Elliptical Plan Research Articles

Global Distribution and Morphology of Small Seamounts

AbstractSeamounts are isolated elevations in the seafloor with circular or elliptical plans, comparatively steep slopes, and relatively small summit area (Menard, 1964). The vertical gravity gradient (VGG), which is the curvature of the ocean surface topography derived from satellite altimeter measurements, has been used to map the global distribution of seamounts (Kim & Wessel, 2011, https://doi.org/10.1111/j.1365-246x.2011.05076.x). We used the latest grid of VGG to update and refine the global seamount catalog; we identified 19,325 new seamounts, expanding a previously published catalog having 24,643 seamounts. Seven hundred thirty‐nine well‐surveyed seamounts, having heights ranging from 421 to 2,500 m, were used to estimate the typical radially symmetric seamount morphology. First, an Empirical Orthogonal Function (EOF) analysis was used to demonstrate that these small seamounts have a basal radius that is linearly related to their height—their shapes are scale invariant. Two methods were then used to compute this characteristic base to height ratio: an average Gaussian fit to the stack of all profiles and an individual Gaussian fit for each seamount in the sample. The first method combined the radial normalized height data from all 739 seamounts to form median and median‐absolute deviation. These data were fit by a 2‐parameter Gaussian model that explained 99.82% of the variance. The second method used the Gaussian function to individually model each seamount in the sample and further establish the Gaussian model. Using this characteristic Gaussian shape we show that VGG can be used to estimate the height of small seamounts to an accuracy of ∼270 m.

A sound from the arena: acoustic reconstruction of a Roman amphitheater located in Avella, south of Italy

In the ancient Rome the shows entertained by gladiators were very numerous, due to the always growing request from the spectators. After the disuse of the amphitheaters, a wide number of philosophers, writers and poets have been experienced to say what happened in these arenas. Nowadays this type of shows represents continuous source of inspiration for different books and movies (e.g. The gladiator, Spartacus). The amphitheaters are characterized by having an elliptical plan layout, which allow to enlarge the capacity of seats other than improving the sight from the steps of the cavea. The most famous Roman amphitheater is the Colosseum with its biggest dimensions that only the capital city of the empire could have, followed by others of smaller volume size. The development of Christianism decreed the immorality of these shows while the barbaric invasions contributed to convert these places into military barracks, if they were not selected to be demolished. This paper deals with the acoustic study of the amphitheater of Avella, which has been found only a few decades ago by archaeological excavations. The geometrical characteristics are typical of other amphitheaters built in Campania during the Imperial age. An acoustic survey has been undertaken in order to understand the main acoustic parameters in accordance with ISO 3382-1, given the functionality of this place in hosting musical shows during the summer seasons. Based on historical sources and discoveries, a virtual model has been realized to represent the architectural features of how the amphitheater would be looked like originally. The model has been used for acoustic simulations by applying the absorption and scattering coefficients of the finish materials, and the results have been assessed to highlight the different acoustic perception between the existing conditions and the original shape.

Acoustic design of a new shell to be placed in the Roman amphitheater located in Santa Maria Capua Vetere

The Roman amphitheatre is one of the architectural building types to be part of the cultural heritage. The development of the elliptical plan layout could give these places a capacity of up to 50,000 seats, being these sites mainly remembered for the shows and fights between gladiators and wild fears. Nowadays some of them are already preserved by hosting musical concerts and artistic performances, but many others, given the state of their ruins, are open to pleasant visits for tourists and amateurs but having no functional activities. This paper is going to illustrate the acoustic characteristics of the amphitheatre located in Santa Maria Capua Vetere nearby Naples. After an extensive acoustic and architectural measurement campaign, in the first instance, the authors present the analysis of the actual conditions as the monument is in its current state. Furthermore, a digital model has been realized in order to understand how the arena could be functioning with a musical performance. An acoustic shell located in the centre of the arena and composed of mountable reflecting panels is one of the options proposed by the authors to give life to this such a wonderful and historical place.

Wind pressure characteristics of elliptical retractable dome roofs

This study investigated the wind pressure characteristics of an elliptical plan retractable dome roof. Wind tunnel experiments were performed on elliptical dome roofs with varying wall height-to-span ratios (0.1–0.5) and opening ratios (0, 10, 30, and 50 %), where the opening ratio was defined as the ratio of the open area of the roof to the total area of the roof. The resulting peak pressure coefficients of the closed dome roof were then compared with those of the Japanese wind load code (AIJ-RLB (2015)) as there are no current peak pressure coefficients for the cladding design code of elliptical dome roofs. The resulting peak pressure coefficients for each elliptical retractable dome roof opening ratio were also compared with those for the cladding design of spherical retractable domes proposed in previous research. Finally, based on the results of the comparative analysis, negative and positive peak pressure coefficients were proposed for the cladding design of elliptical retractable dome roofs.

