Effects of the Loading History on the Local Buckling Behavior and Failure Mode of Welded Beam-to-Column Joints in Moment-Resisting Steel Frames

The cyclic behavior of welded beam-to-column joints for moment-resisting steel frames was assessed by constant amplitude cyclic quasi-static tests. Reanalysis of the results showed that the failure mode of the joints strongly depends on cycle amplitudes. A premature brittle failure of the welds may occur if the cycle amplitude is not large enough to cause local buckling of beam flanges. Influence of both flange and web slenderness ratios on local buckling behavior, investigated through an experimental parametric study, is discussed. Four tests, carried out adopting different variable amplitude displacement histories, confirmed that isolated large amplitude cycles have beneficial effects on the joint response, extending its life; on the contrary, many large cycles clustered together endanger the seismic performance of beam-to-column joints. Numerical analyses allowed interpretation of the experimental data in terms of local stresses and strains. For “large amplitude” cycles numerical results indicate a local state of strain causing a progressive collapse for low-cycle fatigue while, in case of “small amplitude” cycles, brittle failure mode is due to the ratcheting of material.     

Experiments on the Buckling Behavior of Ring-Stiffened Pipelines under Hydrostatic Pressure

Submarine pipelines are deemed as thin-walled structures in which relative external pressure may be created in some cases of fluid transmission. The certain effect of this type of loading is local buckling and its propagation along the considerable length of the line. In this study, an experimental program has been performed, in which the influence of ring stiffeners on the buckling strength of pipelines is investigated. In the tests, only hydrostatic pressure is considered as the major loading case, and the effect of further loads is neglected. The modes of initial buckling, buckling propagation, postbuckling, and development of yield lines and the final collapse of the pipeline have been closely appraised. It is verified that the buckling threshold highly hikes up by attaching some light ring stiffeners. By decreasing the ring spacing, the difference between buckling and failure loads is diminished and torsion-type yield lines at failure mode occur on the pipe skin.     

Postbuckling Response Simulations of Laminated Anisotropic Panels

Numerical simulations are used in conjunction with experiments to study the buckling and postbuckling responses and failure initiation of flat, unstiffened composite panels. The numerical simulations are conducted using two‐dimensional shear‐flexible finite elements. The effect of the laminate stacking sequence on the buckling and postbuckling responses is studied. Correlation between numerical and experimental results is good through buckling, but the numerical models overestimate the postbuckling stiffness of the panels when nominal values of the material properties are used. To explain the discrepancies in the postbuckling stiffnesses, analytic sensitivity derivatives are calculated and used to study the sensitivity of the buckling and postbuckling responses to variations in different material and lamination parameters. Experimental results indicate that failure occurs along a nodal line. Numerical results show that the location of failure initiation corresponds to that of the maximum transverse shear‐strain energy density in the panel, which occurs at the edge of the panel at a nodal line. However, the transverse shear deformation has a negligible effect on the global response characteristics of the panel.     

Interaction between Local and Lateral Buckling on Pultruded I-Beams

This paper presents the results of an experimental work involving pultruded beams. The tests developed attempt to observe the interaction between local and global buckling in open-section beams. A modified three-point bending test with both ends clamped has been used in order to reduce the slenderness of the structural elements. By means of a finite-element model the critical bending moment has been calculated. Special care has been taken to obtain an accurate correspondence between the real test and the finite-element model. The comparison made between test results and critical bending moments showed that the above-mentioned interaction clearly reduces the lateral buckling load in the low slenderness range. Based on the experimental data, Dutheil’s formulation has been adjusted leading to a new design equation. The proposed equation showed a good correlation in the low slenderness range, but did not match well with experimental data from literature developed in the high slenderness range. For high slenderness values, using the critical bending moment seems to be the best design method. Therefore, more experimental work has to be done on pultruded beams in order to establish a suitable formulation to describe the transition between the low and high slenderness ranges’ behaviors.     

