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Master of Science / Department of Architectural Engineering and Construction Science / Kimberly W. Kramer / Prior to the Age of Enlightenment, arches were designed by empirical rules based off of previous successes or failures. The Age of Enlightenment brought about the emergence of statics and mechanics, which scholars promptly applied to masonry arch analysis and design. Masonry was assumed to be infinitely strong, so the scholars concerned themselves mainly with arch stability. Early Age of Enlightenment scholars defined the path of the compression force in the arch, or the shape of the true arch, as a catenary, while most scholars studying arches used statics with some mechanics to idealize the behavior of arches. These scholars can be broken into two categories, those who neglected friction and those who included it. The scholars of the first half of the 18th century understood the presence of friction, but it was not able to be quantified until the second half of the century. The advancements made during the Age of Enlightenment were the foundation for structural engineering as it is known today. The statics and mechanics used by the 17th and 18th century scholars are the same used by structural engineers today with changes only in the assumptions made in order to idealize an arch. While some assumptions have proved to be incorrect, many correctly interpreted behavior and were able to formulate equations for design and analysis that were successfully used to create arches that were structurally sound and more efficient than arches designed by empirical methods. This insight into design during the 18th and 19th centuries can help modern engineers better analyze and restore arches from this era and protect our architectural and engineering history.

Research report submitted to the Faculty of Engineering and the Built Environment, University of Witwatersrand, Johannesburg, in partial fulfilment of the requirements for the degree of Master of Science in Engineering Johannesburg 2017 / This report investigates the seismic response of catenary vaults. Through a series of tests, the inherent seismic resilience of catenary vaults was assessed and a number of reinforcement strategies were investigated to improve this. An analytical model, based on the virtual work method, was developed by Ochsendorf (2002) for the assessment of circular voussoir arches. This model was adapted for catenary vaults. This model is used to calculate the minimum lateral acceleration required to cause the collapse of a catenary vault (λmin) for any catenary profile. The model indicates that there is a linear relationship between cross sectional depth of the arch and λmin until the depth to ratio passes approximately 0.3, where the change in λmin becomes exponential. Using the model, it is also predicted that λmin decreases exponentially with an increase in the height to width ratio up to a value of approximately 1.6. After this point λmin linearly decreases with increased height to width ratios and approaches zero. The first series of tests involved subjecting unreinforced catenary vaults to seismic loading. In these tests the frequency of vibration was varied and the stroke was kept constant. From the results of the tests, it was found that there was no frequency at which the vaults underwent excessive vibration due to resonance. It was observed that during seismic loading, hinges form at locations where pre-existing cracks occur despite the higher computed λmin values for these positions. The tests also indicate that the vaults’ behaviour changes drastically with each hinge that forms. In the next series of tests the frequency was set and the stroke was increased. The vaults were subjected to seismic loading at 2 Hz and 6 Hz, representative of low and high frequencies respectively. The tests indicated that the collapse acceleration of arches subjected to vibration at 2 Hz was lower than that of the vaults subjected to vibrations at 6 Hz. Despite this, the stroke, representing ground movement, required to cause collapse at 2 Hz was substantially higher than that of the 6 Hz tests. This indicates that the duration of load cycles has an effect on the collapse acceleration. In comparing the computed collapse acceleration, λmin, with the actual collapse accelerations, it was found that the computed values are highly conservative. Yet this is expected as the model is based on an infinite duration of lateral loading. It was found that the analytical model was more accurate for low frequency tests as compared to high frequency tests in terms of the predicted hinge locations. Finally, three reinforcement strategies were investigated using basalt fibre geogrid. This was found to be an economical and viable reinforcement material. The first strategy consisted of laying the geogrid over the arch and securing it at the arch base. The second was the same as the first with the addition of anchors which held the geogrid down. The final strategy involved prestressing the arch using the geogrid. The latter 2 methods were found to be the most effective, with observed collapse accelerations being over 60% higher than that of the same unreinforced arch. The anchorage solution was found to be the most viable due to the substantially higher technical input required for the prestressing solution. / MT2017

