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This paper is an extension of a previous one, what was dedicated to the study of the problem of design/verification of reinforcement in two-dimensional concrete structures subjected to in plane forces. Here, the verification of the reinforcement of two-dimensional concrete structures subjected to out-of-plan actions (plates and shells) is reviewed. The presented verification procedure allow us to handle important situations that often appear in reinforced concrete structures. such as reinforcement at plate cornes. combination of in-plane forces and bending stresses occurring at function of cantilever and webs in continuous bridge box sections. The usual alternatives to treat these cases are based oo heuristic procedures or semi-empirical formulae as the Wood. The analysis can be carried out by the use of a simple computer program. The output of this program includes the diagrams of stresses and strains for each of the bar reinforcement families and the principal stresses in the as function of the load amplification factor: Iii this way it is possible to find the safety factor at a point of the reinforced concrete strutctureEste artículo corresponde a la extensión de uno anterior dedicado al estudio del problema de la comprobación y el dimensionamiento de las armaduras de acero en estructuras bidimensionales de hormigón armado tipo laja, cuyos esfuerzos están contenidos en su plano medio. Aquí se consideran las estructuras con cargas normales a su plano medio (placas y láminas), es decir. sometidas a esfuerzos de flexión. El procedimiento de comprobación y dimensionamiento que se propone, permite tratar situaciones importantes como el armado en las esquinas de placa, la combinación de tensiones axiles, rasantes y de flexión que aparecen en los arranques de 10s voladizos en las estructuras de los tableros continuos de puentes, particularmente las zonas sobre apoyos. En estos casos las alternativas actuales son procedimientos heurísticos o fórmulas empíricas como la de Wood. El cálculo, que se lleva a cabo mediante un simple programa de computador; permite obtener en pocos segundos la curva de las tensiones y las deformaciones en cada una de las familias de barras y de las principales en el hormigón en función del factor de amplificación de los esfuerzos. De esta forma se deduce el nivel de seguridad que se alcanza en un punto de la estructura. de hormigón armado.

Typically reinforcement layout in two-dimensional concrete structures (plates and shells) is designed as two steel bar families placed in orthogonal directions. However, in some cases, particularly in zones where high principal stresses do not coincide with the reinforcement directions it is usual to design an extra level of reinforcement oblique to the general reinforcement. Also, in cases of biased plates may be more convenient. from the construction point of view, to design the direction of the bars reinforcement parallel to the sides of the plate than an orthogonal bar layout. However, these situations, that often occur in actual design of reinforced concrete structures, are not contemplated in the majority of concrete Codes and Recommendations. As an example, in the Spanish Code HE reinforcement design and verification of structures different to beams, like two dimensional structures, is scarcely treated. In this work, that is divided into two parts, an unified approach to verify the reinforcement in two dimensional reinforced concrete structures is presented. In this first part the application of this approach to structures type membrane plate and membrane shell, i. e. structures subjected to in-plane stresses. longitudinal and tangential stresses, is shown. As is standard, the stress resultants, that are obtained by means a linear elastic analysis. are amplified by a set of safety coefficients in order to reach the so called verification stress resultants. In this paper the reinforcement verification at a point is assumed to be designed with the maximum generality, i. e. it can have either an arbitrary number of curtains of reinforcement, one in the middle plane or two or more symmetrically placed respect to the middle plane of the structure and for each curtain of reinforcement two or more bar directions. The second part of this work, that is an extension of the presented methodology to the general case of plates and shells subjected to hending and axial stress resultants, will he published in a following issue. In the methodology used in this work the standard elasticity equations, namely, equilibrium, compatibility and constitutive equations, among the known stress resultants, stresses and strains of the two materials, concrete and steel, are applied. In the constitutive equations for the concrete its tension strength is not considered and in order to he specific a parabolic-rectangle diagram with a descendent branch is used. For the steel an elastic-plastic behavior is assumed, that is represented by a bilinear stress-strain diagram and in this way hardening effects can be simulated. In order to carry out the proposed procedure to verify the reinforcement and the concrete the use of a desk-top computer generally is required. By application of a simple computer program it is possible to obtain in a few seconds the curves representing the paths of the strains and stresses of each reinforcement family and the principal stresses in the concrete as function of the amplification factor. In this way the safety level at the point under study of the reinforced concrete structure can be obtained.Las armaduras en estructuras bidimensionales de hormigón (losas y láminas) se suelen disponer en dos direcciones, típicamente ortogonales. Sin embargo, a veces, particularmente en zonas en las que las tensiones principales son elevadas, se disponen más de dos familias de armaduras y si la geometría del contorno de la estructura no es regular o no es rectangular es preciso colocar familias de armaduras formando ángulos oblicuos entre sí. En general, las direcciones de las tensiones principales en un punto de una estructura bidimensional no coinciden con las de las armaduras, lo que implica una incertidumbre acerca del trabajo de éstas. Esta problemática que aparece en el diseño usual de las estructuras de hormigón armado y pretensado, no suele estar recogida en la mayoría de las instrucciones. En particular, el tratamiento que presenta la norma española HE acerca del armado de las estructuras y elementos distintos de los monodimensionales, es decir, de la viga, es muy escaso. Este trabajo, que se ha dividido en dos partes, presenta un tratamiento unificado de comprobación de las armaduras en estructuras bidimensionales. En esta primera parte se recoge su aplicación a estructuras, tipos laja y membrana, sometidas a esfuerzos de extensión, es decir, axiles y rasantes, contenidos en su plano medio en el caso de lajas o en su plano tangente a la superficie media en el punto de comprobación, si se trata de una membrana. Como es usual, los esfuerzos, que se determinan a partir de un cálculo elástico y lineal, se mayoran mediante los pertinentes coeficientes de seguridad para obtener los llamados esfuerzos de cálculo. En este articulo, las armaduras en el punto en el que se comprueba la estructura se disponen con la máxima generalidad, es decir, una o varias familias formando ángulos arbitrarios en planta, y colocadas bien en el plano medio o simétricamente en planos paralelos equidistantes del anterior y separados de las caras superior e inferior de la estructura por los mismos recubrimientos. La segunda parte de este trabajo, que representa una extensión de la metodología al caso general de flexión-extensión, es objeto de una siguiente publicación. La metodología en este trabajo tiene en cuenta las ecuaciones, dadas por la elasticidad, de equilibrio, compatibilidad y constitutivas entre los esfuerzos conocidos y las tensiones y deformaciones en ambos materiales, hormigón y acero. Naturalmente, la ecuación constitutiva del hormigón no considera su resistencia a tracción, y por concreción se utiliza la conocida parábola rectángulo con posibilidad de rama descendente. Para el acero se supone para la relación tensiones-deformaciones un diagrama bilineal, es decir, se tiene en cuenta el posible endurecimiento. El cálculo, que se lleva a cabo mediante un simple programa de computador, permite obtener en pocos segundos las curvas de las tensiones y de las deformaciones en cada una de las familias de barras, así como de las tensiones principales en el hormigón enfunción del factor de amplificación de los esfuerzos. De esta forma se deduce el nivel de seguridad que se alcanza en un punto de la estructura de hormigón armado.