Geometrical Analysis of Oval Domes through Architectural and Mathematical Methods. The Case of the Dome of the Camarín of the Virgin of El Puig (Valencia, Spain)

ABSTRACT The study of oval geometry domes encompasses a broad and interesting field of research that can be approached from multiple points of view. This paper shows the multidisciplinary approach developed for the analysis of the geometry of this type of domes from the architectural and mathematical points of view. This research paper focuses on the geometric study of the dome of the Camarín of the Virgin, of the Monastery of El Puig de Santa Maria (Valencia, Spain), an emblematic building of Valencian history and architecture. It begins with a survey by means of a multi-image photogrammetry and other surveying methods obtaining a point cloud that has served as a base for the geometric analysis. The approach to this analysis is through graphic and mathematical gradients, which allows to determine the graphic layouts and equations that best define the shape of the dome as well as drawing up a geometric construction hypothesis, which is consistent with the data. The conclusion obtained is that the dome is generated by an elliptical plan and five-centered oval arches in the vertical sections and the methodological process developed can applied to other cases.

Wind pressures on a large span canopy roof

Based on wind tunnel tests, this paper investigates the aerodynamic behavior of a large span canopy roof with elliptical plan and hyperbolic paraboloid shape. The statistics of pressure coefficients and the peak factor distributions are calculated for the top and bottom faces of the roof, and the Gaussian or non-Gaussian characteristics of the pressure time-histories in different areas of the roof are discussed. The cross-correlation of pressures at different positions on the roof, and between the top and bottom faces is also investigated. Combination factors are also evaluated to take into account the extreme values of net loads, relevant to the structural design of canopies.

STUDY OF GEOMETRIC DEVIATIONS OF THE LARGE-SPAN SHELL OVER STADIUM STANDS WITH A LARGE NOTCH ON THE ELLIPTICAL PLAN OF DONBAS ARENA

The present article is concerned with determination and research of probable geometric deviations of the large-span shell covering stadium stands with a large notch on the elliptical plan of Donbas Arena in town of Donetsk. The authors implemented a review of previous studies in the field of geometric deviations, erection loads, and other specific factors arising in the process of design → manufacturing → erection → service of steel structures of large-span shells. Determination and analysis of erection and assembly deviations arising during erection of stadium shell unit is done by means of author’s software application - Computing System ‘Dimensional Analysis of Lattice Structures’ (VK RASK). The results of analysis and studies show that the amounts of geometric deviations arising during assembly of shell unit before elevation have been estimated. The authors analysed measures provided by the project of MERO enterprise for compensation of erection and assembly deviations and loads in the roof.

Design pressure coefficients for circular and elliptical plan structures with hyperbolic paraboloid roof

Hyperbolic paraboloid shapes are often used for tensile roofing systems, as they allow covering large spans with a very low self weight. In addition, they can be used in combination with a variety of plan shapes. The aerodynamics, and thus the wind loading of buildings provided with an hyperbolic paraboloid roof is different from that of the same building provided with a different roof shape; previous studies have made this aspect evident for square and rectangular plan buildings, and the differences prove to be even larger in the case of circular and elliptical plans. This paper is focused on the latter two geometries. In particular, two different curvatures of the roof and two different heights of the buildings were tested in the wind tunnel. Envelopes of the experimental pressure coefficients have been obtained, giving rise to simplified load maps for use in design and possible Code implementation. Pressure coefficients on the lateral surfaces have also been measured, and are compared with reference values available for the same plan shape, but different roof geometry.

Roofs of prestressed concrete membranes

Prestressed membrane roofs have been designed from the beginning of prestressed concrete. They are described in basic books written by pioneers of prestressed concrete. For illustration, four architecturally most successful roofs are reminded. The authors are convinced that the prestressed membrane roofs are still modern, structurally efficient and architecturally interesting. If they are assembled of precast members, they can be erected without scaffolding. Recently they have studied different membrane structures from point of view of their architectural and structural arrangement, process of erection and static and dynamic behavior. Deep studies were done for membranes of simple curvature situated above the whole or portion of the rectangle area and selfanchored membranes supported by arches or shells. Also selfanchored suspension membranes situated above the circular or elliptical plans, hypar membranes and membranes of a free form that are suspended on arches or suspension cables were analyzed.