Recent evidence suggests that overfishing of large predatory fishes has resulted in substantial population declines and pelagic longline (PLL) fishing is a major contributor. The primary objective of this dissertation is understanding factors that affect the interactions between marine fish PLL fishing. These factors are important to determine vulnerability of bycatch and target species, especially when PLL catch and effort data are used to estimate stock abundance. Chapter 1 reviews 107 publications/reports on this topic. Results indicate that accurate characterization of PLL gear performance requires empirical measurement of horizontal and vertical gear movement; and pop-up satellite tags (PSATs) are best suited for quantifying pelagic fish vertical habitat use if: (i) sampling resolution and data storage are not a function of tracking duration and (ii) substantial monitoring durations are employed. This review documents the current state of knowledge for these factors and guidance for future research. In Chapter 2, hook time-at-depth was monitored for commercial PLL sets targeting swordfish, Xiphias gladius. Temperature-depth recorders (TDRs) were deployed at the hook, systematically along the entire gear length. Results indicated that: (i) hook depth predictions based on catenary geometry drastically overestimated actual fishing depths and (ii) using catenary geometry fails to capture within- and among-set variability, potentially resulting in biased stock assessments. Chapter 3 used temperature-depth data from PSATs on swordfish and blue marlin (Makaira nigricans) and similar data from TDR monitored near-surface and deep PLL fishing to determine the diel probability of these species encountering PLL hooks. Results indicated that blue marlin and swordfish inhabit surface waters at night with similar probability of encountering PLL hooks but may have different vulnerabilities due to temporal separation in feeding with blue marlin preferring daytime and twilight and swordfish preferring nighttime. Therefore, reducing fishing during daylight hours may reduce blue marlin bycatch during PLL targeting swordfish. Chapter 4 alternated non-offset and 10° offset circle hooks during PLL fishing and compared the relative performance on catch rates, percent mortality, and deep hooking percentage. Results indicated that 10° offset circle hooks can reduce fishing efficiency and conservation benefits commonly associated with circle hooks.

The simulation of seafloor-steel catenary interaction and prediction of riser fatigue life required an accurate characterization of seafloor stiffness as well as realistic description of riser load-deflection (P-y) response. This thesis presents two load-deflection (P-y) models (non-degradating and degradating models) to simulate seafloor-riser interaction. These two models considered the seafloor-riser system in terms of an elastic steel pipe supported on non-linear soil springs with vertical motions. These two models were formulated in terms of a backbone curve describing self-embedment of the riser, bounding curves describing P-y behavior under extremely large deflections, and a series of rules for describing P-y behavior within the bounding loop. The non-degradating P-y model was capable of simulating the riser behavior under very complex loading conditions, including unloading (uplift) and re-loading (downwards) cycles under conditions of partial and full separation of soils and riser. In the non-degradating model, there was a series of model parameters which included three riser properties, two trench geometry parameters and one trench roughness parameter, two backbone curve model parameters, and four bounding loop model parameters. To capture the seafloor stiffness degradation effect due to cyclic loading, a degradating P-y model was also developed. The degradating model proposes three degradation control parameters, which consider the effects of the number of cycles and cyclic unloading-reloading paths. Accumulated deflections serve as a measure of energy dissipation. The degradating model was also made up of three components. The first one was the backbone curve, same as the non-degradating model. The bounding loops define the P-y behavior of extreme loading deflections. The elastic rebound curve and partial separation stage were in the same formation as the non-degradating model. However, for the re-contact and re-loading curve, degradation effects were taken into the calculation. These two models were verified through comparisons with laboratory basin tests. Computer codes were also developed to implement these models for seafloor-riser interaction response.