Dynamic measurements will become a standard for bridge monitoring in the near future. This fact will produce an important cost reduction for maintenance. US Administration has a long term intensive research program in order to diminish the estimated current maintenance cost of US$7 billion per year over 20 years. An optimal intervention maintenance program demands a historical dynamical record, as well as an updated mathematical model of the structure to be monitored. In case that a model of the structure is not actually available it is possible to produce it, however this possibility does not exist for missing measurement records from the past. Current acquisition systems to monitor structures can be made more efficient by introducing the following improvements, under development in the Spanish research Project “Low cost bridge health monitoring by ambient vibration tests using wireless sensors”: (a) a complete wireless system to acquire sensor data, (b) a wireless system that permits the localization and the hardware identification of the whole sensor system. The applied localization system has been object of a recent patent, and (c) automatization of the modal identification process, aimed to diminish human intervention. This system is assembled with cheap components and allows the simultaneous use of a large number of sensors at a low placement cost. The engineer’s intervention is limited to the selection of sensor positions, probably based on a preliminary FE analysis. In case of multiple setups, also the position of a number of fixed reference sensors has to be decided. The wireless localization system will obtain the exact coordinates of all these sensors positions. When the selection of optimal positions is difficult, for example because of the lack of a proper FE model, this can be compensated by using a higher number of measuring (also reference) points. The described low cost acquisition system allows the responsible bridge administration to obtain historical dynamic identification records at reasonable costs that will be used in future maintenance programs. Therefore, due to the importance of the baseline monitoring record of a new bridge, a monitoring test just after its construction should be highly recommended, if not compulsory.

The optimal design of a vertical cantilever beam is presented in this paper. The beam is assumed immersed in an elastic Winkler soil and subjected to several loads: a point force at the tip section, its self weight and a uniform distributed load along its length. lbe optimal design problem is to find the beam of a given length and minimum volume, such that the resultant compressive stresses are admisible. This prohlem is analyzed according to linear elasticity theory and within different alternative structural models: column, Navier-Bernoulli beam-column, Timoshenko beamcolumn (i.e. with shear strain) under conservative loads, typically, constant direction loads. Results obtained in each case are compared, in order to evaluate the sensitivity of model on the numerical results. The beam optimal design is described by the section distribution layout (area, second moment, shear area etc.) along the beam span and the corresponding beam total volume. Other situations, some of them very interesting from a theoretical point of view, with follower loads (Beck and Leipholz problems) are also discussed, leaving for future work numerical details and results.

This paper is a preliminary version of Chapter 3 of a State-of-the-Art Report by the IASS Working Group 5: Concrete Shell Roofs. The intention of this chapter is to set forth for those who intend to design concrete shell roofs information and advice about the selection, verification and utilization of commercial computer tools for analysis and design tasks.The computer analysis and design steps for a concrete shell roof are described. Advice follows on the aspects to be considered in the application of commercial finite element (FE)computer programs to concrete shell analysis, starting with recommendations on how novices can gain confidence and competence in the use of software. To establish vocabulary and provide background references, brief surveys are presented of, first,element types and formulations for shells and, second, challenges presented by advanced analyses of shells. The final section of the chapter indicates what capabilities to seek in selecting commercial FE software for the analysis and design of concrete shell roofs. Brief concluding remarks summarize advice regarding judicious use of computer analysis in design practice.

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.

The theory of guided wave propagation in N-layered media is presented. The derivation of the dispersion equation is obtained from the application of appropriate boundary and continuity conditions to the solution of the general wave propagation. The resulting dispersion equation is given in the form of a determinant of a 4Nx4N coefficient matrix. A numerical procedure is proposed to represent and solve the implicit equation resulting. The validity and efficiency of the proposed numerical model is discussed. Dispersion curves characterizing the N-layered material are obtained and compared to published results. In order to illustrate the use of the model to different practical applications, such as coating problems of plasma spray on a turbine blade, aircraft multiple layers, ice detection, etc. a sensitivity analysis of the dispersion curves respect to depth imperfections is given.

