Geodesic Dome Structural Analysis and Design

1 University of Southern Queensland Faculty of Health, Engineering and Sciences Geodesic Dome Structural Analysis and Design A dissertation submitted by Zhuohao Peng in fulfilment of the requirements of ENG4111 and 4112 Research Project towards the degree of Bachelor of Engineering (Honours) (Civil Engineering) Submitted October, 2016 i Abstract Geodesic dome is one of the simplest forms of structure which has a very unique spherical or partial-spherical shape. The skeleton of the structure consists a number of unequal and straight Structural members to form its many stable triangular elements in order to provide resistance to the gravitational, wind and seismic loads. The Geodesic dome has the capacity to achieve large span without any form of internal posts, load bearing walls or deep beams or trusses, the load is evenly distributed through the surface of the dome. On the other side, a conventional building would require more material and space to achieve larger span, and deflection control and bracing requirement may become a challenge for the conventional form.

2 Whereas, the Geodesic is very effective in limiting deflection, and it is self-braced through its stable triangulated elements. Geodesic domes can be constructed from various materials, ( timber, steel) and a very light PVC cover is applied to the outside of the main structure to shield the dome from weathering. It provides a strength-to-weight ratio that many others could not compete. The fast speed of erection, competitiveness in material costs and its resilience to natural disasters have made dome construction applicable to many agricultural, commercial applications. The purpose of this report is to present the background information about Geodesic dome, also to verify a designing methodology and to develop Design procedure based on the most critical loading, that is wind load for this type of structure. The aid of computational Analysis has been considered as the key tool to obtain Design data from the complex 3D dome model, and then manually checked against steel structure standards AS 4100-1998.

3 In addition, an excel spreadsheet was developed using finite element Analysis method to extract the forces for each element, then the results were compared against the outcomes from computational Analysis method for validation purpose. The spreadsheet was aimed to standardize the Design procedure and to reduce the time required for Analysis and Design in the future, and sensitivity Analysis could also be conducted easily and quickly using the spreadsheet. ii University of Southern Queensland Faculty of Health, Engineering and Sciences ENG4111/ENG4112 Research Project Limitations of Use The Council of the University of Southern Queensland, its Faculty of Health, Engineering & Sciences, and the staff of the University of Southern Queensland, do not accept any responsibility for the truth, accuracy or completeness of material contained within or associated with this dissertation. Persons using all or any part of this material do so at their own risk, and not at the risk of the Council of the University of Southern Queensland, its Faculty of Health, Engineering & Sciences or the staff of the University of Southern Queensland.

4 This dissertation reports an educational exercise and has no purpose or validity beyond this exercise. The sole purpose of the course pair entitled Research Project is to contribute to the overall education within the student s chosen degree program. This document, the associated hardware, software, drawings, and other material set out in the associated appendices should not be used for any other purpose: if they are so used, it is entirely at the risk of the user. iii Certification I certify that the ideas, designs and experimental work, results, analyses and conclusions set out in this dissertation are entirely my own effort, except where otherwise indicated and acknowledged. I further certify that the work is original and has not been previously submitted for assessment in any other course or institution, except where specifically stated. Zhuohao Peng Student Number: 0061056711 iv Acknowledgements I would like to express my appreciations to everyone that has been involved in assisting me prepare and complete this project.

5 The following people and organisations that I would like to make special mention of for without their support I would not have been able to complete this project. Dr Sourish Banerjee for instructive supervision, guidance and suggestions, as well as his valuable time and effort. Bentley sponsorship of a free license of Microstran V9 over the period of the project. Strata Group Consulting Engineers for providing the idea of the project and supporting me completing the project. Family for selfless supports over the years in many ways to encourage and support me. ZHUOHAO PENG v Table of Contents Abstract .. i Certification .. iii Acknowledgements .. iv Table of Contents .. v List of Figures .. viii List of Tables .. x Nomenclature .. xi Novel Aspect .. xiv 1. Introduction .. 1 Background Information .. 1 Project Aim and Objectives .. 2 Scope and Limitation .. 3 2. Literature Review.

6 4 Introduction .. 4 Shell Dome .. 4 Geodesic dome .. 5 History .. 5 Geometry .. 6 Coordinate System .. 9 Strength and weakness .. 10 Structural Analysis of dome .. 10 Failure 11 Loading .. 12 Wind Load .. 12 Seismic load .. 13 Self weight and imposed loads .. 14 vi Snow load .. 14 3. Model Generation and Loading .. 15 Geodesic Model Generation .. 15 Loading .. 16 Wind .. 16 Self-Weight and Imposed 21 Load Combination Cases .. 22 Assumptions .. 23 4 excel Spreadsheet Development .. 24 Introduction .. 24 Flow Chart and Spreadsheet Structure .. 24 data Input .. 25 Nodal Coordinates and Strut Information .. 25 Loading .. 25 Member Stiffness Matrices Construction .. 27 Global Stiffness Matrices Construction .. 31 Solution Procedure .. 33 Post Procedure .. 34 Design Procedure .. 35 5 Microstran V9 Analysis .. 38 Introduction to Microstran V9.

