Computational Science, Engineering and Technology Series: 37

New Trendsin

Seismic Design of Structures

Computational Science, Engineering and Technology Series

Substructuring Techniques and Domain Decomposition MethodsEdited by: F. Magoules

Soft Computing in Civil and Structural EngineeringEdited by: B.H.V. Topping and Y. Tsompanakis

Tall Buildings: Design Advances for ConstructionEdited by: J.W. Bull

Computational Methods for Engineering TechnologyEdited by: B.H.V. Topping and P. Ivanyi

Computational Methods for Acoustics ProblemsEdited by: F. Magoules

Computational Mechanics using High Performance ComputingEdited by: B.H.V. Topping

High Performance Computing for Computational MechanicsEdited by: B.H.V. Topping, L. Lammer

Parallel and Distributed Processing for Computational Mechanics:Systems and ToolsEdited by: B.H.V. Topping

Saxe-Coburg Publications:

Programming Distributed Finite Element Analysis:An Object Oriented ApproachR.I. Mackie

Object Oriented Methods and Finite Element AnalysisR.I. Mackie

Domain Decomposition Methods for Distributed ComputingJ. Kruis

Computer Aided Design of Cable-Membrane StructuresB.H.V. Topping and P. Ivanyi

New Trendsin

Seismic Design of Structures

Edited byN.D. Lagaros, Y. Tsompanakis and M. Papadrakakis

Saxe-Coburg Publications, Stirlingshire, Scotland

published 2015 bySaxe-Coburg PublicationsDun EaglaisStation Brae, KippenStirlingshire, FK8 3DY, UK

Saxe-Coburg Publications is an imprint of Civil-Comp Ltd

Computational Science, Engineering and Technology Series: 37ISSN 1759-3158ISBN 978-1-874672-37-1

British Library Cataloguing in Publication DataA catalogue record for this book is available from the British Library

Printed in Great Britain by Bell & Bain Ltd, Glasgow

Contents

Preface xi

1 Fundamental Properties of Earthquake Input Energy on Single andConnected Building Structures 1I. Takewaki1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Earthquake Input Energy to SDOF Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Constancy of Earthquake Input Energy Based on Time-domain

Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4 Proportionally Damped MDOF Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.5 Connected Buildings (Connected SDOF Models) . . . . . . . . . . . . . . . . . . . . . . . 61.6 Earthquake Input Energy to Connected MDOF Models as Sum of

Input Energies to Subassemblages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.7 Advantageous Features of Frequency-Domain Method (Bound

Estimate) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.7.1 Energy Bound Estimate for Single Buildings (Acceleration-

Velocity Controlled Regions) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.7.2 Energy Bound Estimate for Connected Buildings . . . . . . . . . . . . . . . . 14

1.8 Numerical Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151.8.1 Single-Storey Connected Buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151.8.2 Five-Storey Connected Buildings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181.8.3 Energy Transfer Functions of Single Tall Buildings with and

without Passive Dampers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211.8.4 Velocity Power-Input Energy Relation under Resonant

Sinusoidal Ground Motions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2 Practical Methods for Uncertainty Analysis in Seismic Design 29J.E. Hurtado2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.2 Robust and Reliability-Based Design Options . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

i

2.3 Stochastic Models of Seismic Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332.4 Fundamentals of Random Vibration Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 372.5 Practical Computation of Seismic Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

2.5.1 Moments of Maximum Response. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.5.2 Unconditional Moments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

2.6 Practical Computation of Seismic Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452.6.1 Improving Estimates with the Total Probability Theorem . . . . . . . . 462.6.2 Backward Stratified Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482.6.3 Application to a Base Isolated Building . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

2.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3 Spatial Variability of Earthquake Ground Motion and its Implicationsfor the Dynamic Response of Extended Structures 59A.G. Sextos3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603.2 An Overview of the State-of-the-Art and Practice . . . . . . . . . . . . . . . . . . . . . . . 61

3.2.1 Recent Studies on the Effect of Asynchronous Excitation . . . . . . . 613.2.2 Current Code Provisions and Guidelines . . . . . . . . . . . . . . . . . . . . . . . . . . 623.2.3 Standards and Guidelines Focussing on Seat-Lengths. . . . . . . . . . . . 623.2.4 Eurocode 8 - Part 2 Provisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

3.3 Structure of the Procedure Adopted . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653.3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653.3.2 Step 1: Spatial Variability of Earthquake Ground Motion. . . . . . . . 653.3.3 Step 2: Site Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 703.3.4 Step 3: Soil-Structure Interaction Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . 713.3.5 Step 4: Inelastic Dynamic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

3.4 Overview of the Parametric Analysis Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . 763.5 Impact of Analysis and Design Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 803.6 Asynchronous Seismic Excitation of Extended Byzantine City Walls . 82

3.6.1 Finite Element Modelling of the Wall Section . . . . . . . . . . . . . . . . . . . . 833.6.2 Dynamic Characteristics of the Walls under Study . . . . . . . . . . . . . . . 843.6.3 Seismic Response of Land Walls under Study in the Time

Domain under Synchronous Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . 853.6.4 Seismic Response of Land Walls under Study in the Time

Domain under Asynchronous Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . 863.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

4 SeismologicallyConsistent Stochastic Response Spectra 95S. Sgobba, C.G. Marano, P.J. Stafford and R. Greco4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 964.2 Summary of Previous Work in this Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

ii

4.3 Construction of SSRS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1024.4 Earthquake Ground-Motion Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

4.4.1 Stochastic Simulation of Seismologically ConsistentEarthquake Records . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1054.4.1.1 Deterministic Envelope Function . . . . . . . . . . . . . . . . . . . . . . . 107

4.5 Methodology for SSRS Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1114.5.1 Response Covariance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1124.5.2 Evaluation of Peak Response by Threshold Crossings Theory . . 1154.5.3 Maximum Response Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1184.5.4 Numerical Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

4.6 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1244.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

5 Probabilistic Assessment of the Seismic Performance of Steel BuildingsDesigned According to the LRFD Specification 133C.A. Bermudez, J.E. Hurtado, L.G. Pujades