The simulation of seafloor-steel catenary interaction and prediction of riser fatigue life required an accurate characterization of seafloor stiffness as well as realistic description of riser load-deflection (P-y) response. This thesis presents two load-deflection (P-y) models (non-degradating and degradating models) to simulate seafloor-riser interaction. These two models considered the seafloor-riser system in terms of an elastic steel pipe supported on non-linear soil springs with vertical motions. These two models were formulated in terms of a backbone curve describing self-embedment of the riser, bounding curves describing P-y behavior under extremely large deflections, and a series of rules for describing P-y behavior within the bounding loop. The non-degradating P-y model was capable of simulating the riser behavior under very complex loading conditions, including unloading (uplift) and re-loading (downwards) cycles under conditions of partial and full separation of soils and riser. In the non-degradating model, there was a series of model parameters which included three riser properties, two trench geometry parameters and one trench roughness parameter, two backbone curve model parameters, and four bounding loop model parameters. To capture the seafloor stiffness degradation effect due to cyclic loading, a degradating P-y model was also developed. The degradating model proposes three degradation control parameters, which consider the effects of the number of cycles and cyclic unloading-reloading paths. Accumulated deflections serve as a measure of energy dissipation. The degradating model was also made up of three components. The first one was the backbone curve, same as the non-degradating model. The bounding loops define the P-y behavior of extreme loading deflections. The elastic rebound curve and partial separation stage were in the same formation as the non-degradating model. However, for the re-contact and re-loading curve, degradation effects were taken into the calculation. These two models were verified through comparisons with laboratory basin tests. Computer codes were also developed to implement these models for seafloor-riser interaction response.

Variational techniques are used to develop a theory for the time evolution of a thin strand of viscous fluid suspended from two points. The shape of the strand is approximated to be a parabola and energy conservation is used to derive a differential equation modeling the change in height over time. Data is collected with a high resolution camera and a strobe light to obtain the position and shape of the strand over multiple intervals of time. Three very different and unexpected types of behaviors are observed depending on the initial thickness and shape of the filament. The approximation fits well with one type of behavior but variations in the thickness of the strand, and consequently in the center of mass, need to be factored in to predict the others.

L’alimentation électrique des trains s’effectue en général par une interface pantographecaténairereprésentant un système mécanique couplé complexe. Les phénomènes dynamiques intervenantdans l’interaction entre le pantographe et la caténaire sont encore mal connus. Par ailleurs, le comportementdynamique du système est très variable car sensible à de nombreux paramètres. La premièrecontribution de cette thèse est de proposer une analyse détaillée de l’interaction dynamique pantographecaténaireen étudiant en particulier la réponse dynamique du pantographe à la géométrie de la caténaireainsi que les propagations, réflexions et transmissions des ondes dans cette dernière. Il a ainsi été démontréque la coïncidence spatiale, temporelle ou fréquentielle de ces différents phénomènes est à l’originede la majorité des variations des quantités d’intérêt. Par ailleurs, l’étude des ondes a montré que lespendules entourant le poteau avaient une importance particulière dans l’interaction dynamique et que lesparamètres tels que le rapport des impédances dynamiques et la somme des vitesses des ondes dans lescâbles étaient des variables dimensionnantes dans la caténaire. La seconde contribution a été de réduireles principales incertitudes épistémiques liées au modèle telles que l’amortissement dans la caténaire, laraideur de contact et la taille des éléments. La dernière contribution était d’implémenter des paramètresvariables dans le modèle en utilisant les mesures disponibles. À partir de ce modèle aléatoire, les incertitudesont été classées en utilisant les indices de Sobol sur des critères géométriques et dynamiques.L’absence de corrélation entre les critères géométriques et dynamique observée a des conséquences notablessur la politique de maintenance. Enfin, le grand nombre d’études de sensibilités réalisés a permisde souligner la maturité de l’outil de simulation et de proposer des orientations pour les travaux futurs pourla conception, maintenance ou homologation de pantographes ou de caténaires / In railways, electrical current is generally collected by the train through a complex coupledmechanical system composed of a pantograph and a catenary. Dynamic phenomena that occur duringtheir interaction are still not fully understood. Furthermore, the system behaviour is sensitive to numerousparameters and thus highly variable. The first contribution of this thesis is a detailed analysis of thepantograph-catenary dynamic interaction separating phenomena due to the dynamic response of the pantographto the catenary geometry from wave propagations, reflections and transmissions that occur in thecatenary. The coincidence of frequencies or characteristic times is then shown to explain most variationsin the quantities of interest. Moreover, droppers surrounding the mast have been shown to be particularlyimportant in dynamic interaction. Ratio of wire impedances and sum of wave velocities also appeared tobe dimensioning quantities for catenary design. The second contribution was to reduce epistemic uncertaintylinked with model parameters such as catenary damping, contact stiffness and element size. Thefinal contribution was to use the model in a configuration with random parameters. An initial step was tostatistically characterise physical catenary parameters using available measurements. From this randommodel, ranking of uncertainties using Sobol indices on static and dynamic criteria was shown to be possible.An absence of correlation between geometric and dynamic criteria was also found, which has notableimplications for maintenance policies. The high number of sensitivity studies also gave the occasion tohighlight the maturity of simulation tool and propose directions for further work on design, maintenance orcertification of pantographs and catenaries.

