Browsing by Author "Zingoni, Alphose"

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    Collapse behaviour of double layer grid structures in steel
    (2012) Adams, Jonathan; Zingoni, Alphose
    Flat double layer grid (DLG) structures are efficient modular, structural systems which span in two or more directions and consequently develop their resistance in three dimensions. Although such structures offer many structural, constructional and aesthetic advantages over alternative planar structures, for use in unobstructed roofing applications, they have been observed to have a propensity for sudden collapse behaviour, as witnessed in the collapse of the Hartford Coliseum roof structure in 1978. Previous study of DLG behaviour has been undertaken through experimental and numerical analysis; these studies have confirmed the sudden collapse behaviour and sensitivity of such structures to geometric imperfections for selected cases but have not developed the full spectrum of DLG behaviour. A parameter study was therefore undertaken to identify desirable DLG pre-critical yielding behaviour and post-critical increases in grid structural resistance. The parameter study also served to identify and characterize grid plastic, failure and collapse behaviour for structures representative of those employed in practice; the Structural Eurocodes were used for this purpose.
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    Development of space truss systems in timber
    (2004) Mupona, Gaylord Tonderai; Zingoni, Alphose
    Space trusses are a valuable structural form for architects and structural engineers due mainly to their efficiency in providing large unobstructed areas, associated with faster erection speeds and low maintenance cost. Most space trusses are made of steel and aluminium whilst a few are of timber. Interest is now shifting from the traditional use of timber in plane trusses of relatively short span, to new structural forms for medium to long spans. In adopting such systems in timber for non-traditional roofing applications, the challenge lies in developing structurally sound, visually neat and economically reproducible connectors for 3-dimensional configurations of timber members. The research aimed at developing a new connector for double and triple-layer space grids in timber, intended for medium-span lightweight roofing applications. The origins of the connector date back to 1995, when it was first proposed by Zingoni as the 14FTC-U Timber Space-Truss Connector, and subsequently tested under laboratory conditions over the three years that followed. Unlike connectors for timber space grids proposed by earlier investigators, or the proprietary connector systems that are available for constructions in steel and aluminium, the 14FTC-U connector features a central core of wood in the form of a cuboctahedron or its variants, upon whose faces are attached U-shaped metal brackets that take the timber members. Thus the connector unit is predominantly wood, giving it considerable aesthetic advantages over its all-metal counterparts. While promising, the structural performance of the original connector was not adequate for practical application, hence a programme of further development was embarked upon. As reported in the thesis, the improvements of the connector have culminated in a structurally viable unit that has been successfully employed in a prototype double-layer timber grid.
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    Dynamic modeling and vibration control of high-voltage overhead transmission lines
    (2008) Mtanga, Jameson Joseph; Zingoni, Alphose
    The problem of the dynamic behavior of overhead power transmission lines under wind and other excitations is an important one, since it allows an optimal design and positioning of vibration dampers for the cables. Excessive sway and oscillation of power lines need to be avoided, as they can lead to damage of the lines and power interruptions. The relatively high flexibility of the cables, coupled with the large spans and large sags involved, make the dynamic response of the system highly nonlinear. In this study, we numerically investigate the damped free-vibration response of systems of cables of particularly large spans (120, 200 and 400m).
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    The effect of weld-induced imperfections on the buckling behaviour of spherical and conical shells
    (2005) Steyn, Brett Kenneth; Zingoni, Alphose
    The early research was on general imperfections most commonly in the form of the lowest buckling modes. The use of steel pates to fabricate silos in a regular pattern led to the civil engineering interest in the weld-induced imperfection. This imperfection was found to be in the circumferential direction and the dominant cause for the reduction of the classical buckling load. As previous research was conducted on cylindrical shells the current thesis focused on studying two different shell geometries.
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    The effect of welding on the buckling behaviour of spherical shells : a review and some numerical results
    (2001) Grünitz, L; Zingoni, Alphose
    The purpose of this thesis is to give first a brief review in the area of shell stability with special focus on the effect of imperfections due to the welding process on the buckling behaviour of shell structures.
