Graphical limit state analysis
Application to statically indeterminate trusses, beams and masonry arches
Première édition
The art of structural design requires specific methods and tools. One of those consists in modelling the structural behaviour through a network of straight bars, whether in compression (struts) or in tension (ties), and in expressing its static equilibrium through classic graphic statics reciprocal diagrams... Lire la suite
The art of structural design requires specific methods and tools. One of those consists
in modelling the structural behaviour through a network of straight bars, whether
in compression (struts) or in tension (ties), and in expressing its static equilibrium
through classic graphic statics reciprocal diagrams: a form diagram describing the
geometry of a strut-and-tie network and a force diagram representing the vector
equilibrium of its nodes.
When it comes to statically indeterminate structures, the lower-bound theorem of
Plasticity avoids any overestimation of the load bearing capacity, which allows the
designer to select one of the possible equilibrium states.
Considering that a limit state analysis of these indeterminate equilibriums can better
support the design process when it shares the same graphical environment, the thesis
consists in proposing a graphical methodology for constructing a parametric force
diagram resulting from the combination of independent force diagrams. The stress
distribution is then modified by manipulating the relative position of some vertices
of the force diagram until it reaches limit states; hence, the possibility of identifying
the collapse state and the corresponding load bearing capacity of various types of
structures such as pin-jointed trusses, beams or masonry arches.
The analysis of the admissible geometrical domains for these specific vertices allows
a better understanding of the behaviour of statically indeterminate structures at
limit state and may be helpful when designing them.
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Spécifications
- Éditeur
- Presses universitaires de Louvain
- Auteur
- Jean-François Rondeaux,
- Collection
- Thèses de la Faculté d'architecture, d'ingénierie architecturale, d'urbanisme
- Langue
- anglais
- Catégorie (éditeur)
- Sciences appliquées > Science des matériaux et procédés
- BISAC Subject Heading
- TEC021000 TECHNOLOGY & ENGINEERING / Materials Science
- BIC subject category (UK)
- TG Mechanical engineering & materials
- Code publique Onix
- 06 Professionnel et académique
- CLIL (Version 2013-2019 )
- 3071 Génie civil
- Date de première publication du titre
- 22 mai 2019
- Type d'ouvrage
- Thèse
Livre broché
- Date de publication
- 22 mai 2019
- ISBN-13
- 978-2-87558-805-0
- Ampleur
- Nombre de pages de contenu principal : 166
- Dépôt Légal
- D/2019/9964/19 Louvain-la-Neuve, Belgique
- Code interne
- 98961
- Format
- 16 x 24 cm
- Poids
- 275 grammes
- Type de packaging
- Aucun emballage extérieur
- Prix
- 46,00 €
- ONIX XML
- Version 2.1, Version 3
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Sommaire
Introduction 21
1 Plastic design and limit state analysis 27
1.1 Structural design and analysis . . . . . . . . . . . . . . . . 27
1.2 Theory of Plasticity . . . . . . . . . . . . . . . . . . . . . 29
1.3 Fundamental theorems of Plasticity . . . . . . . . . . . . . 32
1.4 Limit state analysis . . . . . . . . . . . . . . . . . . . . . . 35
1.4.1 Kinematic versus geometric views of statics . . . . 35
1.4.2 Kinematic approaches and upper-bound theorem . 38
1.4.3 Static approaches and lower-bound theorem . . . . 42
1.4.4 Complete limit state analysis . . . . . . . . . . . . 43
1.5 Plastic design . . . . . . . . . . . . . . . . . . . . . . . . . 45
2 Strut-and-tie modelling using graphic statics 51
2.1 Strut-and-tie networks for structural analysis and design . 51
2.2 Classical graphic statics . . . . . . . . . . . . . . . . . . . 54
2.2.1 From parallelogram of forces to form and force diagrams
. . . . . . . . . . . . . . . . . . . . . . . . . 54
2.2.2 Graphical analysis through reciprocal diagrams . . 56
2.2.3 Elasticity and static indeterminacy . . . . . . . . . 59
2.3 Graphical tools for interactive structural design . . . . . . 64
3 Reciprocal diagrams and static indeterminacy 69
3.1 Static indeterminacy in structural design . . . . . . . . . . 69
3.2 Static indeterminacy as a combination of independent stress
states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.3 Geometrical freedom of force diagrams . . . . . . . . . . . 77
3.4 Limit state analysis using reciprocal diagrams . . . . . . . 82
3.5 Designing with indeterminate force diagrams . . . . . . . 89
4 Pin-jointed trusses 95
4.1 Working hypotheses . . . . . . . . . . . . . . . . . . . . . 95
4.2 Complete graphical limit state analysis . . . . . . . . . . . 96
4.3 Optimization procedure on the force diagram . . . . . . . 105
4.4 Case studies: internally and externally statically indeterminate
trusses . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.5 Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . 117
17
5 Beams 123
5.1 Bending and funicular polygons . . . . . . . . . . . . . . . 123
5.2 Statically admissible limit states of funiculars polygons . . 129
5.3 Admissible geometrical domains . . . . . . . . . . . . . . . 137
5.4 Case studies: statically indeterminate beams . . . . . . . 156
6 Masonry arches 167
6.1 Kinematic and static methods for structural assessment of
masonry arches: a short overview . . . . . . . . . . . . . . 167
6.2 Conciliating lower bound theorem and thrust line theory:
the equilibrium approach . . . . . . . . . . . . . . . . . . 176
6.3 Admissible geometrical domains . . . . . . . . . . . . . . . 178
6.4 Graphical safety of masonry arches . . . . . . . . . . . . . 187
6.4.1 Stability under self-weight . . . . . . . . . . . . . . 189
6.4.2 Stability related to the abutments . . . . . . . . . 195
6.5 Current work and perspectives . . . . . . . . . . . . . . . 196
Conclusion 201
List of Figures 205
References 225