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Major steel structures are commonly constructed as frames or trusses. The connections between its beams and columns have a crucial influence on the global behaviour. However, a detailed assessment of the joints is often neglected with rough simplifications, which may lead to poor results. On the other hand, if performing a detailed assessment it is a time-consuming task requiring special expertise. Consequently, the idea stressed in this paper is a novel approach on how to analyse thin-walled steel frames including a detailed assessment of both the joint and beam mechanics. The approach is based on a transformation from standard degrees of freedom into a displacement-based mode formulation. Furthermore, this transformation reduces the total number of degrees of freedom to be computed for advanced joints and beam elements. All this is achieved by adopting an advanced beam element formulation as well as introducing the idea of a ‘joint element’ formulated by finite shell elements. One of the main advantages of this idea is a general formulation of the joint, which makes it valid for many beam-to-column configurations. Furthermore, beam members can either be closed or open sections due to the adopted advanced generalised beam theory. Furthermore, a detailed analysis of the joint element itself is also achieved by this approach. Finally, an increased efficiency is achieved due to reduction of the total amount of degrees of freedom of the advanced model, and a new in-depth knowledge of the joint behaviour is gained from this approach as well, due to the displacement-based mode formulation.

Slotted cold-formed steel studs are used in load bearing external plasterboard walls. The cold-formed steel studs in these walls are supported by and joined to track profiles at the bottom and top level. In this paper the load bearing studs are tested in compression in order to observe the behaviour of the studs and the track joints. The experiments include a joint design with a special web stiffener used in practice. The studs are made of C-profiles and the tracks of U-profiles. Eight different test series are performed. The test series each have different column lengths, thicknesses, and are both with and without web stiffeners to see the influence of these on the joint behaviour and load bearing capacity of the slotted coldformed steel studs.

Results from a detailed numerical investigation of the post-buckling behaviour of rectangular simply supported steel plates subjected to biaxial in-plane loading are presented. The Steel plates are loaded through forced edge displacements. The effects of initial imperfections, aspect ratio, plate slenderness and edge displacement ratio are included in the investigations presented. Capacity interaction curves are established in the bi-axial stress domain. It turns out that for certain stress ratios the imperfections dominating the ultimate capacity are not affine to the lowest classical buckling mode for biaxial stress. It is of great interest that short wave imperfections of a lower magnitude compared to conventionally used imperfections are seen to lower the capacity of the bi-axially loaded plates. The topic is of major concern in the flange plates of long span bridges with multi box girder configurations.

The ultimate state analysis of bridge deck plates at the intersection zone between main girders and transverse beams is complicated by biaxial membrane stresses, which may be in compression or tension in either direction depending on the bridge configuration and the specific location. This paper presents a detailed investigation of the ultimate capacity of simply supported plates subjected to biaxial loads. The full interaction domain of combinations of compressive and tensile loads has been investigated including a large number of imperfections. It was found that non-standard imperfection modes in parts of the interaction domain lead to more critical and lower ultimate capacity than critical buckling mode imperfections.

The non-linear flange curling phenomenon in cold formed profiles is the tendency of slender flanges to deform towards the neutral axis for increasing flexural curvature. Based on Braziers work, Winter proposed a simple engineering formula for determination of the local flange deformation towards the neutral axis. This formula is used in Eurocode to estimate flange curling deformation and give a limit after which flange curling has to be taken into account, however no method or procedure is given for this. The current work presents a new original method, which fits directly into the iterative scheme of Eurocode for determination of effective widths and the neutral axis position in flexure of thin-walled cross sections.

For thin-walled beams, the classic theory for flexural and torsional analysis of open and closed cross-sections can be generalized by including distortional displacements. In a companion paper it is shown that using a novel semi-discretization process, it is possible to determine specific distortional displacement fields which decouple the reduced order differential equations. In this process the cross section is discretized into finite cross-section elements, and the natural distortional modes as well as the related axial variations are found as solutions to the established coupled fourth order homogeneous differential equations of GBT.In this paper the non-homogeneous distortional differential equations of GBT are formulated using this novel semi-discretization process. Transforming these non-homogeneous distortional differential equations into the natural eigenmode space by using the distortional modal matrix found for the homogeneous system, we get the uncoupled set of differential equations including the distributed loads. This uncoupling is very important in GBT, since the shear stiffness contribution from St. Venant torsional shear stress as well as “Bredt's shear flow” cannot be neglected nor approximated by the combination of axial stiffness and transverse stiffness, especially for closed cross sections. The full analytical solutions of these linear non-homogeneous differential equations are given, including four illustrative examples, which illustrate the strength of this novel approach to GBT. This new approach is a considerable theoretical achievement, since it without approximation gives the full analytical solution for a given discretization of the cross section including distributed loading. The boundary conditions considered in the examples of this paper are restricted to built in ends, which are needed for future displacement formulation of an exact first-order distortional beam element.

