Slender Members Research Articles

Analysis of equal leg single-angle section beams subjected to biaxial bending and constant axial compressive force

Single-angle section beams are generally loaded parallel to their geometrical axes and their cross-sections are not symmetrical to their principal axes. Even equal leg angle beams have only one symmetrical axis. Many types of loading cause biaxial bending and axial forces in these members. Since single-angle section beams are slender members, they also need to be analyzed in terms of flexural buckling, lateral torsional buckling and local buckling effects. In this study, a calculation procedure is presented to analyze the nominal loads of equal leg angle section beams loaded vertically to the axis of the beam. It is assumed that the axial force is composed of a constant compressive force. The constant axial force is only taken into consideration for the uniform compressive stress and the second-degree effects caused in the cross-section. Thus only the biaxial bending moments remain. The first yield, full plastic and critical lateral torsional buckling moments for biaxial bending are calculated with respect to the slenderness of the beam and the axial force. The nominal design force on the cross-section is calculated according to the load and resistance factor design rules. The analysis proposed for the constant axial load can also be used for other axial forces, by using an iterative calculation procedure.

Recent developments in the design of cold-formed steel members and structures

Cold-formed steel members and structures are extremely widespread in use at the present time. The design analysis of such structures is often complex, as their behaviour can be influenced by effects, which arise due to the slenderness of members, walls and cross-sections. Prime among these effects are the various types of buckling which can occur, and which may interact with each other to promote failure at loads substantially less than those, which would be obtained in the absence of these effects. The complications induced by such effects must be taken into account in design, if the potential benefits offered by the use of such members are to be realised, and in recent design specifications this has been realised. In this paper the main types of cold-formed steel members are described, the particular characteristics affecting their design are discussed, as are the ways in which design specifications deal with these characteristics.

Location of plastic hinges in axially loaded steel members

Steel structure design standards for both New Zealand and Australia have equations limiting the maximum axial force which can be applied to a yielding steel column as a function of the member slenderness and end moment ratio. These equations were developed to ensure plastic hinge rotation capacity primarily by encouraging flexural yielding to occur at the member ends rather than along the column length. This paper develops an analytical procedure to determine the axial force associated with plastic hinges occurring away from the column ends. It is shown that current code equations conservatively estimate the axial force to ensure yielding at the column ends when the axial force ratio is greater than 0.15, and they are non-conservative for lower axial force ratios. Empirical equations to prevent yielding away from the member ends are developed, and simplifications of these equations are proposed for code adoption.

Application of clan member signal method in structural damage detection

It is well known that in most cases, a reference is necessary for structural health diagnosis, and it is very difficult to obtain such a reference for a given structure. In this paper, a clan member signal method (CMSM) is proposed for use in structures consisting of groups (or clans) that have the same geometry, i.e., the same cross section and length, and identical boundary conditions. It is expected that signals measured on any undamaged member in a clan after an event could be used as a reference for any other members in the clan. To verify the applicability of the proposed method, a steel truss model is tested and the results show that the CMSM is very effective in detecting local damage in structures composed of identical slender members.

Precast Concrete, L-Shaped Spandrels Revisited: Full-Scale Tests

This paper presents results from full-scale testing conducted on 4 precast, prestressed concrete L-shaped spandrels. The 4 L-shaped spandrels were each loaded through 12-ft-long, prestressed double tees that rested on the spandrel ledge at one end and on an independent support at the other. None of the beams were constructed with closed stirrups of mild-steel reinforcement. Rather, different arrangements of transverse L-shaped bars, welded-wire reinforcement, and longitudinal bars were provided to resist the shear and torsion induced in the spandrels. Shear and torsion forces were created by the double-tee reaction forces that were loaded eccentrically to the spandrels. The transverse and longitudinal reinforcement resisted the combined effects of vertical shear and out-of-plane bending of the web and satisfied minimum vertical hanger reinforcement requirements for ledge-to-web attachment. All beams sustained loads in excess of their factored design loads. Eliminating the need for closed reinforcement in slender spandrels would be of significant benefit to the precast concrete industry. This design approach would enhance constructability of slender members, which could increase plant productivity and reduce overall costs. Behavior of all 4 spandrels at various limit states is presented, including crack patterns and failure modes. Researchers used these test results to better understand the fundamental mechanism developed in the L-shaped spandrels to resist shear and torsion.

Rain-wind induced vibrations of cables in laminar and turbulent flow

In the last decades there have been frequent reports of oscillations of slender tension members under simultaneous action of rain and wind - characterized by large amplitudes and low frequencies. The members, e.g. cables of cable-stayed bridges, slightly inclined hangers of arch bridges or cables of guyed-masts, show a circular cross section and low damping. These rain-wind induced vibrations negatively affect the serviceability and the lifespan of the structures. The present article gives a short literature review, describes a mathematical approach for the simulation of rain-wind induced vibrations, sums up some examples to verify the calculated results and discusses measures to suppress the vibrations.