Tangent Stiffness Equations for Laterally Distributed Loaded Members

Tangent stiffness equations for a beam-column, which is subjected to either uniformly or sinusoidally distributed lateral loads, are presented. The equations have been derived by differentiating the slope-deflection equations under axial forces for a member. Thus, the tangent stiffness equations take into consideration axial forces, bowing effect, and laterally distributed loads. As a numerical example, elastic buckling behavior of parallel chord latticed beams with laterally distributed loads is investigated to compare the results obtained from the present method with those from the conventional matrix method in which the distributed loads are considered as a series of concentrated loads at additional intermediate nodes of a member. Furthermore, buckling tests were carried out to confirm the equations derived as well as to clarify the buckling behavior of space frame structures. In conclusion, it can be said that the new equations can provide a good efficient way of estimating the equilibrium paths and buckling loads. They can also lead to a significant savings in core storage and computing time required for the analysis of space frame structures.     

Material Characterisation for Reliable and Efficient Springback Prediction in Sheet Metal Forming

In this paper, a novel experimental‐numerical methodology for an accurate prediction of springback after sheet forming is presented. An advanced phenomenological material model is implemented in the FE‐code ABAQUS. It includes the Bauschinger effect, the apparent reduction of the elasticity modulus at load reversal after plastic deformation, the strain rate dependence and the elastic‐plastic anisotropy and its evolution during the forming process. The required material parameters are determined from stress‐strain curves measured in tension‐compression tests. These tests are carried out with a special test rig designed to avoid buckling of the specimens during compression. The benefits of this procedure for springback prediction are demonstrated. Additionally, parameters for the phenomenological models are determined from texture simulations.     

Inelastic Cyclic Buckling of Aluminum Shear Panels

Cyclic load tests on shear panels of low-yield alloy of aluminum (3003-O) were performed to determine the onset and effect of inelastic web buckling on load-deformation behavior. Yielding of shear panels of aluminum can be used as a means to dissipate energy through hysteresis provided strength deterioration due to inelastic buckling is controlled. Gerard’s formulation for inelastic buckling, as reported in 1948, was found to be in excellent agreement with experimental results and can be used to predict the onset of inelastic shear buckling and to design shear panels so that inelastic buckling does not occur at strains below the design requirements.     

Compression Tests on Cylinders with Circumferential Weld Depressions

The behavior of thin cylindrical shells under axial compression is very sensitive to imperfections in the initial geometry. Local axisymmetric imperfections are among the most detrimental and have been shown to be a regular feature of circumferentially welded joints in civil engineering shell structures such as steel silos and tanks. Many of the experiments on which current design rules are based were performed on elastic Mylar, copper, or aluminum specimens, which have some very different characteristics to those of steel shells. Furthermore, very few laboratory tests have ever examined the consequences of fabrication processes on shell buckling strength, although these strongly influence the amplitudes and forms of geometric imperfections. This paper presents the findings of a careful experimental program on large steel cylinders fabricated with a fully welded circumferential joint. Thorough measurements were made of the initial imperfections and their transformation into a buckling mode. The results are compared with elastic-plastic finite-element predictions and the most recent design standard.     

Characterization of Cemented Sand by Experimental and Numerical Investigations

In this study, the effects of cementation on the stress–dilatancy and strength of cemented sand are investigated through experimental characterizations using triaxial tests and numerical simulations using the discrete element method. At small strains, dilatancy is hindered by the intact bonding network that produces a web-patterned force chain. After yielding, the increase in the dilatancy accelerates. Two competing but intimately related processes determine the peak strength: Bond breakages cause a strength reduction but the associated dilatancy leads to a strength increase. This finding and the experimental observation that the dilatancy at the peak state increases with increasing cement content explain why the measured peak-state strength parameters, c′ and ?p′, are relevant to the cement content. With increasing strain, the force-chain distribution gradually changes to a thick columnar shape, which mostly appears inside the shear band. At the ultimate state, the cementing bonds remain to form clusters, even within the shear band. The existence of clusters not only helps maintain the overall volumetric dilation but also prevents force-chain buckling, which in turn increases the associated strength.     

