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Steel thin-walled profiles are the backbone of modern lightweight construction, offering exceptional efficiency in terms of material use and assembly speed. However, their inherent susceptibility to buckling under complex loading conditions, especially bending torsion, has limited their broader application in advanced structural systems. This paper introduces a groundbreaking method for analyzing the bending-torsion behavior of steel thin-walled C-profile beams, specifically focusing on the critical but often overlooked factor of support warping stiffness. Unlike conventional studies that primarily examine local or global buckling resistance, this research pioneers a comprehensive approach that integrates the warping stiffness of supports into the structural analysis. Through the introduction of novel coefficients—warping (0.377–0.484) and bending (0.616–0.672)—this study established a new paradigm in the design and stability analysis of thin-walled beams. Our findings reveal that incorporating support warping stiffness can dramatically increase normal stresses by 2–4 times within the span, a revelation that significantly alters existing design assumptions. The study also demonstrated how sectorial stiffness, a key parameter, directly enhances the warping stiffness of the supports, while the bending stiffness of the beam has negligible impact on the compliance factor. This novel insight provided a substantial leap forward in accurately predicting the complex interaction between bending and torsion in lightweight steel structures. By addressing a critical gap in the literature, this research not only advances the theoretical understanding of thin-walled profiles but also offers practical implications for optimizing the structural design of modern construction systems, enhancing both performance and safety. • A method was developed for determining the bimoment in beams with support warping stiffness. • A method is proposed for determining the actual reference values of the bending moment and bimoment from numerically obtained values of the reference normal stresses. • Range of values of the coefficients are revealed, considering warping and bending finite stiffness of thin-walled profiles, for the case when stud profiles are supported inside track profiles of various thicknesses and high of 150 mm. • With an increase in the sectorial stiffness of the profile, the support warping stiffness increases, while with increase in bending stiffness of the beam, the compliance bending factor of the support changes insignificantly. • Considering the warping stiffness of the support connection leads to an increase in the obtained normal stresses in the span of a thin-walled profile by 2-4 times, depending on the sectorial stiffness of the profile. [ABSTRACT FROM AUTHOR]

Highlights • Torsion and warping are usually analysed assuming simplified boundary conditions. • Tests of mayor axis joints under torsion about the axis along the length of the beam. • A parametric study is performed to assess the stiffness and resistance by means of FEM. • These joints behave as semi-rigid and full strength when compared with the beam. • A mechanical model and analytical expressions are proposed and checked with FEM. Abstract Torsional effects in joints need to be investigated in order to get a complete model of the joint and also to assess the real boundary conditions for the lateral torsional effects in the beams of structural frames. Phenomena such as: torsion, warping, lateral buckling, etc. are usually analysed assuming simplified boundary conditions, namely pinned or rigid, in frame analysis which can lead to erroneous and non-conservative results. With the aim of knowing the correct boundary conditions and real behaviour of the joints under torsion, an experimental program is carried out consisting of two tests of mayor axis doubled extended bolted end plate joints subjected to torsion about the axis along the length of the beam. These experimental results have allowed the validation of the finite element models carried out using the program Abaqus. Once the models are validated models, a parametric study is performed to assess the stiffness and resistance. This study also verifies that these joints behave in a semi-rigid way when compared with the torsional characteristics of the attached beam. Besides, the beam fails prior to the connection in most cases, and therefore, the joints can be assumed to behave as full-strength. Analytical expressions are proposed and checked with the FEM results proving that the proposed analytical formulae and the proposed mechanical model can predict the stiffness quite accurately, with an average error of 8.5%. Despite these joints can be classified as full-strength under torsion, an assessment of their resistance is done as well. [ABSTRACT FROM AUTHOR]

Practical design of bridges and other structures requires the use of quick and simple calculation methods, rather than the use of tridimensional models using shell or solid finite elements. These methods have to be used for a general loading state, taking into account the different structural mechanisms, and generating the results required to apply the verifications of the structural codes and to understand the structural behavior. In this work, a beam-type element is proposed to adress these objetives for the case of thin walled sections. This element has three nodes, with five-degrees of freedom per node, more than the six degrees of a conventional 3D beam, incorporates the effects of shear lag, torsion and distortion homogeneous and non homogeneous in the distribution of normal stress. Various examples were tested to verify the validity of the beam element according different calculation methods. [ABSTRACT FROM AUTHOR]

