Arches, nonlinear? PDF
Preview Arches, nonlinear?
Arches, nonlinear? Investigating the geometrically nonlinear behaviour of arches in 2D MSc Thesis Ruben Onstein May 2013 Cover illustration: Nijmegen City bridge (source: BAM Infraconsult bv) Arches, nonlinear? Investigating the geometrically nonlinear behaviour of arches in 2D. Thesis submitted to Delft University of Technology for the degree of Master of Science. May 2013 Author: ing. R.C.P. (Ruben) Onstein E-mail: [email protected] Delft University of Technology Faculty: Civil Engineering and Geosciences Department: Structural Engineering Section: Concrete Structures Master’s thesis committee Chairman Prof.dr.ir. J.G.Rots TU Delft – Structural Mechanics Committee members Dr.ir. P.C.J. Hoogenboom TU Delft – Structural Mechanics Dr.ir. M.A.N. Hendriks TU Delft – Structural Mechanics Dr.ir. C. van der Veen TU Delft – Concrete Structures T. Wolvekamp MSc BAM Infraconsult bv Secretary Ir. L.J.M. Houben TU Delft – Road and railway engineering Geometrically nonlinear behaviour of arches in 2D MSc Thesis Contents – general overview Contents – general overview Part 0 – Extended Summary 1. Introduction to Part 0 1 2. Results and Conclusions 4 3. Recommendations for design 6 Part 1 – Introduction and Orientation 5. Design City Bridge Nijmegen 10 6. Design of the approach bridge 12 7. Loads 13 8. Buckling and magnification factors 27 9. Parameter analysis arch buckling 36 Part 2 – Single arch analysis 10. Introduction to Part 2 44 11. Theory of arches 45 12. Analysis single arch 54 13. Solving the differential equations 61 14. Comparing magnification factors 79 15. Different arch geometries 81 16. Conclusions single arch analysis 88 Part 3 – Multiple arch analysis 17. Introduction to Part 3 93 18. Modelling 94 19. Analysis multiple arch models without substructure 97 20. Analysis multiple arch models including substructure 106 21. Approach bridge model 110 22. Conclusion multiple arch analysis 113 Part 4 – Introduction to physical nonlinearity and 3D effects 23. Introduction to Part 4 116 24. Physically nonlinear analysis 117 25. Three dimensional modelling 124 26. Conclusion and recommendation for further research 132 Geometrically nonlinear behaviour of arches in 2D MSc Thesis Acknowledgement This report comprises the results of my Master’s Thesis research at Delft University of Technology. It is a theoretical answer to the practical design question, considering the magnification of bending moments due to second order effects in arch bridges. This topic provided the opportunity to develop more insight into structural behavior of arches and to develop the necessary skills when using software in engineering. I would like to thank my graduation committee, Jan Rots, Cor van der Veen, Pierre Hoogenboom and Max Hendriks for their guidance and feedback while discussing my ideas and results Furthermore, I would like to thank the colleagues at BAM Infraconsult for giving me the opportunity to do the research, for their extensive support and their enthousiasm. Ruben Onstein Gouda, May 2013 Geometrically nonlinear behaviour of arches in 2D MSc Thesis Arched structures? Nonlinear! Part 0: Extended summary Part 0: Extended Summary - Contents Contents – Part 0: Extended Summary 1. Introduction to Part 0 1 1.1 Background 1 1.2 Thesis outline 1 1.2.1 Research questions 2 1.3 Parts 2 1.3.1 Part 1 – Literature and buckling 2 1.3.2 Part 2 – Single arch analysis 2 1.3.3 Part 3 – Multiple arches 3 1.3.4 Part 4 – Further investigation 3 2. Results and Conclusions 4 2.1 Single arch 4 2.2 Multiple arches 5 3. Recommendations for design 6 Geometrically nonlinear behaviour of arches in 2D MSc Thesis Part 0:Extended Summary - Introduction to Part 0 1. Introduction to Part 0 1.1 Background The city of Nijmegen is located at the banks of the river Waal. Heavy traffic on the old Waal bridge (arch bridge, completed in 1936) and the urban road network requires a second river crossing. Based on the architectural look of the bridge, the design competition was won by the consortium. A succession of concrete arches with masonry cladding on the parapets were chosen for the approach bridge, to unite the new bridge with the shape of the existing bridge and with the cities Roman history. Concrete arches are applied in many bridges. Nevertheless, piers supporting the arches and robust end supports to confine these arches is a unique solution. When analysing other concrete arch bridges, either the arches are confined directly by the foundation or tensile ties are applied. The structural verification of the succession of the flexibly supported, slender arches, raised questions on the nonlinear structural behaviour. The axial forces reach values up to of the Euler buckling load and the flexibility of the support leads to high bending moments. In the structural design, the bending moment magnification due to geometrically nonlinear behaviour is based on the design of columns. The well-known engineering formula for geometrically nonlinear behaviour is combined with stability analysis and structural analysis. As the ratio of the Euler buckling load and the design load is , the engineering formula yields a magnification factor of on the bending moments to account for the geometrically nonlinear behaviour. Using this factor, a nonlinear analysis can be left out, which saves time in the design process, but it ignores the true geometrical nonlinearity, the equilibrium of the deformed structure. Figure 1: Side view to Northern approach bridge 1.2 Thesis outline The main objective of the thesis is to provide insight in the theory and analysis of the geometrically nonlinear behaviour of arched structures. The objective splits into two parts. On one hand there is the checking of the design assumption, on the other hand it should guide future design of similar structures. Geometrically nonlinear behaviour of arches in 2D Part 0 - Page 1 of 134 MSc Thesis Part 0:Extended Summary - Introduction to Part 0 The research is carried out within the framework of the Nijmegen city bridge. Loads, soil properties and geometry of the city bridge design are heavily used as backbone of the practical part of the investigation. 1.2.1 Research questions The scope of the investigation is determined by the research questions: - What are the theoretical backgrounds of the geometrically nonlinear behaviour of arched structures? - How do the internal forces change, when geometrically nonlinear behaviour is accounted for in the analysis of arched structures? - Is there a link between Euler buckling and geometrically nonlinear behaviour in arched structures? - How to deal with the geometrically nonlinear behaviour of arched structures in practice? 1.3 Parts The research is carried out and reported in four separate parts, upholding their individual characters and representing the chronology of the research process. Together, the parts provide the answers to the research questions. 1.3.1 Part 1 – Literature and buckling In the first part the orientation phase of the investigation is reported. Obviously, the approach bridge design has been studied, but the main part of the orientation phase consisted of literature study, in which buckling stability was considered. Since in engineering, stability and geometrical nonlinearity are closely related via the factor, studying buckling seemed a good starting point. The theory was extended with a sensitivity analysis to investigate the influence of the different parameters to the Euler buckling capacity of arches. 1.3.2 Part 2 – Single arch analysis As buckling theory did not provide answers to the geometrically nonlinear question in arch analysis, structural behaviour of arches was studied. The differential equation for arch structures provided insight into the linear and nonlinear analysis. In the derivation of the differential equation the effect of the deformations on the arch shape is neglected and the thrust is assumed to be constant , leading to the linear behaviour. The differential equation including the nonlinear effect reads: Geometrically nonlinear behaviour of arches in 2D Part 0 - Page 2 of 134 MSc Thesis
Description:The list of books you might like