Application of system identification techniques in efficient modelling of offshore structural response. Part I: Model development

Offshore structures are exposed to random wave loading in the ocean environment and hence the probability distribution of the extreme values of their response to wave loading is of great value in the design of these structures. Wave loading on slender members of bottom-supported jacket or jack-up structures is frequently calculated by Morison’s equation. Due to nonlinearity of the drag component of Morison wave loading and also due to intermittency of wave loading on members in the splash zone, the response is often non-Gaussian; therefore, simple techniques for derivation of their extreme response probability distribution are not available. Finite-memory nonlinear systems (FMNS) are extensively used in establishing a simple relationship between the output and input of complicated nonlinear systems. In this paper, it will be shown how the response of an offshore structure exposed to Morison wave loading can be approximated by the response of an equivalent finite-memory nonlinear system. The approximate models can then be used to determine the probability distribution of response extreme values with great efficiency. Part I of this paper is devoted to the development of an efficient FMNS model for offshore structural response while part II is devoted to the validation of the developed models.

Strength of biaxially loaded slender I-section beam-columns

The strength of a slender section is governed by local buckling of its elements. The local buckling mode is mainly affected by the width to thickness ratios of elements forming the section and the member slenderness ratio. A nonlinear finite element model was developed in this paper to study the effect of the mentioned factors on the capacity of biaxially loaded slender I-section beam–columns. A group of I sections was selected with varying flange width to flange thickness and web width to web thickness ratios. Different member slenderness ratios were chosen to study the different modes of failure. The results show that the linear interaction equation is safe and provides a good fit to the ultimate capacity of members with intermediate slenderness ratios. It is conservative, however, for short member slenderness ratios. Lastly, compared with the newly developed finite element model, the 1996 edition of the American Iron and Steel Institute specification for cold-formed steel structural members and the European Committee for Standardization Eurocode 3 conservatively predict the capacity of members, especially for large ratios of minor axis to major axis bending.Key words: structural engineering, steel, stability, buckling, biaxial loads, ultimate strength.

Behaviour of fire-exposed concrete-filled steel tubular beam columns repaired with CFRP wraps

This paper presents the test results of fire-exposed concrete-filled steel tubular (CFST) beam columns repaired by unidirectional carbon fibre reinforced polymer (CFRP) composites. Both circular and square specimens were tested to investigate the repair effects of CFRP composites on them. The test results showed that the load-bearing capacity of the fire-exposed CFST beam columns was enhanced by the CFRP jackets to some extent, while the influence of CFRP repair on stiffness was not apparent. The strength enhancement from CFRP confinement decreased with the increasing of eccentricity or slenderness ratio. Ductility enhancement was also observed except those axially loaded shorter specimens with rupture of CFRP jackets at the mid-height, occurred near the peak loads. However, the strengths of all repaired specimens have not been fully restored due to the long exposure time of them in fire. From the test results, it is recommended that, in repairing severely fire-damaged CFST members, slender members or those members subjected to comparatively large bending moments, other appropriate repair measures should be taken.

Stabilization of Surficial Slides Using Recycled Plastic Reinforcement

Surficial slope failures, or nuisance slides, constitute a significant economic and manpower burden for many transportation agencies because of the frequent and recurring nature of the slides. TRB recently estimated that annual costs for stabilization of nuisance slides exceed the costs for repair of major landslides; this estimate suggests that annual costs for repair of nuisance slides on the National Highway System alone exceed $100 million. Recent work has shown the feasibility of using slender recycled plastic members for in situ reinforcement of surficial slides in slopes and embankments. This paper describes the activities performed to evaluate the technique and the results and conclusions derived from the work. Topics covered include the description of five instrumented field test sites, material properties of the recycled plastic members used, construction equipment and techniques used to install the members, general performance observed at the field test sites, and the costs of the technique as compared with other methods.

