Probabilistic Determination of Failure Load Capacity Variations for Lattice Type Structures Based on Yield Strength Variations including Nonlinear Post-Buckling Member Performance

Abstract

With the attempt to achieve the optimum in analysis and design, the technological global knowledge base grows more and more. Engineers all over the world continuously modify and innovate existing analysis methods and design procedures to perform the same task more efficiently and with better results. In the field of complex structural analysis many researchers pursue this challenging task. The complexity of a lattice type structure is caused by numerous parameters: the nonlinear member performance of the material, the statistical variation of member load capacities, the highly indeterminate structural composition, etc. In order to achieve a simulation approach which represents the real world problem more accurately, it is necessary to develop technologies which include these parameters in the analysis. One of the new technologies is the first order nonlinear analysis of lattice type structures including the after failure response of individual members. Such an analysis is able to predict the failure behavior of a structural system under ultimate loads more accurately than the traditionally used linear elastic analysis or a classical first order nonlinear analysis. It is an analysis procedure which can more accurately evaluate the limit-state of a structural system. The Probability Based Analysis (PBA) is a new technology. It provides the user with a tool to analyze structural systems based on statistical variations in member capacities. Current analysis techniques have shown that structural failure is sensitive to member capacity. The combination of probability based analysis and the limit-state analysis will give the engineer the capability to establish a failure load distribution based on the limit-state capacity of the structure. This failure load distribution which gives statistical properties such as mean and variance improves the engineering judgment. The mean shows the expected value or the mathematical expectation of the failure load. The variance is a tool to measure the variability of the failure load distribution. Based on a certain load case, a small variance will indicate that a few members cause the tower failure over and over again; the design is unbalanced. A large variance will indicate that many different members caused the tower failure. The failure load distribution helps in comparing and evaluating actual test results versus analytical results by locating an actual test among the possible failure loads of a tower series. Additionally, the failure load distribution allows the engineer to calculate exclusion limits which are a measure of the probability of success, or conversely the probability