The pantograph - catenary interaction is one of the most important features in high speed trains, and to guarantee a reliable current collection is the target that every railway system must take into consideration in order to speed up trains. The problem that goes against this direction is mainly the variation of the overhead equipment's stiness. To understand the phenomenon a lumped mass model of the pantograph with a rigid body attached to the ground representing the contact wire were built up; in this way a complete lumped mass model is developed. All information regarding both wire and pantograph set up is introduced as lumped parameters. Creating the model, dierent active control strategies as ideal control, PID control and optimal control are introduced. All simulations are made in GENSYS, while the control part is made inSIMULINK; a connection between those two softwares was created as part of the thesis using TCP/IP protocol. Results compared to experimental acquisition are satisfactory in terms of contact force representation. The standard deviation and average value's errors of the contact force are lower than 10%; regarding the control system, typically 20% of reduction of the standard deviation compared to the passive case is achieved. Also a comparison with a nite element program is done in order to better understand the limits of the model compared with a more sophisticated one. The comparison shows a good accordance up to 60 % of the average speed of the wave propagation in the catenary. The last feature analyzed is how the behavior of the controlled system changes introducing a real actuator: results shows that the performance is reduced in dierent ways considering dierent speeds, but no instabilities occur.

No / This paper describes the experimental results of ten fire tests on medium-scale restrained steel sub-frames to investigate the relative behaviour and robustness of different types of steel joint in steel framed structures in fire. The ten fire tests were designed to investigate the effects of two column sizes (simulating two different levels of axial restraint to the connected beam) and five different types of joint, including fin plate, web cleat, flush endplate, flexible endplate and extended endplate connections. Each test frame, in the form of “rugby goalpost” consisting of one beam and two columns, was connected through two identical beam to column joints. All the steelwork was unprotected except for the top flange of the beam which was protected to simulate the effect of a concrete slab in reducing the beam top flange temperature. The column ends were restrained to examine the effects of axial restraint on the beam and the joints. This paper presents the observations of structural fire behaviour, including joint failure modes and beam limiting temperatures, the development of deflections at beam middle span and axial forces in the joints at elevated temperatures. The main conclusions are: (1) failure (fracture) was observed only in joints when the beam was in catenary action and a variety of joint failure modes were observed which provides valuable data in understanding joint behaviour; (2) the medium-scale steel beams were able to undergo very large deflections View the MathML source without failure; (3) the specimens with stronger connections such as extended endplate reached higher than their limiting temperatures, defined as the beam bottom flange temperature at middle span at which the axial load in the beam returned to zero. But the difference in beam limiting temperatures using different types of joint is small, less than 50 °C; also the column size had little effect (less than 30 °C) on the beam limiting temperature; (4) the beams connected to the larger column experienced less deflections, but higher axial force due to the higher axial restraint to the beam, which led to fracture of the joint components in these tests; in contrast, the lighter columns visibly deformed and formed plastic hinges at the joints, but there was little evidence of connection fracture in the test frames using the light columns; (5) the web cleat connection appears to have the best performance.