This paper presents a new approach to the analysis of thin-walled beams. The proposed model is developed by utilizing the eXtended Finite Element Method (XFEM). Global enrichment functions are added to a standard 3D Finite Element (FE) coarse mesh to enhance its performance and reduce the number of degrees of freedom. These analytical functions provide an approximate solution in the longitudinal direction of the beam. The resulting model bridges the gap between the Finite Prism Method (FPM), which provides an efficient approximation to beam bending with analytical functions but has also well-known limitations, and a detailed 3D FE model, which can accurately resolve thin-walled structures but is computationally demanding. Our method can be easily extended for beams with non-prismatic cross-sections (e.g., tapered beams) or with perforations, which makes it more general than other semi-analytical methods, such as the FPM. However, these extensions are not in the scope of this paper. Additionally, one can improve the solution by sectional and/or longitudinal mesh refinements. The performance of the model is investigated on two benchmark problems. The results show that the proposed method captures different global and sectional deformation modes of thin-walled beams when subjected to torsion, including shear-lag and distortion cross-section. Furthermore, convergence studies demonstrate the superior performance of the proposed method as compared to the FPM, and a 3D FE model with a coarse mesh. • A new model is proposed for the analysis of thin-walled beams. • The model is developed based on the extended finite element method. • Global enrichment functions are added based on the free-vibration modes of continuous beams. • An explicit stiffness matrix is formulated for a 3D eight-node brick element with enrichment functions. • The model captures different modes of deformation including shear-lag and distortion of the cross-section. [ABSTRACT FROM AUTHOR]

This work intends to demonstrate the effect of geometrically non-linear cross-sectional analysis of certain composite beam-based four-bar mechanisms in predicting the three-dimensional warping of the cross-section. The only restriction in the present analysis is that the strains within each elastic body remain small (i.e., this work does not deal with materials exhibiting non-linear constitutive laws at the 3-D level). Here, all component bars of the mechanism are made of fiber-reinforced laminates. They could, in general, be pre-twisted and/or possess initial curvature, either by design or by defect. Each component of the mechanism is modeled as a beam based on geometrically non-linear 3-D elasticity theory. The component problems are thus split into 2-D analyses of reference beam cross-sections and non-linear 1-D analyses along the three beam reference curves. The splitting of the three-dimensional beam problem into two- and one-dimensional parts, called dimensional reduction, results in a tremendous savings of computational effort relative to the cost of three-dimensional finite element analysis, the only alternative for realistic beams. The analysis of beam-like structures made of laminated composite materials requires a much more complicated methodology. Hence, the analysis procedure based on Variational Asymptotic Method (VAM), a tool to carry out the dimensional reduction, is used here. The representative cross-sections of all component bars are analyzed using two different approaches: (1) Numerical Model and (2) Analytical Model. Four-bar mechanisms are analyzed using the above two approaches for Ω = 20 rad / s and Ω = π rad / s and observed the same behavior in both cases. The noticeable snap-shots of the deformation shapes of the mechanism about 1000 frames are also reported using commercial software (I-DEAS + NASTRAN + ADAMS). The maximum out-of-plane warping of the cross-section is observed at the mid-span of bar-1, bar-2 and bar-3 are 1.5 mm, 250 mm and 1.0 mm, respectively, for t = 0:5 s. [ABSTRACT FROM AUTHOR]

This paper summarizes the results from an experimental study on the behavior of concrete slabs-on-ground in a controlled environment. The test program characterizes the dimensional properties of selected concrete materials, evaluating their performance as real slabs-on-ground in that they are exposed to the controlled environment on the top surface and to the ground moisture on the bottom surface. The concrete mix designs examined included normal-strength portland cement concrete ( PCC ), high-strength concrete ( HSC ), concrete using shrinkage reducing admixtures ( SRA ), and concrete using calcium sulfoaluminate cement ( CSA ). The data include standard concrete material characterization test results, joint movements, internal relative humidity and temperature over the slab depth. It was found that the concrete using CSA was very stable with no long term shrinkage, cracking or warping, while typical PCC and HSC continued to show crack growth at over 600 days of age. The concrete using SRA had a minor impact at early age and limited impact on long term sectional stability. [ABSTRACT FROM AUTHOR]