Optimum geometry design of nonlinear braced domes using genetic algorithm

Domes are lightweight and cost effective structures that are used to cover large areas. They are mainly comprised of a complex network of triangles made out of slender members. The behaviour of flexible dome is nonlinear under the external loads which makes it necessary to consider the geometrical non-linearity in their analysis to obtain realistic response of these structures. Furthermore, instability check during the nonlinear analysis is of prime importance. In this paper, an algorithm is presented for the optimum geometry design of nonlinear braced domes. The height of crown is taken as design variable in addition to the cross-sectional properties of members. A procedure is developed that calculates the joint coordinates automatically for a given height of the crown. The optimum design algorithm takes into account the nonlinear response of the dome due to the effect of axial forces on the flexural stiffnesses of members. It considers serviceability requirements as well as combined strength limitations set by BS 5950. The solution of the design problem is obtained by genetic algorithm. The elastic instability analysis is then carried out for each individual in the initial population until the ultimate load factor is reached. During this analysis, checks on the overall stability of the dome is conducted. If the loss of stability takes place, this individual is taken out of the population and replaced by a new randomly generated individual. This replacement policy is repeated until an individual is found which does not have instability problem. Once the initial population is established where all the individuals are free of instability problem, the regular genetic operations are applied to generate a new population. Number of design examples are included to demonstrate the application of the algorithm.

Buckling of stainless steel columns and beams in fire

Material properties and their response to elevated temperatures form an essential part of structural fire design. At elevated temperatures, stainless steel displays superior material strength and stiffness retention in comparison to structural carbon steel. Although independently important, the relationship between strength and stiffness at elevated temperature also has a significant influence on the buckling response of structural components. This paper examines existing test results and presents the results of a numerical parametric study, using ABAQUS on stainless steel columns in fire. Sensitivity to local and global initial geometric imperfections, enhancement of corner strength due to cold-work and partial protection of the column ends is assessed. Parametric studies to explore the influence of variation in local cross-section slenderness, global member slenderness and load level are described. Test results are compared with the current design rules in Eurocode 3: Part 1.2, the Euro Inox/SCI Design Manual for Structural Stainless Steel and those proposed by CTICM/CSM. The results of a total of 23 column buckling fire tests, six stub column fire tests and six fire tests on beams have been analysed. Overly conservative results and inconsistencies in the treatment of buckling phenomena and the choice of deformation limits are highlighted. A revised buckling curve for stainless steel in fire, consistent strain limits and a new approach to cross-section classification and the treatment of local buckling are proposed. These revisions have led to a more efficient and consistent treatment of buckling of stainless steel columns and beams in fire. Improvements of 6% for column buckling resistance, 28% for stub column (cross-section) resistance and 14% for in-plane bending resistance over the current Eurocode methods are achieved.

Design basis of Lithuanian steel and aluminium structure codes and their relations to Eurocode

The background in the development of national building technical regulations for the design of steel and aluminium structures is discussed. National Design Standards are under consideration in comparison with the main concepts of EC3 and EC9. Standard features of design parameters of materials, partial safety factors and metallic cross-sections are considered in this article. The resistance criterion of members in combined compression and bending is analysed. The effect of member slenderness and fillet weld connections on design results given by National technical regulations and Eurocodes is illustrated.

Cyclic Behavior of Single Angles for Ductile End Cross Frames

The cyclic inelastic behavior of single angle braces used in bridge cross frames is described in this paper. Based on the results from experiments, it is shown that steel angles can be designed to achieve a ductile response with large inelastic strains prior to failure under cyclic loading. Preventing fracture in the connections as well as satisfying limiting b/t and Kl/r ratios results in good cyclic behavior and maximum cyclic strains greater than 6%. The tensile yield force for the single angles can be confidently predicted. The buckling capacity is shown to be largely dependent on the effective length of the members which, in turn, is dependent on the type of end condition. Where plastic hinging is expected in the gusset plates an effective length factor of 1.0 can be assumed for the member, while if plastic hinging is expected in the member an effective length factor of 0.7 is appropriate, where the length is defined as the distance between the centroids of the connections. It is recommended that Kl/r for single angles in end cross frames of bridges be limited to 120 to preclude the use of slender members for which the buckling strength is sensitive to effective length. By limiting the slenderness ratio to 120, the members are treated like main members for seismic loads based on AASHTO provisions. The b/t ratio should be limited to those specified for special concentrically braced frames from the AISC Seismic Provisions for Structural Steel Buildings. An analytical model was developed to simulate the nonlinear response of the single angles and a simplified bilinear model was developed for design purposes.

Elastic, full plastic and lateral torsional buckling analysis of steel single-angle section beams subjected to biaxial bending

Flexural strength limits of steel single-angle section beams should be calculated based on the full plastic moment capacities, local buckling resistance and lateral torsional buckling capacities of the angle sections. The angle section beams are generally under the effect of external loads applied along the direction of geometrical axes parallel to their legs, so that they cause simultaneous biaxial bending about both principal axes. The behavior of angle sections under biaxial bending is complicated. The stress distribution of the critical points of the section cannot be easily determined since all specific points need to be checked. Furthermore, the design specifications require the consideration of the full plastic moment capacities of angle sections. This brings up the question of determining the required increase in first yield moment in order to attain full plastic moment capacities. Since single-angle section beams are thin walled slender structural members, they cannot be designed only according to their elastic and plastic moment capacities. Lateral torsional buckling and local buckling cases need to be considered in determining nominal design moments. In this study, the bending moment about the minor principal axis is assumed to be less than or equal to the moment about the major principal axis. Under that condition the first yield moment capacities, the interaction diagrams between first yield and full plastic moment capacities and critical lateral torsional buckling moments are calculated. These values are obtained by means of dimensionless coefficients, and design procedures have been given for the case of biaxial bending for single-angle section beams taking LRFD [LRFD Load and resistance factor design of single-angle members. Chicago (IL): American Institute of Steel Construction; 2000] rules into account.