The principal goal in the design of any general engineering structure is to achieve stability. A structure must remain stable and therefore, fit for purpose, throughout its useful life. This requirement can be achieved with the help of structural analysis techniques, which nowadays can be performed using computers. In this paper, the authors consider the three distinct phases of structural analysis, namely Idealisation, Analysis and Interpretation. The idealisation phase describes the process of translating the proposed engineering works into a model that represents the physical response of the structure to applied loading. This model is a simplification of the real structure and only considers the characteristics of the components that have the greatest influence on its stability. In the following phase, the analysis phase, the aforementioned model is used to study and understand how the structure might behave in reality. The framing of this model may draw upon knowledge obtained in many other disciplines, including Applied Mathematics and Materials Science. The significance of the results are determined during the interpretation phase and the engineer either decides that stability can be achieved or works through the process again, modifying the initial idealisation. As computers continue to grow in capability, it is the purpose of this paper to consider the role of computational methods and how they may empower present and future structural engineers.

In this paper a consistent analysis of reinforced concrete (RC) two-dimensional (2-D) structures,namely slab structures subjected to in-plane and out-plane forces, is presented. By using this method of analysis the well established methodology for dimensioning and verifying RC sections of beam structures is extended to 2-D structures. The validity of the proposed analysis results is checked by comparing them with some published experimental test results. Several examples show some of these proposed analysis features, such as the influence of the reinforcement layout on the service and ultimate behavior of a slab structure and the non straightforward problem of the optimal dimension at a slab point subjected to several loading cases. Also, in these examples, the method applications to design situations as multiple steel families and non orthogonal reinforcement layout are commented.

In this paper some topics related to the design of reinforced concrete (RC) shells are addressed. The influence of the reinforcement layout on the service and ultimate behavior of the shell structure is commented. The well established methodology for dimensioning and verifying RC sections of beam structures is extended. In this way it is possible to treat within a unified procedure the design and verification of RC two dimensional structures, in particular membrane and shell structures. Realistic design situations as multiple steel farnilies and non orthogonal reinforcement layout can be handled. Finally, some examples and applications of the proposed methodology are presented.

The optimal design of a column subjected to compression forces is studied. Different support conditions are considered for the column. Also, a point load at the top section, self weight and unifonnly distributed vertical loading may be included in the analysis. The beam is assumed immersed in an elastic Winkler-type soil. Conservative loading has been assumed, i.e. with constant direction and therefore follower loads situation has been disregarded. The optimal column design is described by both cross-section distribution (area; second moment, shear area etc.) along the column span and the corresponding total volume. The optimal design problem consists of detennining the cross-section distribution layout for a beam of given length, so that the column volume becomes minimum, and resultant compressive stresses are admisible. This problem is analyzed assuming a linear elastic material behavior. The column is analyzed by comparing the results obtained from the Navier-Bemoulli beam-column model, and from Timoshenko beam- column model. Special shape functions are introduced in each case.

In this article, a model for the determination of displacements, deformations and tensions of a submarine pipeline during the construction is presented. The process is carried out from an initial floating situation to the final laying position on the seabed. The existence of currents and small waves are also considered. Firstly, this technique, usually applied to polyethylene pipelines, is described in this paper as well as some real world examples, as well as the variables that can be modified to control the behavior of the structure. A detailed description of the actions in this process is considered, specially the ones related to marine environment, as Archimedes force, current and sea waves. The behavior of the pipeline is modeled with a non linear elasto dynamic model where geometric non linearities are taken into account. A 3-D beam model, without cross section deformation effects, is developed. Special care is taken in the numerical analysis, developed within an updated lagrangian formulation framework, with the sea bed contact, the follower forces due to the external water pressures and the dynamic actions. Finally, some subroutines are implemented into ANSYS to simulate the two dimensional case, where the whole construction process is achieved. With this software, a sensibility analysis of the bending moments, axial forces and stresses obtained with different values of the control variables in order to optimize the construction steps. These control variables are, the axial load in the pipe, the inundated inner length and the distance of the control barge from the coast.

In this paper, the main steps necessary to evaluate the seismic risk on a site are discussed. Several examples from the authors practical experience are reported and a systematic procedure to study the seismic risk on a dam site is also shown. The characteristics of the available Spanish seismic information - mainly historical and non instrumental seismic records - are commented. Different types of seismic and geologic techniques to investigate the area under the dam are given. Finally, a probabilistic method to obtain from the given seismic intensities the design earthquake is summarized

En este artículo se muestra la aplicación de un método general de cálculo y dimensionamiento en el E.L.U. de estructuras de hormigón armado bidimensionales. El método presentado utiliza las hipótesis y simplificaciones usuales en el cálculo de vigas de hormigón armado, y su planteamiento desarrollado en [12] se particulariza aquí a estructuras tipo laja, con cargas contenidas en su plano medio. Para establecer los avances que permite el método propuesto se resume el estado actual de los procedimientos de dimensionamiento y comprobación tensional de lajas de hormigón armado. A continuación se indican las hipótesis básicas en las que se fundamenta la teoría y se expone la metodología desarrollada para comprobar y dimensionar una sección. Por último se demuestra la utilidad práctica del método mediante su utilización en la optimización del armado de una serie de elementos estructurales tipo membrana.