In this paper, the analysis of homogenous curved beams of arbitrary cross section (thin- or thick-walled) taking into account the coupling of extension, flexure and torsion, nonuniform warping as well as shear deformation effects (shear lag due to both flexure and torsion) has been studied. The curved beam is subjected to the combined action of arbitrarily distributed or concentrated axial and transverse loading, as well as to bending, twisting and warping moments. Its edges are subjected to the most general boundary conditions. Nonuniform warping distributions are taken into account by employing four independent warping parameters multiplying a shear warping function in each direction and two torsional warping functions, which are obtained by solving corresponding boundary value problems, formulated exploiting the longitudinal local equilibrium equation. Ten one-dimensional boundary value problems are described by second-order differential equations and solved employing the Analog Equation Method (AEM), a boundary element based method, using either constant or quadratic elements for the representation of the adopted fictitious loads. Results are compared with FEM solutions employing curved beam, shell or 3-d solid elements. [ABSTRACT FROM AUTHOR]

An innovative higher-order beam theory, capable of accurately taking into account flexural–shear–torsional interaction, is originally combined with a force-based formulation to derive the corresponding finite element. The selected set of higher-order deformation modes leads to an explicit and direct interaction between three-dimensional shear and normal stresses. Namely, cross-sectional displacement and strain fields are composed of independent and orthogonal modes, which results in unambiguously defined generalised cross-sectional stress-resultants and in a minimisation of the coupling of equilibrium equations. On the basis of work-equivalency to three-dimensional continuum theory, dual one-dimensional higher-order equilibrium and compatibility equations are derived. The former, which govern an advanced form of beam equilibrium, are strictly satisfied via stress fields arising from the solution of the corresponding systems of coupled differential equations. The formulation, which is numerically validated in a companion paper for both linear and nonlinear material response, inherently avoids shear-locking and accurately accounts for span loads. Finally, the superiority of force-based approaches over displacement-based ones, well established for inelastic behaviour, is also demonstrated for the linear elastic case. [ABSTRACT FROM AUTHOR]

The specific features of the proposed force-based formulation derived in the companion paper, which is applied for the first time to higher-order beam theories, are herein thoroughly validated. Introductory numerical examples illustrate the influence of mesh refinement, boundary conditions, and slenderness ratios for isotropic linear elastic response. Specific higher-order effects—unique to the developed element—are then suitably interpreted, as well as the formulation appropriateness to consider distributed loads and to model three-dimensional behaviour, which is verified with solid finite element analyses. Extensive comparisons against existing proposals, namely other refined higher-order beam theories, emphasize the performance of the proposed approach. Finally, the nonlinear response of the element with a multiaxial J2 linear plasticity material model is analysed, highlighting its advantages in relation to a classical force-based Euler–Bernoulli beam using a one-dimensional plastic material model with kinematic hardening. [ABSTRACT FROM AUTHOR]

This paper presents a continuation algorithm based on the Asymptotic Numerical Method (ANM) to study instability phenomena of large torsion of thin-walled open sections beams under various external loadings. The proposed algorithm connects perturbation techniques with a discretization principle and a continuation method without the use of a correction process. In the model, the equilibrium and material constitutive equations are established without any assumption on torsion angle amplitude. In presence of eccentric loads and large torsion context, the right hand side of the equilibrium equations is highly nonlinear and contributes to the tangent stiffness matrix. A 3D beam element having two nodes with seven degrees of freedom is considered in mesh process. Several numerical examples from buckling of thin-walled open sections beams are analyzed to assess the efficiency and the reliability of the method. Comparisons are made with known commercial software. The proposed ANM algorithm is more reliable and less time consuming than other iterative classical methods. [ABSTRACT FROM AUTHOR]

