This study deals with the following two aspects of the response of liquid-filled cylindrical elastic tanks: (a)Dynamic response to a vertical excitation of the base; (b)Statical analysis under antisymmetrical forces of the type obtained in analyses of the dynamic response of the tank to a lateral excitation. The dynamic response of a liquid-tank system is treated in a stepwise fashion by, first examining the free vibrational characteristics of the system and, then, investigating the harmonic and the transient behaviors through a modal superposition procedure. The free vibrational behavior is first investigated on the assumptions that the surface effects associated with the liquid sloshing, and the effect of liquid compressibility, can be neglected. Subsequently, the effects of these quantities are investigated and it is shown that they do not affect the response in any significant way. In the evaluation of the transient response, the effects of the surface sloshing of the liquid and of the liquid compressibility are ignored. The approach to the above analyses consists of satisfying concurrently the equations of motions of the tank and of the contained liquid, subject to the appropriate interface and boundary conditions. Based on the results of the free vibration analysis, approximate models are developed to predict, with acceptable accuracy, some of the modal characteristics of the liquid tank systems. Comprehensive numerical data are presented for analyzing and understanding the behavior of partially and fully filled tanks. The behavior of a partially filled tank is shown to be analogous to that of an equivalent liquid-tank system which is fully filled but has a reduced height corresponding to the depth of the liquid in the partially filled tank. The tank flexibility is found to be of significant importance. In an illustration considered, wherein a fully filled tank of practical dimensions is excited by a broad band vertical excitation, the flexibility of the tank is found to be responsible for effects over three times larger than those induced in a similarly excited rigid tank. Two physically attractive approaches, a displacement approach and a force approach, have been developed for statically analyzing a circular cylindrical tank subjected to the antisymmetrical loadings of the type mentioned in the opening paragraph. Influence coefficients have been furnished to facilitate implementation of the above analyses procedures, which involve application of end displacements or of end forces to correct the deformation/force state associated with membrane state.

First-passage probabilities are investigated for the absolute value of the zero-start response of simple oscillators excited by stationary white noise with a normal probability distribution. Both small-time (non-stationary) and large-time (stationary) behavior are included, but more emphasis is given to the latter. The oscillator responses studied included the linear SDF system, linear 2DF systems, and yielding SDF systems. The basic purposes of this study are, for each oscillator, to investigate the behavior of the first-passage probability by use of Monte Carlo simulation data and theoretical approaches, and to seek empirical formulas which approximate the results adequately for design purposes. Simple procedures are presented for the linear SDF system which allow approximate prediction of the probability of first-passage for both long-time and short-time situations. This includes both the zero-start situation and the stationary-start situation. For a linear 2DF system with nearly equal modal frequencies, an equivalent SDF model is developed by consideration of response correlation coefficients. The model is shown to agree with the 2DF first-passage behavior when modal frequencies differ by less than 20 percent. A diffusion model is developed to approximate the first-passage probability of linear 2DF systems. The procedure is basically parallel to the ideas of Roberts for SDF response. The approximate formulation uses the amplitudes of two response modes as components of a Markov vector to establish a two-dimensional diffusion model. Within any short-time increment the two amplitudes are assumed to evolve independently of each other. The model is simplified to a one-dimensional diffusion when the second frequency is very large. Based on simulation and diffusion results, relatively simple empirical formulas are presented to approximate the long-time first-passage probabilities for 2DF systems. The yielding SDF system studied is the bilinear hysteretic oscillator which has previously been approximated by third-order linear systems and two-mode linear systems in studies of power spectral density and mean-squared response. Here the first-passage statistics of the yielding system are compared with results for the "equivalent" two-mode and third-order linear models. Diffusion results for the two-mode linear system are feasible only when both modes are under-damped, and this excludes approximation of several yielding situations. Diffusion results for the third-order linear model seem to better fit the existing simulation data for the yielding system than do the results for two-mode models.

