Design of Reinforcement in Concrete Shells: a unified Approach

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.

Dimensionamento e análise numérica de cascas de concreto armado para aplicações em plataformas offshore

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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.

Computer analysis and design of concrete shell roofs

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 methodology to calibrate structural finite element models for reinforced concrete structures subject to blast loads

Civil buildings are not specifically designed to support blast loads, but it is important to take into account these potential scenarios because of their catastrophic effects, on persons and structures. A practical way to consider explosions on reinforced concrete structures is necessary. With this objective we propose a methodology to evaluate blast loads on large concrete buildings, using LS-DYNA code for calculation, with Lagrangian finite elements and explicit time integration. The methodology has three steps. First, individual structural elements of the building like columns and slabs are studied, using continuum 3D elements models subjected to blast loads. In these models reinforced concrete is represented with high precision, using advanced material models such as CSCM_CONCRETE model, and segregated rebars constrained within the continuum mesh. Regrettably this approach cannot be used for large structures because of its excessive computational cost. Second, models based on structural elements are developed, using shells and beam elements. In these models concrete is represented using CONCRETE_EC2 model and segregated rebars with offset formulation, being calibrated with continuum elements models from step one to obtain the same structural response: displacement, velocity, acceleration, damage and erosion. Third, models basedon structural elements are used to develop large models of complete buildings. They are used to study the global response of buildings subjected to blast loads and progressive collapse. This article carries out different techniques needed to calibrate properly the models based on structural elements, using shells and beam elements, in order to provide results of sufficient accuracy that can be used with moderate computational cost.

Dynamic analysis of translational shells

This paper presents a Levy-type solution for the natural frequencies of translational shells. A computer program in FORTRAN IV language corresponding to this solution is described. This direct solution is compared with some indirect solutions utilising Galerkin and Rayleigh methods. An extension to the study of forced vibrations is outlined.

A Unique Prestressed Concrete Pedestrian Bridge in Spain

This paper describes the so-called Kiss Bridge. This structure resembles a kiss, a subtle touch of structures. The beams have been structurally designed to adapt the Japanese art of paper folding called "origami." The material used for constructing the floating beams is white reinforced concrete in the form of folded shells. The two geometrically different parts have distinct structural behaviors. The length of the main pathway of both structures is over 60 m. The pedestrian bridge crosses an artificial rainwater channel with a skew of 45° with respect to the referred channel. The joint between the cantilever structure and the Y-shaped one is located over the middle of the channel. Each stretch has different transversal sections. The pedestrian bridge is made with prestressed self-compacting reinforced concrete of 60 MPa. The foundation is shallow, comprising footings and footing beams made of 25 MPa conventional concrete. The cantilever structure with its foundations is designed as a semi-integral bridge whereas the Y-shaped one is an integral structure. The dynamic behavior of the structure was carefully studied to ensure that the dynamic loads generated by pedestrians do not cause excessive vibrations, especially to the cantilever structure, which could present dynamic interactions with the pedestrians walking. The bridge was recognized, in the 2014 edition of the fib Awards for Outstanding Concrete Structures, for having made a valuable contribution to the image and promotion of concrete structures.

The application of expert systems techniques in the design of durable concrete

This thesis describes work done exploring the application of expert system techniques to the domain of designing durable concrete. The nature of concrete durability design is described and some problems from the domain are discussed. Some related work on expert systems in concrete durability are described. Various implementation languages are considered - PROLOG and OPS5, and rejected in favour of a shell - CRYSTAL3 (later CRYSTAL4). Criteria for useful expert system shells in the domain are discussed. CRYSTAL4 is evaluated in the light of these criteria. Modules in various sub-domains (mix-design, sulphate attack, steel-corrosion and alkali aggregate reaction) are developed and organised under a BLACKBOARD system (called DEX). Extensions to the CRYSTAL4 modules are considered for different knowledge representations. These include LOTUS123 spreadsheets implementing models incorporating some of the mathematical knowledge in the domain. Design databases are used to represent tabular design knowledge. Hypertext representations of the original building standards texts are proposed as a tool for providing a well structured and extensive justification/help facility. A standardised approach to module development is proposed using hypertext development as a structured basis for expert systems development. Some areas of deficient domain knowledge are highlighted particularly in the use of data from mathematical models and in gaps and inconsistencies in the original knowledge source Digests.

