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<TitleText>Thèses de l'Université catholique de Louvain (UCL)</TitleText>
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<BiographicalNote textformat="02" language="fre">&#60;p&#62;Shuyuan Han, born in China, is a researcher at the intersection of architecture and structural design. He received a Bachelor (2014) and a Master (2017) in Architecture from Chongqing University and Nanjing University, respectively. Since 2018, he has pursued doctoral research at UCLouvain under Professor Denis Zastavni, focusing on graphical methods for continuous beams and frames, and will obtain his PhD in 2025. As an architect, he has also contributed to award-winning projects, including the restoration of the Chinese Central Stadium Martial Arts Field and the Chinese Garden at the Louvre-Lens.&#60;/p&#62;</BiographicalNote> 
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<Text textformat="02" language="fre">&#60;p&#62;This dissertation revisits historical graphical methods for the elastic analysis of continuous beams and frames, a neglected branch of graphic statics. While graphic statics is celebrated for its clarity in axial-force systems, its application to flexural,&#60;br /&#62;
statically indeterminate structures has been largely overlooked. Between the late 19th and mid-20th centuries, several methods were developed, notably the fixed-points method and trial-closing-string methods, but they have mostly faded from practice and scholarship, and their potential for teaching and design remains unexplored.&#60;br /&#62;
This research reviews their historical development and rationale, focusing on the fixed-points and characteristic-points methods within the trial-closing-string family. Building on this, two graphical methods are proposed: Method I, an enhanced&#60;br /&#62;
characteristic-points method, and Method II, a synthesis of the fixed-points method and Method I, both providing a more intuitive, bidirectional representation of stiffness&#8211; moment relationships. They are accessible to architects and versatile for complex frame structures.&#60;br /&#62;
Within interactive parametric environments, the pedagogical and design potential is explored. Method I offers a dynamic graphical interpretation of classical displacementbased analysis, while Method II develops intuition for stiffness&#8211;moment relationships. Both methods support parametric feasibility assessment in structure design, offering greater transparency, real-time bidirectional control, and clearer geometric constraints than conventional finite element method&#8211;based tools.&#60;/p&#62;</Text>
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<Text language="fre">This dissertation revisits historical graphical methods for the elastic analysis of continuous beams and frames, a neglected branch of graphic statics. While graphic statics is celebrated for its clarity in axial-force systems, its application to flexural, statically indeterminate structures has been largely overlooked. Between the late 19th...</Text>
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<Text textformat="02" language="eng">&#60;p&#62;This dissertation revisits historical graphical methods for the elastic analysis of continuous beams and frames, a neglected branch of graphic statics. While graphic statics is celebrated for its clarity in axial-force systems, its application to flexural,&#60;br /&#62;
statically indeterminate structures has been largely overlooked. Between the late 19th and mid-20th centuries, several methods were developed, notably the fixed-points method and trial-closing-string methods, but they have mostly faded from practice and scholarship, and their potential for teaching and design remains unexplored.&#60;br /&#62;
This research reviews their historical development and rationale, focusing on the fixed-points and characteristic-points methods within the trial-closing-string family. Building on this, two graphical methods are proposed: Method I, an enhanced&#60;br /&#62;
characteristic-points method, and Method II, a synthesis of the fixed-points method and Method I, both providing a more intuitive, bidirectional representation of stiffness&#8211; moment relationships. They are accessible to architects and versatile for complex frame structures.&#60;br /&#62;
Within interactive parametric environments, the pedagogical and design potential is explored. Method I offers a dynamic graphical interpretation of classical displacementbased analysis, while Method II develops intuition for stiffness&#8211;moment relationships. Both methods support parametric feasibility assessment in structure design, offering greater transparency, real-time bidirectional control, and clearer geometric constraints than conventional finite element method&#8211;based tools.&#60;/p&#62;