The objective of this investigation was to contribute to improved understanding of the dynamic response of offshore guyed towers. This was accomplished through studies of the following interrelated problems: (1) Effects of cable and foundation constraints on the natural frequencies and modes of vibration of representative structural systems; (2) Low-amplitude harmonic stiffness and free vibrational characteristics of inclined parabolic cables; (3) Effects of cable-tower interaction on the dynamic response of the tower; and (4) Response of representative guyed tower models to simulated wave loadings. Both the force method and the displacement method are applied to the analysis of the first problem, and the interrelationship of the two methods is elucidated. A study is made of the factors that affect the natural frequencies and modes of vibration of guyed towers, and comprehensive numerical data are presented for a proposed structure which illustrate the sensitivity of the results. Closed-form expressions are presented for the low-amplitude harmonic stiffness of a viscously damped, inclined parabolic cable, and extensive numerical data are included to illustrate the effects of the various parameters involved. Both a complete and an approximate solution are considered, and their interrelationship is examined. In addition, a single-degree-of-freedom model is proposed which reproduces with good accuracy the salient features of the response of the system over a wide range of conditions. The free-vibrational characteristics of simply supported cables are re-examined, and a simple procedure is presented for evaluating the complete spectrum of natural frequencies. Useful closed-form expressions are includedl for certain infinite series involving integrals of the natural modes of vibration of cables. Also described is a finite method of analysis for the problem. The effects of cable-structure interaction are investigated for a harmonic condition of loading using mainly a single-degree-of-freedom representation for the tower. The implications of the results for more complex representations of the tower and for transient excitations are also considered. The nonlinear response of the guyed tower is evaluated by application of the pseudo-force method in combination with the modal method of analysis. Flow charts are included for a computer program developed to implement the analysis. The response of representative structures is evaluated for simulated wave loadings obtained from a Pierson-Moskowitz wave spectrum and Morison's equation for wave forces, and the results are analyzed and discusssed.

The random response of bilinear hysteretic yielding systems subjected to a stationary Gaussian white noise excitation is studied. The responses considered are the root mean square (rms) interfloor displacements of yielding multi-degree-of-freedom (MDF) shear beam type building structures. Simulation results are presented as well as analytical methods to approximate the response levels. Both stationary response levels and the transient build-up of response for systems which are initially at rest are investigated. Nearly elastoplastic 2DF, 4DF and 10DF systems are studied with different stiffness distribution over the height (uniform or tapered) and with different damping ratios. In the simulation studies, the stationary rms interfloor displacement of the yielding MDF bilinear hysteretic system are taken as the time averages of responses to a particular time history (assuming ergodocity). Determining the transient rms interfloor displacements, though, involves computing averages across an ensemble of response time histories. Each response time history is obtained by numerical integration of the equations of motion for a particular time history of excitation. The analytical method presented for predicting the response levels of the yielding MDF system is based on a substitute structure concept. The parameters of the substitute structure are determined from an equivalent third-order system model for single-degree-of-freedom (SDF) structures. That is, each yielding story in the MDF system is replaced by springs and dashpots corresponding to a third-order model for a SDF system. The values of these linear parameters depend on the expected ductility ratio and are determined empirically from simulation data for SDF systems. The Liapunov covariance matrix equation of this higher order linear system is then established to compute the stationary rms interfloor displacements. The stationary results obtained by this method compare very well with those from simulation. The transient rms interfloor displacements of this higher order linear system are also investigated. The Liapunov covariance differential equation is integrated to obtain the transient mean squared responses numerically. The computed results are in good agreement with those from simulation for stories with very high or very low stationary expected ductility factors. . . . (Author's abstract exceeds stipulated maximum length. Discontinued here with permission of school.) UMI

