Experimental observations have shown that the dissipation per cycle in many materials does not depend on the deformation frequency over a wide frequency range. A linear model used frequently to represent this type of mechanical behavior is the concept of hysteretic damping. Herein, time and frequency domain models of hysteretic damping are investigated. The validity of time domain and random vibration analyses of systems with hysteretic damping that is described by a constant complex valued stiffness coefficient was examined. It was shown that, although, this model, can be efficient for frequency domain analysis of harmonic vibration of engineering systems, it does not represent a causal system and thus, is not appropriate for time domain analysis involving transient processes. Using a viscoelastic model, proposed by Biot, a study of dynamic systems with linear hysteretic damping is conducted. These systems results in integro-differential equations in the time domain. A time domain technique for the numerical solution of the integro-differential equation of motion is proposed. The response of a mass supported by Biot's hysteretic element is examined under harmonic excitation and ground motion.

Two new, efficient probabilistic methods are presented for evaluating the reliability of an elastic/perfectly plastic continuous medium exhibiting randomly varying yield strength. Both the Tresca and Mohr-Coulomb yield criteria are considered in the present study. The two probabilistic methods developed are based on the upper and lower bound theorems of plastic limit analysis. By extending these two theorems to probabilistic cases the upper bound and lower bound reliability indices of a safety problem can be calculated for the elastic/plastic medium. Both two and three-dimensional problems are studied. These include a two-dimensional (2-D) wedge loaded on one face and the bearing capacity of a strip footing under constant normal pressure. Both the classical Prandtl and Hill mechanisms are considered for this strip footing problem and the Hill mechanism is found to be more critical probabilistically. The three-dimensional (3-D) problem considered is the extension of the 2-D problem wedge problem. In the 3-D problem the failure length in the longitudinal direction and the resisting strength provided by two vertical end sections play important roles in the reliability calculations, and numerical results are given to illustrate these effects. The spatially varying yield strength is modeled as a Gaussian random field in two or three dimensions, depending on which type of problems is analyzed. Several existing methods to discretize the random fields are reviewed, and their advantages and disadvantages when applied to the plastic random media problems are addressed. It is shown that the limit state functions in the upper bound reliability method can be formulated as linear ones and for the lower bound reliability method the limit state function is formulated as a linear programming problem. The proposed methods provide efficient analytical tools for the probabilistic analysis and design for continuous load-carrying media whose failure is defined by their plastic limit state. The reliability methods presented in this study can be applied to several important classes of problems in geotechnical engineering and are potentially applicable to the plastic failure of plates and shells.

The dynamic behavior of structures of two stacked rigid blocks subjected to ground excitation is examined. Assuming no sliding, the rocking response of the system standing free on a rigid foundation is investigated. The analytical formulation of this nonlinear problem is quite challenging. Its complexity is associated with the continuous transition from one regime of motion to another, each one being governed by a different set of highly nonlinear equations. The behavior is described in terms of the four possible modes of response and impact between the two blocks, or the first block and the ground. The exact (nonlinear) equations governing the rocking response of the system to horizontal and vertical ground acceleration are derived for each mode. Furthermore, a comprehensive model governing impact is derived using classical impact theory. Finally, a computer program is developed to approximate the response of the system under arbitrary base excitation.

A prototype variable fluid damper and stiffness device is evaluated in this study. This damper is capable of providing continuous variation with different levels of system damping and stiffness. The damping and stiffness can be varied independent of each other or simultaneously. The following research is focussed on the evaluation of the effectiveness of such a device, and on determining the effectiveness of incorporation of such a device into a framed structure. The damper properties are determined under cyclic and ramp loadings, and the results are presented. Further experimental research is performed to evaluate the effectiveness of the afore mentioned device in a proposed Scissor-Jack energy dissipation system. This system is incorporated into a typical steel frame; whereupon the variable damping and stiffness system's effectiveness is enhanced by a factor of four. By means of test results of the damper it is shown that the damper is capable of producing continuously and independently variable damping and stiffness. It is shown that a similar variation in frame structure damping and stiffness can be achieved by using the damper in a Scissor-Jack system. The presented device can be an effective means for response reduction of structures under earthquake and/or wind excitation.