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    Influence of geometry on the dynamic behaviour of steel tubular towers for onshore wind turbines
    (2017) Folster, Kaylee; Mudenda, Kenny; Zingoni, Alphose
    South Africa has recently experienced challenges regarding electricity consumption and availability. As part of the country's Integrated Resource Plan, these challenges are to be addressed. This involves a 20 year plan which aims to increase electricity supply capacity as well as reduce the reliance on coal power as part of the global trend to become more environmentally friendly. Wind power, specifically, is to account for a large portion of the renewable energy that is expected to become available by 2030. This results in the need for the understanding of wind turbine design by South African engineers. The dynamic analysis of wind turbine structures, is of particular interest to Civil Engineers. Wind turbine towers are recently of the monopole or tubular type tower, predominantly constructed of either concrete or steel or a combination of both. Steel tubular towers above a height of 80m are generally not recommended for wind turbines owing to cost concerns as well as difficulties in meeting dynamic behaviour requirements. Concrete towers and steel-concrete hybrid towers are recommended for this height regime. The aim of this study was to assess the prospective use of steel tubular towers of varying geometric shape for wind turbines with tower heights of 80m or greater. The study focussed on the analysis of natural frequency and assessing the applicability of steel tubular towers of geometric shapes that have not been previously explored or reported. The turbine of choice for this study was the Vestas V112 3MW type as this is one of the most commonly used and more efficient turbines for towers of this height regime. The results of this study showed that steel monopole towers of heights of 80m and more are still viable options for wind turbine towers. Various geometric tower cases of heights varying from 80m to 120m, produced acceptable fundamental natural frequencies within the allowable frequency range for a Vestas V112 3MW turbine.
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    The lateral load carrying capacity of wall ties used in cavity wall construction in the Western Cape : a comparison between the Butterfly-type wire tie and the Crimped-type wire tie
    (2002) Ebrahim, I; Zingoni, Alphose
    The aim of the testing was to compare the relative positives and negatives of the Butterfly Tie and the Crimped lie as regards to water transfer, tensile and compression strengths based on the Australian Code [AS 2699-l 984] requirements as it is more comprehensive. The reason was because the Butterfly Tie has been promoted in cavity wall construction in South Africa for a number of reasons, for example: * NHBRC (National Home Builders Registration Council) compels contractors to use the Butterfly Tie * SABS 28:l986 and SABS O 164-1 :1980 also compel the use of Butterfly Tie, even though there is an anomalous statement in the specifications. Another reason was because the use of the Crimped Tie was not being promoted in cavity wall construction in South Africa mainly because of a lack of information regarding characteristic strength and its resistance to water transfers. The following tests, based on the Australian Code, which is more stringent than the South African Codes were then carried out on the Butterfly Tie and the Crimped Tie: * Tests for water transfer * Tests tor compression and tensile strengths using couplets * Tests for compression and tensile strengths using ties only. Although the testing showed that the Butterfly Tie and the Crimped Tie fulfilled the requirements of the Australian Code, there were negative aspects relating to the Butterfly Tie. It is recommended that serious considerations be given by the South African Bureau of Standards to include the Crimped Tie in its Code of Practice for Cavity Walls.