The use of stochastic process theory in a structural dynamic analysis is usually restricted to normal processes. Recent studies have shown that the influence of nonnormality on both fatigue failures and first-excursion failures cannot be neglected. Basically, the aim of this study is to understand the effects of nonnormality on structural dynamics and fatigue, particularly as related to offshore structures. Several related aspects of the problem are studied. The fourth order cumulant function is taken as a reasonable measure of the departure of a process from normality. However, in practice, it is not easy to see the degree of nonnormality of a process directly from the fourth order cumulant function, because of its multidimensional nature. Therefore, the kurtosis or the coefficient of excess is used as a simpler index to represent the degree of nonnormality. The study significantly extends the usual description of wave forces by deriving a description for the nonnormal part of the wave force. An approximation for the fourth cumulant function (and corresponding three-dimensional power spectral density) of a wave force is obtained. Because the degree of nonnormality of the response of a linear structure subjected to a wave force is not easily obtained, analytical studies are also made for a linear SDF structure subjected to somewhat simpler nonnormal forces. An efficient technique for calculating the response kurtosis is derived. Another aim of this study is to estimate the effect of nonnormality of fatigue damage. Both analytical and simulation results confirm that the effect of nonnormality should not be neglected. Simulation studies are also made for the dynamic response of an idealized structure subjected to a stochastic wave force. It is found the degree of nonnormality of the response is quite substantial, but never exceeds the degree of nonnormality of the excitation, at least for the situations considered.

The objectives of the studies reported in this dissertation are: (1) to develop improved techniques for evaluating the dynamic response of viscously damped linear systems, and (2) to contribute concepts and information which will lead to an improved insight into the dynamic response of such systems. The dissertation consists of two major parts. The first part, reported in Chapters II through IV, deals with the analysis of the response of nonclassically damped discrete systems. A critical evaluation is first made of the generalized modal superposition method of analysis for such systems, with special emphasis on identifying the physical significance of the various terms in the solution and simplifying its implementation. Next, the response spectrum variant of the procedure is examined for base-excited systems. The interrelationship of the spectral values of deformation and relative velocity of single-degree-of-freedom systems is identified, and simple practical rules are presented for defining the design spectra for relative velocity for such systems. These rules are similar to those available for defining the corresponding spectra for maximum deformation. Finally, a recently proposed procedure for interrelating the steady-state and transient responses of classically damped systems is extended to nonclassically damped systems. The second part of this dissertation, comprised of Chapters V and VI, deals with the application of the Discrete Fourier Transform (DFT) method of dynamic analysis. The limitations and principal sources of potential inaccuracies of this approach are identified, and an evaluation is made of the nature and magnitudes of the errors that may result from its indiscriminate use. Two versions of a modification are then presented which dramatically improve the efficiency of the procedure, and the relative merits of the two techniques are examined. The concepts involved are developed by reference to single-degree-of-freedom systems and are then extended to the analysis of multi-degree-of-freedom systems.

A critical examination is made of the dynamic response of a realistic guyed-tower structure to wave-induced excitations. The tower is modeled as a cantilever, discrete, stick-like system, and due consideration is given in the analysis to the nonlinear behavior of the guylines and foundation. The wave forces are defined by Morison's equation in combination with a Pierson-Moskowitz wave spectrum and linear wave theory. The response of the system is evaluated in the time domain by application of the concept of pseudo-forces and the modal method of analysis. The effects of numerous factors on the dynamic response of the structure are investigated. The factors considered include: (1) the relative contribution of the modes of vibration of the system to its response; (2) the effects of damping and fluid-structure interaction; (3) the nonlinear effects of the guying and foundation systems; (4) the P-Delta effects of the vertical loading; (5) the effects of variations in the values of the drag and inertia coefficients; and (6) the influence of the random phase angles used in the generation of the random sea. The response quantities examined are the lateral displacements of the structure, the associated shear forces and bending moments, and the guyline reaction. Particular emphasis is placed on the maximum values of these response quantities. The results are presented in graphs and tables and they are interpreted in a manner that is believed to provide valuable insight into the dynamic action of this type of structure. An exploratory study of the applicability of the response spectrum approach to design for waves is also reported. The results of this study demonstrate the potential of the approach as a practical design tool for offshore structures in general.

