Graphical limit state analysis
Application to statically indeterminate trusses, beams and masonry arches
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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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- Publisher
- Presses universitaires de Louvain
- Author
- Jean-François Rondeaux,
- Language
- English
- BISAC Subject Heading
- TEC021000 TECHNOLOGY & ENGINEERING / Materials Science
- BIC subject category (UK)
- TG Mechanical engineering & materials
- Onix Audience Codes
- 06 Professional and scholarly
- CLIL (Version 2013-2019)
- 3071 Génie civil
- Title First Published
- 22 May 2019
- Subject Scheme Identifier Code
- : Science des matériaux et procédés
Paperback
- Product Detail
- 1
- Publication Date
- 22 May 2019
- ISBN-13
- 9782875588050
- Extent
- Absolute page count : 166
- Code
- 98961
- Dimensions
- 16 x 24 cm
- Weight
- 275 grams
- Packaging Type
- No outer packaging
- List Price
- 46.00 €
- ONIX XML
- Version 2.1, Version 3
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Contents
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