Structural Analysis of Thin Tile Vaults and Domes: The Inner Oval Dome of the Basilica de los Desamparados in Valencia

The inner oval dome of the Basílica de la Virgen los Desamparados, built in 1701, is one of the most slender masonry vaults ever built. It is a tile dome with a total thickness of 80 mm and a main span of 18.50 m. It was built without centering with great ingenuity and economy of means, thirty three years after the termination of the building in 1667. The dome is in contact with the external dome only in the inferior part with the projecting ribs of the intrados, the lunettes of the windows, and, in the upper part, through 126 inclined iron bars. This unique construction was revealed in the 1990's in the studies previous to the restoration of the Basílica, and has given rise to different theories about the mode of construction and the structural behaviour and safety of the dome. The present contribution aims to provide a plausible hypothesis about the mode of construction and to explain the safety of the inner dome which has stood, without need of repairs or reinforcement, for 300 hundred years.

The Islamic Crossed-Arch Domes in Cordoba: Geometry and Structural Analysis of the “Capilla de Villaviciosa”

Crossed-arch domes are a singular type of ribbed vaults. Their characteristic feature is that the ribs that form the vault are intertwined, forming polygons or stars, leaving an empty space in the centre. The earliest known vaults of this type are found in the Great Mosque of Córdoba, built ca. 960 a.C. The type spread through Spain, and the north of Africa in the 10th to the 16th Centuries, and was used by Guarini and Vittone in the 17th and 18th Centuries in Italy. However, it was used only in a few buildings. Though the literature about the structural behaviour of ribbed Gothic vaults is extensive, so far no structural analysis of crossed arch domes has been made. The purpose of this work is, first to show the way to attack such an analysis within the frame of Modern Limit Analysis of Masonry Structures (Heyman 1995), and then to apply the approach to study the stability of the dome of the Capilla de Villaviciosa. The work may give some clues to art and architectural historians to understand better the origin and development of Islamic dome architecture.

Chemical and structural analysis of Eucalyptus globulus and E. camaldulensis leaf cuticles: a lipidized cell wall region

The plant cuticle has traditionally been conceived as an independent hydrophobic layer that covers the external epidermal cell wall. Due to its complexity, the existing relationship between cuticle chemical composition and ultra-structure remains unclear to date. This study aimed to examine the link between chemical composition and structure of isolated, adaxial leaf cuticles of Eucalyptus camaldulensis and E. globulus by the gradual extraction and identification of lipid constituents (cutin and soluble lipids), coupled to spectroscopic and microscopic analyses. The soluble compounds and cutin monomers identified could not be assigned to a concrete internal cuticle ultra-structure. After cutin depolymerization, a cellulose network resembling the cell wall was observed, with different structural patterns in the regions ascribed to the cuticle proper and cuticular layer, respectively. Our results suggest that the current cuticle model should be revised, stressing the presence and major role of cell wall polysaccharides. It is concluded that the cuticle may be interpreted as a modified cell wall region which contains additional lipids. The major heterogeneity of the plant cuticle makes it difficult to establish a direct link between cuticle chemistry and structure with the existing methodologies.

A large displacement structural analysis of a pipeline subjected to gravity and buoyancy forces

A nonlinear analysis of an elastic tube subjected to gravity forces and buoyancy pressure is carried out. An update lagrangian formulation is used. The structural analysis efficiency in terms of computer time and accuracy, has been improved when load stiffness matrices have been introduced. In this way the follower forces characteristics such as their intensity and direction changes can be well represented. A sensitivity study of different involved variables on the final deformed pipeline shape is carried out.