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    Lateral-torsional buckling behaviour of monosymmetric steel sections formed with flange upstands
    (2023) Mudenda, Kenny; Zingoni, Alphose
    The study of the lateral-torsional buckling behaviour of steel beams has been largely focused on doubly symmetric beams and less so on monosymmetric sections. Monosymmetric sections, however, do offer some advantages over doubly symmetric beams if the monosymmetry is applied in a way that it can be exploited. This is because the effects of monosymmetry can work to increase or decrease the moment capacity. Identifying these cases is therefore essential. In the current study the behaviour of a monosymmetric section produced by introducing flange upstands as stiffeners is explored. The upstands convert a standard doubly symmetric section into a monosymmetric section. The change in member properties is first explored with the movement of shear center relative to the geometric centroid being of particular interest. It is observed that the shear center initially moves away from the centroid towards the stiffened flange, reaches a stationery point and then starts to move away from this flange. This leads to the shear center then intersecting the centroid so that for a monosymmetric section, at a certain upstand height, the shear center and centroid are coincident. This results in a monosymmetric section taking on a property typically associated with a doubly symmetric section. A study of the change in the monosymmetry constant of the section also reveals that at a given upstand height the monosymmetric section also takes on another property associated with doubly symmetric sections, that of the monosymmetry constant having a value of zero. Further study of the critical elastic moment change with change in upstand height reveals that the section initially has a significant increase in the value of the critical elastic moment with upstand height followed by a trend of diminishing increase rate. In some cases, this trend then reverses so that with an increase in upstand height the critical elastic moment starts to decrease. The region where the monosymmetry acts beneficially to increase section capacity represents a target domain before the monosymmetry then starts working to diminish the member capacity. This second region represents an undesirable domain for the use of these upstands. This observed behaviour, therefore, leads to identification of a domain of upstand heights in which the positive effect of monosymmetry can be exploited. The junction between the two regions, given by a critical upstand height, can be reasonably approximated based on the upstand height at which the shear center and centroid coincide. Engineers who may want to make use of flange stiffeners need to be aware of these trends to better manage the strengthening of doubly symmetric members so that material is used economically and not wasted in regions were the returns are minimal or diminishing. The application of this domain has been demonstrated for linear elastic buckling cases as well as for inelastic buckling cases so that real member behaviour is also simulated. Although applied for strengthening cases in the current study the principle can be used for section optimization at member selection stage should members with upstands be an option. Equations obtained using the Rayleigh-Ritz energy method were employed for the elastic critical buckling study for two transverse load cases. Finite element models were then employed for the nonlinear analysis for the inelastic buckling cases. Residual stresses have not been included in the finite element models. Geometric imperfections as well as material constitutive behaviour were incorporated in the models. This gives a realistic picture of ‘real' member behaviour despite not including residual stresses. The results from the nonlinear study support those from the linear elastic study in demonstrating how the beneficial domain can be exploited.
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    Modelling of crowd-induced vibrations in stadium terraces
    (2005) Nhleko, Sifiso P; Zingoni, Alphose
    Human-induced vibrations are increasingly becoming an issue of great concern in the design of civil engineering structures. In this research work, three major trends that contribute to the prevalence of human-induced vibrations in public structures were identified. While the focus has been mainly on sports stadia, the known effects of humans on the vibration behaviour of structures in general were also reviewed. Existing design and theoretical models for predicting the effects of humans on structures were examined with two issues being raised. Firstly, the existing force model for describing load impulses resulting from jumping has been found to be unable to predict the correct shape of the impulse or its dominant harmonic for jumping frequencies that are significantly less than 2 Hz. Secondly, there is experimental evidence to show that active humans not only excite a structure through footfall-induced forces, but that they also affect the dynamic properties of the structural system, namely its natural frequencies and damping. However, the existing modelling approach assumes that humans engaged in continuous movement can act only as an input force in the dynamics of the vibrating system. To address both these issues, a new modelling approach, termed 'the pseudo-variable mass model' has been proposed in this study. This method is based on the treatment of the structure-jumper system as a pseudo-variable mass system. The predictions of both the existing and the proposed models were compared with the actual results of experimental investigations involving 10 jumpers, jumping on a lightweight-flexible structure at frequencies of 1 Hz and 1.5 Hz. Comparisons with other findings in the literature were also made. This study showed that the proposed model can adequately predict four observed phenomena, namely, the impulse shape, the dominant harmonic of the impulse, the dominant harmonic in the acceleration response and the effect on the fundamental frequency. Thus, for safe and economic design of lightweight and flexible structures, the proposed model may be used to simulate the effects of jumping at frequencies that are significantly less than 2 Hz.
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    Moment - Rotation characteristics of boltedc beam - to - column aluminium connections
    (2009) French, Vandy; Zingoni, Alphose
    Structural aluminum provides a unique option to engineers by virtue of both its unique strength to weight ratio and its well known corrosion resistance properties. The development of the Eurocode 9 provides an insight to the design of aluminum structures based on results from various researchers worldwide. However the area of connections remains very sparse with regards to research material as compared to steel as provided by Eurocode 3 part 1-8. This work involves the analysis of the performance of aluminum end plate beam column connections with regards moment rotation behavior as well as the main connection classification criteria, strength, stiffness and ductility. A parametric study is done with the use of the non- linear finite elements program ADINA in which the effects of connection geometry is observed under incremental loading.