The classical Vlasov theory for torsional analysis of thin-walled beams with open and closed cross-sections can be generalized by including distortional displacement fields. We show that the determination of adequate distortional displacement fields for generalized beam theory (GBT) can be found as part of a semi-discretization process. In this process the cross-section is discretized into finite cross-section elements and the axial variation of the displacement functions are solutions to the established coupled fourth order differential equations of GBT. We use a novel finite-element-based displacement approach in combination with a weak formulation of the shear constraints and constrained wall widths. The weak formulation of the shear constraints enables analysis of both open and closed cell cross-sections by allowing constant shear flow. We use variational analysis to establish and clearly identify the homogeneous differential equations, the eigenmodes, and the related homogeneous solutions. The distortional equations are solved by reduction of order and solution of the related eigenvalue problem of double size as in non-proportionally damped structural dynamic analysis. The full homogeneous solution is given as well as transformations between different degree of freedom spaces. This new approach is a considerable theoretical improvement, since the obtained GBT equations found by discretization of the cross-section are now solved analytically and the formulation is valid without special attention also for closed single or multi cell cross-sections. Further more the found eigenvalues have clear mechanical meaning, since they represent the attenuation of the distortional eigenmodes and may be used in the automatic meshing of approximate distortional beam elements. The magnitude of the eigenvalues thus also gives the natural ordering of the modes.

The interaction between structural reinforcement and the surrounding concrete matrix in tension is a governing mechanism in the structural response of reinforced concrete members. The tension stiffening process, defined as the concrete ´s contribution to tensile response of the composite, has been investigated using an image-based deformation measurement and analysis system. This allowed for detailed view of surface deformations and the implications on the resulting response of the member in tension. In this study, conventional concrete and a ductile, strain hardening cement composite, known as Engineered Cementitious Composite (ECC), have been combined with steel and glass fiber reinforced polymer (GFRP) reinforcement to contrast the effects of brittle and ductile cement matrices as well as elastic/plastic and elastic reinforcement on the tension stiffening process. Particular focus was on the deformation process and transverse crack formation in the cementitious matrix at increasing tensile strain.

This paper presents a comprehensive experimental analysis of lateral forces generated by single pedestrians during continuous walking on a treadmill. Two different conditions are investigated; initially the treadmill is fixed and then it is laterally driven in a sinusoidal motion at varying combinations of frequencies (0.33-1.07 Hz) and amplitudes 4.5-48 mm). The experimental campaign involved seventy-one male and female human adults and covered approximately 55 km of walking distributed between 4954 individual tests. When walking on a laterally moving surface, motion-induced forces develop also at the frequency of the movement and are herewith quantified as equivalent velocity and acceleration proportional coefficients. Their dependency on both the vibration frequency and amplitude is presented, both in terms of mean values and probabilistically to illustrate the randomness associated with both intra and inter-subject variability. It is shown that the motion induced portion of the pedestrian load (on average) inputs energy into the structure in the frequency range (normalised by the average walking frequency) between approximately 0.6 and 1.2. Furthermore, it is shown that the load component in phase with the acceleration of the treadmill depends on the frequency of the movement, such that pedestrians (on average) add to the overall modal mass for low frequency motion and subtract from the overall modal mass at higher frequencies.

This paper investigates the phenomenon of excessive pedestrian-induced lateral vibrations as observed on several high-profile footbridges. The vibrations are a consequence of human-structure interaction, in which the forces generated by the pedestrians depend strongly on the vibration of the underlying pavement. An extensive experimental analysis has been carried out to determine the lateral forces generated by pedestrians when walking on a laterally moving treadmill. Two different conditions are investigated; initially the treadmill is fixed and then it is laterally driven in a sinusoidal motion at varying combinations of frequencies (0.33-1.07 Hz) and amplitudes (4.5-48 mm). The component of the pedestrian-induced force which is caused by the laterally moving surface is herewith quantified through equivalent velocity and acceleration proportional coefficients. It is shown that large amplitude lateral vibrations are the results of correlated pedestrian forces in the form of negative damping, with amplitudes that depend on the relationship between the step frequency and the frequency of the lateral movement.

This paper presents a generalization of the classic theory for thin-walled beams by including distortional displacements. A condensed presentation of the novel finite-elementbased displacement approach in [1,2] is given, where specific distortional displacement fields, which decouple the differential equations for generalized beam theory (GBT), are determined via a semi-discretization procedure. The distortional displacement fields are found as solutions to a distortional homogeneous eigenvalue problem which produce distortional displacement eigenmodes. Using the distortional modal matrix found for the homogeneous system the final uncoupled set of distortional differential equations including the load terms are presented and the full solution is given, including an illustrative example. This new approach is an alternative to the traditional first order GBT method.

The typical use of triangular and quadrangular facets in doubly curved facetted shells requires the use of triangulated truss systems or quadrangular truss framing with diagonals or cross tension cabling. In such a structure, the load carrying ability is based on concentrated forces in the framing system, while the glass merely serves as a separation of the inside environment from the outside. In this paper facetted glass shell structures with three way vertices, i.e. with three adjoining edges in each vertex are considered, since the load carrying ability of such a structure is achieved primarily by in-plane forces in the facets and the transfer of distributed in-plane forces across the joints. It is described how these facets work structurally, specifically how bending moments develop and cause possible stress concentrations in the corners, which are subjected to uplift. Apart from local bending moments from distributed load, other types of bending moments are likely to occur, especially if the shell has areas of low stiffness, for example along a free edge. A facetted shell structure has been modelled in a finite element program, and the resulting stresses are presented and discussed.

An improved and codifiable footbridge response evaluation is presented herewith, in which peak vertical accelerations are provided as a function of load return period in the form of response spectra. To achieve this, a series of Monte Carlo simulations are employed to generate vertical loads induced by a "random" crowd that are subsequently used in linear timehistory analyses of the response of bridges with varying fundamental frequencies. The peak accelerations are presented as a function of return period and it is shown that the acceleration response due to a crowd is lower than $\sqrt{N}$ times the response of a single pedestrian, which is often referred to as a conservative estimate for crowds.