An interactive web-based learning assistant for structural analysis of continuous beams

There are significant levels of concern about the relevance and the difficulty of learning some issues on Strength of Materials and Structural Analysis. Most students of Continuum Mechanics and Structural Analysis in Civil Engineering usually point out some key learning aspects as especially difficult for acquiring specific skills. These key concepts entail comprehension difficulties but ease access and applicability to structural analysis in more advanced subjects. Likewise, some elusive but basic structural concepts, such as flexibility, stiffness or influence lines, are paramount for developing further skills required for advanced structural design: tall buildings, arch-type structures as well as bridges. As new curricular itineraries are currently being implemented, it appears appropriate to devise a repository of interactive web-based applications for training in those basic concepts. That will hopefully train the student to understand the complexity of such concepts, to develop intuitive knowledge on actual structural response and to improve their preparation for exams. In this work, a web-based learning assistant system for influence lines on continuous beams is presented. It consists of a collection of interactive user-friendly applications accessible via Web. It is performed in both Spanish and English languages. Rather than a “black box” system, the procedure involves open interaction with the student, who can simulate and virtually envisage the structural response. Thus, the student is enabled to set the geometric, topologic and mechanic layout of a continuous beam and to change or shift the loading and the support conditions. Simultaneously, the changes in the beam response prompt on the screen, so that the effects of the several issues involved in structural analysis become apparent. The system is performed through a set of web pages which encompasses interactive exercises and problems, written in JavaScript under JQuery and DyGraphs frameworks, given that their efficiency and graphic capabilities are renowned. Students can freely boost their self-study on this subject in order to face their exams more confidently. Besides, this collection is expected to be added to the "Virtual Lab of Continuum Mechanics" of the UPM, launched in 2013 (http://serviciosgate.upm.es/laboratoriosvirtuales/laboratorios/medios-continuos-en-construcci%C3%B3n)

A framework for adaptive e-learning for continuum mechanics and structural analysis

This paper presents a project for providing the students of Structural Engineering with the flexibility to learn outside classroom schedules. The goal is a framework for adaptive E-learning based on a repository of open educational courseware with a set of basic Structural Engineering concepts and fundamentals. These are paramount for students to expand their technical knowledge and skills in structural analysis and design of tall buildings, arch-type structures as well as bridges. Thus, concepts related to structural behaviour such as linearity, compatibility, stiffness and influence lines have traditionally been elusive for students. The objective is to facilitate the student a teachinglearning process to acquire the necessary intuitive knowledge, cognitive skills and the basis for further technological modules and professional development in this area. As a side effect, the system is expected to help the students improve their preparation for exams on the subject. In this project, a web-based open-source system for studying influence lines on continuous beams is presented. It encompasses a collection of interactive user-friendly applications accessible via Web, written in JavaScript under JQuery and Dygraph Libraries, taking advantage of their efficiency and graphic capabilities. It is performed in both Spanish and English languages. The student is enabled to set the geometric, topologic, boundary and mechanic layout of a continuous beam. While changing the loading and the support conditions, the changes in the beam response prompt on the screen, so that the effects of the several issues involved in structural analysis become apparent. This open interaction with the user allows the student to simulate and virtually infer the structural response. Different levels of complexity can be handled, whereas an ongoing help is at hand for any of them. Students can freely boost their experiential learning on this subject at their own pace, in order to further share, process, generalize and apply the relevant essential concepts of Structural Engineering analysis. Besides, this collection is being added to the "Virtual Lab of Continuum Mechanics" of the UPM, launched in 2013 (http://serviciosgate.upm.es/laboratoriosvirtuales/laboratorios/medios-continuos-en-construcci%C3%B3n)

Some examples of the simultaneous use of closed-form and numerical solutions in shell structural analysis

The computational advantages of the use of different approaches -numerical and analytical ones- to the analysis of different parts of the same shell structure are discussed. Examples of large size problems that can be reduced to those more suitable to be handled by a personal related axisyrometric finite elements, local unaxisymmetric shells, geometric quasi-regular shells, infinite elements and homogenization techniques are described

The folded plate model in structural analysis. Elastic, plastic and dynamic formulations for nonprismatic structures

A specific numerical procedure for the analysis of arbitrary nonprismatic folded plate structures is presented. An elastic model is studied and compared with a harmonic solution for a prismatic structure. An extension to the plastic analysis is developed, and the influence of the structural geometry and loading pattern is analyzed. Nonprismatic practical cases, with arbitrary geometry and loading are shown, as well in the elastic range as in the plastic one. Finally, a dynamic formulation is outlined