Numerical Simulations of Dynamic Instability of Elastic-Plastic Beams

This paper numerically investigates the dynamic instability of different elastic-plastic beams subjected to transverse pulse load. Two types of beam dynamic instability, i.e., symmetrical and asymmetrical instabilities, are studied. The unstable responses of the elastic-plastic beams are illustrated by investigating the modal participation factors of the lowest nine vibration modes, which are determined by inverse derivation of the numerically simulated beam deflection response. The critical pulse loads for the beam symmetrical and asymmetrical instabilities are obtained with respect to different load durations. Characteristic diagrams for beams with different boundary conditions and subjected to different type pulse loads are given. The present study conforms that not only axial compressive load induces instability of slender members, but also transverse pulse load results in instability of elastic-plastic beams.

Shear Strength of Reinforced Concrete Members Subjected to Monotonic Loads

A model to calculate the shear strength of reinforced concrete members subjected to monolonic loading was developed. The proposed model includes the contribution of the most significant mechanisms of shear transfer in reinforced concrete members identified in the research literature. The shear strength is calculated by the superposition of components related to arch action, truss action, friction, and the contribution of the uncracked compression zone. A procedure to calculate the shear strength of members in the transition phase from deep to slender members is formulated, so that the proposed expression can be used for members with geometric configurations varying from squat to slender members. The proposed model was found to provide good estimates of strength for members with and without transverse reinforcement, and having a wide range of geometric configurations and concrete compressive strengths.

Shake table testing of tubular steel bracing members

An experimental study on the seismic response of cold-formed steel tubular members functioning as bracing members in concentrically braced frames is described. A number of shake table tests were carried out to examine member and storey performance under earthquake loads. Three different square and rectangular hollow cross-sections were utilised for the bracing members. It is shown that maximum brace tensile forces can be over 30% higher than those estimated using the actual yield strength, due to strain hardening and strain rate effects. Moreover, the experimental storey shear can exceed that predicted by design procedures by more than 50%. The tests also indicate that the ductility demand under seismic loading can be estimated reasonably well for the frame models using a conventional equal-energy idealisation. In addition, the results illustrate generally satisfactory performance for braces with member slenderness exceeding typical limits in seismic codes.

Shrinkage and creep response of slender reinforced concrete columns under moment gradient: theory and test results

Slender structural members experience geometric non-linearities under eccentric axial compression. Reinforced concrete columns under sustained compression also experience material non-linearities owing to the viscoelastic effects attributable to shrinkage and creep. This paper presents a technique based on expanding the deflected shape of an eccentrically loaded column as a Fourier series to study the response of rectangular reinforced concrete columns under a sustained compressive force applied at each end with unequal eccentricities. The technique allows for the coupling of geometric non-linearity and viscoelasticity, and includes cracking of the concrete. Test results are reported on five slender columns of square cross-section (with L/D ratios of 33·3) under sustained axial compression applied eccentrically, and it is shown that the numerical scheme predicts the experimental results with good accuracy. These test results also add to the smallish pool of accurately conducted experiments on slender columns under sustained loading, and especially provide benchmark test data for unequal end eccentric loading for which test results seem somewhat scarce.

Shrinkage and creep response of slender reinforced concrete columns under moment gradient: theory and test results

Slender structural members experience geometric non-linearities under eccentric axial compression. Reinforced concrete columns under sustained compression also experience material non-linearities owing to the viscoelastic effects attributable to shrinkage and creep. This paper presents a technique based on expanding the deflected shape of an eccentrically loaded column as a Fourier series to study the response of rectangular reinforced concrete columns under a sustained compressive force applied at each end with unequal eccentricities. The technique allows for the coupling of geometric non-linearity and viscoelasticity, and includes cracking of the concrete. Test results are reported on five slender columns of square cross-section (with L/D ratios of 33·3) under sustained axial compression applied eccentrically, and it is shown that the numerical scheme predicts the experimental results with good accuracy. These test results also add to the smallish pool of accurately conducted experiments on slender columns under sustained loading, and especially provide benchmark test data for unequal end eccentric loading for which test results seem somewhat scarce.