In this paper a review of two main groups of structural damage identification methods by dynamic tests is presented. The first group is concerned with metallic thin structures damages or imperfections and the second one with reinforced concrete beam structures damages. 1. The first group is addressed to the detection of potential imperfections, fissures and cracks appearing in industrial machines, aeronautical structures and motor engines. They are typically metallic structures and the tests are carried under controlled environment conditions, such as in a laboratory. The application of body waves, and more often, guided waves, as Rayleigh and Lamb waves, as dynamic excitation in order to detect the damage, is described. The studied imperfections have been divided into three classes. • Cracks, related to the structural safety. They are penetrating a significant part of the plate thickness. • The second class of imperfections are small cracks or fissures, and they can be called partially penetrating ones because they are extended only to a small part of the plate thickness. Imperfections of this class are difficult to detect, because sometimes they can not be observed on the plate surfaces. • Finally, the third class of imperfections are the superficial cracks and they are more related to the durability of the structure than to its safety. These imperfections are more connected to structural protection to the environment, i.e. to protective painting and coating. Dynamic models used to detect the first class of imperfections have been Kirchhoff or Reissner bending thin plate. The crack detection can be achieved quite accurately by comparison between the first spatial derivatives of the mode shapes of the uncracked and cracked plates. Partially penetrating and superficial cracks have been identified by application as dynamic input of Lamb and Rayleigh waves respectively. The use of these guide waves seems to be a very promising technique for imperfection detection. However, computational problems appear. They are related to the small time step and the large number of the finite elements needed in order to reach a suitable accuracy level. 2. The second part of the paper treats a different group of dynamic identification and location of damage in civil and building structures. In particular the damage in reinforced concrete beams,typically used in bridge and building structures is studied. Detection procedures in this part differ of the first ones, because the existing structure is tested in the field and reinforced concrete is rather heterogenous material in comparison to metallic material. Normally, potential cracks are detected, during the free vibrations of the structure, by estimation of the changes either of its natural frequencies, or in its mode shapes or in the measure of its dynamic flexibility. However,in general, the differences of these values between uncracked and cracked beams are small and in some cases they can not be distinguished from the inherent measurement errors occurring during the tests. After reviewing several different models applied to crack detection, one based on the linear elasticity has been developed. In this model the cracks are assumed to remain open and the rest of the structure to behave elastically, Using this model a sensitivity analysis of the presence of cracks,depth and location, respect to the variation of the structure natural frequencies and modes shapes can be carried out. Using this approach a crack identification methodology is proposed. Finally,some possible modifications of the proposed methodology aimed to improve the accuracy and reliability of the obtained results are discussed.

The problem of design/verification of reinforcement in concrete shells is reviewed. Methods of analysis are classified, and the elastic-plastic approach is described in detail in the general case of shells subjected to both bending and membrane action. The procedure is then reduced to membrane shells (applicable also to concrete walls) and to pure bending, as in the case of plates. The procedure, which is based on previous research,generally requires the use of a desk-top computer.

Se describe someramente el procedimiento de colocación por fondeo de una tubería de polietileno en un emisario submarino. El problema estructural se plantea en grandes movimientos pero con material elástico y deformaciones pequeñas. Se estudian las distintas acciones actuales: peso propio, inundación del tubo, oleaje, corriente marina, tiro de arrastre y modificaciones del esquema estructural. Algunas de las acciones anteriores son de persecución (follower forces) y por lo tanto, generalmente no son conservativas. Por otra parte, se establecen las pertinentes condiciones de contorno, algunas no lineales con carácter unilateral como es la representada por la existencia del fondo marino. Se determinan los esfuerzos y movimientos en las distintas etapas de un proceso de inmersión del emisario, desde su posición inicial de flotación hasta su colocación en el fondo del mar. El modelo presentado se aplica al estudio de unos casos simples de colocación del emisario en el lecho marino.

This paper is an extension of a previous one, what was dedicated to the study of the problem of design/verification of reinforcement in two-dimensional concrete structures subjected to in plane forces. Here, the verification of the reinforcement of two-dimensional concrete structures subjected to out-of-plan actions (plates and shells) is reviewed. The presented verification procedure allow us to handle important situations that often appear in reinforced concrete structures. such as reinforcement at plate cornes. combination of in-plane forces and bending stresses occurring at function of cantilever and webs in continuous bridge box sections. The usual alternatives to treat these cases are based oo heuristic procedures or semi-empirical formulae as the Wood. The analysis can be carried out by the use of a simple computer program. The output of this program includes the diagrams of stresses and strains for each of the bar reinforcement families and the principal stresses in the as function of the load amplification factor: Iii this way it is possible to find the safety factor at a point of the reinforced concrete strutcture, Este artículo corresponde a la extensión de uno anterior dedicado al estudio del problema de la comprobación y el dimensionamiento de las armaduras de acero en estructuras bidimensionales de hormigón armado tipo laja, cuyos esfuerzos están contenidos en su plano medio. Aquí se consideran las estructuras con cargas normales a su plano medio (placas y láminas), es decir. sometidas a esfuerzos de flexión. El procedimiento de comprobación y dimensionamiento que se propone, permite tratar situaciones importantes como el armado en las esquinas de placa, la combinación de tensiones axiles, rasantes y de flexión que aparecen en los arranques de 10s voladizos en las estructuras de los tableros continuos de puentes, particularmente las zonas sobre apoyos. En estos casos las alternativas actuales son procedimientos heurísticos o fórmulas empíricas como la de Wood. El cálculo, que se lleva a cabo mediante un simple programa de computador; permite obtener en pocos segundos la curva de las tensiones y las deformaciones en cada una de las familias de barras y de las principales en el hormigón en función del factor de amplificación de los esfuerzos. De esta forma se deduce el nivel de seguridad que se alcanza en un punto de la estructura. de hormigón armado.

