Optimal Structural Standardization
W. B. Hall*
University of Illinois

For economical reasons, many structural members are produced in fixed sizes rather than in a continuous supply of structural shapes. This presents an interesting optimization problem, namely, how to design an assortment of profiles or sizes to best satisfy a structural demand. One solution approach is to minimize the material waste from overdesign that occurs when standardized sizes are selected rather than "made-to-order" cross sections. Related problems include the modeling of economy of scale and the optimal consolidation of production materials.

Probabilistic Assessment of Structural Control Robustness
W. B. Hall,* L. A. Bergman (Aero. & Astro. Engr.)
University of Illinois

The ability of a structural control system to maintain stability is measured by its robustness. When parameter uncertainty is modeled by a probability distribution, robustness becomes analogous to system reliability, in which the joint distribution is of dimension equal to the number of uncertain parameters and the failure boundary is defined by the onset of instability. In the approach taken, root loci provide a mapping of system performance into the parameter space, defining failure boundaries. System reliability methods are then used to assess system robustness from the set of all modal failure regions. A further benefit is the ability to revise the robustness measure when new information from testing or observation is obtained.

Probabilistic Evaluation of Test Results
W. B. Hall*
University of Illinois

Reliability models of structural design are extended to cover the use of load testing for design of new structures or evaluation of existing structures. Approaches are being developed to incorporate into decision making the information from sample tests, single-mode or multimode proof tests, and other sources. These and other load-testing models allow both test and nontest information on strength and safety to be used in the evaluation of a structure. Procedures for design by testing can be assessed for their likely effects on achieved reliability, and design resistance factors can be found that account for test uncertainties.

Reliability Allocation in Structural and Mechanical Systems
W. B. Hall*
University of Illinois

Strategies for allocation of reliability to components of a system are being investigated. In general, a uniform allocation of reliability to individual components will not efficiently achieve system reliability goals, whereas optimized schemes show potential for cost savings and improved consistency in reliability control. Promising strategies depend on the type of system, the costs of component reliabilities, and other factors. Current structural design codes, which seek to control reliability at the component level, appear to be inconsistent at the system level. Practical methods to improve reliability allocation in design are being sought.

Singular Configurations of Structural Systems
E. N. Kuznetsov*
University of Illinois

Singular configurations exist only in underconstrained structural systems, including systems with infinitesimal mobility. This work addresses a critical, yet so far unexplored, aspect of singular configurations-their realizability. It has been found that the only generic, physically realizable type of a singular configuration is a system with first-order infinitesimal mobility, and even this cannot be constructed without inducing prestress of finite magnitude. All other singular configurations (unprestressable first-order mechanisms; higher-order mechanisms; and singular configurations of finite mechanisms) are unrealizable. Moreover, except for exact or symbolic calculation, they are also noncomputable, which explains numerous failed attempts at their analysis.