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Angle profiles belong to the most common steel profiles used in several types of civil engineering structures, such as in lattice towers. Although, in such towers, they are usually considered as axially loaded (truss) members, an additional bending moment develops due to the eccentricity between the point of load application and the gravity center of the profile. Therefore, this paper focuses on the buckling resistance of single-angle members subjected to combined compression and bending. The investigations have been performed through numerical parametrical studies and have been compared to different normative documents where interaction equations are provided. [ABSTRACT FROM AUTHOR]

The buckling behavior of latticed columns had been widely investigated based on the theory of Euler, Engesser and Timoshenko shear beam. Although these methods had been formulated and proved to be accurate in case of special assumptions, the influences of lacing bars on the buckling behavior of latticed columns were unclear. This paper modeled a general four-legged latticed column to study the influence of the cross-section characteristics of lacing bars along with their imperfections on the buckling capacity of latticed columns. Three loading conditions and four geometric imperfect models were built to testify the performance of lacing bars. To calculate the buckling load of latticed columns with imperfections accurately, advanced nonlinear analytical procedures using Newton-Raphson incremental-iterative method (ANAP-NR) and Risk arc-length incremental-iterative method (ANAP-Risk) were developed, and then validated by FE software ABAQUS. The current data in the paper show the maximum variation on the critical buckling load of latticed columns, caused by the cross-section area, the bending moment of inertia outer lacing plane, and the imperfections of lacing bars, could reach 68%, 30%, and 25%. The analytical results indicate the great importance of lacing bars on the buckling capacity of latticed columns. [ABSTRACT FROM AUTHOR]

This paper studies the critical issue of thin-walled beams with laterally fixed ends. The method for defining the formulae of twist moment for the beams subjected to combined loads was elucidated. Based on this, the governing differential equations of the beam were developed. The procedure for determining the critical state of the beam by the energy method was presented. With this procedure, the critical state of the beam concerned under three types of loadings such as axial force F , bending moment M and distributed load q (or concentrated load P) was examined deliberately. The outcomes were presented in explicit closed-form, which can be illustrated in 2D and 3D graphs. Also, the analytical solution obtained was in agreement with the numerical one obtained by the commercial software NX Nastran. Furthermore, the analytical solutions were applied straightforwardly to explore the stability and design optimization of the tooth-blade for the new frame-type saw machine under an eccentric load. The result can also be promisingly used to study problems of thin-walled beams with laterally fixed ends subjected to other types of loads. [ABSTRACT FROM AUTHOR]

This paper presents an exact solution for the boundary-value problem which describes the linear buckling of axially compressed circular cylindrical panels with stringers attached to the straight edges. The boundary conditions differ from the classical simply supported ones, often assumed for design purposes, in the sense that the torsion resisted by the stringers are also taken into account. The presence of the stringers makes the results reported herein of practical interest and valuable as benchmark data. [ABSTRACT FROM AUTHOR]

A computationally efficient framework is presented to design fibre steered laminates in cylindrical shells, stiffened with longitudinal stiffeners, optimally. The framework is comprised of a semi-analytical analysis approach and a multi-step optimisation framework, and is applied for maximum buckling capacity design of fibre steered laminates of two stiffened cylinders, with different thickness to radius ratios, under bending moment. If the maximum buckling capacity designs are material failure critical, strength is imposed as a constraint in the optimisation problem. Comparisons of buckling capacity of steered fibre laminates with those of straight fibre laminates are shown and validated. Finally, to gain in-depth understanding of the way buckling capacity is improved by fibre steering, the axial section load and the critical buckling modes of straight and steered fibre laminates are compared. [ABSTRACT FROM AUTHOR]

The lateral buckling analysis of cold-formed thin walled beams subjected to pure bending moments has been performed. The critical buckling loads are estimated based an optimization criteria. The estimated critical buckling stresses are compared with the published results, they show excellent agreement. The effect of the beam length, radius and thickness of the flanges and the length of the extended open flanges, on the critical buckling stresses have been studied for several combinations of the geometric parameters of the beam. Among the three beams, the critical buckling moments for the beam with the extended open flanges are found to be the maximum. However, considering the material and manufacturing costs, beams with rounded cross section are efficient in resisting the buckling loads. [ABSTRACT FROM AUTHOR]

Buckling of a bar of an elastoplastic material is studied. It is shown that for any ( σ- ɛ) diagram of the bar material, the limit load (the longitudinal external force) in dimensionless variables that the bar can withstand does not exceed the current bending stiffness of the most loaded (in terms of the bending moment) section. [ABSTRACT FROM AUTHOR]

Abstract: In this study, linear buckling analysis of unstiffened plates under interacting patch loading and bending moment is developed. The study focuses on estimation of the elastic critical load due to patch load, and concomitant linearly variable compressive stress in the normal direction, with analysis of mechanisms of plate instability. The present work proposes simple design equations for the elastic critical load of rectangular plates subjected to both patch load, and uniform compressive stress, and also patch load with linearly varying compressive stresses for the serviceability limit state. The proposed analytical relationship, obtained on the basis of parametric numerical analyses, is validated by comparing analytical predictions with experimental tests from the literature, and full numerical models; good agreement was obtained for practical situations in steel bridge design, such as the erection of steel bridges with the launching construction technique. In the launch phase, web panels of the open-section girders are subjected to concentrated loads applied to the lower flange, and considerable bending moment. [Copyright &y& Elsevier]