In this paper current bridge design development is reviewed and different acting mechanisms in this process are identified. Some of the bridge design ingredients are discussed in the different paper sections. In the first section, the use of modern materials in bridge design is commented. Structural concrete, in its different versions, several forms of steel: bars, cable, beams and, finally, composite materials, i.e., the ones combining in their best use, concrete and steel. The second section is related with the extensive typology of bridges, i. e. compression structures (columns, arch, membranes, and shell systems), bending (beams, plates, cable stayed), combination of stresses (portal frame, vierendel, Maillart) and tension (suspension bridge or inverted arch) among others. In the following and in connection to the previous one bridge analysis is discussed. Next, the important topic of construction in the conceptual bridge design is studied, because frequently, during its construction the bridge suffers more severe loading conditions than during its service life and design details must be considered according to the construction procedure considered. Separate attention is paid to the specific methods of staging, push-out and cantilever. The next two sections are devoted to the currently Important items of new bridge functions, environment consideration, aesthetic and technical efficiency in bridge design (urban bridges) and bridge management in its aspects of extraordinary traffIC control, maintenance, early damage detection and repairing. Finally, in the framework of the above ideas some recent examples of bridge design are described.

Este artículo corresponde a la extensión de uno anterior dedicado al estudio del problema de la comprobación y el dimensionamiento de las armaduras de acero en estructuras bidimensionales de hormigón armado tipo laja, cuyos esfuerzos están contenidos en su plano medio. Aquí se consideran las estructuras con cargas normales a su plano medio (placas y láminas), es decir. sometidas a esfuerzos de flexión. El procedimiento de comprobación y dimensionamiento que se propone, permite tratar situaciones importantes como el armado en las esquinas de placa, la combinación de tensiones axiles, rasantes y de flexión que aparecen en los arranques de 10s voladizos en las estructuras de los tableros continuos de puentes, particularmente las zonas sobre apoyos. En estos casos las alternativas actuales son procedimientos heurísticos o fórmulas empíricas como la de Wood. El cálculo, que se lleva a cabo mediante un simple programa de computador, permite obtener en pocos segundos la curva de las tensiones y las deformaciones en cada una de las familias de barras y de las principales en el hormigón en función del factor de amplificación de los esfuerzos. De esta forma se deduce el nivel de seguridad que se alcanza en un punto de la estructura de hormigón armado.

The paper is divided in the following parts. First, the problem of design/verification of reinforcement in concrete membrane, p1ate and shell structures is reviewed. Methods of analysis are classified , and the elastic-plastic approach is described and used in the development of an unified approach to verify the reinforcement in two dimensional reinforced concrete structures. Then, the developed methodology is applied to structures type membrane plate and membrane shell (applicable also to concrete walls) and to pure bending, as in the case of plates. Its application to the general case of folded plate and shell structures subjected to bending and axial stress resultants is shown. The methodology applied in this work is based on the standard elasticity equations,namely, equilibrium, compatibility und constitutive equations. Non linear constitutive equations of concrete and steel are considered. Namely, the tension strength concrete is not considered and a parabolic-rectangle diagram with a descendent branch is used. For the steel an elastic-plastic behavior is assumed, that is represented by a bilinear stress-strain diagram and in this way hardening effects can be simulated. At each section of the structure two or more reinforcement families are considered and they can be placed in plan along arbitrary directions. In this way many practical design situations, that are not contemplated in the majority of the Concrete Codes and Recommendations and are different to typical cases of orthogonal two steel bar families,are envisaged. An example of these cases are zones of high stress concentration where extra reinforcement families are demanded. Based on the presented methodology a computer program has been written. The main re sult is the set of curves representing the paths of the strains and stresses of each reinforcement family and the principal stresses in the concrete as function of the amplification factor. In this way the safety level at the point under study of the reinforced concrete structure can be obtained.

Se estudia una placa tipo Mindlin, reforzada con nervios distribuidos de forma periódica según direcciones arbitrarias, mediante técnicas de homogeneización basadas en métodos de desarrollos asintóticos en escalas múltiples. Se obtiene de esta forma la matriz de rigidez de la placa homogeneizada que resulta ser dependiente de las características geométricas de la celda periódica, es decir, de su oblicuidad, forma en planta, variación de espesores etc., así como de las constantes elásticas del material. El cálculo de esta matriz se lleva a cabo mediante un promedio sobre el dominio de la celda de una combinación lineal de soluciones de diferentes problemas de contorno deflexión de placa sobre el dominio de la celda y con condiciones de contorno de tipo periódico. Cada uno de estos problemas de contorno corresponde a unas cargas aplicadas sobre la placa que son derivadas de las funciones D y Do constantes de flexión y de cortante de la placa. Finalmente se presenta un ejemplo que ilustra la aplicación de esta metodología.

A Mindlin plate with periodically distributed ribs patterns is analyzed by using homogenization techniques based on asymptotic expansion methods. The stiffness matrix of the homogenized plate is found to be dependent on the geometrical characteristics of the periodical cell, i.e. its skewness, plan shape, thickness variation etc. and on the plate material elastic constants. The computation of this plate stiffness matrix is carried out by averaging over the cell domain some solutions of different periodical boundary value problems. These boundary value problems are defined in variational form by linear first order differential operators on the cell domain and the boundary conditions of the variational equation correspond to a periodic structural problem. The elements of the stiffness matrix of homogenized plate are obtained by linear combinations of the averaged solution functions of the above mentioned boundary value problems. Finally, an illustrative example of application of this homogenization technique to hollowed plates and plate structures with ribs patterns regularly arranged over its area is shown. The possibility of using in the profesional practice the present procedure to the actual analysis of floors of typical buildings is also emphasized.

