Buckling Length Research Articles

Effective buckling length of steel column members based on elastic/inelastic system buckling analyses

This study presents an improved method that uses the elastic and inelastic system buckling analyses for determining the K-factors of steel column members. The inelastic system buckling analysis is based on the tangent modulus theory for a single column and the application is extended to the frame structural system. The tangent modulus of an inelastic column is first derived as a function of nominal compressive stress from the column strength curve given in the design codes. The tangential stiffness matrix of a beam-column element is then formulated by using the so-called stability function or Hermitian interpolation functions. Two inelastic system buckling analysis procedures are newly proposed by utilizing nonlinear eigenvalue analysis algorithms. Finally, a practical method for determining the K-factors of individual members in a steel frame structure is proposed based on the inelastic and/or elastic system buckling analyses. The K-factors according to the proposed procedure are calculated for numerical examples and compared with other results in available references.

Experimental investigation of conditions of lateral shear reinforcements in RC columns accompanied by buckling of longitudinal bars

AbstractThis study presents a cyclic load test of four RC columns to obtain data on stresses and strains on lateral shear‐reinforcing bars that contact buckled longitudinal reinforcing bars. The specimens include columns laterally jacketed with all‐elastic fibre‐reinforced polymer (FRP) sheets. The buckling lengths and modes in the longitudinal bars of the four column specimens stabilized at a buckling deflection (= lateral deformation of buckled longitudinal bar) from 0.3 to 0.6 mm. The yield portion ratio rby of shear reinforcement around the buckled longitudinal bars was introduced as an index of the development of buckling conditions. Here, the yield portion ratio rby was defined as the ratio of the length of the region where the shear reinforcements yield lby, to the buckling length lb. The rby values of the tested columns ranged from 0.45 to 0.76. The test results show that the buckling stress and the specific compressive stress of the longitudinal bars in the columns were smaller than those of the bare bars. Copyright © 2007 John Wiley & Sons, Ltd.

Buckling length of a steel column for fire design

The Eurocode 3 part 1-2 gives some simple rules to determine the buckling length l f i of a steel column for fire design. In the case of a braced frame in which each storey comprises a separate fire compartment with sufficient fire resistance, Eurocode 3 suggests that the buckling length may be taken as l f i = 0.5 L in an intermediate storey and as l f i = 0.7 L in the top storey, where L is the system length in the relevant storey. Stability analyses for the evaluation of the buckling length and critical load of columns in braced frames show that the Eurocode 3 rule may be rather inaccurate in many practical situations. The authors propose alternative formulas to determine the buckling length at elevated temperatures, as an improvement of the actual rule of the Eurocode 3 part 1.2.

液状化地盤において杭頭水平変位を伴う鋼管単杭の曲げ座屈応力度

In our previous paper, the possibility of flexural bucking of slender piles in liquefied soil was presented, and the buckling stress for the AIJ design code is estimated. Then the boundary conditions were assumed to be pinned support, but in the real structures, the pile heads will move laterally during earthquake. This paper describes the evaluation of the buckling length of slender piles with roller supports on the pile head when the soil liquefies and then the distribution of the coefficient of the subgrade reaction is assumed to be unified or triangular. The relationship between the buckling length of the slender piles and the soil-pile interaction is presented.

굴착순서에 따른 Top Down 선기둥 지지력 산정

Top Down method is more widely used in downtown construction, recently. As underground construction constitutes a significant portion of the total construction cost and time in Top Down construction, it is important to develop a construction method to reduce the time required in underground works. The purpose of this study is to analyze load carrying capacity of Top Down prefounded columns on different excavation schedule. When several floors are excavated, the valid buckling length of prefounded column is increased and allowable buckling stress is decreased. The result shows that all columns are safe in buckling down to B3 story whether 2 or 3 stories are excavated. However, several columns are not safe from B4 story when 2 or 3 stories are excavated straightly. With these results, a process can be designed that the first three stories in the basement are excavated, and then excavate B4 story after placing concrete on B1 and B2 floor.

