| Summary: | 博士 === 國立臺灣大學 === 土木工程學研究所 === 91 === According to their behaviors after deformation, reinforced concrete structures can be divided into two categories: B regions and D regions. The regions where the Bernoulli hypothesis of linear strain distribution is valid are usually referred to as B regions. As a result, the beam theory can be applied in B regions to get a conservative analysis or design. The remaining regions are called D regions (meaning discontinuity or disturbance), which usually occur near geometrical discontinuities or concentrated forces. D regions are usually designed using empirical approaches or detailing practices. Therefore, most structural failures occur in D regions.
Numerous researches have dedicated to investigating methods for designing D regions, and one of the most commonly used approaches is the strut-and-tie model. In this method, the complex flow of internal forces in D-regions is realized as a truss-like structure carrying the imposed loading to adjacent B regions or to its supports. Compressive and tensile members of the truss model are understood as ‘struts’ and ‘ties’, and the place where tensile and compressive elements meet as ‘nodes’. In general, struts and nodes consist of concrete to resist compressive forces, and ties, composed of reinforcement or prestressed tendons, are used to resist tensile forces.
Through truss analyses, engineers can obtain member forces of the strut-and-tie model and select reinforcement that is necessary to provide the required tie capacity. Depending on crack direction in struts and bearing types of nodes, struts and nodes can be divided into different types. Each has its own compressive strengths in codes and guidelines. Once the compressive strength is obtained, it can be used to compute the effective widths for struts, which, in turn, will determine the shapes and dimensions of nodes. Finally, the truss model with finite widths is examined to see whether it is suitable for the configuration of the selected structure. If not, the strut-and-tie model is considered unable to resist the external loads and the selected strut-and-tie model has to be modified.
Although conceptually simple, the strut-and-tie model has a few drawbacks that may hinder its practice. Firstly, due to the lack of automation, the development of such a model depends considerably on the experiences of engineers. Nonetheless, since a reinforced concrete structure can produce more than one strut-and-tie model, it may be difficult for designers to decide which model is the most appropriate one. Secondly, there is still much debate on the compressive strength of struts and nodes; the strength values specified in codes and guidelines are far from being universally accepted. Thirdly, checking struts and nodes is time-consuming and tedious, especially when the strut-and-tie model is complex.
In this thesis a refined evolutionary structural optimization (RESO) method is proposed to generate strut-and-tie models automatically. The relative stiffness of each member is readily obtained from the evolutionary topology of the considered structure. Furthermore, concrete failure criteria, instead of the conventional effective strength, are employed to check the bearing capacity of struts and nodes. Finally, two interactive computer graphic programs, ADSTM-2D and ADSTM-3D, are developed with the RESO method and concrete failure criteria to automate two-dimensional and three-dimensional strut-and-tie designs and analyses. As the evolutionary process can be observed clearly from windows, users can establish the corresponding strut-and-tie model accordingly. In addition, after analyzing member forces in the strut-and-tie model, the programs can automatically work out the required reinforcements and development length.
ADSTM is not only valuable in the designs of reinforced concrete structures but is also instrumental for structural ultimate strength estimation. For a structure whose design details are known, users can exploit ADSTM to calculate the compressive and tensile strength factors and estimate the ultimate strength of the structure. Numerical examples show that such estimations are satisfactorily accurate when compared with experimental values.
In this thesis, ADSTM is also extended to deal with topology optimization having multiple load cases and elastic-plastic topology optimization problems. Since conventional evolutionary structural optimization method (ESO) cannot tackle multiple load cases with different magnitudes, ‘weight factor’ is proposed to consider the magnitude of each load case. Numerical examples demonstrate that the optimal topology under multiple load cases is different from that of all load cases applied simultaneously, and the differences can be reasonably reflected using the proposed weight factor.
For elastic-plastic topology optimization, nonlinear performance indices are derived in this thesis to compare the material efficiency of structures during different evolutionary stages and to serve as a stop criterion for the evolutionary process. It is found that the optimal topology of elastic-plastic material and that of linear elastic material can be significantly different. In addition, the elastic-plastic topology is in general much better than the elastic topology in terms of load-carrying capacities and stored internal energies.
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