure mode in mechanical and structural systems. Reliability methods are appropriate for managing the large uncertainties that exist in fatigue design factors. In this paper, methods of fatigue reliability analysis are reviewed with emphasis on recent work, for which time variant reliability methods are used to model fatigue-weakened structures.