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COM.ONIXSUITE.9782875588050 03 02 i6doc 01 SKU 98961 02 2875588052 03 9782875588050 15 9782875588050 02 01 00 BC 00 01 9.45 in 02 6.30 in 08 9.70 oz 01 24 cm 02 16 cm 08 275 gr BE 01 01 Graphical limit state analysis Application to statically indeterminate trusses, beams and masonry arches 1 A01 01 Onixsuite Contributor ID 20949 01 Onixsuite Contributor ID 6435 Jean-François Rondeaux Rondeaux, Jean-François Jean-François Rondeaux Jean-François Rondeaux graduated in 2006 from the School of Engineering of theUCLouvain (EPL) with a Master in Architectural Engineering. As practitioner in structural engineering, he has also been teaching at the Faculty of Architecture, Architectural Engineering, Urban planning (LOCI), where he conducted his research on graphical limit state analysis under the supervision of Prof. Denis Zastavni. 01 eng 07 166 03 10 TEC021000 12 TG 29 2012 3071 Génie civil 24 Science des matériaux et procédés 01 06 03 00 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. 02 00 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... 03 00 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. 02 00 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... 04 00 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 01 00 03 02 01 D502 02 2819 03 1878 06 1a1e28bb7683b47cfd2300ea11e1fa76 07 436731 https://i6doc.com/resources/titles/28001107715590/images/6f221fcb5c504fe96789df252123770b/HIGHQ/9782875588050.jpg 17 20190524T1209Z 02 01 D502 02 188 03 125 06 6aee842a8b752174419444e1d4dff987 07 20988 https://i6doc.com/resources/titles/28001107715590/images/6f221fcb5c504fe96789df252123770b/THUMBNAIL/9782875588050.jpg 17 20190524T1209Z 09 00 03 02 01 D502 https://i6doc.com/resources/publishers/35.jpg 10 00 03 02 01 D503 https://i6doc.com/resources/publishers/73.png 06 3052405007518 Presses universitaires de Louvain 01 01 Dilicom PULOUVAIN 06 3052405007518 Presses universitaires de Louvain 01 Presses universitaires de Louvain http://pul.uclouvain.be/ Louvain-la-Neuve BE 04 01 20190522 11 20190522 02 WORLD 02 01 GCOI 28001107715590 WORLD 04 03 06 3012405004818 CIACO - DUC 33 www.i6doc.com http://www.i6doc.com 01 2 20 1 02 00 02 02 STD 02 46.00 01 R 6.00 43.40 2.60 EUR