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    Nonlinear vibration of beams and plates resting on elastic foundations having nonlinear stiffness properties
    (2023) Feulefack, Songong Edwige; Zingoni, Alphose
    Beam elements are used to model components in which one dimension (the length) is significantly greater than the other two dimensions. On the other hand, a plate is a structural element char- acterised by its thickness being very small compared with the other two dimensions. Beams and plates find civil and mechanical engineering applications and are mostly used to construct build- ings, bridges, floors, pavements, and runways. Investigating the vibration of beams and plates is an ongoing topic, and researchers are becoming more interested in it. Because the structure foundation is the most important part of the building process, engineers and designers dedicate more attention to that part of the structure. This contributes to the desire to build strong, safe, and economic structures for a sustainable environment. Beams and plates on elastic foundations (BPoEFs) also find many applications in civil engi- neering. They are frequently used to design structural members of buildings, railroads, airports, highways, and railway tracks. For example, when studying railway track behaviour, a beam on an elastic foundation (BoEF) theory is often employed, and the study can be extended to track dynamics, noise, and vibration. Winkler (1867) was the first to introduce the topic of BPoEFs and developed these to analyse railroad tracks. Since then, many other researchers have extended the concept, giving rise to other foundation types. The foundation can be linear or nonlinear, depending on the purpose for which the structure will be used. For example, to model the interaction between the beam or plate and an elastic foundation, the entire beam or plate and the foundation are modelled without modelling the foun- dation itself. Then, the modelling can become easy or difficult depending on the foundation type and property (linear or nonlinear). Therefore, linear analysis is appropriate for easier cases, while nonlinear analysis is left for other complex cases. Nevertheless, it is important to note that linear analysis is limited to simple structures and is only valid for design. As a result, nonlinear analysis is recommended because it can be used for design and realisation purposes. Beams and plates on linear elastic foundations (BPoLEFs) have been extensively studied, whereas beams and plates resting on nonlinear elastic foundations (BPoNEFs) have been ne- glected and constitute the interest of the current thesis. A beam simply supported at both ends and a rectangular plate also simply supported are considered. Linear and nonlinear foundations are considered to capture the beam and plate behaviour and response. The foundation is assumed to be an assembly of discrete linear or nonlinear springs or connectors. First, the beam on a linear foundation is studied as the basis and then extended to the beam on a nonlinear foundation. Three cases of nonlinearities are discussed: quadratic, cubic, and the combination of quadratic and cubic. The straightforward expansion method (SEM) is used to find solutions to the governing nonlinear differential equation. Finally, the natural frequencies and the corresponding mode shapes of the system beam-foundation are derived. We note that the overall thesis only focuses on free vibration analyses. A rectangular plate on an elastic foundation (PoEF) is studied to extend the research on beams. Here also, linear and nonlinear foundations are considered. The same analyses as those of the beam are carried out on the plate to cover all structure types. Both studies on BoEFs and PoEFs revealed that the natural frequencies of the system increase with the increase of the nonlinear stiffness parameter of the foundation. Interestingly, the same increase in the nonlinear stiffness of the foundation tends to decrease the beam and the plate temporal vibration amplitude. Comparing linear to nonlinear results reveals that neglecting the nonlinearity of the foundation produces differences which are more significant at lower modes. This confirms the fact that, if the model of a beam or a plate resting on a nonlinear elastic foundation is simplified to a linear one, the results obtained from the linear analysis might not accurately represent the real system. Finite Element Analysis (FEA) in Abaqus is used for the numerical analysis. Here also, the natural frequencies and corresponding mode shapes of the beam and the plate with foundation are derived. Extensive parametric studies conducted on the beam and plate vibration reveal that the foundation's nonlinear stiffness is indispensable because it lowers the beam and plate vibration amplitude. Having validated the results from Abaqus, they are used as a benchmark to validate the analytical results. Satisfactory agreement is found between the results of the two methods, with details of each method shown. The results from this thesis show that the nonlinear foundation can accurately be used to control the vibrations of the beam and plate model. The findings further reveal that adding nonlinear quadratic or cubic or mixed parity stiffness properties in the foundation when studying BPoEFs is beneficial and should be adapted for design and realisation purposes.
