Cold-Formed Steel Examples to the Theory and Finite Element Implementation of Plasticity

This paper presents two examples to the theory and finite element implementation of plasticity. The first example is on the cross-sectional behavior of trapezoidal sheeting subjected to a concentrated load. It is shown that the number of elements (and thus the number of integration points) along the corner radius are important for the correct modeling of this static problem. The second example is on the failure of first-generation sheeting subjected to a concentrated load and a bending moment. This problem, especially for large span lengths, can be solved only with explicit dynamic simulations. These are, for our research field, for the first time published here. The explicit simulations normally function with a rather simple integration scheme for plasticity; is shown that our sheeting results are very sensitive to this

Untersuchung der Parameterempfindlichkeit bei Problemen der Strukturoptimierung

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Analytical and finite element modelling of long plate mode jumping behaviour

Trapezoidal sheeting of thin-walled steel is applied frequently for roofing and cladding. As such, it is loaded by a concentrated load (at the support) and a bending moment. A recently developed model to predict the sheeting's failure behaviour leaves the question open whether mode jumping (the phenomenon that a plate dynamically changes its buckling mode during an increasing load) should be taken into account in the model. This article presents the analytical and finite element modelling of square and long plates, which, depending on the boundary conditions, may represent the compressed flange of trapezoidal sheeting. The analytical modelling is based on the combination of several displacement functions and using the principle of minimal potential energy. Hereafter the stability of each part of the resulting equilibrium curves is determined. A spin-off of the analytical model is an analytical expression for a current curve-fitted based prediction formula for the post/pre buckling stiffness ratio by Rhodes. Furthermore, the accuracy range of a solution by Williams and Walker for the far-post buckling behaviour can be confirmed. The finite element modelling has been carried out by implicit dynamic, and explicit (dynamic) simulations. Both for the load levels and the buckling mode sequences, the analytical and finite element models give equivalent results. It is concluded that for the specific boundary conditions that represent the situation of a compressed flange for trapezoidal sheeting, it is very likely that mode jumping will not occur

Analytical and finite element modelling of long plate mode jumping behaviour

Trapezoidal sheeting of thin-walled steel is applied frequently for roofing and cladding. As such, it is loaded by a concentrated load (at the support) and a bending moment. A recently developed model to predict the sheeting's failure behaviour leaves the question open whether mode jumping (the phenomenon that a plate dynamically changes its buckling mode during an increasing load) should be taken into account in the model. This article presents the analytical and finite element modelling of square and long plates, which, depending on the boundary conditions, may represent the compressed flange of trapezoidal sheeting. The analytical modelling is based on the combination of several displacement functions and using the principle of minimal potential energy. Hereafter the stability of each part of the resulting equilibrium curves is determined. A spin-off of the analytical model is an analytical expression for a current curve-fitted based prediction formula for the post/pre buckling stiffness ratio by Rhodes. Furthermore, the accuracy range of a solution by Williams and Walker for the far-post buckling behaviour can be confirmed. The finite element modelling has been carried out by implicit dynamic, and explicit (dynamic) simulations. Both for the load levels and the buckling mode sequences, the analytical and finite element models give equivalent results. It is concluded that for the specific boundary conditions that represent the situation of a compressed flange for trapezoidal sheeting, it is very likely that mode jumping will not occur

Composite Behaviour of Steel Frames with Precast Concrete Infill Panels

This paper presents preliminary experimental and numerical results of an investigation into the composite behaviour of a steel frame with a precast concrete infill panel (S-PCP) subject to a lateral load. The steel-concrete connections consist of two plates connected with two bolts which are loaded in shear only. The connections are designed for a failure mechanism consisting of ovalisation in the bolt holes due to bearing of the bolts to avoid brittle failure. Experimental pull-out and shear tests on individual frame-panel connections were performed to establish their stiffness and failure load. A full scale experiment was performed on a onestorey one-bay 3 by 3m infilled frame structure horizontally loaded at the top. With the known characteristics of the frame-panel joints from the experiments on individual connections, a numerical analysis was performed on the infilled frame structure taking nonlinear behaviour of the structural components into account. The finite element model yields reasonably accurate results and indicates a connection failure sequence similar to experimental failure

The generation of hierarchic structures via robust 3D topology optimisation

Commonly used building structures often show a hierarchic layout of structural elements. It can be questioned whether such a layout originates from practical considerations, e.g. related to its construction, or that it is (relatively) optimal from a structural point of view. This paper investigates this question by using topology optimisation in an attempt to generate hierarchical structures. As an arbitrarily standard design case, the principle of a traditional timber floor that spans in one direction is used. The optimisation problem is first solved using classical sensitivity and density filtering. This leads indeed to solutions with a hierarchic layout, but they are practically unusable as the floor boarding is absent. A Heaviside projection is therefore considered next, but this does not solve the problem. Finally, a robust approach is followed, and this does result in a design similar to floor boarding supported by timber joists. The robust approach is then followed to study a floor with an opening, two floors that span in two directions, and an eight-level concrete building. It can be concluded that a hierarchic layout of structural elements likely originates from being optimal from a structural point of view. Also clear is that this conclusion cannot be obtained by means of standard topology optimisation based on sensitivity or density filtering (as often found in commercial finite element codes); robust 3D optimisation is required to obtain a usable, constructible (or in the future: 3D printable) structural design, with a crisp black-and-white density distribution

Elastic post-buckling behaviour of uniformly compressed plates

In this paper it is discussed how existing analytical and semi-analytical formulas for describing the elastic-post-buckling behavior of uniformly compressed square plates with initial imperfections, for loads up to three times the buckling load can be simplified and improved. For loads larger than about twice the buckling load the influence of changes in the buckling shape, assumed sinusoidal, cannot be neglected anymore. These changes can be taken into account by using the perturbation approach. The existing and improved formulas are compared to the results of finite element simulations

Experiments investigating concrete floor punching using specific reinforcement

To reduce the surface crack width and to optimize the ultimate punching load of warehouse concrete floors, fibre reinforcement and special reinforcement mats above piles are used. Due to the special reinforcement mats, current design rules cannot be used to correctly predict the surface crack width and the ultimate punching load. Therefore, full-scale experiments have been carried out for six different reinforcement types. A fibre-reinforced floor with circular pile mat is the best solution, both for reducing the surface crack width and for optimizing the ultimate punching load