Prestressed concrete columns generally have a much smaller amount of longitudinal reinforcement compared to reinforced concrete columns and the confinement of the core is thus provided mainly by the lateral reinforcement. The main objective of this study was to evaluate the need for lateral reinforcement and its influence on the confinement in short prestressed concrete columns. In the experimental part of this investigation, twenty-three specimens were tested under axial loading. Primary variables were the type and amount of lateral reinforcement. Three types of lateral reinforcement were investigated: conventional ties, continuous square spiral and the welded wire mesh. The volumetric ratio of lateral reinforcement to concrete core was varied between 1.09% and 2.18%. Experimental results showed that lateral reinforcement was much more effective in increasing the ductility than the strength. It was also found that the currently available analytical confinement models did not accurately represent the behavior of prestressed concrete columns and considerably overestimated the strength in the post-peak loading region. Therefore, based on the observed behavior, an analytical model for predicting the stress-strain relation of confined concrete in axially loaded precast prestressed concrete columns with rectilinear lateral reinforcement is proposed. The ascending part of the model consists of a second degree parabola followed by a linear segment and an exponentially decreasing curve. This model takes into account any increase in strength and ductility resulting from lateral reinforcement, and more realistically represents the post-peak behavior. Finally, some design implications are suggested and the concept of strain ductility factor as a measure of ductility is proposed.

Thirty-nine welded steel specimens have been tested under variable amplitude loadings to determine the extent to which fatigue life is affected by the amplitude variability of the loading and by the high frequency components in the psd of the loading. Constant amplitude tests have also been run to determine the S-N curve so that comparisons can be made between the variable amplitude results and the commonly used analytical techniques such as rainflow analysis, the Rayleigh approximation and the peak counting method. Analytical predictions are based on an S-N curve corrected for the effect of weld residual stress. The twelve different variable amplitude loadings are classified into two groups. The variability of the amplitude of the group I loadings depends on the correlation between the successive extrema. The loadings vary from broadband to extremely narrowband, having peak to adjoining valley correlation values from zero to $-0.995$. Most of these loadings have Rayleigh distributed peaks and valleys. The group II loadings deal with the effect of high frequency components of psd for Gaussian processes. This includes variation of the relative frequency location of the high frequency component in a bimodal psd, and variation of the frequency of truncation of a smooth psd curve. The experimental fatigue lives for group I loadings are all significantly smaller than the predictions by either the Rayleigh approximation or rainflow analysis. The lowest fatigue life found is only 35% of the Rayleigh approximation. The experimental results for group II loadings indicate that the presence of a high frequency component can reduce the fatigue life substantially (as much as 46% for one case studied). Furthermore, it is found that neither of the commonly used analytical techniques can consistently predict the effect of high frequency components. A new damage model is also developed in an attempt to obtain predictions in agreement with the experimental results. The new theoretical results are in very good agreement with the experimental results for group I loadings and group II loadings with unimodal psd's. However, for the two group II loadings with bimodal psd's, the new damage model gives quite conservative predictions.

An ultraviolet pilot plant was installed at the Montreal Urban Community Wastewater Treatment Plant (MUCWTP) to assess the feasibility of employing a full scale UV disinfection system. Wastewater characteristics such as suspended solids (SS), turbidity, iron content, transmittance at 254 nm, and dissolved organic carbon were monitored to assess their effect on UV disinfection. Fecal coliforms were used as indicators to measure disinfection performance. UV disinfection was capable of reducing the fecal coliform counts from typical values of 0.2-3 million CFU/100ml (depending on the process and season) to thousands, hundreds or tens per 100 ml, depending on the dose applied, the process used for phosphorus removal, and wastewater quality. High turbidity values yielded higher surviving microbial counts; disinfection effectiveness decreased by 10% for each NTU of turbidity increase. SS in the wastewater scattered the UV light, leading to dose underestimations and the illusion that higher SS would yield better disinfection effectiveness. A photoreactivation increase of 8.1 and 11.7 fold was observed for iron-treated and alum-treated effluents respectively. Dark repair increases were very different for iron-treated and alum-treated effluents; however, in terms of dark repaired fraction, both effluents had values within the same range. UV disinfection was not found to cause any additional toxicity in the wastewater.