Flexural-torsional Buckling Resistance Research Articles

Laboratory testing and numerical modelling of pin-ended hot-rolled stainless steel angle section columns failing by flexural-torsional buckling

The flexural-torsional buckling behaviour and resistances of pin-ended hot-rolled stainless steel angle section columns have been studied in the present paper, based on laboratory testing and numerical modelling. The testing programme adopted four hot-rolled stainless steel angle sections and included initial global and torsional geometric imperfection measurements and twelve pin-ended column tests. The key obtained test results, including the failure loads and deformations at the failure loads, the load–mid-height lateral deflection curves and failure modes, were fully reported and discussed. Strong interaction between flexural-torsional buckling about the major principal axis and flexural buckling about the minor principal axis was observed for each pin-ended hot-rolled stainless steel angle section column specimen during and upon testing. The testing programme was followed by a numerical modelling programme; finite element models were developed and validated against the test results, and afterwards used to perform parametric studies to generate further numerical data over a wide range of cross-section dimensions and member lengths. On the basis of the experimentally and numerically obtained data, the accuracy of the codified design methods, as adopted in Europe, America and Australia/New Zealand, and a recently proposed DSM-based design approach for pin-ended hot-rolled stainless steel angle section columns susceptible to flexural-torsional buckling, were evaluated. Overall, it may be concluded that (i) all the three considered design codes result in conservative flexural-torsional buckling resistance predictions, (ii) the current European code leads to more accurate resistance predictions for pin-ended columns with non-slender hot-rolled stainless steel angle sections, but a lower degree of design accuracy for pin-ended columns with slender hot-rolled stainless steel angle sections, in comparison with the American specification and Australian/New Zealand standard, and (iii) the DSM-based design approach yields substantially improved resistance predictions, due to the rational consideration of the length-dependent characteristic of flexural-torsional buckling and the interaction of flexural-torsional buckling with minor-axis flexural buckling, but with many predictions lying on the unsafe side.

Flexural-torsional buckling behaviour and resistances of fixed-ended press-braked S690 high strength steel angle section columns

The flexural-torsional buckling behaviour and resistances of fixed-ended press-braked S690 high strength steel angle section columns have been studied based on testing and numerical modelling, and reported in this paper. A testing programme, employing four different equal-leg angle section sizes, was firstly conducted, and comprised material tensile coupon tests, initial global and torsional geometric imperfection measurements and twelve fixed-ended column tests. The column test setup and procedures were thoroughly presented, and the key obtained test results, including the failure loads and deformations at the failure loads, load–end shortening curves, load–mid-height torsional rotation curves and failure modes, were fully reported and discussed. This was followed by a numerical modelling programme, where finite element models were initially developed to simulate the experimental responses and then adopted to perform parametric studies to generate further numerical data over a wide range of cross-section dimensions and member lengths. The obtained test and numerical data were then used to evaluate the accuracy of the relevant codified design rules, given in the European code, North American specification and Australian/New Zealand standard, and a recently proposed DSM-based design approach. The results of the evaluation revealed that all the codified design rules yield excessively conservative and scattered flexural-torsional buckling resistance predictions for fixed-ended press-braked S690 high strength steel angle section columns, while the DSM-based design approach leads to substantially improved resistance predictions, owing to the rational consideration of the length-dependent characteristic of flexural-torsional buckling and the interaction of flexural-torsional buckling with minor-axis flexural buckling.

Flexural-torsional buckling behaviour of fixed-ended hot-rolled austenitic stainless steel equal-leg angle section columns

The present paper shows an experimental and numerical modelling investigation of the flexural-torsional buckling behaviour and load-carrying capacities of fixed-ended hot-rolled austenitic stainless steel equal-leg angle section columns. The testing programme was conducted on four austenitic stainless steel angle sections and involved material testing, initial global and torsional imperfection measurements and sixteen fixed-ended column tests. This was followed by a numerical simulation study, where the numerical models were firstly developed to validate against the experimental data and then utilised to perform numerical parametric studies to generate additional results over a broader range of member lengths and cross-section geometric dimensions. The derived test and finite element results were carefully analysed and then utilised to evaluate the accuracy of the established design rules in Europe, America and Australia/New Zealand. Comparisons of the failure loads derived from the experimental and numerical studies with the corresponding codified flexural-torsional buckling strength predictions revealed an unduly high level of conservatism and scatter. Extension of the direct strength method to carbon steel equal-leg angle section columns has been recently made, and the applicability of the approach to fixed-ended hot-rolled austenitic stainless equal-leg steel angle section columns was also assessed. The new approach was generally shown to yield more precise flexural-torsional buckling resistance predictions than the existing design standards, but a large portion of the predictions were unsafe, indicating that further improvements are required.