Exact static analysis of partially composite beams and beam-columns

The ordinary differential equations and general solutions for the deflection and internal actions and, especially, the pertaining consistent boundary conditions for partially composite Euler–Bernoulli beams and beam-columns are presented. Static loading conditions, including transverse and axial loading and first- and second-order analyses are considered. The theoretical procedure is applicable to general loading and boundary conditions for uniform composite beams and beam-columns with interlayer slip. Further, the exact closed form characteristic equations and their associated exact buckling length coefficients for composite columns with interlayer slip are derived for the four Euler boundary conditions. It is shown that these coefficients are the same as those for ordinary fully composite (solid) columns, except for the Euler clamped-pinned case. For the clamped-pinned case, the difference between the exact buckling length coefficient and the corresponding value for solid columns is less than 1.8% depending on the so-called composite action parameter and relative bending stiffness parameter. Correspondingly, the maximum deviation between the exact and approximate buckling load is at most 2.5%. These small differences can in most practical cases be neglected. Also, the maximum theoretical range for the relative bending stiffness for partially composite beams and beam-columns is derived. An effective bending stiffness, valuable in the determination of the critical buckling load for partially composite members, is derived. This effective bending stiffness is also suitable for analysing approximate deflections and internal actions or stresses in composite beams with flexible shear connection. The beam-column analysis is applied to a specific case. The difference in the approaches to the first- and second-order analysis is illustrated and the results clearly show the magnification in the actions and displacements due to the second-order effect. The magnification of the internal axial forces is different from magnifications obtained for the other internal actions, since only that portion of an internal axial force that is induced by bending is magnified by the second-order effect.

Dynamic buckling of elastic-plastic column impacted by rigid body

The dynamic buckling of an elastic-plastic column subjected to an axial impact by a rigid body was discussed by using the energy law. The traveling process of elastic-plastic waves under impact action was analyzed by characteristics method. The equation of lateral disturbance used to analyze the problem was developed by taking into account the effect of elastic-plastic stress wave. The power series solution of this problem has been the power series approach. The buckling criterion of this problem was proposed by analyzing the characteristics of the solution. The relationship among critical velocity and impact mass, critical buckling length, hardening modulus was given by using theoretical analysis and numerical computation.

Buckling strength of multi-story sway, non-sway and partially-sway frames with semi-rigid connections

The objective of this paper is to propose a simplified approach to the evaluation of the critical buckling load of multi-story frames with semi-rigid connections. To that effect, analytical expressions and corresponding graphs accounting for the boundary conditions of the column under investigation are proposed for the calculation of the effective buckling length coefficient for different levels of frame sway ability. In addition, a complete set of rotational stiffness coefficients is derived, which is then used for the replacement of members converging at the bottom and top ends of the column in question by equivalent springs. All possible rotational and translational boundary conditions at the far end of these members, featuring semi-rigid connection at their near end as well as the eventual presence of axial force, are considered. Examples of sway, non-sway and partially-sway frames with semi-rigid connections are presented, where the proposed approach is found to be in excellent agreement with the finite element results, while the application of codes such as Eurocode 3 and LRFD leads to significant inaccuracies.

Mechanics and Dynamics of Actin-Driven Thin Membrane Protrusions

Motile cells explore their surrounding milieu by extending thin dynamic protrusions, or filopodia. The growth of filopodia is driven by actin filament bundles that polymerize underneath the cell membrane. We compute the mechanical and dynamical features of the protrusion growth process by explicitly incorporating the flexible plasma membrane. We find that a critical number of filaments are needed to generate net filopodial growth. Without external influences, the filopodium can extend indefinitely up to the buckling length of the F-actin bundle. Dynamical calculations show that the protrusion speed is enhanced by the thermal fluctuations of the membrane; a filament bundle encased in a flexible membrane grows much faster. The protrusion speed depends directly on the number and spatial arrangement of the filaments in the bundle and whether the filaments are tethered to the membrane. Filopodia also attract each other through distortions of the membrane. Spatially close filopodia will merge to form a larger one. Force-velocity relationships mimicking micromanipulation experiments testing our predictions are computed.

Stiffness of joints in bolted connected cold-formed steel trusses

Web members in cold-formed steel trusses are usually assumed to have pinned connections at the ends, but the latest AISI Cold-Formed Steel Truss Design Standard allows for the joint stiffness to be considered in design. The paper summarizes experimental research performed for several years at the University of Timisoara, Romania, aimed at evaluating the real behaviour of bolted joints in cold-formed steel trusses. By means of tests on single lap joints and on truss sub-assemblies, a theoretical model for joint stiffness was proposed. The formula for the joint stiffness, from which the buckling length of web members was further determined, was also validated through a test on a full-scale truss.

