Nonlinear Mechanics of Prestressed Stayed Columns
Lead Research Organisation:
Imperial College London
Department Name: Civil & Environmental Engineering
Abstract
Advancements in the fields of digital design and fabrication have facilitated the development of complex architectural concepts that are driving equally novel structural solutions for these to be realised. This scenario is exemplified in the design and fabrication of doubly-curved plates which are currently limited by the European design code for steel structures, which does not provide guidance for the structural design of curved plates. While recent studies considering the behaviour of cylindrically-curved plates (i.e. plates having a constant radius of curvature in one plane) under various load conditions have been published, there is very limited research considering the behaviour of doubly-curved plates under in-plane loading and this is the primary aim of this research project. The currently described problem will be tackled initially by deriving and investigating nonlinear analytical models of hyperbolic paraboloidal shaped plates, the objective being to provide an understanding of the mechanical behaviour of the doubly-curved plate to the loading and boundary conditions considered. These analytical models will be verified and validated against numerical models formulated using the Finite Element Method. This well-established methodology will provide confidence in the results of a parametric study, which will test the influence of additional parameters, such as the effects of initial geometric imperfections, plate thickness, plate aspect ratio and residual stresses from manufacturing, on the load-carrying capacity of the plates.
The ultimate aim of this research project is to formulate design recommendations for doubly-curved plates under various loading conditions, in a manner that such recommendations can be implemented in future versions of the design codes for use by practising engineers.
Research Questions
What is the mechanical behaviour of doubly curved plates under various in plane loading conditions?
How can engineers design for the failure modes to ensure safe and efficient performance of such structural forms?
Approach
Analytical models will be derived, using established energy principles that consider the hyperbolic paraboloid shaped plates under a variety of in plane loading and boundary conditions.
The analytical models will be additionally verified and validated against numerical models formulated using the Finite Element Method.
A parametric study that tests the influence of additional parameters, such as the effects of initial geometric imperfections, plate thickness, plate aspect ratio and residual stresses from manufacturing, on the load-carrying capacity of the plates.
Identify correlations between the parameters explored and derive relationships that allow such considerations to be implemented into the design codes for use in industrial practice
Complex geometries are becoming more prevalent in engineering with advancements in both design and fabrication technologies. The safety and reliability of these structures require fundamental mechanical principles to understand the behaviour of such geometries under loads encountered in practice, which this research project aims to address.
EPSRC Research areas: Engineering Design, Non-linear systems, Structural Engineering
EPSRC Priority areas: Engineering sciences, Lightweight systems, Structural integrity and materials behaviour
The ultimate aim of this research project is to formulate design recommendations for doubly-curved plates under various loading conditions, in a manner that such recommendations can be implemented in future versions of the design codes for use by practising engineers.
Research Questions
What is the mechanical behaviour of doubly curved plates under various in plane loading conditions?
How can engineers design for the failure modes to ensure safe and efficient performance of such structural forms?
Approach
Analytical models will be derived, using established energy principles that consider the hyperbolic paraboloid shaped plates under a variety of in plane loading and boundary conditions.
The analytical models will be additionally verified and validated against numerical models formulated using the Finite Element Method.
A parametric study that tests the influence of additional parameters, such as the effects of initial geometric imperfections, plate thickness, plate aspect ratio and residual stresses from manufacturing, on the load-carrying capacity of the plates.
Identify correlations between the parameters explored and derive relationships that allow such considerations to be implemented into the design codes for use in industrial practice
Complex geometries are becoming more prevalent in engineering with advancements in both design and fabrication technologies. The safety and reliability of these structures require fundamental mechanical principles to understand the behaviour of such geometries under loads encountered in practice, which this research project aims to address.
EPSRC Research areas: Engineering Design, Non-linear systems, Structural Engineering
EPSRC Priority areas: Engineering sciences, Lightweight systems, Structural integrity and materials behaviour
Organisations
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/R513052/1 | 01/10/2018 | 30/09/2023 | |||
| 2109376 | Studentship | EP/R513052/1 | 01/10/2018 | 31/03/2022 | Luke Lapira |
| Description | The hyperbolic paraboloid (hypar) geometry has been frequently implemented in long-span roof structures, as the surface loads applied to these structures are resisted by an efficient load-path, identified as membrane shear, while minimising bending stresses. In the current work, a size effect has been identified where, once the scale of the hyperbolic paraboloid is reduced from a long-span roof to a small element for use as part of a smaller structure, bending stresses become highly significant and must be addressed for its safe design. Initial research into a phenomenological model that replicated the behaviour of the hypar subject to in-plane loads showed potential. This involved discretising the hypar into a series of inter-connected axially loaded arches and cables, inspired by previous research and a fundamental understanding of how flat plates resist shear. This model was investigated using both analytical and numerical models, to determine if such simplifying assumptions were valid or otherwise. It was shown that the lattice was unable to replicate an increase in stiffness shown by the plate, attributed to an over-simplification of the confinement offered by the continuous plate as opposed to the artificial representation of this in the analytical model. Hence, this modelling approach was not pursued but it did provide some valuable information in terms of the limitations of the phenomenological approach. The hypar subjected to edge shear loads was in parallel to above approach being simulated using finite element (FE) models to provide an insight into the actual behaviour. It was clearly observed that the hypar behaved in a similar manner to an imperfect plate. Hence, a more exacting nonlinear analytical model is implemented, compared to the approach described previously, which treats the initial double-curvature as a deliberately imposed imperfection to the flat plate geometry, that was subsequently stress relieved. Comparisons with the FE model exhibit excellent correlation across a range of plate slenderness and degrees of initial hypar curvature. The benefit of the analytical model is that the contributions of the individual harmonic functions are easily identified and their influence on the behaviour of the hypar is established. This provides a new mechanical insight onto the behaviour of the hypar throughout loading and establishes a framework on which design guidance can be established, while the analytical modelling approach has the potential to be extended to different load cases and practical doubly-curved plate geometries. |
| Exploitation Route | The work described above has laid the foundation to pursue the objectives of this research further, particularly to establish design guidance for the hypar subject to edge shear loading. To achieve this objective, ongoing research is addressing key issues such as examining the behaviour across a wider range of plate aspect ratios, as well as considering other practical loading cases that are expected in practice. Once the design guidance has been established, it can be implemented in future revisions of the design codes such that practising engineers can use them for their designs. Furthermore, the nonlinear analytical model that has been developed can also be implemented to other loading cases and doubly-curved geometries. This approach can be pursued by other researchers to develop an understanding of how such geometries behave when subjected to loading and provide the insights necessary to develop design guidance for the cases considered. |
| Sectors | Construction |