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This two-part contribution presents a novel theory of bending of thin-walled beams with influence of shear (TBTS). The theory is based on the Vlasov’s general beam theory as well as on the Timoshenko’s beam bending theory. The theory is valid for general thin-walled open beam cross-sections. Part I is devoted to the theoretical developments and part II discusses analytical and obtained numerical results. The theory is based on a kinematics assuming that the cross-section maintains its shape and including three independent warping parameters due to shear. Poison’s effect is ignored, as well as warping constrains due to shear (as it known, those effect have small and for engineering praxis neglected influence on the stresses and displacements). Closed-form analytical results are obtained for three-dimensional expressions of the normal and shear stresses. Under general transverse loads, reduced to the cross-section principal pole, the beam will be subjected to bending with influence of shear and in addition to torsion due to shear with respect to the cross-section principal pole and to tension/compression due to shear, in the case of non-symmetrical cross-sections. The beam will be subjected to bending with influence of shear (i) in the plane of symmetry under the loads in that plane and in addition to tension/compression due to shear, (ii) in the plane through the principal pole orthogonal to the plane of symmetry under the loads in that plane and in addition to torsion with respect to the principal pole, in the case of the mono-symmetrical cross-sections. The beam will be subjected to bending with influence of shear in the principal planes, in the case of the bi-symmetrical cross-sections. The principal cross-section axes as well as the principal pole are defined by the classical Vlasov’s theory of thin-walled beams of open section. The analytical and numerical analyses presented in part II include comparisons with the classical beam theory, Euler-Bernoulli’ theory (EBBT) as well as comparisons with the finite element method (FEM). [ABSTRACT FROM AUTHOR]

This paper presents experimental and finite element analyses of the ultimate strength and buckling collapse behaviours of a single- and a double-hull girder with a large deck opening subjected to cyclic ultimate bending moments. The cyclic ultimate bending moments here means that the external load in every cycle exceed the ultimate load bearing capacity of the specimens; the aim is to understand how the structures behave under this kind of extreme but not unusual load condition. The results showed that, in general, the plastic deformation would be accumulated under the cyclic loads, and the buckling collapse would expand from the deck plates to the broadside plates in both specimens. However, even if overall buckling occurred on both specimens, the specimens still preserved most of the load bearing capacity for the next ultimate loading cycles, but the double-hull specimen had a higher safety stock. In addition, the different behaviours of these two types of specimens were recorded, and the reasons behind were deeply analysed, which has helped us gain a deeper understanding of how these complex engineering structures perform under this kind of extreme but not well-studied load condition. The conclusions drawn in this works would be beneficial to improve the structural safety of ship hull girders and other similar thin-walled structures. • The collapse behaviours of box type hull girder under cyclic ultimate moments were analysed by experiments and FEM. • Coupled effect of structural complexity and loading condition on the collapse behaviour of the girders was investigated. • The difference between single- and double-hull girders regarding the collapse behaviours was compared and deeply analysed. • Suggestions on how to improve the structural safety under extreme load condition were provided. [ABSTRACT FROM AUTHOR]

Abstract: 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 where 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. [Copyright &y& Elsevier]

Abstract: In a recent paper (Gonçalves and Camotim, 2013 [1]), the authors presented an investigation concerning the buckling (bifurcation) behaviour of uniformly compressed thin-walled tubes with regular polygonal cross-sections (RCPS). The present paper complements the previous work by addressing the local and distortional buckling behaviour of RCPS members subjected to bending or torsion and aims at providing a novel insight into these phenomena. In particular, the specialization of Generalized Beam Theory (GBT) for RCPS, as recently proposed in Gonçalves and Camotim (2013) [2], is employed to obtain closed-form analytical solutions and also to carry out parametric studies by means of numerical analyses which are both computationally efficient (due to the small number of d.o.f. involved) and clarifying (due to the modal decomposition features of GBT). For validation purposes, solutions taken from the literature and also standard shell finite element model results are employed. [Copyright &y& Elsevier]

Abstract: For the coupled static and dynamic buckling of thin walled beam subjected to various forces, such as axial force, uniform bending moment, and bending moment due to concentrated and distributed lateral forces, the spline finite element method is employed to obtain the dynamic stiffness matrix. Second order effects of the axial force and moment are considered. A doubly symmetric cantilever beam with uniform cross-section is investigated. Extensive static and dynamic interaction diagrams are plotted. The effects of warping rigidity, torsional rigidity, axial tension and compression on moment buckling, moment on axial buckling compression, higher buckling modes are discussed in detail. The spline finite element method is proved to be very efficient for the present problem and many interaction diagrams can be plotted easily. Some new results are presented. The methodology is based on finite element formulation and therefore it can be easily extended to analyze structural frames. [Copyright &y& Elsevier]

Abstract: This paper presents a beam formulation for large displacement analysis of beam-type structures with flexible connections. Within the framework of updated Lagrangian incremental formulation and the nonlinear displacement field of thin-walled cross-sections, which accounts for restrained warping and the second-order displacement terms due to large rotations, the equilibrium equations of a straight beam element are firstly developed. Due to the nonlinear displacement field, the geometric potential of semitangential moment is obtained for both the internal torsion and bending moments, respectively. Material nonlinearity is introduced for an elastic-perfectly plastic material through the plastic hinge formation at finite element ends. To account for the flexible connection behaviour, a special transformation procedure is developed. The numerical algorithm is implemented in a computer programme and its reliability is validated trough several test examples. [Copyright &y& Elsevier]

Abstract: This paper presents a crashworthiness design of regular multi-corner thin-walled columns with different types of cross-sections and different profiles, including straight octagonal columns and curved hexagonal columns. In this paper, the straight octagonal section columns are first optimized, which mainly take axial crash loads during crashes. Next, the curved hexagonal section columns are optimized following the same approach, which are subject to bending moment when impact occurs. During the design optimizations, specific energy absorption (SEA) is set as the design objective, side length of the cross-sections and wall thickness are selected as design variables, and maximum crushing force (P m) is set as the design constraint. Both the objective and constraint are formulated using the response surface method (RSM) based on sets of finite element (FE) results obtained from FE analyses (FEA). After obtaining the optimal designs, parametric studies are performed to investigate the influences of the design variables on the crash performance of such multi-corner thin-walled columns. [Copyright &y& Elsevier]