COLLAPSE AND FLEXURAL-TORSIONAL BUCKLING TEMPERATURES AT FIRE FOR BEAMS IN STEEL FRAMES

When a steel beam arranged in a steel frame is exposed to fire, compressive force, that is thermal stress, is generated in it with member temperature increase, because the liner thermal expansion is restricted by the adjacent members. It is, however, well known that the generated thermal stress is attenuated by plastic deformation occurred in the steel frame at elevated temperature, finally disappears when the heated beam exhibits collapse mode. The collapse temperature is independent of the thermal stress in case of stable plastic collapse mode. On the other hand, there is a possibility that the open cross-section beam unstiffened in the out-of-plane direction exhibits flexural-torsional buckling in the process of fire by acting the large compressive force. Since the flexural-torsional buckling resistance depends on the compressive force, it is considered that the member temperature at the flexural-torsional buckling depends on the thermal stress. The main purpose of this study is to clarify the flexural-torsional buckling behavior of the beam at the fire arranged in the steel frame and propose theoretical solutions on the flexural-torsional buckling temperature considering influence on the thermal stress. Three dimensional finite element analyses are conducted to verify the theoretical solutions. A line element being capable of analyzing the flexural-torsional behavior of the member is used. Both geometrical and material nonlinearity are considered in the numerical analysis. Three types of partial frame models including a fire compartment room are analyzed and their numerical flexural-torsional buckling and collapse temperatures are estimated, respectively. By comparison of the theoretical solution with the analytical results obtained by the parametric analyses, the following 1) and 2) were clarified. 1) The unstiffned beam at the fire exhibits the flexural-tosional buckling and the large buckling deformation in both in-plane and out-of-plane directions occurs with the temperature increase. The flexural-torsional buckling temperature becomes lower when the liner thermal expansion is strongly restricted by the adjacent members. However, the beam can sustain vertical loads after the buckling. The thermal stress is attenuated by the plastic deformation in both in-plane and out-of-plane directions generated in the buckled beam. The beam can resist up to the temperature when the thermal stress disappears. The collapse temperature is higher than the flexural-torsional buckling temperature, however, the plastic deformation in the out-of-plane direction is very large. 2) The flexural-torsional buckling temperature of the heated beam at the fire can be safely estimated by the theoretical solution proposed in this study. The collapse temperature of the beam after the buckling can be estimated by the theoretical collapse temperature based on the simple plastic theory. It is considered that fire resistance of the beam in the case when the plastic deformation in the out-of-plane direction cannot be allowed, for instance, in the case when the heated beam adjoins fire compartment walls, should be estimated by the theoretical flexural-torsional buckling temperature.

Flexural-Torsional Buckling Resistance Design of Circular Arches with Elastic End Restraints

This paper presents the flexural-torsional buckling resistance and design of steel circular arches subjected to uniform compression with elastic end bending restraints by using finite element (FE) numerical analyses. Firstly, effects of geometric and mechanical parameters such as initial imperfections, section types, material properties, slenderness, rise-to-span ratios, and end restraints on flexural-torsional buckling resistances of arches are investigated and are found to be eliminated to a large extent by introducing the normalized slenderness. Then, on the basis of extensive numerical results, a design method is proposed to predict the flexural-torsional buckling resistances of circular arches in uniform compression with elastic end restraints by the column curves according to the normalized slenderness and a specific section type, namely curve ‘a’ for hollow sections, curve ‘b’ for welded box sections, and curve ‘c’ for welded I-sections. Next, the flexural stiffness of an arch is studied, taking the destabilizing effect of the axial force into account to calculate the end restraining provided by adjacent arch segments to the adverse segment in a laterally-braced arch in uniform compression to obtain the flexural-torsional buckling resistance using the normalized slenderness and the column curve analytically. The result shows a good agreement with that gained from finite element numerical analyses, and proves it very conservative when the adverse segment is assumed to be hinged without any end restraining.

A FURTHER STUDY OF FLEXURAL-TORSIONAL BUCKLING OF ELASTIC ARCHES

This paper uses both a virtual work approach and a static equilibrium approach to study the elastic flexural-torsional buckling of circular arches under uniform bending, or under uniform compression. In most studies of the elastic flexural-torsional buckling of arches under uniform compression produced by uniformly-distributed radial loads, the directions of the radial loads are conventionally assumed not to change but to remain parallel to their initial directions during buckling. In practice, the uniform compression may be produced by hydrostatic loads or by uniformly-distributed radial loads that are directed to a specific point during buckling. In addition, there are discrepancies between existing solutions for the elastic flexural-torsional buckling moment and load of arches under uniform bending or under uniform compression which need to be clarified. Closed form solutions for the buckling moment and load are developed. The discrepancies among the existing solutions for the elastic flexural-torsional buckling moment and load of arches are clarified and the sources for the discrepancies are identified. It is found that the lateral components of hydrostatic loads and of uniformly-distributed radial loads that are always directed toward the center of the arch increase the flexural-torsional buckling resistance of an arch under uniform compression. It is also found that first-order buckling deformations are sufficient for static equilibrium approaches for the flexural-torsional buckling analysis of arches. The rational static equilibrium approach for the flexural-torsional buckling in the present study is effective.

