Finite Strip Analysis of Bridges

364 Pages·1996·13.615 MB·English

by  M.S. Cheung, W. Li, S.E. Chidiac

Finite Strip Analysis of Bridges
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Finite Strip Analysis
of Bridges
M.S. Cheung
Director, Ottawa-Carleton Bridge Research Institute
and
Adjunct Professor,
Department of Civil Engineering,
University of Ottawa,
Ottawa, Canada
W. Li
Post-Doctoral Fellow,
Department of Civil Engineering,
University of Ottawa,
Ottawa, Canada,
and
S.E. Chidiac
Research Officer,
Structures Laboratory,
Institute for Research in Construction,
National Research Council Canada,
Ottawa, Canada
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© 199 6 M.S. Cheung, W. Li and S.E. Chidiac
ISBN 0 41 9 1915 0 X
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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