<p>The results of this work are the closed-form expressions for the tangent and secant stiffness matrices of the 3-node Mindlin frame element. From the study of two solution methods and the behavior of the three elements, several conclusions have been made as follows:</p> <a>1. Because the Mindlin frame element uses quadratic polynoms for the interpolation functions, at least two elements are needed for modelling a member of a plane frame structure.</p> <p> 2. The Mindlin frame element will give a more flexible structure due to the shear deformation effect, but the effect is not always significant.</p> <p> 3. The Mindlin frame element requires about twice degree-of-freedoms than the Bernoulli-Euler frame element requirement.</p> <p> 4. The formulation of tangent stiffness matrix can be simplified, in condition that the internal forces calculations are done using the appropriate nonlinear formulation. The calculation of the tangent stiffness matrix and the internal element forces can be done using different formulations.</p> / Master of Science

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.

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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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

The aim of a structural designer, whether dealing with buildings, bridges, airplanes, or some other type of structure, is to design the most economical structure that will do the job required of it with safety. In the latter part of the nineteenth century and the early part of the twentieth century, many designers went to great lengths to make their structures statically determinate and often inserted pins and.hinges in the structure in order to achieve this end. With the advent of reinforced concrete and welded steel structures, however, it became evident that continuous, hence statically indeterminate structures were easier and cheaper to build and methods for designing them were devised. One of the methods of analysis used extensively since its introduction to this country in 1915 by George A. Maney is the slope-deflection method, in which the rotations and translations of the joints are redundants and must be determined before the bending moments can be calculated. This method, as well as the other classical methods, involves the solving of simultaneous linear equations18 - a procedure which can become very tedious in a structure of any size. Another method, perhaps typical of newer methods of analysis, which has won wide acceptance and a great deal of popularity in its relatively short existence is Hardy Cross's moment distribution. The use of this method gives the analyst a physical picture of joint movements and at the same time saves a great deal of time in the analysis of many structures. The usual procedure when analysing a building frame or other three-dimensional structure is to consider it as a series of planar structures and ignore the effects of torsion in the members. The use of an appropriate factor of safety, or factor of ignorance, as many insist, makes this an acceptably safe procedure, but can also cause quite a waste of materials. The effect of torsion upon concrete has been found worthy of notice and several papers have been written on analysis of three-dimensional rigid frames, but as yet nothing has been developed that would interest very many practicing design engineers. If rigid frames are to be analyzed in their true three-dimensional form, a convenient method of analysis must be devised. The classical methods of analysis are much too tedious, and even the most elementary type of three-dimensional frame analyzed using moment distribution is rather a tremendous undertaking, in spite of the saving of time gained by the use of this method. / Master of Science

The Linked Column Frame (LCF) is a new brace-free lateral structural steel system intended for rapid return to occupancy performance level. LCF is more resilient under a design level earthquake than the conventional approaches. The structural system consists of moment frames for gravity that combines with closely spaced dual columns (LC) interconnected with bolted links for the lateral system. The LC links are sacrificial and intended to be replaced following a design level earthquake. The centerpiece of this work was a unique full-scale experiment using hybrid simulation testing; a combination of physical test of a critical sub-system tied to a numerical model of the building frame. Hybrid simulation testing allows for full scale study at the system level accounting for the uncertainties via experimental component and having the ability to model more conventional behavior through numerical simulation. The experimental subsystem consisted of a two story LCF frame with a single bay while the remainder of the building was numerically modeled. Two actuators per story were connected to the specimen. The LC links have been designed to be short and plastically shear dominated and the LCF met the design intent of 2.5% inter-story drift limits. For evaluating the LCF response, hybrid testing was performed for ground motion at three different intensities; 50%, 10% and 2% probability of exceedence in 50 years for Seattle, Washington ground motions. The system overall had exhibited three distinct performance levels; linearly elastic, rapid return to occupancy where only the replaceable links would yield, and collapse prevention where the gravity beam components also became damaged. Results demonstrated a viable lateral system under cyclic and seismic loading, offering a ductile structural system with the ability to rapidly return to occupancy.

Thesis (Ph. D.)--University of Washington, 2006. / Vita. Includes bibliographical references (leaves 266-272).

Most of the current optimization techniques for the design of light-weight structures are unable to generate structural alternatives at the concept stage of design. This research tackles the challenge of developing an optimization method for the early stage of design. The main goal is to propose a procedure to optimize material and shape of stiff shafts in torsion. / Recently introduced for bending stiffness design, shape transformers are presented in this thesis for optimizing the design of shafts in torsion. Shape transformers are geometric parameters defined to classify shapes and to model structural efficiency. The study of shape transformers are centered on concept selection in structural design. These factors are used to formulate indices of material and shape selection for minimum mass design. An advantage of the method of shape transformers is that the contribution of the shape can be decoupled from the contribution of the size of a cross-section. This feature gives the designer insight into the effects that scaling, shape, as well as material have on the overall structural performance. / Similar to the index for bending, the performance index for torsion stiffness design is a function of the relative scaling of two cross-sections. The thesis examines analytically and graphically the impact of scaling on the torsional efficiency of alternative cross-sections. The resulting maps assist the selection of the best material and shape for cross-sections subjected to dimensional constraints. It is shown that shape transformers for torsion, unlike those for bending, are generally function of the scaling direction. / The efficiency maps ease the visual contrast among the efficiency of open-walled cross-sections and that of close-walled cross-sections. As expected, the maps show the relative inefficiency of the former compared to the latter. They can also set the validity range of thin- and thick-walled theory in torsion stiffness design. The analytical results are validated with the numerical data obtained from ANSYS to guarantee the consistency of the models. The thesis concludes with three case studies that demonstrate the method.