Elastic flexural-torsional buckling of fixed arches

This paper is concerned with the elastic flexural-torsional buckling of laterally fixed circular arches that are subjected to uniform axial compression, and to uniform bending. The finite strains and the energy equation for the flexural-torsional buckling of arches have been derived based on an accurate orthogonal rotation matrix. Closed form solutions for the elastic flexural-torsional buckling resistance of laterally fixed arches in uniform compression and in uniform bending have been obtained, which are quite different from those of pin-ended and simply supported arches. The results demonstrate that the routine 'effective length' approach, which is often useful for determining the buckling response of straight members, is not suitable for the elastic flexural-torsional buckling response of fixed arches.

Effects of prebuckling deformations on the elastic flexural-torsional buckling of laterally fixed arches

The effect of the prebuckling in-plane deformations on the elastic flexural-torsional buckling of laterally fixed circular arches is studied in this paper. The finite strains and the energy equation for the flexural-torsional buckling of arches have been derived based on an accurate orthogonal rotation matrix. A closed form solution for the elastic flexural-torsional buckling resistance of laterally fixed arches in uniform bending, including the effects of the prebuckling deformations, is obtained. It is found that the notion that the prebuckling deformations increase the flexural-torsional buckling moment of an arch or of a beam is not necessarily correct for a laterally fixed arch or beam in uniform bending, in deference to a laterally pinned arch. When a laterally fixed arch is subjected to positive uniform bending, the effects of the prebuckling deformations decrease the buckling moment, and the reduction of the buckling moment increases with an increase of the included angle and of the out-of-plane slenderness ratio of the arch. When a laterally fixed arch is subjected to negative uniform bending, the effects of the prebuckling deformations decrease the absolute value of its buckling moment when the included angle is very small, but increase the absolute value of the buckling moment when the included angle exceeds a certain value. The increase in the absolute value of the buckling moment increases with an increase of the included angle and of the out-of-plane slenderness ratio of the arch. When the ratio of the out-of-plane to the in-plane second moments of area of the cross-section is not small, both the reduction of the buckling moment of a laterally fixed arch in positive uniform bending and the increase of the buckling moment of a laterally fixed arch in negative uniform bending, are substantial.

Flexural-torsional buckling of stepped beams subjected to pure bending

The cross sections of continuous multi-span beams are sometimes increased suddenly, or stepped, at interior supports of continuous beams to resist high negative moments. An investigation of the elastic flexural-torsional buckling (FTB) behavior of I-shaped stepped beams was conducted using finite element method (FEM) and resulted in the development of design equations for beams having singly or doubly stepped cross sections within a laterally unbraced length. The finite element models are subjected to pure bending moment in the entire beam span. Results from the design equations were demonstrated with comparisons between the proposed equations or the weighted average approach (WAA) and FEM results for doubly and singly stepped beam spans of existing highway bridges. The new equations proposed definitely improve current design methods for the FTB problem and increase efficiency in building and bridge design. The proposed solutions can be easily used to develop new design equation for FTB resistance of stepped beams subjected to general loading condition such as a concentrated load, a series of concentrated loads or uniformly distributed load.

Elastic Flexural-Torsional Buckling of Discretely Restrained Arches

This paper presents a study of the effects of elastic discrete restraints on the elastic flexural-torsional buckling of arches in uniform bending and compression. It was found that established results for the elastic flexural-torsional buckling of restrained beams in uniform bending cannot be used directly for restrained arches in uniform bending, nor can those for elastic flexural or torsional buckling of restrained columns in uniform compression be used directly for restrained arches in uniform compression. Because of the curved profile of an arch, restraints are more effective in increasing the elastic buckling resistance of an arch than that of the corresponding straight member. Approximate formulas for the threshold values of the stiffness of the central torsional and lateral-translational restraints for a restrained arch in uniform bending and for the threshold value of stiffness of the lateral-translational restraints for a restrained arch in uniform compression at which the flexural-torsional buckling mode changes from being symmetric to antisymmetric are proposed. Approximate formulas for elastic flexural-torsional buckling resistance of centrally or end restrained arches in uniform bending and in uniform compression are also proposed. Finite element results show that these proposed formulas are accurate.

Torsional Restraint against Elastic Lateral Buckling

It is well known that a central elastic torsional restraint restricts the lateral buckling shape of an elastic I-beam and increases its elastic flexural-torsional buckling resistance. However, available information on the effects of torsional restraints on elastic buckling are either incomplete, or in some cases inaccurate. This paper investigates the effects of moment distribution and load height on the elastic flexural-torsional buckling of beams with central torsional restraints. The effects of off-center and continuous restraints are also studied, and design approximations and procedures are developed.