The main objective of this study was to determine whether Limit Design could be applied to low-rise unbraced concrete frames. The investigation was carried out both analytically and experimentally. In the analytical part, two mathematical models were used to determine the behavior of unbraced frames. The first method used a nonlinear computer program, which takes into account the material and geometric nonlinearities of concrete frames. Several cases of frames with different reinforcement ratios and under different beam to column load ratios were investigated. For each frame the gravity loads were increased proportionately to 3/4 of the ultimate frame capacity. Then, lateral load was applied to failure while keeping the beam and column loads constant. The second mathematical model solved for the frame stability equation by assuming elasto-plastic moment curvature relationships for members. Also, the stability solution was carried out by reducing the frame to a column attached to a linear spring. In the experimental part, two frames were designed for the same loading conditions but by two different methods; and were tested to failure. Frame USD-1 was designed by the Ultimate Strength Design, while Frame LD-1 by a Limit Design method. The columns were 21-in high while the beam was 84-in long. The loading procedure consisted of proportionately loading the beam and columns up to the design load, and then applying the lateral load to failure. The computer study and the stability model solution showed that frames subjected to low column thrusts remained in stable equilibrium until two plastic hinges form, thus constituting a mechanism. The two experimental frames remained in stable equilibrium until two plastic hinges formed in the beams. The ultimate lateral loads of Frames USD-1 and LD-1 exceeded the design lateral load by 66% and 33%, respectively. Based on this investigation, it appears that Limit Design may be used for low-rise unbraced reinforced concrete structures.

The study applies an ethnography of speaking to the study of a bilingual child, with the construct of a frame as the unit of analysis. The child was observed and tape recorded playing a commercial game in Chinese with her mother, and in English with her father. Both activity frames and conceptual frames were analyzed toward answering (1) what frames were performed during game play (2) how those frames differed between Chinese and English (3) what conceptual frames were produced in languages spoken and (4) how those conceptual frames differed between each language. In brief, the study applied an ethnographic perspective toward describing how the organization of activity and language compared between both languages, through the play of a single game. The study discovered that each parent enacted different roles with the daughter during the play of the game. Whereas the mother, who had previous experience with game, performed an expert-novice role during game play, the father with his lack of experience in playing the game, took a novice-expert stance with respect to the daughter. The activity frames and conceptual frames followed accordingly, with the games in Chinese dominated by frames featuring directing and reporting on the part of the mother. In contrast, the English games reported the daughter dominating talk with informing and reporting functions of frames. Of the conceptual frames, Chinese presented game objects and events as changes of state; objects were evaluated according to notions of permission and convention. Conversely, English conceptualized objects as independent things existing with attributes, and events as discrete objects with defined spans of time. The study discovered a tight relationship between utterance, its function, and its frame for embedding topic-relationships. This relationship hints at dual activity-conceptual systems among bilingual children, warranting further attention by educators to integrate three dimensions into language classroom instruction: grammar form, speech function, and conceptual contents. As this study demonstrates, bilingual children do much more than talk in two languages. / Ph. D.

Recent proposed rafter slenderness limits, to prevent snap-through of plastically designed pitched-roof portal frames, incorporate the elastic snap-through buckling load of such frames. It has been suggested that the elastic snap-through buckling load used in the proposals is over-estimated making these slenderness limits unconservative. This is supported by a more rigorous elastic analysis. To test the proposals, model frames lying on or close to the slenderness limits were tested to failure in the laboratory. Frame dimensions were chosen so that the frames were only susceptible to snap-through instability. Failure loads far lower than the expected plastic collapse loads were measured, showing that the elastic snap-through buckling load is over -estimated . Since plastic analysis is easily applied to portal frames, these slenderness limits are best replaced by a similar limit incorporating a more accurate elastic snap-through buckling load. A new limit is outlined which must still be tested by further research