Las armaduras en estructuras bidimensionales de hormigón (losas y láminas) se suelen disponer en dos direcciones, típicamente ortogonales. Sin embargo, a veces, particularmente en zonas en las que las tensiones principales son elevadas, se disponen más de dos familias de armaduras y si la geometría del contorno de la estructura no es regular o no es rectangular es preciso colocar familias de armaduras formando ángulos oblicuos entre sí. En general, las direcciones de las tensiones principales en un punto de una estructura bidimensional no coinciden con las de las armaduras, lo que implica una incertidumbre acerca del trabajo de éstas. Esta problemática que aparece en el diseño usual de las estructuras de hormigón armado y pretensado, no suele estar recogida en la mayoría de las instrucciones. En particular, el tratamiento que presenta la norma española HE acerca del armado de las estructuras y elementos distintos de los monodimensionales, es decir, de la viga, es muy escaso. Este trabajo, que se ha dividido en dos partes, presenta un tratamiento unificado de comprobación de las armaduras en estructuras bidimensionales. En esta primera parte se recoge su aplicación a estructuras, tipos laja y membrana, sometidas a esfuerzos de extensión, es decir, axiles y rasantes, contenidos en su plano medio en el caso de lajas o en su plano tangente a la superficie media en el punto de comprobación, si se trata de una membrana. Como es usual, los esfuerzos, que se determinan a partir de un cálculo elástico y lineal, se mayoran mediante los pertinentes coeficientes de seguridad para obtener los llamados esfuerzos de cálculo. En este articulo, las armaduras en el punto en el que se comprueba la estructura se disponen con la máxima generalidad, es decir, una o varias familias formando ángulos arbitrarios en planta, y colocadas bien en el plano medio o simétricamente en planos paralelos equidistantes del anterior y separados de las caras superior e inferior de la estructura por los mismos recubrimientos. La segunda parte de este trabajo, que representa una extensión de la metodología al caso general de flexión-extensión, es objeto de una siguiente publicación. La metodología en este trabajo tiene en cuenta las ecuaciones, dadas por la elasticidad, de equilibrio, compatibilidad y constitutivas entre los esfuerzos conocidos y las tensiones y deformaciones en ambos materiales, hormigón y acero. Naturalmente, la ecuación constitutiva del hormigón no considera su resistencia a tracción, y por concreción se utiliza la conocida parábola rectángulo con posibilidad de rama descendente. Para el acero se supone para la relación tensiones-deformaciones un diagrama bilineal, es decir, se tiene en cuenta el posible endurecimiento. El cálculo, que se lleva a cabo mediante un simple programa de computador, permite obtener en pocos segundos las curvas de las tensiones y de las deformaciones en cada una de las familias de barras, así como de las tensiones principales en el hormigón en función del factor de amplificación de los esfuerzos. De esta forma se deduce el nivel de seguridad que se alcanza en un punto de la estructura de hormigón armado.

This paper is part of a set of publications related with the development of mathematical models aimed to simulate the dynamic input and output of experimental nondestructive tests in order to detect structural imperfections. The structures to be considered are composed by steel plates of thin thickness. The imperfections in these cases are cracks and they can penetrate either a significant part of the plate thickness or be micro cracks or superficial imperfections. The first class of cracks is related with structural safety and the second one is more connected to the structural protection to the environment, particularly if protective paintings can be deteriorated. Two mathematical groups of models have been developed. The first group tries to locate the position and extension of the imperfection of the first class of imperfections, i.e. cracks and it is the object of the present paper. Bending Kirchoff thin plate models belong to this first group and they are used to this respect. The another group of models is dealt with membrane structures under the superficial Rayleigh waves excitation. With this group of models the micro cracks detection is intended. In the application of the first group of models to the detection of cracks, it has been observed that the differences between the natural frequencies of the non cracked and the cracked structures are very small. However, geometry and crack position can be identified quite accurately if this comparison is carried out between first derivatives (mode rotations) of the natural modes are used instead. Finally, in relation with the analysis of the superficial crack existence the use of Rayleigh waves is very promising. The geometry and the penetration of the micro crack can be detected very accurately. The mathematical and numerical treatment of the generation of these Rayleigh waves present and a numerical application has been shown.

In a Finite Element (FE) analysis of elastic solids several items are usually considered, namely, type and shape of the elements, number of nodes per element, node positions, FE mesh, total number of degrees of freedom (dot) among others. In this paper a method to improve a given FE mesh used for a particular analysis is described. For the improvement criterion different objective functions have been chosen (Total potential energy and Average quadratic error) and the number of nodes and dof's of the new mesh remain constant and equal to the initial FE mesh. In order to find the mesh producing the minimum of the selected objective function the steepest descent gradient technique has been applied as optimization algorithm. However this efficient technique has the drawback that demands a large computation power. Extensive application of this methodology to different 2-D elasticity problems leads to the conclusion that isometric isostatic meshes (ii-meshes) produce better results than the standard reasonably initial regular meshes used in practice. This conclusion seems to be independent on the objective function used for comparison. These ii-meshes are obtained by placing FE nodes along the isostatic lines, i.e. curves tangent at each point to the principal direction lines of the elastic problem to be solved and they should be regularly spaced in order to build regular elements. That means ii-meshes are usually obtained by iteration, i.e. with the initial FE mesh the elastic analysis is carried out. By using the obtained results of this analysis the net of isostatic lines can be drawn and in a first trial an ii-mesh can be built. This first ii-mesh can be improved, if it necessary, by analyzing again the problem and generate after the FE analysis the new and improved ii-mesh. Typically, after two first tentative ii-meshes it is sufficient to produce good FE results from the elastic analysis. Several example of this procedure are presented.