Abstract: The durability of thermal barrier coatings (TBCs) employed in most turbine engines is limited by delamination, both within the coating and at the coating–substrate interface. A test used for evaluating the mixed-mode toughness pertinent to such delaminations has been fully-analyzed by determining the steady-state energy release rate, the mode mixity and the critical length for buckling. An analytic solution based on beam theory establishes basic estimates and scaling relationships. Selected finite-element calculations have been used to affirm the fidelity of the results. The energy release rate attains steady-state, but the phase angle changes throughout because of a small (but significant) bending moment induced at the supports. The coating buckles at a critical delamination length, whereupon the energy release rate increases rapidly and violates steady state. The solutions are used to re-interpret measurements reported in the literature for an electron beam physically deposited TBC. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Although steel single angle sections are commonly used as beams to support distributed loads which cause biaxial bending and torsion, their behavior may be extremely complicated, and the accurate prediction of their strengths very difficult. Further, many design codes do not have design rules for torsion, while some recommendations are unnecessarily conservative, or are of limited application, or fail to consider some effects which are thought to be important. This paper is one of a series on the behavior and design of single angle section steel beams. Two previous papers have studied the biaxial bending and torsion of restrained beams, a third has studied the lateral buckling of unrestrained beams, a fourth the biaxial bending of unrestrained beams, and a fifth and sixth the buckling and torsion of unrestrained beams. In each paper, simple design methods have been developed. In this present paper, an approximate method of predicting the second-order deflections and twist rotations of steel equal angle section beams under biaxial bending and torsion is developed. This method is then used to determine the approximate maximum biaxial bending moments in such beams, which are then used with the section moment capacity proposals of the first paper and the lateral buckling proposals of the third paper to approximate the member capacities. [ABSTRACT FROM AUTHOR]

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Unsymmetrical loads along the frame beams produce unequal axial forces in columns together with primary bending moments in the frame members. The combined effect of these two factors on the elastic buckling loads of the frames is studied. The case of one concentrated load acts at different locations on the frame beams is chosen as an example to study the effect of aforementioned factors. The analysis is applied on different types of structural systems such as braced and unbraced multistory frames. Parameters such as fixed and hinged bases, beam to column bending stiffness ratios, and beam span to column height ratios are considered. In addition, the effect of the axial stiffness of the bracing elements is taken into account. The matrix displacement method of analysis has been used throughout the study. The geometric nonlinear behavior of the members is considered by using the stability functions to modify the stiffness matrix of the individual members. Results clearly show that the combined action of the primary bending moments along with the variation of loads ratios on columns has considerable effect on the elastic buckling loads of the braced planar frames. [ABSTRACT FROM AUTHOR]

Abstract: In this study, conditions for bifurcation buckling of functionally graded plates were investigated by using classical plate theory. Since functionally graded plates were produced generally in an unsymmetrical form with respect to mid-plane, flatness of this type of plate before buckling should be considered as in un-symmetrically laminated composite plates [Leissa, Compos Struct 1986;6:261–70]. It was found that a bending moment is required for simply supported functionally graded plates to remain flat under in-plane loading. Clamped boundary conditions provide the necessary moment conditions. [Copyright &y& Elsevier]

Tubular steel towers are the most common design solution for supporting medium-to-high-rise wind turbines. Notwithstanding, historical failure incidence records reveal buckling modes as a common type of failure of shell structures. It is thus necessary to revisit the towers' performance against bending-compression interactions that could unchain buckling modes. The present investigation scrutinises buckling performances of a cylindrical steel shell under combined load, by means of the energy method. Within the proposed framework, the differential equations to obtain dimensionless expressions showed the energy-displacement relations taking place along the shell surface. Furthermore, shell models integrated with initial imperfection have been embedded into finite element algorithms based on the Riks method. The results show buckling evolution paths largely affected by bending moments lead to section distortions (oval-shaped) that in turn change the strain energy dissipation routine and section curvature. The shell geometrical parameters also show a strong influence on buckling effects seemingly linked to a noticeable reduction of the shell bearing capacity during the combined loading scenarios. [ABSTRACT FROM AUTHOR]

• Cantilevers are very different from simply supported beams. • Cantilevers have different restraints and moment and yielding patterns. • Yielding in steel cantilevers varies with moment distribution and residual stresses. • Yielding reduces out-of-plane section rigidities. • Lateral buckling resistance is affected by moment distribution and reduced rigidities. • Beam buckling design rules are inappropriate for cantilevers. Steel cantilevers are very different from the simply supported beams under uniform bending which provide the basis for designing steel members against lateral buckling. Cantilevers have different end restraint conditions, while the most critical loading condition for cantilevers is one of concentrated end load leading to a linear moment distribution. Thus the elastic lateral buckling formulations for uniform bending of simply supported beams used more generally for design are inappropriate for cantilevers. The mono-symmetric yield patterns in simply supported beams with residual stresses in uniform bending are of opposite sense to those of cantilevers because of the opposite sense of the bending moments. Thus formulations which take account of the effect of mono-symmetry on the inelastic lateral buckling of simply supported beams are inappropriate for cantilevers. Further, the linear cantilever moment distribution leads to very localised yielding instead of the uniform yielding of beams under uniform bending. This paper studies the inelastic lateral buckling of cantilevers in order to produce better design guidance than that currently based on the inelastic buckling of simply supported beams in uniform bending. The effects of mono-symmetry on the elastic buckling of beams and cantilevers are first investigated, and then the effects of the mono-symmetric non-uniform yielding patterns which complicate the prediction of the inelastic buckling resistances of cantilevers are studied. Cantilevers with reduced (instead of rigid) end warping restraints occur in overhanging beams, and so the effects of yielding on overhanging segments are also studied. These studies are used to develop simple approximate methods for designing cantilevers and overhanging segments against inelastic lateral buckling. [ABSTRACT FROM AUTHOR]