7 38 Model Setup .. 38 Load Input .. 39 Structural Analysis .. 40 6 Conclusion .. 42 Comparison of Outcomes .. 42 Future Work and Improvements .. 44 Reference .. 1 Appendices A Project Specification .. 3 vii Appendices B Supporting Documents .. 5 Appendices C Spreadsheet .. 9 Appendices D Microstran V9 Outcomes .. 10 viii List of Figures Figure 1: Translation shell dome (Ketchum) .. 4 Figure 2: Regular Octahedron (Kenner 2003) .. 6 Figure 3: Modified Octahedron (Kenner 2003) .. 7 Figure 4: Class and frequency (Salsburg) .. 7 Figure 5: 31 great circles (Pacific Domes 1971) .. 8 Figure 6: Icosahedron and great circle (Kenner 2003) .. 8 Figure 7: Six great circles on the spherical icosahedron (Kenner 2003) .. 9 Figure 8: The spherical co-ordinates (Ramaswamy 2002) .. 9 Figure 9: Strut buckling (Lewis 2005) .. 11 Figure 10: Wood dome on shake table (Clark 2014) .. 13 Figure 11: 6m V2 Geodesic dome model generated CADRE Geo.

8 15 Figure 12: Illustration of wind acting on dome structure (Susila 2009) .. 16 Figure 13: Elevation of circular dome (Susila 2009) .. 17 Figure 14: External Pressure coefficient Cp, e for y/d = 1/2 (Susila 2009) .. 17 Figure 15: External Pressure Coefficient (Cp, e) Curved Roof (AS/NZS 2011) 18 Figure 16: Dome wind zone divisions .. 19 Figure 17: Elevation of dome and tangent line .. 19 Figure 18: Tributary areas of a node .. 22 Figure 19: Flow chart of FEA procedures .. 24 Figure 20: Nodal coordinates and reference diagram .. 25 Figure 21: Wind loads local and global axis .. 26 Figure 22: Loads of primary and combined load cases .. 27 Figure 23: Load displacement relationship .. 27 Figure 24: Three-dimensional system .. 29 Figure 25: Member stiffness matrix .. 30 Figure 26: Node designation of the Geodesic dome .. 31 Figure 27: Strut designation of the Geodesic dome .. 32 Figure 28: Structure global stiffness matrix assembling.

9 33 Figure 29: Global stiffness matrix and partition .. 33 Figure 30: Calculation of nodal deflection .. 34 Figure 31: Calculation of strut axial force .. 35 Figure 32: Effective length factors for members for idealized conditions of end restraint (AS4100:1998) .. 36 Figure 33: Member Design and result .. 37 ix Figure 34: Microstran V9 model with selected CHS size .. 38 Figure 35: Dead load assignment (G) .. 39 Figure 36: Imposed load assignment (Q) .. 39 Figure 37: Wind load assignment (Wind) .. 40 Figure 38: Axial force diagram .. 40 Figure 39: Deflection under wind load .. 41 Figure 40: Geodesic dome with two section sizes .. 44 Figure 41: Project Gantt Chart .. 8 x List of Tables Table 1: Relationship between NZS3604 wind zones, site wind speeds and basic pressures Table 2: excel and Microstran V9 outcomes comparison xi Nomenclature A Cross section area Ag Gross cross section area An Net cross section area Cp Wind pressure coefficient Cp, e External wind pressure coefficient Cp, i Internal wind pressure coefficient Cfig Aerodynamic shape factors CHS Circular Hollow Section d depth of Geodesic dome d Local displacement matrix dN Local displacement at near end dF Local displacement at far end DOF Degree of freedom D Global displacement matrix DXF AutoCAD drawing interchange format DNx Global displacement in x axis at near end DNy Global displacement in y axis at near end DNz Global displacement in z axis at near end DFx Global displacement in x axis at far end DFy Global displacement in y axis at far end DFz Global displacement in z axis at far end Du Nodal deflections matrix Dk Boundary condition of nodes matrix E Modulus of Elasticity (MPa)

10 Fy Steel yield strength fu Steel tensile strength FEA Finite element Analysis G Dead load h height of Geodesic dome k Member stiffness matrix kc,i Internal combination factor kc,e External combination factor ka Area reduction factor kf Form factor xii kl Local factor kp Porosity factor ke Effective length factor kt Correction factor kPa Kilopascal kg Kilogram kN Kilo newton K Structure stiffness matrix L Length of strut Ns Nominal section capacity NC Nominal member capacity NC- excel Maximum Axial compression force from excel NC-Microstran Maximum Axial compression force from Microstran Nt Nominal tensile capacity NT- excel Maximum Axial tensile force from excel NT-Microstran Maximum Axial tensile force from Microstran PVC Polyvinyl Chloride q Axial force qN Local axial force at near end qF Local axial force at far end Q Live load / Imposed load QNx Global force in x axis at near end QNy Global force in y axis at near end QNz Global force in z axis at near end QFx Global force in x axis at far end QFy Global force in y axis at far end QFz Global force in z axis at