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A method for the incorporation of continuum modeling in the optimization of large discrete structures is presented. The use of a continuum model facilitates decomposition of optimization problems and augments the scope and applicability of the multilevel decomposition method. This new concept is demonstrated by the optimization of slender, multi-bay, beam-like trusses with large numbers of members. An algorithm for the continuum model optimization of the truss is developed and tested against a traditional algorithm that might be used to solve the problem. Data are presented that reflect the advantages of the continuum model method over the traditional in the areas of computational efficiency and robustness. Additionally, design results for the beam-like truss are presented. / Master of Science

The probabilistic approach to design optimization has received increased attention in the last two decades. It is widely recognized that such an approach should lead to designs that make better use of the resources than designs obtained with the classical deterministic approach by distributing safety onto the different components and/or failure modes of a system in an optimal manner. However, probabilistic models rely on a number of assumptions regarding the magnitude of the uncertainties, their distributions, correlations, etc. In addition, modelling errors and approximate reliability calculations (first order methods for example) introduce uncertainty in the predicted system reliability. Because of these inaccuracies, it is not clear if a design obtained from probabilistic optimization will really be more reliable than a design based on deterministic optimization. The objective of this work is to provide a partial answer to this question through laboratory experiments — such experimental validation is not currently available in the literature. A cantilevered truss structure is used as a test case. First, the uncertainties in stiffness and mass properties of the truss elements are evaluated from a large number of measurements. The transmitted scatter in the natural frequencies of the truss is computed and compared to experimental estimates obtained from measurements on 6 realizations of the structure. The experimental results are in reasonable agreement with the predictions, although the magnitude of the transmitted scatter is extremely small. The truss is then equipped with passive viscoelastic tuned dampers for vibration control. The controlled structure is optimized by selecting locations for the dampers and for tuning masses added to the truss. The objective is to satisfy upper limits on the acceleration at given points on the truss for a specified excitation. The properties of the dampers are the primary sources of uncertainties. Two optimal designs are obtained from deterministic and probabilistic optimizations; the deterministic approach maximizes safety margins while the probability of failure (i.e. exceeding the acceleration limit) is minimized in the probabilistic approach. The optimizations are performed with genetic algorithms. The predicted probability of failure of the optimum probabilistic design is less than half that of the deterministic optimum. Finally, optimal deterministic and probabilistic designs are compared in the laboratory. Because small differences in failure rates between two designs are not measurable with a reasonable number of tests, we use anti-optimization to identify a design problem that maximizes the contrast in probability of failure between the two approaches. The anti-optimization is also performed with a genetic algorithm. For the problem identified by the anti-optimization, the probability of failure of the optimum probabilistic design is 25 times smaller than that of the deterministic design. The rates of failure are then measured by testing 29 realizations of each optimum design. The results agree well with the predictions and confirm the larger reliability of the probabilistic design. However, the probabilistic optimum is shown to be very sensitive to modelling errors. This sensitivity can be reduced by including the modelling errors as additional uncertainties in the probabilistic formulation. / Ph. D.

A fully automated computer program is developed for the optimum design of steel space trusses acting compositely with a concrete slab placed on top. The program sizes the truss members to meet the requirements of the load and resistance factor design specification of the American Institute of Steel Construction using the load combinations of ANSI. Earthquake loading is not considered. The optimum size is based on minimum cost, regarding the amount of welding required at the joints and of the member itself. The total cost is based on all steel work in the truss. Once the truss configuration has been defined, and it has been ensured that linear elastic behavior exists, the structure is analyzed for the construction process, to make sure that no overstressing will take place in any structural element at any time during construction and service. The analysis and design principles are presented and an actual design case is solved. (Abstract shortened with permission of author.)

Thesis (MScEng (Civil Engineering))--Stellenbosch University, 2008. / The Southern African Institute of Steel Construction expressed concern with regard to the unit definition of the effective length factor, K, stipulated for compressive elements of parallel chord trusses in Clause 15 of SANS 10162-1:2005 - Limit state design of hot-rolled steelwork. The simplified method for truss design specified in the code assumes all compression members are pin-connected, which allows for greater design simplicity and reduces the amount of code interpretation required by the designer. In addition to this, Clause 15 requires the additional reduction in resistance of the first web compression members by a factor of 0.85. However, this approach may be considered overly conservative and in current design practice the effective length factor is often reduced to less than 1.0. This research investigates the effective length factor of web compression members in parallel chord trusses, by means of investigative structural analyses of representative trusses using ANGELINE and Prokon analytical programs, and by designing, constructing and testing six representative trusses, using current design practices. A comparative study of a number of different countries’ codified approaches to truss design is also included. The structural analyses revealed that in-plane buckling of the web compression members was the consistent mode of failure, however at a much greater applied load than the design load determined according to SANS 10162-1:2005. Contrary to the expected mode of failure, all six tests performed on the representative trusses exhibited elastic out-of-plane buckling, or strongaxis buckling, of the web compression members, but still at a much greater applied load than the design load. The unexpected out-of-plane buckling of the web members is due to the inplane stiffness of the end connections used. In order to stay true to current design practice, gusset plates and longitudinal welds were used to join the web members to the chords. The stiffness of the gusset plates therefore significantly reduced the effective length of the web compression members in-plane, but did not reduce the effective length out-of-plane. Despite the unanticipated behaviour of the tests performed, certain conclusions can still be drawn from the results. The unit definition of the effective length factor for in-plane buckling of web compression members is too conservative and a K factor of 0.8 is recommended. In addition to this an effective length factor for out-plane-buckling of web compression members of 1.1 is recommended for trusses with welded connections. The necessity of the reduction in resistance of 0.85 of the first web compression members requires further investigation. The most important conclusion to be drawn is that out-of-plane buckling of web compression members can be the dominant failure mode, which is not taken into consideration in current design practice.