Analysis of the railway track as a spatially periodic structure

This article presents a new and computationally efficient method of analysis of a railway track modelled as a continuous beam of 2N spans supported by elastic vertical springs. The main feature of this method is its important reduction in computational effort with respect to standard matrix methods of structural analysis. In this article, the whole structure is considered to be a repetition of a single one. The analysis presented is applied to a simple railway track model, i.e. to a repetitive beam supported on vertical springs (sleepers). The proposed method of analysis is based on the general theory of spatially periodic structures. The main feature of this theory is the possibility to apply Discrete Fourier Transform (DFT) in order to reduce a large system of q(2N + 1) linear stiffness equilibrium equations to a set of 2N + 1 uncoupled systems of q equations each. In this way, a dramatic reduction of the computational effort of solving the large system of equations is achieved. This fact is particularly important in the analysis of railway track structures, in which N is a very large number (around several thousands), and q = 2, the vertical displacement and rotation, is very small. The proposed method allows us to easily obtain the exact solution given by Samartín [1], i.e. the continuous beam railway track response. The comparison between the proposed method and other methods of analysis of railway tracks, such as Lorente de Nó and Zimmermann-Timoshenko, clearly shows the accuracy of the obtained results for the proposed method, even for low values of N. In addition, identical results between the proposed and the Lorente methods have been found, although the proposed method seems to be of simpler application and computationally more efficient than the Lorente one. Small but significative differences occur between these two methods and the one developed by Zimmermann-Timoshenko. This article also presents a detailed sensitivity analysis of the vertical displacement of the sleepers. Although standard matrix methods of structural analysis can handle this railway model, one of the objectives of this article is to show the efficiency of DFT method with respect to standard matrix structural analysis. A comparative analysis between standard matrix structural analysis and the proposed method (DFT), in terms of computational time, input, output and also software programming, will be carried out. Finally, a URL link to a MatLab computer program list, based on the proposed method, is given

Numerical analysis of shell and spatial structures

Since the advent of the computer into the engineering field, the application of the numerical methods to the solution of engineering problems has grown very rapidly. Among the different computer methods of structural analysis the Finite Element (FEM) has been predominantly used. Shells and space structures are very attractive and have been constructed to solve a large variety of functional problems (roofs, industrial building, aqueducts, reservoirs, footings etc). In this type of structures aesthetics, structural efficiency and concept play a very important role. This class of structures can be divided into three main groups, namely continuous (concrete) shells, space frames and tension (fabric, pneumatic, cable etc )structures. In the following only the current applications of the FEM to the analysis of continuous shell structures will be discussed. However, some of the comments on this class of shells can be also applied to some extend to the others, but obviously specific computational problems will be restricted to the continuous shells. Different aspects, such as, the type of elements,input-output computational techniques etc, of the analysis of shells by the FEM will be described below. Clearly, the improvements and developments occurring in general for the FEM since its first appearance in the fifties have had a significative impact on the particular class of structures under discussion.

Numerical methods in Nonlinear Analysis of shell structures

The design of shell and spatial structures represents an important challenge even with the use of the modern computer technology.If we concentrate in the concrete shell structures many problems must be faced,such as the conceptual and structural disposition, optimal shape design, analysis, construction methods, details etc. and all these problems are interconnected among them. As an example the shape optimization requires the use of several disciplines like structural analysis, sensitivity analysis, optimization strategies and geometrical design concepts. Similar comments can be applied to other space structures such as steel trusses with single or double shape and tension structures. In relation to the analysis the Finite Element Method appears to be the most extended and versatile technique used in the practice. In the application of this method several issues arise. First the derivation of the pertinent shell theory or alternatively the degenerated 3-D solid approach should be chosen. According to the previous election the suitable FE model has to be adopted i.e. the displacement,stress or mixed formulated element. The good behavior of the shell structures under dead loads that are carried out towards the supports by mainly compressive stresses is impaired by the high imperfection sensitivity usually exhibited by these structures. This last effect is important particularly if large deformation and material nonlinearities of the shell may interact unfavorably, as can be the case for thin reinforced shells. In this respect the study of the stability of the shell represents a compulsory step in the analysis. Therefore there are currently very active fields of research such as the different descriptions of consistent nonlinear shell models given by Simo, Fox and Rifai, Mantzenmiller and Buchter and Ramm among others, the consistent formulation of efficient tangent stiffness as the one presented by Ortiz and Schweizerhof and Wringgers, with application to concrete shells exhibiting creep behavior given by Scordelis and coworkers; and finally the development of numerical techniques needed to trace the nonlinear response of the structure. The objective of this paper is concentrated in the last research aspect i.e. in the presentation of a state-of-the-art on the existing solution techniques for nonlinear analysis of structures. In this presentation the following excellent reviews on this subject will be mainly used.