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    A parametric investigation into the membrane stresses of hydrostatically loaded circular and elliptic toroidal shells
    (2017) Govender, Nishalin; Zingoni, Alphose
    This study explores the membrane stresses of hydrostatically loaded elliptical and circular toroidal tanks. Equations are derived, using the membrane theory of shells, to obtain equations which can accurately describe the meridional and hoop stress behaviour at locations sufficiently far away from any bending disturbance occurring within the shell. The derived expressions are validated using the finite element software ADINA, indicating excellent agreement between the analytical and numerical solutions. A parametric study is undertaken, whereby the membrane profiles for prolate, oblate and circular toroidal shells is investigated. Parameters which are varied are the opening and aspect ratio of toroidal shells. Stress resultant profiles are shown for numerous cases in order to aid designers on suitable ratios to minimise membrane stresses for use when designing hydrostatically loaded toroidal shells. Lastly, numerical examples are investigated, keeping the volume constant and comparing the surface area due to a variation of opening and aspect ratios. It was found that when investigating toroidal shells, considerations are required when choosing the aspect ratio and opening ratios. Based on the results obtained, compromises between prolate and circular cross-sections with relatively small opening ratios are recommended in order to minimise the cost and maximise the structural efficiency, based on the membrane stresses occurring within the shell.
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    Parametric study of stiffened steel containment shell structures
    (2008) Masendeke, Rugare B; Zingoni, Alphose
    A FEM-based parametric study is undertaken to investigate the buckling behavior of meridionally and circumferentially stiffened steel cylindrical and conical shell frustum subjected to different load cases. This situation arises in different steel shell applications such as storage vessels (liquid, solid and gas) and in certain configurations of industrial process facilities. The stiffeners are flat strips of rectangular section welded on to the outer surface of the shell, either over the whole length of the shell meridian or around the circumference of the shell. It is required to establish how the elastic buckling load and mode shapes vary with respect to certain key parameters of the problem. The parameters of interest in the study include the number of stiffeners around the shell circumference and along the meridian, the stiffener-depth to shell-thickness ratio, and the stiffener depth-to-width ratio. This thesis reports the findings of the parametric study and also presents some results of experimental tests on laboratory small-scale models of stiffened cylindrical and conical frusta.
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    Parametric study of stresses in cooling-tower shells
    (2002) Ajayi, Olugbenga Olumide; Zingoni, Alphose
    Many attempts have been made in studying the structural behaviour of cooling tower shells, focusing more on the effect of wind on the structure and shape imperfections. However, little has been investigated on the most basic loading condition, i.e. self-weight load. This thesis focuses on a cooling tower with uniform thickness where several geometric parameters like the hyperbolic axis ratio (bla), top opening angle , offset parameters (A), and scale of the structure are varied one at a time, to investigate the effect these parameters have on the meridional and hoop stresses. A general-pwpose finite element programme, ABAQUS, was used to create models of the cooling tower structure. The model results were verified using closed-form analytical membrane solutions as reported by Zingoni. The model considers constraining the base against rotation in all directions while the top is made to be free. The predicted numeric meridional and hoop stresses compare favourably well with the closed-form analytical results, except at the critically stressed zone near the base that exhibits some bending disturbances. Parametric investigation shows that an increase in the hyperbolic axis ratio, the top opening angle, and offset paramete also increases meridional and hoop stresses. It is concluded that lower blao, and zero offset parameters be adopted for preliminary design purposes. Finally, recommendations are made on the need for further investigations.
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    Parametric study on the buckling behaviour of singly and doubly curved concrete arch dams
    (2011) Mokhuthu, Batho; Zingoni, Alphose
    This study explores the buckling behaviour of thin walled and curved concrete arch dams investigated as a function of various parameters of interest, the focus being on the influence of dam thickness on the elastic buckling behaviour.
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    Performance of cold formed welded tubular steel joints under moment loading
    (2008) Mudenda, Kenny; Zingoni, Alphose
    Although exhibiting many superior properties to open sections structural hollow sections (SHS) have seen limited application in structures where joints resist moments. Their application has remained largely in truss type and lattice type structures where pinned joints are assumed. However, SHS have wide potential for use in structures with moment resisting joints. Much still needs to be done, however, to develop an understanding of joint behaviour under moment loads. It is also desirable to come up with means of developing design tables that can simply the design process. The purpose of the research was to investigate the behavior of SHS joints under moment loading through experimental tests as well as using finite element modeling.