Transition from progressive to global buckling of aluminium extrusions – a numerical study

Numerical simulations using LS-DYNA were carried out in order to study the transition between progressive and global buckling of axially loaded aluminium extrusions in alloy AA6060 temper T6. A numerical model was validated against experimental tests and good agreement was found between the progressive buckling pattern in the numerical simulations and experimental tests. The numerical simulations were capable of giving a relatively accurate prediction of the collapse mode found in the experimental tests. The critical global slenderness is defined as the global slenderness, or length to width ratio (L/b), where direct global buckling or a transition from progressive to global buckling occurs. The validated numerical model was used in a parametric study where the influence on the critical global slenderness from impact velocity and material properties has been studied. The means to stabilize the response and increase the critical global slenderness has been investigated. It was found that the introduction of a heat affected zone at the impacted end increased the critical buckling length.

Improved stiffness distribution factors for evaluation of effective buckling lengths in multi-story sway frames

The objective of this paper is to propose improved expressions for the effective buckling length coefficient of columns in multi-story sway frames. To that effect, a complete set of rotational stiffness coefficients are derived, which are then used for the replacement of members converging at the bottom and top ends of the column in question by equivalent springs. All possible rotational and translational boundary conditions at the far end of these members, as well as the eventual presence of axial force, are considered. An analytical expression and a corresponding graph similar to those used by Eurocode 3 are then proposed for the calculation of the effective buckling length coefficient. Examples of three-story sway frames are presented, where the proposed approach is found to be in excellent agreement with finite element results, while applications of Eurocode 3 and LRFD lead to significant inaccuracies.

Transition from progressive buckling to global bending of circular shells under axial impact––Part I: Experimental and numerical observations

The influence of impact velocity and material characteristics on the dynamic buckling response of circular shells subjected to axial impact loads is studied. It is shown experimentally that the critical buckling length, which marks the transition between progressive and global buckling of aluminium alloy circular tubes, is significantly influenced by the axial impact velocity. A finite element analysis is undertaken to further explore the effects of material yield stress, strain hardening and strain rate sensitivity on the transition phenomenon. It is observed that circular tubes made of ductile alloys with a high yield stress and low strain hardening characteristics have a better performance as energy absorbers than tubes made of alloys with a low yield stress and high strain hardening characteristics. Theoretical analysis of some particular features of the dynamic buckling transition is presented in Part II [International Journal of Solids and Structures (2004)].

A Stability Analysis of Risers Subjected to Dynamic Compression Coupled With Twisting

Risers anchored in a floating system and excited by a moderate sea state are often subjected to dynamic compression near the touchdown point, since the static tension in this region is usually very small. An analytical expression for the critical load of dynamically compressed risers was recently derived by Aranha et al. [1], whose results were compared with numerical simulations, showing a good agreement in several cases. This paper extends Aranha’s results by showing that the well-known Greenhill formula can be used to predict stability conditions in cables/risers having an initial curvature and subjected simultaneously to dynamic compression and twisting. This is done by extending Aranha’s reasoning, of a “local buckling length scale,” a little further, therefore creating a general procedure that enables one to obtain the buckling number n appearing in the classical Greenhill formula. An application to rigid risers is presented and discussed.

Computational p -element method on the effects of thickness and length on self-weight buckling of thin cylindrical shells via various shell theories

This paper is concerned with the development of a global p-element method for the analysis of self-weight buckling of thin cylindrical shells. Such buckling problems occur when cylindrical shells are subject to high-g acceleration, for instance the launching of rockets and missiles under high propulsive power. The cylindrical shells may have any combination of free, simply supported and clamped ends. A p-element computational method has been developed based on various thin shell theories including Donnell, Sanders and Goldenveizer-Novozhilov models. The strain energy for the global element during buckling is formulated and an eigenvalue equation is derived. Unlike the conventional buckling problem where the eigenvalue is directly solved, a pre-determined buckling parameter is fixed at the outset for a geometric-dependent stiffness and a recursive numerical procedure is developed to compute the effect of critical buckling length. The critical buckling length is found to be proportional to thickness to a power of approximately 0.9. The effects of shell thickness and length on buckling parameter are also investigated. Comparison of results from various shell theories indicates solutions of the Sanders and Goldenveizer-Novozhilov shell theories are in excellent agreement while the Donnel shell theory is good for buckling of short cylindrical shells.