The semi-active variable stiffness tuned mass damper (SAIVS-TMD), developed in this thesis, is capable of continuously varying its stiffness and retuning its frequency due to real time control, and is robust to changes in building stiffness and damping. In comparison, the passive tuned mass damper (TMD) can only be tuned to a fixed frequency, which is the first mode frequency of the building. The building fundamental frequency can change due to damage or other reasons. The developed SAIVS-TMD overcomes the limitations of the TMD by retuning the frequency in real time. Real time instantaneous frequency identification and control algorithms are developed in this thesis based on time-frequency techniques. Real time tuning algorithms that identify and tune the instantaneous frequency of the SAIVS-TMD are developed based on Hilbert Transform (HT), Short Time Fourier Transform (STFT) and Empirical Mode Decomposition (EMD). A new method for smoothing the end effects of EMD algorithm is proposed and verified through numerical examples. The mathematical formulation of the linear time varying (LTV) system is developed. A new predictor-corrector algorithm is proposed for the LTV system. The LTV analytical model is developed to study the response of SAIVS-TMD under harmonic, sinesweep, random, wind and earthquake excitation. The effectiveness of the SAIVS-TMD and new identification and control algorithms is verified by means of shake table tests of a three-story 1:10 scale steel model. The confirmation of the performance of the SAIVS-TMD and the real time controller is studied analytically in a 76-story benchmark tall building. The results confirm the robust performance of the SAIVS-TMD, even in cases with +/-15% building stiffness uncertainty. The effectiveness of the SAIVS-TMD in reducing the responses of the structures excited by much stronger seismic ground motion is also presented. The effectiveness of the instantaneous frequency identification algorithm, based on EMD/HT method, in offshore structures is also presented.

Elastomeric base isolation systems, consisting of laminated rubber bearings, are very effective in reducing seismic response due to lateral flexibility, which results in longer fundamental period and reduced forces in the superstructure. Such a strategy is aimed at far fault earthquakes that are predominant in the short period range. Longer period near fault earthquakes tend to produce larger base displacements in elastomeric base isolated structures. Introduction of semi-active variable stiffness and damping is expected to reduce the base displacement and interstory drifts. The objective of this thesis is to analytically study the effectiveness of both variable damping devices, such as Magneto-Rheological dampers, and variable stiffness devices such as Semi-Active Variable Stiffness system (SAIVS) in reducing the seismic response. Various control algorithms for MR dampers are evaluated and reductions in response are evident. A new control algorithm is developed based on Time-Frequency principles and Short Term Fourier Transform (STFT) for the SAIVS device and the simulated results demonstrate significant potential for seismic response reduction.

The behavior of reinforced concrete beams under pure torsion was studied. Six reinforced concrete beams were designed with stirrup spacing as the principal variable and tested under monotonic loading up to failure. Loads, angles of twist and reinforcing steel strains were recorded. Based on the experimental results, methods to predict the response of the beams were examined and an equation for torsional capacity was proposed. Three of the predamaged beams were repaired by adding external steel bands bonded to concrete which was proved to be a very practical and efficient way for retrofitting damaged torsion beams. Experimental data on strength, stiffness, steel strain of the repaired beams were obtained, and comparisons between the repaired and the unrepaired control beams were made. Repair by external steel bands is shown to increase torsional capacity, restore the degraded stiffness of the beams and decrease the reinforcement stress levels.

An analytical closed-form solution has been developed for steady-state lateral response of concrete-face rockfill dams built in rectangular canyons. The canyon is assumed to be rigid, while the dam is idealized as a three-dimensional linearly-hysteretic elastic body deforming in shear and bending. Both free and base induced oscillations are studied for various canyon geometries. A parametric study of the effects of the canyon narrowness and the dam slope on the response is undertaken. Finally, a more rigorous numerical formulation is used for verification of the closed-form solution.

This thesis is concerned with passive control systems for seismic protection of building structures, with special emphasis on elastomeric bearings, viscous dampers and tuned mass dampers. Both mathematical modeling and earthquake response analysis techniques are presented for this class of problems. Earthquake response simulations are carried out for a six-story L-shaped building equipped with these protective systems and subjected to three real earthquake ground excitations, namely the El Centro 1940, Orion Blvd 1971 and Capitola 1989 earthquake records. Both deterministic and stochastic earthquake ground excitations are considered. The performance and effectiveness of these passive protective systems are studied mainly in the time domain with some considerations of the frequency domain. Based on all analyses performed and for the particular building structure considered, it is found that base isolation is very effective in reducing the seismic structural response, especially if it exhibits a nonlinear hysteretic behavior, since in addition to decoupling the frame structure from the ground motion, it dissipates the earthquake input energy through hysteretic action. Tuned-mass damping is less effective than viscous damping in reducing the structural response to earthquake excitations. The results also show that the characteristics of the earthquake ground excitation represent a very important factor which influences the performance of the three passive earthquake protective systems studied herein, especially of the tuned-mass damper system.

The stability of elastic/plastic columns and circular rings with random geometric imperfections is investigated. Columns are analyzed for axial loading and rings for uniform external pressure. A procedure is developed to evaluate the reliability of imperfect elastic/plastic columns and rings against instability. The geometric imperfections are modeled as Gaussian random field in one dimension with given mean, variance, and covariance functions. The random field is discretized by the method of orthogonal series expansion using a Fourier series. The weak form of the boundary value problems for column and ring is formulated using Galerkin's method. A mixed finite element is used in which the primary degrees of freedom are transverse deflection and bending moment. For illustration purposes the material behavior is taken as elastic/perfectly plastic. The computationally efficient first- and second-order reliability methods are used to evaluate the failure probabilities and Monte Carlo simulation is used as a check. The variation of the probability of failure of columns and rings over a range of applied loads is presented for different amounts of random geometric imperfections.