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In the frame analysis, the local analysis model of the joint must follow the behavior of the joint. When completing the elastic global analysis, the initial rotational stiffness of the joints should be known to obtain the reliable moment distribution between the members of the frame. This paper evaluates the existing calculation approach for the initial rotational stiffness of welded rectangular hollow section T joints. Validation with the experiments shows that the current calculation approach significantly underestimates their initial rotational stiffness. Based on the existing experimental data, the paper proposes the improvement for determining the initial stiffness. The second part of the article investigates the effect of the axial force in the main member on the initial rotational stiffness of the joint. The conducted numerical study on square hollow section T joints shows that the reduction of their initial stiffness can reach 50%, when the main member experiences the normal stresses close to yielding. Using the curve fitting approach, the paper proposes and validates a corresponding chord stress function, similar to the existing ones for the moment resistance. acceptedVersion

Seismically designed mid- to high-rise steel moment resisting frames in the United States are commonly constructed with the lowest portion of the first story column embedded into a concrete footing to transfer large moments and forces. Despite their prevalence, these Embedded Column Base (ECB) connections have not been experimentally examined until recently, such that strength estimation methods for other types of connections are usually adapted for their design. Based on recent experiments, current approaches for designing ECB connections are examined, and a new strength characterization method is presented. Mechanisms for internal force transfer within the connection are postulated; these include horizontal bearing of the column flange against the concrete, panel zone shear, and vertical bearing of the embedded base plate against the concrete. The proposed approach has two components: (1) a process for moment distribution between the horizontal and vertical bearing mechanisms, and (2) idealized stress distributions for estimation of associated limit states. The proposed method is able to characterize the experimentally observed specimen strengths with good accuracy, such that the average test-predicted ratio is 1.01, with a coefficient of variation 0.06. No significant bias in accuracy of the method is observed with respect to test variables. Limitations of the study are discussed; these arise from its empirical aspects which may not be generally extrapolated to configurations significantly different from the experiments upon which the method is based.

The paper describes 36 experimental tests conducted on rectangular and square tubular columns filled with normal and high strength concrete and subjected to a non-constant bending moment distribution with respect to the weak axis. The test parameters were the nominal strength of concrete (30 and 90 MPa), the cross-section aspect ratio (square or rectangular), the thickness (4 or 5 mm) and the ratio of the top and bottom first order eccentricities e top/e bottom (1, 0.5, 0 and - 0.5). The ultimate load of each test was compared with the design loads from Eurocode 4, presenting unsafe results inside a 10% safety margin. The tests show that the use of high strength concrete is more useful for the cases of non-constant bending moment, whereas if the aim is to obtain a more ductile behavior the use of concrete-filled columns is more appealing in the cases of normal strength concrete with non-constant bending moments because, although they resist less axial force than the members with HSC, they obtain a softened post-peak behavior. © 2011 Elsevier Ltd., The authors wish to express their sincere gratitude to the Spanish Ministry of Education for the help provided through projects BIA2005_255 and BIA2009_9411, and to the European Community for FEDER funds.

Steel portal frames were traditionally designed assuming that beam-to-column joints are ideally pinned or fully rigid. This simplifies the analysis and structural design processes, but at the expense of not obtaining a detailed understanding of the behaviour of the joints, which in reality, have finite stiffness and are therefore semi-rigid. The last century saw the evolution of analysis methods of semi-rigid joints, from the slope-deflection equation and moment distribution methods, to matrix stiffness methods and, at present, to iterative methods coupling the global and joint structural analyses. Studies agree that in frame analysis, joint rotational behaviour should be considered. This is usually done by using the moment–rotation curve. Models such as analytical, empirical, experimental, informational, mechanical and numerical can be used to determine joint mechanical behaviour. The most popular is the mechanical model, with several variances (e.g. Component Method). A summary is given of the advantages and disadvantages and principal characteristics of each model. Joint behaviour must be modelled when analysing semi-rigid frames, which is associated with a mathematical model of the moment–rotation curve. Depending on the type of structural analysis required, any moment–rotation curve representation can be used; these include linear, bilinear, multilinear and nonlinear representations. The most accurate representation uses continuous nonlinear functions, although the multilinear representation is commonly used for mechanical models. This article reviews three areas of steel joint research: (1) analysis methods of semi-rigid joints; (2) prediction methods for the mechanical behaviour of joints; (3) mathematical representations of the moment–rotation curve.