Aerodynamic and Pedestrian-Level Wind Characteristics of Super-Tall Buildings with Various Configurations

Recent super-tall building design has been released from the spell of compulsory symmetric shape design, and freestyle design is increasing. This is mainly due to architects’ and structural designers’ challenging demands for novel and unconventional expressions. Another important aspect is that rather complicated sectional shapes are basically good with regard to aerodynamic properties for cross-wind responses. A series of wind tunnel tests have been carried out to determine aerodynamic performance and pedestrian-level wind characteristics of many super-tall buildings with various configurations: square plan, rectangular plan, elliptic plan, with corner cut, with corner chamfered, tilted, tapered, inverse tapered, with setbacks, helical, openings and so on. Dynamic wind-induced response analyses of these models have also been conducted. The results of these tests have led to comprehensive discussions on the aerodynamic and pedestrian level wind characteristics of various tall building configurations.

Improving the Acoustical Properties of an Elliptical Plan Space with a Cable Net Membrane Roof

Textile roofs are particularly suited for covering large open spaces. They are used to make buildings that are able to dynamically change their functions. Their strengths are their great lightness and thinness. These characteristics are optimal for their load bearing function, as a roof covering, but they are not so good for the acoustic performance of the structure. This aspect is important because it makes it difficult to transform a sports arena, for example, into a music hall or auditorium. The possibility having these transformations is economically important for this kind of building. This paper is focused on the acoustic performance of a building covered with a flexible roof made of a cable net and membrane. In this specific case, the roof has a hyperbolic paraboloid geometry, and the building footprint is elliptical. The interaction between shape and acoustic performance is investigated. An acoustic improvement is proposed for the double functional aim of satisfying both speech and music. This improvement is obtained using acoustic absorbing and diffusing panels.

The extension of Rome׳s Capitoline Museums and the design of a new Hall on the site of the ancient ‘Giardino Romano’

The new Hall of Marcus Aurelius in the Capitoline Museums, located within the ancient site of Giardino Romano, displays the original statue of the Roman emperor of the 2nd century AD. The idea of extending the Capitoline Museums by including this site came about in the framework of its general redevelopment.11The chronology of the design work stretches from 1993 to 2002; the works have been achieved between 2004 and 2005. The design leader was Carlo Aymonino and his collaborators architects Maria Luisa Tugnoli, Geneviève Hanssen, Raffaella Castrignanò. The structural design is by engineer Antonio Michetti, with Giuseppe Silvetti and architect Marco Astolfi. The new Hall is the result of a long and complicated process (1988–2005) considering the exceptional importance of the site and the many changes brought to the museum programme during the said period (Figures 1 and 2).In fact, the new Hall was originally supposed to display the marbles of the Temple of Apollo Sosianus, the foundation wall of the Temple of Capitoline Jupiter, embedded within the structures of the Palazzo Caffarelli, opposite the Giardino Romano. However, in 1997, the plan for the Capitoline Museum changed radically as the statue of Marcus Aurelius, which had been restored following the blast of a bomb attack in 1979, was determined to be the focus of the Hall. The project finally consisted of a steel and glass structure on an elliptic plan andshaped around the foundations of the Temple, with the statue at its center.

Building Envelope Pressure Manipulation for Streamlined High-Rise Buildings

Methods of manipulating building envelope wind pressure distributions for application in the natural ventilation of high-rise buildings are presented using computer simulation methods. CFD was used to simulate the external flow while the multi-zone method was used to compute the flow distribution in the building interior. First, a 2–D CFD study was conducted to explore various techniques of manipulating the building envelope wind pressure distribution. This study indicated that the use of externally mounted flow-resistance devices is an effective method of manipulating the wind pressure distribution. It was demonstrated that this technique is well suited for application to buildings of streamlined cross-section (e.g. elliptical plan form). Next, a 3–D CFD study was conducted in order to investigate the performance of the flow resistance device concept applied to a full-scale building. The results indicated that it is possible to significantly alter the pressure distributions at different heights of the building by utilizing flow resistance devices. Manipulating the wind pressure distribution was shown to confer the ability to control the direction of the airflow exchange (i.e. intake versus exhaust) in the interior zones of a building.

NEW APPROACHES TO ANALYSIS AND DESIGN OF A STATIONARY COVERING ABOVE THE STADIUM TRIBUNES

The stationary covering above tribunes of a stadium is reviewed as a truncated rod shell of positive curvature in the elliptical plan. The system of dimensionless spatially‐rigid parameters is obtained for this structure, and it stipulates features of stressed and deformed state of structure under the influence of assumed loads. The results of numerical and experimental studies, original positions of the suggested engineering procedure of design and calculation, results of experimental designing are adduced.