Energy Absorption Characteristics of Metallic and Composite Shells

Metallic and composite shells of different sizes and tubes were subjected to axial compression in an Instron Machine. Their progressive failure modes and energy absorption capacities have been studied. In the case of metallic shells, analytical expressions are derived to find the mean collapse load and the fold length based on the formation of plastic hinges. Theoretical results have been compared with experimental results wherever possible. The effect of internal folding on the post-collapse behaviour of round tubes has been discussed and expressions for fold length and post-collapse load compression curves are derived as a function of internal folding. Based on the experimental observations, analysis has been carried out to find the progressive crushing load and crush length in a cycle of round and conical shells. The shells are infilled with polyurethane foam and subjected to axial compression. The effect of foam on the crushing behaviour is also studied. Conical shells of different cone angles varied from 8.5 to 45 and the effect of cone angle on the crushing mode of the conical shells has been studied. Also, a comparative study of metallic and composite shells has been carried out based on the deformation and energy absorption characteristics. The different parameters considered for analysis include effective crushing length and total energy absorbed during the crushing process and the Euler buckling length in metallic shells.

A thermomechanical model for adhesion reduction of MEMS cantilevers

Presents a thermomechanical model that describes adhesion reduction in MEMS structures using laser heating. A fracture mechanics model is developed where the interface between the stiction-failed microcantilever and the substrate is treated as a crack, and the energy release rate is calculated using elastic theory. In order to include the effect of a temperature difference between the microcantilever and the substrate, an associated thermal strain energy is included in the fracture model. If the free length is longer than the critical buckling length, the beam buckles decreasing the strain energy of the system. For surface-micromachined polycrystalline silicon cantilevers with an initial crack length of 400 /spl mu/m, the model predicts that a temperature difference of 100 K repairs microcantilevers as long as 1300 /spl mu/m. The peeling of adhered beams from the substrate after laser irradiation is experimentally shown with measured crack lengths within 15% of predicted values indicating that the proposed model establishes the mechanism of adhesion reduction by laser irradiation.

Reinforcement Stability and Fracture of Cover Concrete in Reinforced Concrete Members

The main aim of this study is to propose a simple and reliable method to predict the buckling length of longitudinal reinforcing bars and also to predict the spalling of cover concrete in reinforced concrete members. Stability analysis is conducted giving due consideration to both geometrical and mechanical properties of the longitudinal reinforcing bars and lateral ties. The tie stiffness required to hold longitudinal reinforcing bars in different buckling modes is derived from energy principles, and it is compared with actual tie stiffness to determine the stable buckling mode. The buckling length is computed as the product of the stable buckling mode and the tie spacing. The proposed buckling length determination method is experimentally verified for various cases. A design method for lateral ties to avoid buckling-induced strength degradation is also recommended. The effect of lateral deformation of longitudinal bars is quantitatively evaluated and incorporated in the simulation of cover concrete spal...

Dynamic elastic local buckling of piles under impact loads

A dynamic elastic local buckling analysis is presented for a pile subjected to an axial impact load. The pile is assumed to be geometrically perfect. The interactions between the pile and the surrounding soil are taken into account. The interactions include the normal pressure and skin friction on the surface of the pile due to the resistance of the soil. The analysis also includes the influence of the propagation of stress waves through the length of the pile to the distance at which buckling is initiated and the mass of the pile. A perturbation technique is used to determine the critical buckling length and the associated critical time. As a special case, the explicit expression for the buckling length of a pile is obtained without considering soil resistance and compared with the one obtained for a column by means of an alternative method. Numerical results obtained show good agreement with the experimental results. The effects of the normal pressure and the skin friction due to the surrounding soil, self-weight, stiffness and geometric dimension of the cross section on the critical buckling length are discussed. The sudden change of buckling modes is further considered to show the 'snap-through' phenomenon occurring as a result of stress wave propagation.

ANTI-OPTIMIZATION PROBLEMS ARISING IN OPTIMIZATION OF STRUCTURAL STEELWORK

In this paper a structural optimization technique based on a genetic algorithm (GA) is presented. The technique is developed to deal with discrete structural optimization of 2D steel frame structures. Also from a structural point of view, the paper explores the maximum ratio of the effective buckling length when using the finite element approach and that by the British Standard (BS 5950) approach. In order to consider realistic steelwork design problems, the developed technique has been linked to a system of structural design rules (British Standards BS 5950 and BS 6399), interacting with a finite element package (ANSYS). In the formulation of the optimization problem, the objective function is the maximum ratio of the effective buckling length of a column evaluated by FEM and that by BS5950. The cross-sectional properties of the structural members, which form the set of design variables, are chosen from two separate catalogues (universal beams and columns covered by British Standards BS 4). The constraints are imposed on the design criteria stipulated by BS 5950. Two 2D steel frame structures having different number of design variables and subjected to multiple loading cases are analyzed. These examples show that the developed technique based on GA can be successfully incorporated in discrete structural optimization problems of steel frame structures.