Funicularity and equilibrium for high-performance conceptual structural design

Las estructuras que trabajan por forma se caracterizan por la íntima e indisociable relación entre geometría y comportamiento estructural. Por consiguiente, la elección de una apropiada geometría es el paso previo indispensable en el diseño conceptual de dichas estructuras. En esa tarea, la selección de las posibles geometrías antifuniculares para las distribuciones de cargas permanentes más habituales son más bien limitadas y, muchas veces, son criterios no estructurales (adaptabilidad funcional, estética, proceso constructivo, etc.) los que no permiten la utilización de dichas geometrías que garantizarían el máximo aprovechamiento del material. En este contexto, esta tesis estudia la posibilidad de obtener una estructura sin momentos flectores incluso si la geometría no es antifunicular para sus cargas permanentes. En efecto, esta tesis presenta un procedimiento, basado en la estática gráfica, que demuestra cómo un conjunto de cargas adicionales, introducidas a través de un sistema de pretensado exterior con elementos post-tesos, puede eliminar los momentos flectores debidos a cargas permanentes en cualquier geometría plana. Esto se traduce en una estructura antifunicular que proporciona respuestas innovadoras a demandas conjuntas de versatilidad arquitectónica y optimización del material. Dicha metodología gráfica ha sido implementada en un software distribuido libremente (EXOEQUILIBRIUM), donde el análisis estructural y la variación geométrica están incluidos en el mismo entorno interactivo y paramétrico. La utilización de estas herramientas permite más versatilidad en la búsqueda de nuevas formas eficientes, lo cual tiene gran importancia en el diseño conceptual de estructuras, liberando al ingeniero de la limitación del propio cálculo y de la incomprensión del comportamiento estructural, facilitando extraordinariamente el hecho creativo a la luz de una metodología de este estilo. Esta tesis incluye la aplicación de estos procedimientos a estructuras de cualquier geometría y distribución inicial de cargas, así como el estudio de diferentes posibles criterios de diseño para optimizar la posición del sistema de post-tesado. Además, la metodología ha sido empleada en el proyecto de maquetas a escala reducida y en la construcción de un pabellón hecho enteramente de cartón, lo que ha permitido obtener una validación física del procedimiento desarrollado. En definitiva, esta tesis expande de manera relevante el rango de posibles geometrías antifuniculares y abre enormes posibilidades para el diseño de estructuras que combinan eficiencia estructural y flexibilidad arquitectónica.Curved structures are characterized by the critical relationship between their geometry and structural behaviour, and selecting an appropriate shape in the conceptual design of such structures is important for achieving materialefficiency. However, the set of bending-free geometries are limited and, often, non-structural design criteria (e.g., usability, architectural needs, aesthetics) prohibit the selection of purely funicular or antifunicular shapes. In response to this issue, this thesis studies the possibility of achieving an axial-only behaviour even if the geometry departs from the ideally bending-free shape. This dissertation presents a new design approach, based on graphic statics that shows how bending moments in a two-dimensional geometry can be eliminated by adding forces through an external post-tensioning system. This results in bending-free structures that provide innovative answers to combined demands on versatility and material optimization. The graphical procedure has been implemented in a free-downloadable design-driven software (EXOEQUILIBRIUM) where structural performance evaluations and geometric variation are embedded within an interactive and parametric working environment. This provides greater versatility in finding new efficient structural configurations during the first design stages, bridging the gap between architectural shaping and structural analysis. The thesis includes the application of the developed graphical procedure to shapes with random curvature and distribution of loads. Furthermore, the effect of different design criteria on the internal force distribution has been analyzed. Finally, the construction of reduced- and large-scale models provides further physical validation of the method and insights about the structural behaviour of these structures. In summary, this work strongly expands the range of possible forms that exhibit a bending-free behaviour and, de facto, opens up new possibilities for designs that combine high-performing solutions with architectural freedom.