The book represents a very interesting example of the possibility to combine in a single publication basic theory of structures and quite advanced topics on the same subject. The author fulfills this objective in a reasonable size book, less than 400 pages divided into 15 chapters averaging 20 pages each plus 9 short appendices. A diskette is also included in the book. This diskette contains training as well practical executable programs on different aspects of structural analysis, such as cross-sections properties,general-purpose computer programs for the static, dynamic and stability analysis of simple bar structures, etc. The book figures are didactic and have been carefully drawn.

In this work we introduce a new mathematical model for elastic beams with a cross-section of constant width and longitudinally variable depth, obtained from the classical three-dimensional linear elasticity problem by using an asymptotic expansion method. We characterize the first- and second-order displacements and the first-order stress field, giving results related to existence, uniqueness and convergence for the limit model solution. Finally, we present the computations for a classical example.

In this work, some results obtained by Trabucho and Viaño for the shear stress distribution in beam cross sections using asymptotic expansions of the three-dimensional elasticity equations are compared with those calculated by the classical formulae of the Strength of Materials. We use beams with rectangular and circular cross section to compare the degree of accuracy reached by each method.

Using the 3-D equations of linear elasticity and the asylllptotic expansion methods in terms of powers of the beam cross-section area as small parameter different beam theories can be obtained, according to the last term kept in the expansion. If it is used only the first two terms of the asymptotic expansion the classical beam theories can be recovered without resort to any "a priori" additional hypotheses. Moreover, some small corrections and extensions of the classical beam theories can be found and also there exists the possibility to use the asymptotic general beam theory as a basis procedure for a straightforward derivation of the stiffness matrix and the equivalent nodal forces of the beam. In order to obtain the above results a set of functions and constants only dependent on the cross-section of the beam it has to be computed them as solutions of different 2-D laplacian boundary value problems over the beam cross section domain. In this paper two main numerical procedures to solve these boundary value pf'oblems have been discussed, namely the Boundary Element Method (BEM) and the Finite Element Method (FEM). Results for some regular and geometrically simple cross-sections are presented and compared with ones computed analytically. Extensions to other arbitrary cross-sections are illustrated.

El libro Apología de un matemático de G. H. Hardy (1877-1947), uno de los mejores matemáticos de este siglo, ha vuelto a ser publicado recientemente en español, dentro del año de la Matemática que estamos celebrando (…)

There are different methods of construction of outfall pipelines, all of them have to solve the problem of placing a tube over a known location in sea bed. This process has sometimes to be done in difficult conditions as waves, current or depths greater than 30 metres, where a diver cannot go safely beyond. Also the placement of the pipeline must be carried out without any damage to the tube, therefore a close control of the deflections and stresses in the structure must be performed. The importance of this control should be not diminished because a damage during the construction would imply a very difficult and expensive repair, that should be avoided with a proper design of the construction process. This paper is focused in the analysis of the tube during its placement according to a very well known construction method consisting in placing the tube from a boat, where all the connections between consecutive tube segments are performed, and also the whole process is controlled. This method is used for outfall as well as offshore pipelines, and it will be described in Section 2

The objective of this lecture is try to predict the future of this important type of spatial structures. In this way the activities of the different IASS Technical Working Groups can be stimulated and coordinated in order to play a more relevant role in this future. To grasp a possible evolution of bridges it is convenient a reflection on the bridge history and on their present situation, particularly in relation to the different existing achievements.

In this paper, a set of design parameters, such as the slopes of upstream and downstream faces of the dam, radius of the upper arch, width of the dam at the top level and height of the vertical upper part of the dam, are given as function of the valley characteristics when the dam is situated, such as its geometry and its geotechnical properties. These tables have been obtained using a regression of the design parameters of an arch-gravity dam with a minimum concrete volume, placed in a large number of valleys with different characteristics and properties. Elasticites for these design parameters are also discussed.

Arch gravity dams are massive structures of important environment impact and economic investments with a complex structural behavior. This behavior is usually simulated by means 3-D Finite Elements with several layers across the dam thickness. Due to limited experienced existing for this type of dams a set of preliminary formulae have been obtained in order to compute the key parameters of the design definition, such as the slopes of upstream and the downstream faces of the dam, radius of the upper arch, with of the dam at the top level, etc. The methodology used to find the formulae consist in assuming a quadrilateral cross section for the valley where the dam will be located. The values to define the valley geometry are given as data. From these data and the concrete material properties, an arch gravity dam supporting a set of loadings combinations can automatically be designed with a minimum weight. In the analysis of this design the obtained stresses should be layed between some specified admissible limits. First and second order optimization procedures have been applied to a large set of valley configurations and the corresponding arch gravity designs have been found. Using this correspondence a regression analysis has been performed and the corresponding graph, design curves and regression polynomial functions between the valley data and the different dam design parameters have been obtained. Some conclusions about the importance of the data on the design parameters of an arch gravity dam are also presented.

