Finite Element Design of Concrete Structures: A Practical Guide by G.A. Rombach
Finite element design of concrete structures is a book that aims to help structural engineers use computer software for the computational design of concrete structures. The book, written by G.A. Rombach, a professor of structural engineering at the Technical University of Hamburg-Harburg, Germany, covers various types of concrete structures, such as truss and beam structures, shell structures, slabs, and three-dimensional building models. The book also explains the general problems of numerical analysis of concrete structures, such as nonlinear material behavior, cracking, creep, shrinkage, and reinforcement detailing.
The book is based on the second edition of Finite-element Design of Concrete Structures: Practical problems and their solutions, published by ICE Publishing in 2011. The book is compatible with Eurocode 2 Part 1, the European standard for the design of concrete structures. The book contains numerous worked examples of real-life structures that show how to check numerical calculations and avoid errors in computational analysis. The worked examples are prepared using commonly available software systems, such as ANSYS, ABAQUS, and DIANA. The book also provides references to relevant literature and standards for further reading.
The book is intended for practicing structural engineers who use computer software for the design of concrete structures, as well as students of structural engineering who want to learn more about the finite element method and its applications. The book can also help software developers to appreciate the importance of practical understanding in addition to computer power. The book is available in PDF format from various online sources.
In this article, we will review some of the main topics covered in the book Finite Element Design of Concrete Structures by G.A. Rombach. We will also provide some examples of the code and output from the software systems used in the book.
Introduction to FEM
The finite element method (FEM) is a numerical technique for solving problems involving complex geometries, materials, and loads. The FEM divides the domain of interest into smaller subdomains called finite elements, which are connected by nodes. The behavior of each element is described by a set of equations that relate the displacements, strains, and stresses at the nodes. The equations for all the elements are assembled into a global system of equations that can be solved for the unknown nodal displacements. The strains and stresses at any point in the domain can then be computed from the nodal displacements using interpolation functions.
The FEM can handle various types of problems, such as linear or nonlinear, static or dynamic, elastic or plastic, and so on. The FEM can also model different types of boundary conditions, such as fixed supports, prescribed displacements, loads, and temperature changes. The FEM can also account for different types of material properties, such as isotropic or anisotropic, homogeneous or heterogeneous, and linear or nonlinear.
The FEM is widely used for the analysis and design of concrete structures, as it can capture the complex behavior of concrete and its interaction with reinforcement. However, the FEM also has some limitations and challenges, such as mesh generation, convergence, accuracy, stability, and computational cost. Therefore, it is important for the structural engineer to understand the basic principles and assumptions of the FEM, as well as its advantages and disadvantages.
Truss and beam structures
Truss and beam structures are common types of concrete structures that consist of slender members connected by joints. Truss structures are composed of axial members that carry only axial forces, while beam structures are composed of flexural members that carry both axial and bending forces. Truss and beam structures can be modeled by one-dimensional finite elements that have two nodes with two or three degrees of freedom (DOF) each. The DOF represent the translational or rotational displacements at the nodes.
The book Finite Element Design of Concrete Structures provides several examples of truss and beam structures, such as a simple truss bridge, a continuous beam bridge, a portal frame building, and a cable-stayed bridge. The book shows how to model these structures using different software systems, such as ANSYS, ABAQUS, and DIANA. The book also shows how to apply different types of loads and boundary conditions to these structures, such as dead loads, live loads, wind loads, temperature changes, support settlements, and prestressing forces. The book also shows how to check the results of the analysis for convergence, accuracy, and consistency.
For example, Figure 1 shows a simple truss bridge modeled by ANSYS. The bridge has a span of 30 m and a height of 6 m. The cross-sectional area of each member is 0.1 m2. The material properties are E = 30 GPa and Î = 0.2 for concrete. The bridge is subjected to a uniform load of 10 kN/m along its length. The bridge is supported by fixed supports at both ends.
Figure 1: Truss bridge modeled by ANSYS
The code for creating this model in ANSYS is shown below: