Finite Element Analysis for Building Assessment

Advanced Use and Practical Recommendations

Paulo B. Lourenço, Angelo Gaetani

• Publisher: Routledge
• Year: 2022
• eBook ISBN: 9781000563146
• Edition: 1
• Topic: Architecture
• Subtopic: Architecture Methods & Materials

Existing structures represent a heterogeneous category in the global built environment as often characterized by the presence of archaic materials, damage and disconnections, uncommon construction techniques and subsequent interventions throughout the building history. In this scenario, the common linear elastic analysis approach adopted for new buildings is incapable of an accurate estimation of structural capacity, leading to overconservative results, invasive structural strengthening, added intervention costs, excessive interference to building users and possible losses in terms of aesthetics or heritage values. For a rational and sustainable use of the resources, this book deals with advanced numerical simulations, adopting a practical approach to introduce the fundamentals of Finite Element Method, nonlinear solution procedures and constitutive material models. Recommended material properties for masonry, timber, reinforced concrete, iron and steel are discussed according to experimental evidence, building standards and codes of practice. The examples examined throughout the book and in the conclusive chapter support the analyst's decision-making process toward a safe and efficient use of finite element analysis.

Written primarily for practicing engineers, the book is of value to students in engineering and technical architecture with solid knowledge in the field of continuum mechanics and structural design.

Chapter 1 Fundamentals of the finite element method

DOI: 10.1201/9780429341564-1

Introduction

This chapter provides a brief description of the Finite Element Method (FEM) in the framework of linear elasticity. This type of problem includes two assumptions: small displacements (with respect to the characteristic dimensions of the body) and a linear elastic stress–strain relationship (meaning that the relations between stresses and strains are given by a fixed set of constants; these relations are univocal, with no dependence on the load path). In practice, the first assumption states that geometrical changes after load application to the body are so small that they may be neglected, while the second assumption means that the effects of different loads can be superimposed on each other. In this framework, a linear proportion between causes and effects holds, as first stated in 1675 by Robert Hooke (1635–1703) by means of a succinct Latin anagram standing for “ut tensio, sic vis”, i.e. “as the extension, so the force”. Basically, if the external load (understood as a point load or the full set of forces applied to a body) doubles, so do the effects, namely, displacements, strains and stresses. Although linear elasticity is a simplification with respect to the goal of the book, which is nonlinear analysis, linear elasticity allows a simple presentation of the FEM, providing the basis for further insight discussed in the next chapters. Here, applications of FEM to simple problems are also discussed and verified with respect to theoretical considerations.

1.1 Equilibrium of a three-dimensional body in elasticity

In the analysis of quasi-static problems (i.e. when inertia effects can be neglected and quantities are allowed to vary only slowly in time), the goal of structural engineering can be summarized as follows:

For a given system of body forces b and surface tractions t, imposed displacements u_S, initial strains ε₀ (with no evident relation with stress, e.g. temperature change or shrinkage) and initial (residual) stresses σ₀ applied to a constrained structure of a certain geometry and materials, calculate the compatible displacement field u and strain state ε, as well as the equilibrated stress state σ and constraint reactions r.

This statement can be applied to the masonry bridge shown on the left of Figure 1.1. Its geometrical schematization, depicted on the right, highlights the physical quantities involved in the problem. In particular, body forces b are...

Table of contents

• Cover
• Half Title Page
• Title Page
• Copyright Page
• Table of Contents
• Foreword
• Preface
• Authors
• 1 Fundamentals of the finite element method
• 2 Nonlinear structural analysis
• 3 Constitutive models
• 4 Recommended properties for advanced numerical analysis
• 5 Guidelines for practical use of nonlinear finite element analysis
• Index