New approaches to analysis and design of a stationary covering above the stadium tribunes

Abstract The stationary covering above tribunes of a stadium is reviewed as a truncated rod shell of positive curvature in the elliptical plan. The system of dimensionless spatially‐rigid parameters is obtained for this structure, and it stipulates features of stressed and deformed state of structure under the influence of assumed loads. The results of numerical and experimental studies, original positions of the suggested engineering procedure of design and calculation, results of experimental designing are adduced.

Caspar David Friedrich als Architekt fur eine Kapelle zu Vitt? Uberlegungen zu seinen Nurnberger Entwurfen fur einen Kirchenbau

The writer discusses nine architectural drawings by Caspar David Friedrich (designs for a church with a tower), now in the Germanisches Nationalmuseum in Nuremberg, Germany. The numbered drawings, some of which are colored, are thought to date from 1805–06. They include an elliptical ground plan, interior and exterior views, and furnishing details. The writer considers evidence that casts doubt on the thesis that the drawings relate to a chapel in Vitt, Germany.

Optimum shapes of a cable dome structure

The present paper reports a study on optimization for maximum stiffness of a full-scale cable dome, which has a 240×190 m elliptic plan and is roofed with membrane. The optimization performed in this study indicated that the optimum shape of the dome depends greatly on the length of the outermost posts. It was thus found that the vertical displacement in the area along the minor axis, which is usually big and difficult to reduce for an elliptic cable dome, can be reduced 25∼35% by increasing 20% of the length of the outermost posts. The dependence of the optimality upon the design parameters were represented in terms of: (1) the slope of the descent path of the objective function during optimization iteration; (2) the slope of the surface of optima. Such a representation is very helpful for designers to evaluate the dependence of the optimality upon the design parameters so as to make design decisions accordingly.

Numerical modelling of the hydro-mechanical behaviour of fractured rock masses

The Pont-Ventoux underground Power Plant is a 150 MW hydroelectric project in the North-West part of the italian Alps. During the geological survey, necessary for the definition of the mechanical parameters, it was found that the original project location was unsuitable due to a fault zone. The power station complex was therefore relocated to a new area with better mechanical conditions. As a result the project of the cavern was modified and a new shape created. The project engineers designed three-dimensional egg-shaped cavern with two abses on both ends of the cavern and an elliptical plan well. To study and research such an innovative shape several numerical analysis were carried out. An hybrid approach F.E.M.-B.E.M. (finite elements method-boundary elements method) was used. The results obtained from these numerical analysis confirmed the validity of the whole idea. The new cavern is therefore supported mainly by means of untensioned grouted dowels and shotcrete.

A new design for a large cavern in the Alps

The Pont-Ventoux underground Power Plant is a 150 MW hydroelectric project in the North-West part of the italian Alps. During the geological survey, necessary for the definition of the mechanical parameters, it was found that the original project location was unsuitable due to a fault zone. The power station complex was therefore relocated to a new area with better mechanical conditions. As a result the project of the cavern was modified and a new shape created. The project engineers designed three-dimensional egg-shaped cavern with two abses on both ends of the cavern and an elliptical plan well. To study and research such an innovative shape several numerical analysis were carried out. An hybrid approach F.E.M.-B.E.M. (finite elements method-boundary elements method) was used. The results obtained from these numerical analysis confirmed the validity of the whole idea. The new cavern is therefore supported mainly by means of untensioned grouted dowels and shotcrete.

Three Dimensional Flow Analysis for the Cavitating-Hydrofoils of Finite Span by Combining with the Lifting-Line. 2nd Report, Cavitating-Line Theory.

A method of flow analysis is developed by combining the formerly proposed cavitating-line theory with the well-known lifting-line one for obtaining the three dimensional characteristics of the cavitating hydrofoils. of finite span. Its main theoretical features are enumerated as follows (1) Three dimensional effects due not only to the finite hydrofoil but also to the finite cavity are reasonably taken into account in the analysis. (2) A theoretical basis for spanwise determination of the two dimensional cavity model adopted is shown clearly under the mutual interferences between the cavitating-line and lifting-line. Some notable effects of aspect ratio on the hydrofoil characteristics (lift, drag, induced drag) and cavity characteristics (effective cavitation number, cavity length, cavity termination thickness, cavity drag, induced drag) are clarified in some details through numerical examples of wide range for the super-cavitating hydrofoils of elliptic plan form.