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    Predicting variations in the areas of circular leaks in water pipes due to changes in pressure
    (2016) Nsanzubuhoro, Rene Mathias Nsanzintore; Van Zyl, Jakobus E; Zingoni, Alphose
    Leak openings in water distribution system pipes are not static, but have areas that vary with pressure. These changes in area affect the way that leakage respond to changes in pressure, and was thus important for municipal engineers to understand. This study focussed on round hole leak openings that can exist as pipe failures. In this study, a finite element analysis (FEA) study was carried out to model the behaviour of round holes in pipes with varying pressure under elastic conditions. It was found that the areas of the holes vary as linear functions of pressure in the pipe. The slope of this linear function, also referred to as the head-area slope m, was identified as a critical element to investigate because this head-area slope essentially gives an indication of the extent to which the leak area is sensitive to pressure. The FEA was then used to better understand the factors that affect the head-area slope m. In order to understand which parameters affect the head-area slope m, a parametric study was conducted. This parametric study was done by varying each parameter in turn to study the effect of that parameter on the head-area slope of the pipe. The parameters investigated in the study include the pipe material (elastic modulus, Poisson's ratio and longitudinal stress), pipe geometry (wall thickness and internal diameter) and hole diameter. It was found in this study that of the five aforementioned geometric and material parameters, the elastic modulus, wall thickness and internal diameter had the most significant effect on the head-area slope m. The extent to which these parameters influenced m depended on the hole diameter. It was found that as the hole diameter increased the effect of the parameter was more significant. Solid mechanics theory was then used to develop an equation to predict the head-area slope of round holes in different pipes and materials. Various techniques were used in the development of the equation. To calibrate and validate this equation the head-area slopes calculated from the equation were compared and plotted against the finite element head-area slopes. A reasonable expression was found that can be used in further research and practice. The head-area slopes m obtained from this equation was compared to the head-area slopes m obtained in the FEA analysis. It was found that this expression predicts the finite element model analysis reasonably well, producing trends that are similar to those found from the finite element models.
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    Stability behaviour and dynamic response of cooling towers subjected to wind loading
    (2016) Kucherera, Grant Tarwirei; Zingoni, Alphose
    In this study, a linear eigenvalue buckling parametric analysis is presented for various cooling tower shell geometries. The shells are subjected to increasing wind pressures (speeds) to observe the trends in the critical buckling pressures/speeds at which the shell first buckles and the corresponding buckling modes. The cooling tower's geometry is changed in a systematic manner to obtain the relationship between critical wind speeds associated with the first mode of buckling and the cooling tower's geometry. Geometrical parameter ratios of the cooling tower's dimensions are considered in order to cover a wider spectrum of the cooling tower's geometry. The critical wind speed versus height curve is observed to be similar to the Euler buckling curve. There appears to be a certain optimum throat height to total height ratio of about 0.75 for any cooling tower at which the critical wind speed is maximum. The critical wind speed varies linearly with the cooling tower thickness and non-linearly with all diameter ratios. A linear eigenvalue vibration parametric analysis is presented for various cooling tower shell geometries to observe trends in the free vibration response (natural frequencies and mode shapes). The forced response of the cooling tower to various forcing frequencies of wind gusts is analysed using the mode superposition method. The shells are subjected to increasing wind gust periods of the same speed to obtain the trends in the forced vibration response (response frequencies and modes). The cooling tower's geometry is changed in a systematic manner to obtain the free and forced vibration behaviour. The natural frequencies and their corresponding bandwidths for the first ten different modes reduce with increasing height. They are generally invariant with the height to top diameter ratio, but the bandwidth increases with increasing height to top diameter ratio. The response frequencies and their corresponding bandwidths generally decrease with increasing height as well as the height to top diameter ratios. The response frequency generally decreases with decreasing forcing frequency, but not for all the cooling tower geometries. The findings can be used as a basis for further research and establishment of conceptual design guidelines when considering stability, free and forced vibration cooling tower behaviour.