Examples of global solutions of the shell equations are presented, such as the ones based on the well known Levy series expansion. Also discussed are some natural extensions of the Levy method as well as the inherent limitations of these methods concerning the shell model assumptions, boundary conditions and geometric regularity. Finally, some open additional design questions are noted mainly related to the simultaneous use in analysis of these global techniques and the local methods (like the finite elements) to finding the optimal shell shape, and to determining the reinforcement layout.

This paper describes the development of an improved numerical technique for the prediction of time-dependent effects in prestressed concrete bridges. The purpose of the research project was to enhance the prediction of bridge deflections and strains. This was achieved by the development of an on-site recalibration procedure by which a numerical model describing the development of time-dependent effects can be updated and improved during the construction process. The numerical technique has been developed and tested on prestressed concrete balanced cantilever and integrally constructed portal frame bridges.

The option value problem with two costs is written as a variational inequality. The advantage of this formulation is that it takes place in a fixed domain. Thus no front tracking is needed for numerical approximation of the free boundary. An iterative algorithm is proposed which can be used to solve the nonlinear system obtained by finite differences or finite elements procedures. Especial care has to be taken in the design of differences finites schemes o finite elements due to the degeneracy of the differential operator. These schemes can be absortion or convection dominated nearly to the axis. This is a preliminary note to the study of this kind of problems.

First a brief introduction about nonlinear analysis of structures and its implications on their design is given. Then a description of an already built structure, namely a cantilever roof for a toll station in the motorway Tarrasa-Manresa, composed by cables stiffened by prestressed is presented. The static analysis of the structure, that is modelled as a plan frame, is carried out in order to evaluate its response during the service and ultimate load states. In the assumed Ioading combinations the self weight, dead load, snow load and wind actions are included. The obtained results have been admissible in accordance to the design conditions and they have been in good agreement with the results found in the original design of the structure. In the initial design analysis the structure was modelled as a plane truss with stiffening bar effects due to the existence of traction forces.

Se describen someramente las características de diversos programas de intercambio de estudiantes universitarios, en particular del ERASMUS, el cual pronto va a ser sustituido por otro más amplio denominado SÓCRATES. También se van a comentar algunas posibles dificultades que pueden aparecer en el desarrollo de los mismos y finalmente se expondrán las conclusiones que de forma provisional ha extraído el autor a partir de su experiencia como actor en alguno de ellos, primeramente en la Universidad de Cantabria y más tarde en la Universidad Politécnica de Madrid. La información obtenida del Vicerrectorado de la UPM se reconoce con especial agradecimiento

In this paper a method for automatic design of the prestress in continuous bridge decks is presented. In a first step of the procedure the optimal prestressed force for a completely geometrically defined and feasible prestress layout is obtained by means of linear programming techniques. Further on, in a second step the prestress geometry and minimum force are automatically found by step descent optimization techniques. Finally this methodology is applied to two span continuous bridge decks and from the obtained results some preliminary design rules can be drawn.

Tras una breve introducción sobre la clasificación de los cálculos no lineales en estructuras y sus implicaciones en el diseño, se presenta una estructura ya construida, formada por cables rigidizados mediante pretensado y que corresponde a una marquesina de la autopista de Tarrasa-Manresa. El cálculo estático de la estructura, supuesto un entramado plano, se llevó a cabo con objeto de evaluar su respuesta para las situaciones de servicio y de carga última. Las hipótesis consideradas incluían las cargas de peso propio, carga permanente, nieve y viento. En el cálculo se tuvieron en cuenta los grandes desplazamientos, la rigidización de las barras por tracción y la no linealidad del material. Los resultados obtenidos han sido aceptables con las condiciones de diseño y concordantes con los deducidos en la fase de proyecto, en la que se calculó como una estructura celosía plana, con efectos rigidizantes en las barras, debidos a las tracciones.

Se plantea el problema de conseguir un método que, partiendo de una malla inicial en elementos finitos, genere una malla próxima a la óptima, conservando el mismo número de grados de libertad y, por consiguiente, sin penalizar los tiempos de análisis por ordenador. La bondad de una malla se mide por un funcional determinado (Energía Potencial Total, Error Cuadrático Medio, etc.) La Técnica de gradiente descendente, aplicada al funcional de Energía Potencial Total (1) permite, a partir de una inicial dada, obtener una malla mejorada. No obstante, este método requiere un esfuerzo de computación muy grande. Como consecuencia de la aplicación del método del gradiente descendente a numerosos casos, se ha observado que la geometría que adopta la malla mejorada, se aproxima a la de una malla tal que sus nudos se sitúen sobre las líneas isostáticas (envolventes de las tensiones principales) y generen elementos regulares (de lados iguales) o cuasirregulares. La conclusión más importante es, precisamente, que a partir de una malla inicial, razonablemente regular, se puede realizar un único análisis y definir las isostáticas correspondientes a este modelo. Ajustando una malla, con el mismo número de nudos que la inicial, a las líneas isostáticas con nudos situados de forma regular, se obtiene otra que está próxima a la óptima. A la malla así obtenida, se la denomina isostática isométrica. Esta conclusión se ha probado que es válida para los diferentes funcionales que se utilizan para evaluar la bondad de la malla en elementos finitos.

El artículo presenta una formulación sencilla que permite obtener los seis primeros períodos propios de vibración de una presa bóveda simétrica diseñada según las recomendaciones del U.S. Bureau of Reclamation. Se indican las expresiones polinómicas aproximadas de estos períodos, tanto para embalse vacío como para embalse lleno. El efecto del embalse se modeliza mediante la técnica de Westergaard modificada. Asimismo se indica una expresión que intenta tener en cuenta, de modo tentativo, el efecto de la flexibilidad del terreno

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.