How To Do Seismic Analysis Using Finite Elements

Phil Cooper, Philip Hoby, Nawal Prinja

First Published November 2007
Softback, 86 Pages

Earthquake is only one of many hazards which must be considered in the design or assessment of structures and equipment. Successful seismic design relies not only on knowledge of the performance of the structure or plant under consideration but also requires a good understanding of the nature of earthquakes.

Modern Finite Element Analysis (FEA) software and hardware capabilities enable engineers to perform very sophisticated analyses, but this ability is no substitute for a sound understanding of the underlying classical engineering principals. FEA should not be seen as a panacea for safe design.

Structural analysis has become more sophisticated in recent years principally due to the availability of powerful computers rather than a perceived inadequacy of earlier simpler methods. Consequently, the analysis and design functions have tended to become separated, often performed by different people. There is a danger here that the analyst becomes more concerned with the analytical process rather than the ‘correct’ simulation of the structure. Separation of the analysis and design can lead to the analysis driving the design. In an ideal world the design and analysis would be done by the same person. Close collaboration of analyst and designer is a realistic compromise and is strongly encouraged.

Until the early 1980s the conventional approach to earthquake design was to use a quasi-static method to determine the dynamic effects of seismic loading. Dynamic analysis software is now commonplace and various forms of dynamic analysis are now the norm. The generalized approach to dynamic analysis is to develop a model of the structural system and impose a time dependant input motion based on measurements of real earthquake motions. There are many methods available to solve this problem, ranging from elastic response spectra methods to inelastic time history analysis incorporating soil structure interaction. Some models may need to account for soil behaviour, material non-linearity, geometric non-linear effects, high levels of damping and other complex behaviour. Thus seismic analysis presents a considerable challenge to the engineer.

Many advances in earthquake engineering have been made from the observation of the performance of real structures that have been subject to a severe earthquake. Analytical modelling, including FEA, has an important role, but its limitations must be recognized. For many engineered structures, satisfactory seismic performance requires careful attention to design, detailing and good construction practice. This is particularly so for buildings expected to undergo inelastic deformation. Safety is thus achieved by the successful integration of analysis, design and construction.

Given the wide range of assumptions and approximations in seismic design it is worth remembering the value of simple analytical approaches in helping gain an understanding of structural response.

Purpose

This book aims to provide practical guidance on the application of FEA to the seismic analysis of structures and equipment, and to inform the reader generally about seismic analysis.

The intended audience is the practicing engineer (and to a lesser degree engineering managers). It is assumed that the reader has some understanding and experience of seismic engineering and FEA.

Examples of actual applications of FEA to safety critical structures and plant are used to illustrate some of the techniques and guidelines given within this document.

There is much literature on the subject of FEA, including other NAFEMS publications, and there is an abundance of literature on the subject of seismic engineering. In particular, the reader is referred to ASCE 4-98 [Ref 1], and its successor document ASCE/SEI 43-05 [Ref 2].  Although geared to seismic analysis of safety related nuclear structures, this publication offers good practical guidance that is generally applicable to seismic analysis.

Scope

This document covers the basics of seismic analysis using FEA, including input motion, practical aspects of modelling, damping, analysis methods and results combination.  Modelling of inelastic behaviour of reinforced concrete structures is discussed, as is soil-structure interaction.

Contents

1        Introduction

1.1        General
1.2        Purpose
1.3        Scope
1.4        Document Layout

2        Glossary

Part I: General

3        Earthquakes and Seismic Response

4        Seismic Input

4.1        Equivalent Static Method
4.2        Response Spectra
4.3        Time Histories
4.4        Orientation of Input Motion
4.5        Subsystems

5        Modelling

5.1        General
5.2        Discretisation
5.3        Stiffness
5.4        Mass
5.5        Damping
5.6        Coupling

6        Analysis

6.1        Choice of Analysis Method

Part II: Modelling Techniques

7        Foundations and Soil Structure Interaction

7.1        Fixed Base Models
7.2        Equivalent Springs
7.3        Shear Beam Models
7.4        Finite Elements (Continua)
7.5        Specification of Boundary Motion
7.6        Soil Material Properties

8        Building Structures

8.1        General
8.2        Floors (Diaphragms)
8.3        Framed Structures
8.4        Walls
8.5        Reinforced Concrete Structures
8.6        In-filled Frames
8.7        Hysteretic Behaviour
8.8        Tanks
8.9        Dams
8.10     Base Isolated Structures

Part III: Examples

9        Examples

9.1        Analysis of a Cantilever Subject to Earthquake Motion
9.2        Response Spectra of a 3-D Frame Building
9.3        Seismic Analysis of a Concrete Gravity Dam
9.4        Seismic Assessment of GFRP Pipes

10          References