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    Stresses in egg-shaped sludge digesters in the form of ellipsoidal shells of revolution
    (2019) Naidoo, Pranava; Zingoni, Alphose
    Anaerobic sludge digesters of the squat cylindrical shape have inherent flaws which drive up maintenance costs, limits its ability to maintain optimum environmental conditions and is not shaped for efficient mixing. The egg-shaped sludge digester is an effective solution to these flaws. However, the analysis of these structures are complex and design guides are not readily available to designers of anaerobic sludge digesters. In previous studies, various shells of revolution were considered as egg-shaped sludge digester geometries. In terms of stress behaviour, these studies found the geometries to be suitable to act as egg-shaped sludge digesters. This thesis extends the list of geometries explored and considers the stress behaviour in an ellipsoid of revolution. First, only the membrane stress distributions were considered by varying a parameter e (the major axis radius over the minor axis radius) of the ellipsoidal shell. To conduct the study, closed form solutions for the meridional and hoop stresses were derived. The stress distributions of the varying ellipsoidal geometries were then compared and analysed. Additionally, the parametric study considered structural efficiency of the shell. Following this, in order to judge the effectiveness of the geometry, it was compared to findings of previous studies on different geometries. The study compared the geometries on the bases of volume, smoothness and maximum hoop stresses. It was found that the ellipsoidal geometry faired extremely well against the other geometries in the volume and maximum hoop stress criteria. Due to the limitations of the membrane theory of shells to predict bending stresses at supports and other discontinuities, a finite element study was conducted to achieve a complete shell stress distribution. Special attention was paid to bending at the support region where large meridional stress peaks occur as well as bending stresses seen at the apexes. Following this, various support conditions were tested to gather a full understanding of how this affects the total stress distribution in the shell. Finally based on findings of the study a design guide for egg-shaped digesters of ellipsoidal geometry was given.
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    Structural Investigation of Negative Gaussian Curvature Shells as Liquid-Storage Vessels
    (2023) Mahlelebe, Hlasoa; Zingoni, Alphose
    Shells of negative Gaussian curvature, such as hyperboloid of revolution, can be seen in most parts of the world in application in the energy industry as cooling towers supported on the large surface area on the ground (Zingoni, 2018). Hyperboloid of revolution shell has been found to resist self-weight stresses better when used as a cooling tower, and it is constructed to heights up to 200m or even more (Zingoni, 1999). Concrete can be moulded into almost any shape, provided the formwork is well constructed to give the desired shape. This makes it possible to be built into a large-capacity supersized tank (Zingoni, Mokhothu & Enoma, 2015). Some research has emerged on the analysis and design aspects of some elevated liquid containment vessels such as cylindrical, spherical, conical, and an Inze tank (a tank of compound geometry comprising of spherical top closure, vertical cylindrical sides, a conical transition in a lower part and a spherical bottom closure). The current study explores the structural investigation of hyperboloidal shells of revolution when used on a different application as a form of elevated liquid-containing vessel, making the current study novel in liquid containment application. In the current study, closed-form analytical solutions for membrane stress resultants due to hydrostatic loading have been developed and were used to conduct the structural investigation. The solutions developed were based on the membrane theory for shells of revolution for the concrete vessel and can be used to assess the membrane stress state at any point on the hyperboloidal vessel subjected to hydrostatic loading. It was found that increasing the geometric ratio of b/a decreased the maximum membrane meridional stress resultant from vessel to vessel. However, the same increase of b/a increased the maximum hoop stress resultants. The hoop stress resultants were 2.3 times the meridional stress resultant for the geometric ratio b/a =2.1 and 4.4 times for b/a = 2.8. Therefore, the hoop stresses were taken as governing the structural design. The Finite Element Method (FEM) using ABAQUS software was also used to check the accuracy of the derived closed-form solutions. These were in good agreement with an error of less than 5% for both hoop and meridional stresses, hence the developed equations are reliable in predicting stresses in the vessel due to hydrostatic loading. Furthermore, the FEM method using ABAQUS software was used to conduct a linear eigenvalue buckling analysis for zones that experience significant compressive stresses in the hyperboloidal vessel. The meridional stresses were entirely in compression throughout the vessel for all eight tested vessels from a b/a ratio of 2.1 to a b/a ratio of 2.8. It was found that increasing the geometric ratio of b/a increases the linear buckling capacity of the vessel when subjected to hydrostatic loading. The eigenvalues occurred in pairs, which resembles a feature of symmetry of symmetrical structural systems.