Incremental launching is a common and convenient methodology to build continuous girder bridges on several piers. Although it has mainly been applied to straight bridges with box sections, today it is also used for construction of horizontally curved bridges with concrete and composite steel-concrete closed or open sections like I-girders. In these cases the contribution of torsion to the stress state becomes of primary importance when the construction stages of these bridges are analysed. Moreover, the presence of thin-walled cross-sections, makes the analysis of non-uniform torsion fundamental when the angle of twist per unit length is not constant or warping is prevented in those sections where rigid internal diaphragms occur. Consequently the stress state in the launching phases can be strongly influenced by non-uniform torsion, especially for the evaluation of axial stresses in I-girder bridges, where non-uniform torsion presents its maximum influence. In this paper a methodology for the repetitive analysis of launching steps is proposed, based on the Hamiltonian Structural Analysis method, which takes into account the internal characteristics of non-uniform torsion (warping and bimoment) in order to evaluate the influence of prevented warping on the stress state at each stage of launching. The methodology is convenient because it can be considered a sort of generalised beam theory and presents a reduced computational burden with respect to finite element or boundary element procedures, with fast solution of many bridge launching static schemes. A validation of the method is given through a comparison with finite element procedures and literature data. An application is presented on a bridge with different typologies of cross-section in order to compare the different behaviours of thin-walled sections and the different degree of influence of non-uniform torsion on the stress state. The results are given in the form of envelope graphs of internal forces and stresses for the entire launching sequence and for the different cases examined. [ABSTRACT FROM AUTHOR]

A distortional theory is developed for the analysis of doubly symmetric and mono-symmetric wide flange beams under general loading. The governing differential equations of equilibrium and associated boundary conditions are derived based on the principle of potential energy. The theory captures shear deformation effects in the web and local and global warping effects. In contrast to classical beam theories, the present study captures web distortion by accounting for its flexibility within the plane of the cross-section while considering the flanges as Euler-Bernoulli beams. The formulation yields two systems of coupled differential equations of equilibrium in seven displacements fields. The first system governs the longitudinal transverse response and involves three displacement fields, and the second system governs the lateral torsional response and involves four displacement fields. Closed form solutions are then developed for both coupled systems under general loading. Numerical solutions for practical problems are then provided to illustrate the applicability of the formulation. Comparisons to results based on 3D shell finite element solutions show the validity of the results. The theory preserves the relative simplicity of one dimensional beam theories while effectively capturing the three-dimensional distortional phenomena normally captured within computationally expensive 3D FEA. [ABSTRACT FROM AUTHOR]

Beam-type elements based on the theories of Euler–Bernoulli, Timoshenko, and Vlasov are widely used in civil engineering. However, shell and solid finite elements are often used when the effects on normal stresses of either shear deformation or distortion are considered important. Numerically validated in an earlier study with finite element models for shell-type structures, the same one-dimensional finite element model is further developed in this study with a low number of degrees of freedom per node that includes all the structural mechanisms without using 3D finite element models. Laboratory testing of an instrumented steel box girder is conducted, to improve validation of the goodness of fit of the finite element model with real structural behavior. • Calculation of the resistant modes of sections (shear, torsion and distortion). • Improvement of the description of the new beam element by applying energetic methods. • Laboratory testing of an instrumented steel box girder. • Validation of fitting with a one-dimensional finite element of the real behavior. [ABSTRACT FROM AUTHOR]

Highlights: [•] Bars under general torsional boundary conditions and loading. [•] Investigation of secondary torsional moment deformation effect. [•] Assessment of EC3 – part 1.1 guidelines related to torsion. [•] Necessity of employing a torsional shear correction factor is studied. [•] Reliability of Thin Tube Theory in open- and closed-shaped section bars. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a new beam finite element is presented, with an accurate representation of normal stresses caused by “shear lag” or restrained torsion. This is achieved using an enriched kinematics, representing cross-section warping as the superposition of “warping modes”. Detailed definitions and computational methods are given for these associated “warping functions”. The exact solution of the equilibrium equations is given for a user-defined number of warping modes, though elastic results are totally mesh-independent. [Copyright &y& Elsevier]

Abstract: In this paper a general solution to the geometrically nonlinear analysis of plates stiffened by arbitrarily placed parallel beams of arbitrary doubly symmetric cross section, subjected to arbitrary loading is presented. The plate–beam structure is assumed to undergo moderate large deflections and the nonlinear analysis is carried out by retaining nonlinear terms in the kinematical relations. According to the proposed model, the stiffening beams are isolated from the plate by sections in the lower outer surface of the plate, while the arising tractions in all directions at the fictitious interfaces are taken into account. These tractions are integrated with respect to each half of the interface width, yielding two interface lines along which the loading of the beams as well as the additional loading of the plate is defined. Their unknown distribution is established by applying continuity conditions at the interfaces, in all directions. The utilization of two interface lines for each beam enables the nonuniform distribution of the interface transverse shear forces and the nonuniform torsional response of the beams to be taken into account. Six boundary value problems are formulated and solved using the Analog Equation Method (AEM), a BEM based method. Application of the boundary element technique leads to a system of nonlinear and coupled algebraic equations which is solved using iterative numerical methods. The adopted model permits the evaluation of the shear forces at the interfaces in both directions, the knowledge of which is very important in the design of prefabricated ribbed plates. [Copyright &y& Elsevier]

