Finite Strip Analysis of Bridges JOIN US ON THE INTERNET VIA WWW, GOPHER, FTP OR EMAIL: WWW: http://www.thomson.com GOPHER: gopher.thomson.com ^ servjc e FTP: ftp.thomson.com w EMAIL: [email protected] OTHER BOOKS ON STRUCTURES FRO M E & FN SPO N Aluminium Alloy Structures F. M. Mazzolani Alternative Materials for the Reinforcement and Prestressing of Concrete Edited by J.L. Clark e Bridge Bearings and Expansion Joints D. J. Lee Bridge Deck Behaviour E. C. Hambl y Bridge Management 3 Edited by J. Harding, G.A.R. Parke and M.J. Ryall Building the Future Innovation in design, materials and construction Edited by F. K. Garas, G. S. T. Armer and J. L. Clarke Computer Methods in Structural Analysis J. L. Meek Concrete Structure s Stresses and deformation s A. Ghali and R. Favre Concrete under Severe Condition s Environment and loading Edited by K. Sakai, N. Banthia and O.E. Gjorv Constructional Steel Desig n An international guide Edited by P. J. Dowling, J. E. Harding and R. 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Chidiac Research Officer, Structures Laboratory, Institute for Research in Construction, National Research Council Canada, Ottawa, Canada m E & FN SPON An Imprint of Chapman & Hall London • Weinheim • New Yor k • Tokyo • Melbourne • Madras Published by E & FN Spon, an imprint of Chapman & Hall, 2-6 Boundary Row, London SE1 8HN, UK Chapman & Hall, 2-6 Boundary Row, London SE1 8HN, UK Chapman & Hall GmbH, Pappelallee 3, 69469 Weinheim, Germany Chapman & Hall USA, 115 Fifth Avenue, New York, NY 10003, USA Chapman & Hall Japan, ITP-Japan, Kyowa Building, 3F, 2-2-1 Hirakawacho, Chiyoda-ku, Tokyo 102, Japan Chapman & Hall Australia, 102 Dodds Street, South Melbourne, Victoria 3205, Australia Chapman & Hall India, R. Seshadri, 32 Second Main Road, CIT East, Madras 600 035, Indi a First edition 199 6 © 199 6 M.S. Cheung, W. Li and S.E. 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A catalogue record for this book is available from the British Library To our families Contents Preface x i Notation xii i Part I Mathematica l Approac h 1 1 Introductio n 3 1.1 Bridg e analysis by refined methods 3 1.2 Developmen t o f the finite stri p method 5 1.3 Readin g suggestion s 7 2 Basi c concepts of numerica l method s 9 2.1 Introductio n 9 2.2 Proble m formulatio n 1 0 2.3 Direc t approach 1 3 2.4 Variationa l method 1 5 2.5 Weighte d residual metho d 2 7 2.6 Finit e element method 3 1 2.7 Convergenc e requirements fo r interpolation functions 3 2 2.8 Generalize d procedur e for a finite elemen t solution 3 3 2.9 Finit e strip method 3 6 3 Numerica l error s 3 7 3.1 Introductio n 3 7 3.2 Definitio n of computational error s 3 8 3.3 Assessin g computational error s 3 9 3.4 Assessin g discretization errors 4 1 3.5 Concludin g remarks 4 9 Part I I Finit e Stri p Method 5 1 4 Finit e strip metho d 5 3 4.1 Introductio n 5 3 4.2 Energ y approac h for a simple beam 5 4 viii Contents 4.3 Plat e strip 5 6 4.4 Plan e stress strip 6 9 4.5 Fla t shell strip 7 5 4.6 Boundar y condition s alon g nodal lines 7 8 4.7 Continuou s structures : flexibility approac h 8 0 4.8 Continuou s structures : stiffnes s approac h 8 1 4.9 Numerica l examples 8 4 5 Highe r orde r finit e strip s 9 1 5.1 Introductio n 9 1 5.2 Plat e strip H02 wit h curvatur e continuit y 9 1 5.3 Plat e strip H03 wit h a n internal nodal line 9 3 5.4 Plan e stress strip H03 9 7 5.5 Fla t shell strip H03 9 9 5.6 Choic e of approach 9 9 5.7 Numerica l examples 9 9 6 Splin e finit e stri p metho d 10 5 6.1 Introductio n 10 5 6.2 Splin e function interpolation 10 7 6.3 Fla t shell spline finite strip 10 9 6.4 Analysi s of arbitrarily shaped plates 11 2 7 Compoun d stri p metho d 12 1 7.1 Introductio n 12 1 7.2 Rectangula r compoun d stri p 12 2 7.3 Rectangula r B-splin e compound stri p 12 6 7.4 Numerica l examples 12 7 8 Finit e laye r method ; finit e pris m metho d 13 3 8.1 Introductio n 13 3 8.2 Finit e layer method 13 4 8.3 Finit e prism method 13 6 8.4 Circularl y curved finite prism 14 1 8.5 Numerica l examples 14 2 9 Vibratio n and stabilit y analyse s 14 9 9.1 Introductio n 14 9 9.2 Vibratio n finite strip analysis 14 9 9.3 Mas s matrix of a finite strip 15 0 9.4 Mas s matrix of a plate stri p 15 1 9.5 Mas s matrix of a plane stress strip 15 2 9.6 Mas s matrix of a flat shel l strip 15 2 9.7 Bendin g and in-plan e interaction 15 3 Contents i x 9.8 Stabilit y analysis of plates 15 5 9.9 Stabilit y analysis of thin-walled structures 15 5 9.10 Numerica l examples 15 7 10 Nonlinea r analysi s 16 7 10.1 Introduction 16 7 10.2 Nonlinea r solution procedure 16 7 10.3 Elastoplasti c analysis 17 1 10.4 Analysi s of reinforced concrete slabs 18 0 10.5 Geometricall y nonlinear analysis 19 0 11 Combine d analysis 20 3 11.1 Introduction 20 3 11.2 Combine d FS/FE analysi s of irregular plates 20 4 11.3 Combine d FS/BE analysis of irregular plates 20 9 11.4 Combine d BE/FS analysi s of slab girder bridges 21 3 Part II I Finit e Strip Analysis of Bridges 22 3 12 Sla b and slab-on-girder bridge s 22 5 12.1 Introduction 22 5 12.2 Stiffnes s matri x of a longitudinal beam 22 6 12.3 Deformatio n and settlement o f support 22 8 12.4 Numerica l examples 22 8 13 Curve d an d skewe d bridge s 24 1 13.1 Introduction 24 1 13.2 Circularl y curved plate strip 24 1 13.3 Curve d compound strip 24 4 13.4 Curve d strip for box bridges 24 7 13.5 Skewe d plate strip 25 0 13.6 Analysi s of skewed box girder bridges 25 2 13.7 Numerica l examples 25 2 14 Bo x girde r bridges 26 3 14.1 Introduction 26 3 14.2 Elasti c properties of constituent plates 26 4 14.3 Intermediat e supports an d diaphragm 26 6 14.4 Prestressin g force s 27 0 14.5 Loca l bending moment 27 2 14.6 Numerica l examples 27 3 15 Continuou s haunched bridge s 289 15.1 Introduction 289