Preliminary Study and Proposal for Restoring a Jesuit College at Saragossa, Spain

A historical study and a construction pathology survey were conducted prior to proposing a solution for restoring the upper windows on the south side of Old San Carlos College at Saragossa (16th-17th centuries), wich had been forteited to add a third storey to the cloister. Althought initially designed to a simple large hall format, the church is a harmonius blend of Aragonese Gothic architecture and typical Jesuit scheme, consisting in a central nave flanket by chapel-confessional and raised galleries for the community. A subsequent enlargement of the roof, wich rests on the original framing over the central nave, reduced the mechanical strength of the principal rafters on the opposite side, prompting a concomitant imbalance of forces that has affected the entire structure. In view of the foregoing, in addition to restituting the upper window, the proposal solution envisages restoring the roof over the central nave to its original design, and with the interior lighting in the church.

Shower approach in the simulation of ion scattering from solids

An efficient approach for the simulation of ion scattering from solids is proposed. For every encountered atom, we take multiple samples of its thermal displacements among those which result in scattering with high probability to finally reach the detector. As a result, the detector is illuminated by intensive “showers,” where each event of detection must be weighted according to the actual probability of the atom displacement. The computational cost of such simulation is orders of magnitude lower than in the direct approach, and a comprehensive analysis of multiple and plural scattering effects becomes possible. We use this method for two purposes. First, the accuracy of the approximate approaches, developed mainly for ion-beam structural analysis, is verified. Second, the possibility to reproduce a wide class of experimental conditions is used to analyze some basic features of ion-solid collisions: the role of double violent collisions in low-energy ion scattering; the origin of the “surface peak” in scattering from amorphous samples; the low-energy tail in the energy spectra of scattered medium-energy ions due to plural scattering; and the degradation of blocking patterns in two-dimensional angular distributions with increasing depth of scattering. As an example of simulation for ions of MeV energies, we verify the time reversibility for channeling and blocking of 1-MeV protons in a W crystal. The possibilities of analysis that our approach offers may be very useful for various applications, in particular, for structural analysis with atomic resolution.

Obtaining carbonation depth of concrete used two different procedures standard EHE-08

In the Standard EHE 08, for the first time, durability acquires the status of Limit State. Article 8 provides that the term Durability limit state, produced by physical and chemical actions, different loads and actions of structural analysis, which can degrade the concrete and reinforcement to unacceptable limits. The verification of this limit state can be done through a procedure set out in the provisions of the Standard. This procedure is based on the use of tables that, depending on the aggressiveness of the environment in which the structure is the concrete strength and the life of the project, setting the quality of the concrete cover (minimum thickness and maximum water cement ratio of concrete used) and the maximum crack width. This procedure, simple in its application, provides highly secure solutions. In addition, on Annex 9, the Standard EHE 08 offers models for testing the durability limit state in cases of corrosion of reinforcement due to carbonation of concrete or entry of chloride ions. The results obtained with these models are tighter than those obtained with the procedure of the articles. In this paper we use both methods in the study of reinforced concrete structures with potential problems of corrosion of reinforcement due to carbonation of concrete. Later checking the results obtained by both procedures. Results demonstrate that the use of the models listed in Annex 9 of Standard EHE 08 offer cheaper solutions than those obtained using the procedure of the articles