Methods used for the design of steel beams supported at both ends are not well suited for the design of cantilevers against lateral buckling. The end restraints are very different for cantilevers, and the maximum displacements and twist rotations take place at the free ends, instead of near mid-span. Consequently, their buckling modes are very different to those of supported beams. The methods of allowing for the effects of the moment distribution on the elastic and inelastic buckling of supported beams use a mean of the moment distribution, which is weighted to allow for the maximum deformations being near mid-span. These methods are clearly inappropriate for cantilevers whose deformations are greatest at the free ends. Lateral buckling design methods for cantilevers are modifications of the methods for supported beams, but are of doubtful accuracy, and may be over conservative. In some cases there is little or no design guidance. This paper summarizes information on the effects of the moment distribution and load height on the elastic buckling of cantilevers which can be used in the method of design by buckling analysis. It then extends a method of designing supported beams by inelastic buckling analysis to allow for the effects of the moment distribution on the inelastic buckling of cantilevers. This extended method is then used to provide improved design methods for cantilevers which are consistent with those for simply supported beams. A worked example is summarized.

A simple model of the elastic buckling of steel beams with rigid and continuous lateral restraints has been developed. It is based on a method of displacements that associate lateral restraint conditions. A numerical procedure for resolving the resulting partial differential equations is proposed in which rotations are approximated by trigonometric functions. The effects of moment distribution and continuous restraints on the elastic flexural–torsional buckling of beams are also studied and design approximations and procedures developed. This study also highlights that the restraint of the tensioned part of the beam is not sufficient to limit lateral buckling. The use of these solutions is demonstrated by two examples.

Floorbeams of orthotropic plated bridge decks are generally elements with a low slenderness, especially in the case of railway bridges. When loaded, such elements generate not only flexural deformations but shear deformations as well. Depending on the configuration, these shear deformations can be considerably large and should certainly not be neglected. In a design according to the Pelikan–Esslinger method, this deformation is taken into account in the second stage of the calculation of the orthotropic deck. At this stage, the additional bending moments, shear forces and floorbeam reactions due to the floorbeam flexibility are evaluated. The deflection of a directly loaded floorbeam creates a distribution of the load to adjacent non-loaded floorbeams. In addition, the deflection will affect the longitudinal ribs, increasing the sagging moments at midspan and decreasing the bending moments at the supports of the ribs provided by the floorbeams. In this paper a method is developed to take the shear deformation in the floorbeam into account, thus correcting the Pelikan–Esslinger method. The correction is especially important since the floorbeam web is frequently further weakened by cutouts for the longitudinal ribs and in some cases additional cope holes. The floorbeam web resisting the shear deformation is further reduced by these openings, increasing the importance of shear deformations even for more slender floorbeams. The validity of the proposed method is checked by full finite element calculation using shell elements which inherently comprise shear deformation. The effect of the correction on the calculations in the second stage of the calculation are relatively small for the floorbeam reactions; on the contrary, it can be quite large for the additional bending moments in the longitudinal ribs. In that case, the effect is worth considering.

Steelwork design standards consider lateral–torsional buckling as one of the ultimate limit states that must be checked for steel members in bending. The buckling resistance assessment is usually based on buckling curves and requires the computation of the elastic critical moment, which is strongly dependent on both the bending moment distribution and restrictions at end supports. This paper focuses on the equivalent uniform moment factor (EUMF) which is used to compute the elastic critical moment. A review of EUMF values given by modern steelwork standards and their comparison with recent results presented in the literature shows that whilst codes may lead to very conservative values for simply supported beams, non-conservative values are obtained in the case of support types designed to restrict lateral bending and warping. In order to clarify situations where EUMF values proposed by modern codes appear contradictory with recent computational results, the paper presents a significant set of EUMF values obtained using both finite difference and finite element techniques. Particular attention has been given to instances where lateral bending and warping are prevented at beam supports since very few results from these cases have been published. A major advantage of codes, such as the American AISC LRFD and the British BS 5950-1, is that they provide closed-form expressions to compute the EUMF for any moment distribution. Unfortunately, these closed-form expressions do not take into account changes in the EUMF due to end support restrictions. This paper presents a general closed-form expression that not only delivers similar advantages but also improves the results given by those codes for some loading cases.

A general procedure for incorporating the effects of joint flexibility into standard methods for the analysis of frames is presented. The method can allow for joint flexibility associated with all six degrees of freedom normally considered when analysing three-dimensional frames, including coupling between deformations. It can also allow for the finite size and exact location of connections. Simple examples using the moment distribution technique, slope deflection equations and matrix stiffness method illustrate the application of the proposal. Additional examples to illustrate the effects of connection length on the frame moment distribution, lateral drift and column load capacities are also present.

This paper describes an experimental study of the inelastic flexural-torsional buckling behaviour of restrained continuous beam-columns typical of those found in multi-storey steel frames. Nine specimens were tested (and five re-tested) under a variety of loading conditions to provide experimental data on the effects of force and moment distribution, continuity, and end restraints. The experimental data will provide benchmark results for future theoretical analyses on the inelastic buckling behaviour of continuous beam-columns. Results presented include failure load combinations, variations of in-plane and out-of-plane displacements with applied load, measurements of geometrical and material imperfections, and results of subsidiary tests to determine the full plastic moment and squash load. A preliminary assessment of present design rules for beam-columns is carried out.