Fred Moses

Structural optimization by methods of feasible directions

Abstract A general design algorithm based on methods of feasible directions is presented. Zoutendijks method of feasible directions is first presented as applied to structural design. This method is modified to improve numerical stability of the design process and is then further modified to deal efficiently with infeasible designs. The algorithm requires the analytic gradient of the objective function and the constraint functions which are active at a given stage in the design process. Gradient information is not required for nonactive constraints. Complex constraint functions may be ignored in the initial design stages because violation of these constraints is efficiently overcome later in the design process. The algorithm is demonstrated with elastic design of redundant trusses.

System reliability developments in structural engineering

Abstract Two major limitations occur in present structural design code developments utilizing reliability theory. The notional system reliabilities may differ significantly from calibrated component reliabilities. Secondly, actual failures are often due to gross errors not reflected in most present code formats. A review is presented of system reliability methods and further new concepts are developed. The incremental load approach for identifying and expressing collapse modes is expanded by employing a strategy to identify and enumerate the significant structural collapse modes. It further isolates the importance of critical components in the system performance. Ductile and brittle component behavior and strength correlation is reflected in the system model and illustrated in several examples. Modal combinations for the system reliability are also reviewed. From these developments a system factor can be addended to component safety cheking equations. Values may be derived from system behavior by substituting in a damage model which accounts for the response range from component failure to collapse. Other strategies are discussed which emphasize quality assurance during design and in-service inspection for components whose behavior is critical to the system reliability.

A sequential response surface method and its application in the reliability analysis of aircraft structural systems

Abstract The reliability analysis of aircraft structural systems is difficult to evaluate due to the complexity of the g-function g(x), the probability density function ƒ(x) and the dimension m of the problem. In many cases, the g-function can be very complex and the number of evaluation of g(x) may dominate the computation cost. Response Surface Methods may alleviate the problem by giving a simple approximation, g′(x), to the true g-function, which can then be used instead of g(x) for the reliability analysis. In this paper, a new Sequential Response Surface Method together with Monte Carlo Importance Sampling (MCIS) is suggested. Based on the method, a reliability analysis program RSM for aircraft structural systems is developed. Several examples are presented to illustrate the method.

Optimum design, redundancy and reliability of structural systems

Abstract The need for structural safety under a variety of loading and accident conditions has focused attention on redundancy, ductility and reliability of structural systems. The concepts of component reserve strength and system residual strength, system reliability and system residual reliability and their application are described. Several different structural configuration examples are illustrated in which component sizes are optimized. Design models for extreme loading and accident conditions for both brittle and ductile models are developed. System design methods are recommended.

Structural system reliability and optimization

Abstract Structural reliability research concentrates on probabilistic descriptions of phenomena and application to code oriented safety design. Alternatively, optimization research works toward efficient algorithms for locating optima particularly in large-scale systems using prescribed deterministic constraints. This paper attempts to unify these efforts. Optimization procedures should explicitly consider safety either directly in its cost function or as one of its primary constraints. In the design of structural elements it is easier to establish the connection between optimization and reliability. Examples of element optimization in concrete structures and highway bridge girders elements subject to fatigue loading are discussed. In structural system problems, the complex interrelationship of elements and failure modes has made structural reliability analysis extremely difficult. The paper emphasizes the importance of characterizing systems with regard to a reliability oriented model including parallel, series, ductile, brittle, independent and correlated strength behavior. Following the developments in reliability formulation for elements the paper derives a second-moment reliability analysis for framewords leading to a step-by-step evaluation of the system reliability with a series of reanalysis of the structure. Since the reliability evaluation only requires a few reanalyses in most cases, the method is feasible for application in system optimization.

Problems and prospects of reliability-based optimization

Reliability has long been recognized as a safety constraint in structural engineering. That is, an optimum design should balance both cost and safety. Nevertheless, applications of reliability analysis in recent years have been primarily aimed at establishing the basis for code factors. Similarly, most optimization studies have used accepted code safety factors without introducing reliability as explicit design constraints. This paper reviews the methodology of component and system reliability analysis and examples of their inclusion in optimization applications. The limitations in the explicit use of reliability in optimization are discussed.

A Method of Structural Optimization Based on Structural System Reliability

ABSTRACT An optimality criterion based on structural system reliability is presented for optimizing component sizes to satisfy a system reliability constraint. In this paper, optimality criteria and iterative formulas are developed. Some results in reliability optimization are presented and illustrated. An incremental loading approach is adopted for identifying failure modes and computing system reliability. For a number of illustrative examples, optimal designs were obtained within 3 to 5 iterations. With the aid of several examples, optimal weight characteristics of statically determinate and statically indeterminate structures are explained. These structures are loaded under both a single group of loads and different groups of loads.

Redundancy and robustness of highway bridge superstructures and substructures

Major advances have been recently achieved in developing methodologies for the structural analysis of cascading failures and in understanding the behaviour of different types of systems under suddenly applied extreme loads. Yet, a main issue related to defining objective measures of redundancy and quantifying the levels of redundancy that exist in structural systems remains vastly unresolved. This paper reviews the work done by the authors and their colleagues on the quantification of system redundancy of typical highway bridges and reassesses previously made proposals for including system redundancy and robustness during the structural design and safety evaluation of bridge superstructure and substructure systems. These proposals, which are based on system reliability principles, consider structural system safety, system redundancy and system robustness in comparison to member safety, and account for the uncertainties associated with determining member and system strengths as well as future loads in a consistent and rational manner.

Cost and safety optimization of structural design specifications

Abstract The design of buildings, bridges, offshore platforms and other civil infrastructure systems is controlled by specifications whose purpose is to provide the engineering principles and procedures required for evaluating the safety of structural systems. The calibration of these codes and specifications is a continuous process necessary to maintain a safe national and global infrastructure system while keeping abreast of new developments in engineering principles, and data on new materials, and applied loads. The common approach to specification calibration is to use probabilistic tools to deal with the random behavior of materials and to account for the uncertainties associated with determining environmental and other load effects. This paper presents a procedure to calibrate load factors for a structural design specification based on cost and safety optimization. The procedure is illustrated by determining load factors that may be applicable for incorporation in a bridge design specification. Traditional code calibration procedures require a set of pre-determined safety levels that should be used as target values that each load combination case should satisfy. The procedure in this paper deduces the failure cost implied in present designs, and provides consistent safety levels for all load combination cases. For greater accuracy, load effects showing variance in time have been modeled by separating them into two random variables; time dependent r.v. (wind speed, vehicular loads, etc.) and time independent r.v. (modeling uncertainties). The total expected lifetime cost is used in the optimization to account for both initial construction cost and future equivalent failure costs.

Protocols for Collecting and Using Traffic Data in Bridge Design

This report provides a set of protocols and methodologies for using available recent truck traffic data to develop and calibrate vehicular loads for load and resistance factor design (LRFD) superstructure design, fatigue design, deck design, and design for overload permits. The protocols are geared to address the collection, processing, and use of national weigh-in-motion (WIM) data. The report also gives practical examples of implementing these protocols with recent national WIM data drawn from states/sites around the country with different traffic exposures, load spectra, and truck configurations. The material in this report will be of immediate interest to bridge engineers. This report replaces NCHRP Web Document 135.