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Since the discovery in the early 1950's, frames have emerged as an important tool in signal processing, image processing, data compression and sampling theory etc. Today, powerful tools from operator theory and Banach space theory are being introduced to the study of frames producing deep results in frame theory. In recent years, many mathematicians generalized the frame theory from Hilbert spaces to Hilbert C*-modules and got significant results which enrich the theory of frames. Also there is growing evidence that Hilbert C*-modules theory and the theory of wavelets and frames are tightly related to each other in many aspects. Both research fields can benefit from achievements of the other field. Our purpose of this dissertation is to work on several basic problems on frames for Hilbert C*-modules. We first give a very useful characterization of modular frames which is easy to be applied. Using this characterization we investigate the modular frames from the operator theory point of view. A condition under which the removal of element from a frame in Hilbert C*-modules leaves a frame or a non-frame set is also given. In contrast to the Hilbert space situation, Riesz bases of Hilbert C*-modules may possess infinitely many alternative duals due to the existence of zero-divisors and not every dual of a Riesz basis is again a Riesz basis. We will present several such examples showing that the duals of Riesz bases in Hilbert $C^*$-modules are much different and more complicated than the Hilbert space cases. A complete characterization of all the dual sequences for a Riesz basis, and a necessary and sufficient condition for a dual sequence of a Riesz basis to be a Riesz basis are also given. In the case that the underlying C*-algebra is a commutative W*-algebra, we prove that the set of the Parseval frame generators for a unitary group can be parameterized by the set of all the unitary operators in the double commutant of the unitary group. Similar result holds for the set of all the general frame generators where the unitary operators are replaced by invertible and adjointable operators. Consequently, the set of all the Parseval frame generators is path-connected. We also prove the existence and uniqueness of the best Parseval multi-frame approximations for multi-frame generators of unitary groups on Hilbert C*-modules when the underlying C*-algebra is commutative. For the dilation results of frames we show that a complete Parseval frame vector for a unitary group on Hilbert C*-module can be dilated to a complete wandering vector. For any dual frame pair in Hilbert C*-modules, we prove that the pair are orthogonal compressions of a Riesz basis and its canonical dual basis for some larger Hilbert C*-module. For the perturbation of frames and Riesz bases in Hilbert C*-modules we prove that the Casazza-Christensen general perturbation theorem for frames in Hilbert spaces remains valid in Hilbert C*-modules. In the Hilbert space setting, under the same perturbation condition, the perturbation of any Riesz basis remains a Riesz basis. However, this no longer holds for Riesz bases in Hilbert C*-modules. We also give a complete characterization on all the Riesz bases for Hilbert C*-modules such that the perturbation (under Casazza-Christensen's perturbation condition) of a Riesz basis still remains a Riesz basis.

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In this thesis, a method of predicting the steady state, dynamic, electromechanical behavior of stack actuators (both electrostrictive and piezoelectric) integrated within complex structures is developed and experimentally verified. This research was motivated by a need to accurately predict transmission force, velocity output, and power consumption for a wide range of applications both terrestrial and space based. The relevant transduction equation / parameters are derived from basic principles. These results are experimentally verified with a PZT stack active member. The derivations are then extended to incorporate the effects of integrating the actuator within a host structure. Specifically, the equations needed to predict actuator output force, resulting velocity and drawn current are derived. To implement and test these results in a structure, the equivalent host structure impedance must be determined. This is done experimentally for a complex truss structure representative of a small satellite. These results are then used to prepare theoretical predictions which compare well with experimentally measured output force. Finally, the derivations are extended to the electrical behavior of active members integrated within truss structures. It is now possible to predict the electrical load imposed by the active member on the power supply system including the effects of coupling with the host structure dynamic boundary conditions. Two implications of this are considered. First, the required power demands directly influence the design and sizing of amplifiers, applied voltage levels and power systems. Second, the dissipative power from actuation losses contributes directly towards raising the internal temperature of an operating stack actuator. / Master of Science

Recent developments in the philosophy of structural steel design have led to design specifications that incorporate second-order geometric effects. The use of second-order elastic analysis (SOEA) in the design of structural frameworks may lead to more economically designed structures and increased knowledge of structural stability. The research presented here concerns economy of design between the available steel design specifications as they apply to the metal building industry. Since these buildings are primarily for industrial use, their optimization suggests the use of gabled rigid frames with tapered elements to provide the required load carrying capacity. Results of the research indicate that elastic stability considering geometric nonlinearity is not a primary concern for these types of frames. Rather, the fully-stressed design approach leads to the optimally designed frame. / Master of Science