Complementary Energy Based Formulation for Torsional Buckling of Columns

A unique formulation for the elastic torsional buckling analysis of columns is developed in this paper based on the principle of stationary complementary energy. It is well known that in displacement based numerical formulations, discretization errors lead to stiffer behavior; hence convergence from above. On the other hand, discretization errors in complementary energy based numerical formulations lead to softer behavior in linear elasticity problems, which is a desired feature from the engineering view point. However, complementary energy based formulations can only overpredict the buckling loads for the flexural buckling problems of columns unless the physical conditions are compromised. In this study a formulation based on the principle of stationary complementary energy is considered for the elastic torsional buckling analysis of columns. The complementary energy expression is obtained from the well known total potential energy functional by using Frederichs’ transformation. In contrast to flexural buckling analysis of columns, it is shown that when the principle of stationary complementary energy is used, the torsional buckling loads can be underpredicted. A mathematical proof is provided to elucidate this property. The convergence behavior of the approximate solutions is illustrated through numerical examples for several columns with different boundary conditions.     

Scale Effect of Strip and Circular Footings Resting on Dense Sand

This paper presents the results of a research program of strip and circular footings resting on dry dense sand. The scale effect on the bearing capacity and the shape factor s;gg of the footings is investigated numerically and experimentally. The footings are analyzed using the method of characteristics. A wedge failure mechanism has been adopted. Triaxial compression tests conducted under confining pressures up to 2,500 kPa show that the friction angle of dense sand decreases with stress level. The stress-dependent friction angle of soil is adopted in the characteristics analysis. The numerical results indicate that the bearing capacity increases exponentially with footing size. With increasing footing size, the bearing capacity factor N;gg is reduced, while the shape factor s;gg is increased. Centrifuge tests of strip and circular footings with dimensions up to the equivalent of 7 m have been conducted. The experimental work verified the numerical analysis through the consistency of results.     

Shear Buckling Resistance of GFRP Plate Girders

Thin webs of glass-fiber-reinforced polymer (GFRP) girders are sensitive to shear buckling, which can be considered an in-plane biaxial compression-tension buckling problem, according to the rotated stress field theory. An extensive experimental study was performed, which shows that an increasing transverse tension load significantly increases the buckling and ultimate loads caused by a decrease in the initial imperfections and additional stabilizing effects. The stacking sequence also greatly influenced the buckling behavior. Higher bending stiffness in the compression direction increased the buckling and ultimate loads, while higher bending stiffness in the tension direction changed the buckling mode shape. The general solution obtained using the Fok model accurately modeled the experimental results, while the simplified solution (modified Southwell method) provided accurate results only at higher tension loads.     

Ductility Evaluation of Concrete-Encased Steel Bridge Piers Subjected to Lateral Cyclic Loading

An experimental and analytical study was conducted to investigate the ductility of concrete-encased steel piers, referred to as “steel-reinforced concrete (SRC) construction.” Based on the cyclic lateral loading tests of SRC column specimens, the restorable and ultimate limit states are defined as the point when concrete cover spalling occurs (equivalent to longitudinal bar buckling) and the point when flange buckling of the H-shaped steel occurs, respectively. To estimate the lateral displacement capacity at both the restorable and ultimate limit states, the curvature distribution of the column was calculated based on the buckling analysis of the longitudinal bar, which was restrained by a concrete cover and transverse reinforcement, and of the steel flange encased in concrete. The lateral displacement was obtained by integrating the curvature distribution. Comparison of the computed results with experimental results, including other writers’ reports, confirmed that the proposed method can appropriately estimate the lateral displacement at the restorable and ultimate limit states, and it can accurately evaluate the buckling characteristics of the longitudinal bar and steel flange components of SRC column specimens.     

Optimal Stabilization of Column Buckling

Linear buckling of column structures is an important design constraint in many structures, particularly where weight is a primary concern. Active strengthening is the application of feedback control to increase the critical buckling load of the structure. An important feature of this control problem is that the structure is inherently unstable when the axial load surpasses the critical buckling load. This research presents a design method for creating optimal buckling control systems using state or static output feedback. The primary feature of this method is the ability to select the designed closed loop, actively strengthened, critical buckling load. The stability of the resulting controllers is determined using Lyapunov methods. Simulation and experimental demonstration of this algorithm is performed using a column employing piezoelectric actuators, and MEMS-based strain sensors. The optimal buckling controllers developed are able to increase the critical buckling load by a factor of 2.9. The closed loop system is able to support lower axial loads indefinitely (>30 min).     