Abstract: In this paper a boundary element method is developed for the evaluation of warping shear stresses of bars of an arbitrary doubly symmetric constant cross section undergoing nonuniform torsional vibrations taking into account the effect of geometrical nonlinearity. The bar is subjected to arbitrarily distributed or concentrated conservative dynamic twisting and warping moments along its length, while its edges are supported by the most general torsional and axial boundary conditions. The transverse displacement components are expressed so as to be valid for large twisting rotations (finite displacement — small strain theory), thus the arising governing differential equations and boundary conditions are in general nonlinear. Employing a variational approach, a coupled nonlinear initial boundary value problem with respect to the main unknown kinematical components and two boundary value problems with respect to the primary and secondary warping functions are formulated. The solution of the last two problems is performed by a pure BEM approach requiring exclusively boundary discretization of the bar’s cross section and leading to the evaluation of the warping shear stresses. The arising linear system of equations related to the secondary warping function is singular and a special technique is used to perform its regularization. The validity of the negligible axial inertia assumption is examined for the problem at hand. [Copyright &y& Elsevier]

Abstract: In this paper, the effect of axial restraint in the elastic–plastic uniform torsion analysis of cylindrical bars taking into account the effect of geometric nonlinearity is presented employing the boundary element method. The bar is axially elastically supported at the centroids of its end cross sections, treating the cases of free axial boundary conditions (vanishing axial force), restrained axial shortening or given axial force as special ones. The cross section of the bar is an arbitrary doubly symmetric composite one, consisting of materials in contact, each of which can surround a finite number of inclusions, while the case of a homogeneous cross section is treated as a special one. The stress–strain relationships for the materials are assumed to be elastic–plastic-strain hardening. The incremental torque–rotation relationship is computed based on the finite displacement (finite rotation) theory, that is the transverse displacement components are expressed so as to be valid for large rotations and the longitudinal normal strain includes the second-order geometrically nonlinear term, often described as the “Wagner strain”. The proposed formulation does not stand on the assumption of a thin-walled structure and therefore the cross section’s torsional rigidity is evaluated exactly without using the so-called Saint-Venant’s torsional constant. The torsional rigidity of the cross section is evaluated directly employing the primary warping function of the cross section depending on both its shape and the progress of the plastic region. A boundary value problem with respect to the aforementioned function is formulated and solved employing a BEM approach. The developed procedure retains most of the advantages of a BEM solution over a pure domain discretization method, although it requires domain discretization, which is used only to evaluate integrals. The significant increase of the torsional rigidity of the bar and the arising axial force due to the axial restraint are concluded. [Copyright &y& Elsevier]

Abstract: In this paper a general solution for the dynamic analysis of plates stiffened by arbitrarily placed parallel beams of arbitrary doubly symmetric cross section subjected to an arbitrary dynamic loading is presented. According to the proposed model, the stiffening beams are isolated from the plate by sections in the lower outer surface of the plate, taking into account the arising tractions in all directions at the fictitious interfaces. These tractions are integrated with respect to each half of the interface width resulting two interface lines, along which the loading of the beams as well as the additional loading of the plate is defined. Their unknown distribution is established by applying continuity conditions in all directions at the interfaces. The utilization of two interface lines for each beam enables the nonuniform distribution of the interface transverse shear forces and the nonuniform torsional response of the beams to be taken into account describing better in this way the actual response of the plate–beam system. The analysis of both the plate and the beams is accomplished on their deformed shape taking into account second-order effects. The method of analysis is based on the capability to establish a flexibility matrix with respect to a set of nodal mass points, while a lumped mass matrix is constructed from the tributary mass areas to these mass points. Six boundary value problems are formulated and solved using the Analog Equation Method (AEM), a BEM based method. Both free and forced damped or undamped transverse vibrations are considered and numerical examples with great practical interest are presented. The discrepancy in the obtained eigenfrequencies using the presented analysis (which approximates better the actual response of the plate–beam system since it permits the evaluation of the shear forces at the interfaces in both directions) and the corresponding ones ignoring the inplane forces and deformations justify the analysis based on the proposed model. Three additional finite element models using beam, shell or solid finite elements are also employed for the verification of the accuracy of the results of the proposed model. [Copyright &y& Elsevier]