&#60;p&#62;&#60;/p&#62;</Text>
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<Text language="eng">This dissertation revisits historical graphical methods for the elastic analysis of continuous beams and frames, a neglected branch of graphic statics. While graphic statics is celebrated for its clarity in axial-force systems, its application to flexural, statically indeterminate structures has been largely overlooked. Between the late 19th...</Text>
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<Text textformat="02">&#60;p&#62;CHAPTER 1 INTRODUCTION 1&#60;br /&#62;
1.1 Background  3&#60;br /&#62;
1.2 Problem statement and existing research  14&#60;br /&#62;
1.3 Objectives of the research  18&#60;br /&#62;
1.4 Organisation of the content  20&#60;br /&#62;
CHAPTER 2 THE PRECURSOR AND EMERGENCE OF CONTINUOUS BEAMS AND&#60;br /&#62;
FRAMES 23&#60;br /&#62;
2.1 The functions of continuous beams and frames  25&#60;br /&#62;
2.2 Knee-braced timber and cast-iron frames: the predecessors of rigid frames 28&#60;br /&#62;
2.3 The emergence of rigid frame and engineered continuous beam  42&#60;br /&#62;
2.4 Vierendeel girder: transition between rigid frame and continuous frames  84&#60;br /&#62;
2.5 The continuous frame full-fledged in both construction, function, and engineering 94&#60;br /&#62;
2.6 Summary 104&#60;br /&#62;
CHAPTER 3 A REVIEW OF THE FIXED-POINTS METHOD  107&#60;br /&#62;
3.1 The fixed-points method  109&#60;br /&#62;
3.2 The evolution of the fixed-points method  110&#60;br /&#62;
3.3 The theoretical foundation of fixed-points method  126&#60;br /&#62;
3.4 The principles and determination of the fixed points  132&#60;br /&#62;
3.5 The fixed-points method for continuous beams 140&#60;br /&#62;
3.6 The fixed-points method for continuous frames  146&#60;br /&#62;
3.7 Robert Maillart's application in the analysis of bridge frames  151&#60;br /&#62;
3.8 Discussion 157&#60;br /&#62;
3.9 Summary 159&#60;br /&#62;
CHAPTER 4 A REVIEW OF THE TRIAL-CLOSING-STRING METHODS  161&#60;br /&#62;
4.1 The trial-closing-string method 163&#60;br /&#62;
4.2 The history of the trial-closing-string method 164&#60;br /&#62;
4.3 The theoretical foundation of the trial-closing-string methods 170&#60;br /&#62;
4.4 Greene's semi-graphical method 175&#60;br /&#62;
4.5 Filder&#8217;s characteristic points method  178&#60;br /&#62;
4.6 Wolfe&#8217;s method 185&#60;br /&#62;
4.7 Comparison and discussion 192&#60;br /&#62;
4.8 Summary  196&#60;br /&#62;
CHAPTER 5 METHOD I &#8211; DEVELOPING CHARACTERISTIC-POINTS METHOD 199&#60;br /&#62;
5.1 The advantages and limitations of Filder&#8217;s characteristic points method  201&#60;br /&#62;
5.2 Enhancing the visual distinction of the characteristic points method diagram  204&#60;br /&#62;
5.3 The location of the characteristic points  207&#60;br /&#62;
5.4 The characteristic moment: formula, meaning, and sign  215&#60;br /&#62;
5.5 Applications for the analysis of structures  218&#60;br /&#62;
5.6 Reverse approach: deriving member stiffness from predefined inner force 233&#60;br /&#62;
5.7 Summary  236&#60;br /&#62;
CHAPTER 6 METHOD II &#8211; SYNTHESIZING FIXED-POINTS METHOD WITH METHOD I 241&#60;br /&#62;
6.1 Complementary potential of Method I and fixed-points method  243&#60;br /&#62;
6.2 Load-induced bending moment and its distribution  246&#60;br /&#62;
6.3 Bending moment induced by transverse displacement at joint  256&#60;br /&#62;
6.4 Reverse approach: deriving member stiffness from predefined bending moment 260&#60;br /&#62;
6.5 Comparison 262&#60;br /&#62;
6.6 Summary  267&#60;br /&#62;
CHAPTER 7 APPLICATION: EXPLORING THE PEDAGOGICAL RELEVANCE OF METHOD I AND II  269&#60;br /&#62;
7.1 Pedagogical potential of method I and II  271&#60;br /&#62;
7.2 Method I: interactive diagram for intuitively illustrating deflection methods  274&#60;br /&#62;
7.3 Method II: interactive diagram for intuitive stiffness-moment exploration  297&#60;br /&#62;
7.4 Summary and discussion  302&#60;br /&#62;
CHAPTER 8 APPLICATION: EXPLORING THE DESIGN RELEVANCE OF METHOD I AND II 305&#60;br /&#62;
8.1 Introduction  307&#60;br /&#62;
8.2 Implementing in a parameterized environment 311&#60;br /&#62;
8.3 Re-sizing of the L-frame of the Garstatt Bridge  315&#60;br /&#62;
8.4 Re-sizing the frame of the Weissensteinstrasse Overpass  322&#60;br /&#62;
8.5 Summary and discussion  327&#60;br /&#62;
CHAPTER 9 GENERAL CONCLUSION 329&#60;br /&#62;
9.1 Summary of results 330&#60;br /&#62;
9.2 Contributions 332&#60;br /&#62;
9.3 Limitations and future work  337&#60;br /&#62;
REFERENCES  341&#60;br /&#62;
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