Buckling Experiments on Cone-Cylinder Intersections under Internal Pressure

Cone-cylinder intersections are used in many shell structures including tanks, silos, pressure vessels, and piping, and internal pressurization is often an important loading condition. For the intersection of the large end of a cone and a cylinder, internal pressurization causes large circumferential compressive stresses in the intersection. These stresses can lead to failure of the intersection by either axisymmetric collapse or nonsymmetric buckling. This paper presents the first carefully conducted experimental study on these intersections. Following a brief summary of the experimental setup, the experimental results are presented together with finite-element predictions. Both experimental and numerical results show that the postbuckling behavior of internally pressurized cone-cylinder intersections is stable, but the postbuckling growth of deformations and associated strains can cause rupture failure at welds. The experimental buckling load can be closely approximated by the nonlinear bifurcation load of the perfect geometry, indicating that the effect of initial imperfections is very limited.     

Failure of Web-Flange Junction in Postbuckled Pultruded I-Beams

A numerical procedure for analyzing a common and catastrophic failure mode in pultruded composite material I-beams is presented in this paper. Pultruded wide-flange profiles (often referred to as I-beams) exhibit a number of different failure modes when loaded in flexure or axial compression. The particular failure mode of interest to this paper is that due to the local separation of the flange from the web of the profile following local buckling of the flange. A node-separation technique is used to simulate the progressive failure of the joint between the flange and the web of the wide-flange beam in the postbuckled regime. The procedure has been implemented in NIKE3D, a multipurpose nonlinear implicit finite-element code. The fundamentals of the separation algorithm and the mechanics of the implementation in NIKE3D are described. The results of simulations using the proposed procedure are compared with experimental observations.     

Membrane Effects in Biaxial Compression Tests

The effects of the confining membrane in laboratory tests on soil specimens have been the subject of numerous experimental, analytical, and numerical studies over the past half-century. This technical note expands the existing knowledge base by presenting a methodology and the associated results from an experimental study that has quantified the effect of the confining membrane in biaxial shear tests conducted on medium sand. The applicability of the method of biaxial tests on clay specimens is also presented. The results show that for both tests on sands and clays, the effect of the membrane on the shear stress on the failure plane are significant and should be accounted for in the interpretation of biaxial shear test results where localization occurs.     

Global and Local Buckling of a Sandwich Beam

A two-dimensional mechanical model is developed to predict the global and local buckling of a sandwich beam, using classical elasticity. The face sheet and the core are assumed as linear elastic isotropic continua in a state of planar deformation. The core is assumed to have two deformation modes: antisymmetrical and symmetrical with respect to the core geometric midplane. Characteristics of the two deformation modes and the corresponding buckling behavior are shown and it appears that they are identical when the buckling wavelength is short. The present analysis is compared with various previous analytical studies and corresponding experimental results. On the basis of the model developed here, validation and accuracy of several previous theories are discussed for different geometric and material properties of a sandwich beam. The results presented in this paper, verified through finite-element analysis and experiment, are an accurate prediction of the overall buckling behavior of a sandwich beam, for a wide range of material and geometric parameters.     

Spatial Stability of Nonsymmetric Thin-Walled Curved Beams. II: Numerical Approach

In a companion paper, for spatial stability of nonsymmetric thin-walled curved beams, a general formulation was derived based on a displacement field considering the second-order terms of semitangential rotations. Closed-form solutions were newly derived for in-plane and out-of-plane buckling of simply supported curved beams with monosymmetric sections subjected to pure bending or uniform compression. In this paper, to get numerical solutions for the buckling of thin-walled curved beams subjected to general loadings, finite-element procedures are developed using thin-walled curved beam elements and straight frame elements with nonsymmetric sections. Numerical examples for the spatial buckling of doubly symmetric, monosymmetric, and nonsymmetric thin-walled circular beams are presented and compared with previously published solutions to illustrate the accuracy and the practical usefulness of the analytical solutions and numerical procedures.