• Exact analysis of non-uniform torsion is difficult. • Addition of uniform and warping torsion stiffnesses leads to approximate solutions. • Computer programs are not needed. • Approximations are generally of acceptable accuracy. • Superposition allows solutions for many torque distributions. It is difficult to obtain closed form exact solutions for the non-uniform torsion of beams. Advanced finite element methods easily produce very accurate solutions, but simple programs are not widely available. One simple program is validated by comparing its solutions with closed form solutions. A simple approximate method is proposed which combines the uniform and warping torsion stiffness approximations. The determination of the warping stiffness approximation is simplified by using the moment-area method. The approximate twist rotations are compared with the accurate solutions, are shown to be of generally acceptable accuracy, and in most cases to be conservative. Approximate solutions for the central twist rotations of simply supported beams with off-centre torques can be combined using superposition to find solutions for a wide range of torque loadings. A worked example is given. [ABSTRACT FROM AUTHOR]

• More torsional restraint in a system improves agreement between analyses types. • At lower loading, doubly symmetric response can agree with more detailed methods. • Non-symmetric behavior was more impactful at higher loading and lead to variations. • Doubly symmetric analyses fail prematurely with stability problems without warping. • Ignoring non-symmetric properties can cause conservative and unconservative results. Cold-formed steel components exist in a variety of structural systems including wall, floor, and roofing systems. A common feature of these cross sections is that they are often open and singly symmetric or point symmetric. While design requirements for these cross-sections account for the relevant effects resulting from their lack of symmetry, structural analysis programs do not always consider these effects. Engineers will use structural analysis programs to calculate the appropriate load sharing among members in the structural system. Accounting for the appropriate stiffness of each member and the related deformations is a vital component to determining the final distribution of bending moment, forces, and displacements. Many common structural analysis programs treat all sections as doubly symmetric without warping. Removing this assumption causes non-symmetric cross sections to exhibit nonplanar displacements and complicates the stability limits. The analysis of two structural systems composed of non-symmetric members was completed with varying member modeling assumptions utilizing multiple finite element software programs. A single channel portal frame was investigated that was subjected to simulated gravity load and wind loading with varying bracing support. Additionally, a roofing system with Z-section or channel purlins and channel bracing was investigated. The finite element analysis results were compared among the various modeling assumptions and existing experiments where available. It was observed that good agreement between the doubly symmetric and the more complex analyses was obtained in some instances, particularly when the members were loaded to low levels and highly constrained. However when loading is closer to the elastic limits and members can more freely move out-of-plane, the inclusion of non-symmetric section properties becomes a critical factor in determining an accurate response for both internal forces and displacements. The variations between these different analysis methods were found to be difficult to predict due to the cumulative effect of the competing mechanical behaviors that could result in either conservative or unconservative responses when ignoring non-symmetric behavior. [ABSTRACT FROM AUTHOR]

• Major-axis end plate joints with additional plates are tested under torsion. • A parametric study is performed to assess the stiffness by means of FEM. • This research verifies that these joints behave as semi-rigid and full strength. • They improve the behaviour of those without additional plates. • A mechanical model and analytical expressions are proposed and checked. This investigation deals with the characterization of the torsional behaviour of major axis steel joints with doubled extended end-plate and additional plates welded to the column flanges at the height of the beam flanges. One aim of this research is to provide the real joint torsional boundary conditions under which the beam elements behave for frame analysis and stability checks, thus avoiding the need for simplifications such as pinned or rigid joint conditions. Another objective is to characterize the stiffness of 3D joints, which requires knowledge of each of the individual components, such as the ones studied in this investigation. With this purpose two experimental tests were done, followed by a parametric study performed with calibrated finite element models that led to the analytical expressions of the components that characterize the torsional stiffness of this kind of joints. After a detailed analysis, these joints were found to behave as semi-rigid and full-strength. The semi-rigid behaviour is due to the torsional warping effects transmitted by the beam. The results are also compared with those of the same joints but without additional plates (described in a recent publication) and it is shown that the additional plates increase the joint stiffness significantly. [ABSTRACT FROM AUTHOR]