Catenary Vaults: A solution to low-cost housing in South Africa Ivanka Bulovic A research report submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in partial fulfilment of the requirements for the degree of Master of Science in Engineering. Johannesburg 2014 The financial assistance of the National Research Foundation (N R F) towards this research is hereby acknowledged. Opinions expressed and conclusions arrived at, are those of the author and are not necessarily to be attributed to the NRF. Table of Contents Table of Contents ................................................................................................................................. 1 Declaration ............................................................................................................................................ 5 Abstract .................................................................................................................................................. 6 Acknowledgements .............................................................................................................................. 7 List of Figures ....................................................................................................................................... 8 List of Tables ....................................................................................................................................... 13 List of Symbols ................................................................................................................................... 14 1. Introduction .................................................................................................................................. 16 1.1. Problem Statement ............................................................................................................ 16 1.2. Objectives ............................................................................................................................ 17 1.3. Scope ................................................................................................................................... 18 2. Literature Review ....................................................................................................................... 20 2.1. Introduction .......................................................................................................................... 20 2.2. Materials .............................................................................................................................. 23 2.2.1. Tiles .............................................................................................................................. 23 2.2.2. Bricks and Blocks ....................................................................................................... 26 2.2.3. Surface Protection ...................................................................................................... 29 2.3. Forms, Modelling and Spacing ......................................................................................... 31 2.4. Construction Methods ........................................................................................................ 38 2.4.1. With Formwork ............................................................................................................ 39 2.4.2. Without Formwork ...................................................................................................... 42 2.5. Conclusion ........................................................................................................................... 44 3. Layout and shape establishment ............................................................................................. 46 3.1. Design Considerations ...................................................................................................... 46 3.2. Design Selection ................................................................................................................. 49 4. Materials Investigation ............................................................................................................... 54 4.1. Introduction .......................................................................................................................... 54 4.2. Production process ............................................................................................................ 55 4.2.1. Soil Selection .............................................................................................................. 55 4.2.2. Mix ratios ..................................................................................................................... 56 1 4.2.3. Production ................................................................................................................... 57 4.2.4. Problems in production .............................................................................................. 59 4.3. Material properties ............................................................................................................. 59 4.3.1. Dry-stack interlocking Blocks .................................................................................... 60 4.3.2. Splitter-Brick Block ..................................................................................................... 62 5. Method of Analysis for a Catenary Curve ............................................................................... 64 5.1. Introduction .......................................................................................................................... 64 5.2. Mathematical definition ...................................................................................................... 64 5.3. The Graphical method ....................................................................................................... 64 5.4. Segmental Equilibrium Method ........................................................................................ 67 5.4.1. Introduction .................................................................................................................. 67 5.4.2. Theoretical basis ........................................................................................................ 67 5.4.3. The Middle-Third concept ......................................................................................... 69 5.4.4. Method of Design ....................................................................................................... 71 5.5. Finite Element Method ....................................................................................................... 77 6. Structural Analysis and Design of Catenary Vaults .............................................................. 79 6.1. Introduction .......................................................................................................................... 79 6.2. Case study: Bapong ........................................................................................................... 79 6.2.1. Introduction .................................................................................................................. 79 6.2.2. Finite Element Results ............................................................................................... 83 6.3. Loading ................................................................................................................................ 85 6.4. Loading Combinations and Patterns ............................................................................... 91 6.5. Design Process using the Segmental Equilibrium Method .......................................... 94 6.5.1. Dead Load Design...................................................................................................... 94 6.5.2. Dead Load, Live Load and Wind Load Analysis .................................................. 100 6.6. Finite Element Analysis ................................................................................................... 109 6.6.1. Verification Phase .................................................................................................... 109 6.6.2. Analysis of Temperature Loading .......................................................................... 113 6.7. Discussion of Results ...................................................................................................... 115 6.7.1. Thrust Line Analysis ................................................................................................. 115 6.7.2. Finite Element Analysis ........................................................................................... 120 6.8. Conclusion ......................................................................................................................... 120 2 7. Structural Member Design ...................................................................................................... 121 7.1. Slab..................................................................................................................................... 121 7.1.1. Introduction ................................................................................................................ 121 7.1.2. Design ........................................................................................................................ 121 7.2. Masonry wall design .......................................................................................................