BENEFICIAL REUSE OF LOCALLY-AVAILABLE WASTE MATERIALS AS LIGHTWEIGHT AGGREGATE IN LIGHTWEIGHT CONCRETE

This study investigated the physical characteristics of lightweight concrete produced using waste materials as coarse aggregate. The study was inspired by the author’s Peace Corps service in Kilwa, Tanzania. Coconut shell, sisal fiber, and PET plastic were chosen as the test waste products due to their abundance in the area. Two mixes were produced for each waste product and the mix proportions designed for resulting compressive strengths of 3000 and 5000 psi. The proportions were selected based on guidelines for lightweight concrete from the American Concrete Institute. In preparation for mixing, coconut shells were crushed into aggregate no larger than 3/4 inch, sisal fiber was cut into pieces no longer than 3/8 inch, and PET plastic was shredded into 1/4 inch-wide strips no longer than 6 inches. Replicate samples were mixed and then cured for 28 days before they were tested for compressive strength, unit weight, and absorption. The resulting data were compared to ASTM Standards for lightweight concrete masonry units to determine their adequacy. Based on these results, there is potential for coconut shell to be used as coarse aggregate in lightweight concrete. Sisal fiber was unsuccessful in producing the appropriate compressive strength. However, the reduction in spalling of the hardened concrete and the induction of air in the mixes incorporating sisal fiber suggests that it has the potential to improve other characteristics of lightweight concrete. Concrete mixes using PET plastic as aggregate resulted in adequate compressive strengths, but were too dense to be considered ‘lightweight’ concrete. With some adjustments to slightly decrease absorption and unit weight, the PET plastic concrete mixes could be classified as medium weight concrete and, therefore, achieve many of the same benefits as would be seen with lightweight concrete.

High performance concrete applied to storage system buildings at low temperatures

According to some estimates, world's population growth is expected about 50% over the next 50 years. Thus, one of the greatest challenges faced by Engineering is to find effective options to food storage and conservation. Some researchers have investigated how to design durable buildings for storing and conserving food. Nowadays, developing concrete with mechanical resistance for room temperatures is a parameter that can be achieved easily. On the other hand, associating it to low temperature of approximately 35 °C negative requires less empiricism, being necessary a suitable dosage method and a careful selection of the material constituents. This ongoing study involves these parameters. The presented concrete was analyzed through non-destructive tests that examines the material properties periodically and verifies its physical integrity. Concrete with and without incorporated air were studied. The results demonstrated that both are resistant to freezing.

Unconstrained Finite Element for Geometrical Nonlinear Dynamics of Shells

This paper presents a positional FEM formulation to deal with geometrical nonlinear dynamics of shells. The main objective is to develop a new FEM methodology based on the minimum potential energy theorem written regarding nodal positions and generalized unconstrained vectors not displacements and rotations. These characteristics are the novelty of the present work and avoid the use of large rotation approximations. A nondimensional auxiliary coordinate system is created, and the change of configuration function is written following two independent mappings from which the strain energy function is derived. This methodology is called positional and, as far as the authors' knowledge goes, is a new procedure to approximated geometrical nonlinear structures. In this paper a proof for the linear and angular momentum conservation property of the Newmark beta algorithm is provided for total Lagrangian description. The proposed shell element is locking free for elastic stress-strain relations due to the presence of linear strain variation along the shell thickness. The curved, high-order element together with an implicit procedure to solve nonlinear equations guarantees precision in calculations. The momentum conserving, the locking free behavior, and the frame invariance of the adopted mapping are numerically confirmed by examples. Copyright (C) 2009 H. B. Coda and R. R. Paccola.

A positional FEM Formulation for geometrical non-linear analysis of shells

This work presents a fully non-linear finite element formulation for shell analysis comprising linear strain variation along the thickness of the shell and geometrically exact description for curved triangular elements. The developed formulation assumes positions and generalized unconstrained vectors as the variables of the problem, not displacements and finite rotations. The full 3D Saint-Venant-Kirchhoff constitutive relation is adopted and, to avoid locking, the rate of thickness variation enhancement is introduced. As a consequence, the second Piola-Kirchhoff stress tensor and the Green strain measure are employed to derive the specific strain energy potential. Curved triangular elements with cubic approximation are adopted using simple notation. Selected numerical simulations illustrate and confirm the objectivity, accuracy, path independence and applicability of the proposed technique.

Parametric model for the analysis of concrete expansion due to alkali-aggregate reaction

The alkali-aggregate reaction (AAR) is a chemical reaction that provokes a heterogeneous expansion of concrete and reduces important properties such as Young's modulus, leading to a reduction in the structure's useful life. In this study, a parametric model is employed to determine the spatial distribution of the concrete expansion, combining normalized factors that influence the reaction through an AAR expansion law. Optimization techniques were employed to adjust the numerical results and observations in a real structure. A three-dimensional version of the model has been implemented in a finite element commercial package (ANSYS(C)) and verified in the analysis of an accelerated mortar test. Comparisons were made between two AAR mathematical descriptions for the mechanical phenomenon, using the same methodology, and an expansion curve obtained from experiment. Some parametric studies are also presented. The numerical results compared very well with the experimental data validating the proposed method.

Dynamical Casimir effect for a massless scalar field between two concentric spherical shells with mixed boundary conditions

In this work we analyze the dynamical Casimir effect for a massless scalar field confined between two concentric spherical shells considering mixed boundary conditions. We thus generalize a previous result in literature [Phys. Rev. A 78, 032521 (2008)], where the same problem is approached for the field constrained to the Dirichlet-Dirichlet boundary conditions. A general expression for the average number of particle creation is deduced considering an arbitrary law of radial motion of the spherical shells. This expression is then applied to harmonic oscillations of the shells, and the number of particle production is analyzed and compared with the results previously obtained under Dirichlet-Dirichlet boundary conditions.