Buckling of a Weakened Column

The buckling problem of a column weakened at an interior location is studied for the first time. The weakness is modeled by a rotationally restrained junction. Exact buckling load values are obtained for the weakened column with various end conditions. Depending on the end conditions of the column, the buckling loads show sensitivity (and insensitivity) to junction location and rotational stiffness. The optimum location of the junction could be at the midpoint, at the ends, or somewhere in between.     

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 of Column with Base Attached to Elastic Half-Space

Buckling of a heavy elastic column loaded by a concentrated force at the top is analyzed. It is assumed that the base of the column is fixed to a rigid circular plate that is positioned on a homogeneous, isotropic, linearly elastic half-space. The plate has adhesive contact with the half-space. The constitutive equations for the column are assumed in the form that allows axial compressibility and takes into account the influence of shear stresses. It is shown that eigenvalues of the linearized equations determine the bifurcation points of the full nonlinear system of equilibrium equations. The type of bifurcation at the lowest eigenvalue is examined and is shown that it could be super- or subcritical. The postcritical shape of the column is determined by numerical integration of the equilibrium equations.     

Effect of Base Fixity on Buckling of Heavy Column with End Load

This paper studies the effect of a rotationally restrained base on the buckling of a standing column subjected to both its own weight and a tip load. The characteristic equation is derived analytically in terms of Bessel functions. The results show stability is greatly compromised when the base is not securely fixed. Rotational spring constants for some simple base constraints are estimated.     

Restraining Steel Brace Buckling Using a Carbon Fiber-Reinforced Polymer Composite System: Experiments and Computational Simulation

This paper presents an experimental and computational study of the buckling behavior of steel members strengthened with carbon fiber-reinforced polymer (CFRP) wraps. In the proposed strengthening system, steel members are first sandwiched within a core comprised of mortar or PVC blocks and then the entire system is wrapped with CFRP sheets. A matrix of specimens is tested under monotonic compression to investigate the parameters that influence system response. Test results show that the proposed strengthening method can provide enough lateral support to a steel bar member to allow it to reach yield in compression and to continue deforming inelastically beyond. Key failure modes are identified in the test program. Important parameters that influence behavior are also pinpointed and studied in more detail through a computational simulation model that is validated using the test data. Parameters identified as influential in the experimental and computational studies include: number of CFRP layers, core thickness, bond between CFRP layers and the core, bond between the core and the inner steel member, and strength of transverse sheets at the member ends.     

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.     

Simulation of Upward Seepage Flow in a Single Column of Spheres Using Discrete-Element Method with Fluid-Particle Interaction

The interaction between soil particles and pore water makes the behavior of saturated and unsaturated soil complex. In this note, upward seepage flow through a granular material was idealized using a one-column particle model. The motion of the individual particles was numerically simulated using the discrete-element method taking the interaction with the fluid into account. The fluid behavior was simulated by the Navier-Stokes equation using the semi-implicit method for pressure-linked equation. This approach has already been applied in powder engineering applications. However, there are very few studies that have used this approach in geotechnical engineering. This note first describes the qualitative and quantitative validation of this method for hydraulic gradients below the critical one by comparing the results with an analytical solution. Then, the ability of the method to simulate the macroscale behavior due to the interaction between particles and pore water at hydraulic gradients exceeding the critical hydraulic gradient is discussed.     

预裂-缓冲爆破中柱状孔间应力波作用分析

利用新型全息动光弹,以南芬矿高台阶靠帮控制爆破的现场参数为实验模拟基础,研究了两预裂孔间应力波迭加的动态变化过程。在两炮孔均实行孔底和孔口同时起爆(四起爆点),并对孔底进行加强装药条件下,获得了不同时刻的等差条纹图。发现沿炮孔方向应力波分布有很大不同,提出了初始P波与后出现的S波迭加形成的波是所有波中最重要的部分。研究表明,孔底加强装药是深孔孔底产生预裂效果的关键因素,孔底连线上应力场强度不受端部效应影响。     

Buckling of Columns with Intermediate Elastic Restraint

This paper presents a comprehensive set of exact stability criteria for Euler columns with an intermediate elastic restraint. A subset of this class of problem is the buckling problem of columns with an intermediate rigid support where the elastic restraint takes on an infinite stiffness. Also, this study reiterates the existence of a critical elastic restraint stiffness in which the buckled mode switches to a higher-buckling mode of the corresponding column without an intermediate support. It is clear that this critical stiffness value exists only when the restraint is placed at the node of the higher-buckling mode and the buckling load associated with this critical stiffness value is the maximum achievable value that can be attained with an intermediate elastic restraint.     

Lateral-Torsional Buckling of Stepped Beams with Continuous Bracing

Continuous span multibeam steel bridges are common along the state and interstate highways. The top flange of the beams is typically braced against lateral movement by the deck slab, and in many bridges the cross section is stepped at discrete points along the span. Design equations for lateral–torsional buckling (LTB) resistance in the American Association of State Highway and Transportation Officials “Load and resistance factor design bridge design specifications” are for prismatic beams and ignore the lateral restraint provided by the bridge deck. A new design equation is proposed that can be applied to I-shaped stepped beams with continuous top flange lateral bracing. By including the effects of the change in cross section size and the continuous top flange bracing, the calculated LTB resistance is significantly increased. Critical bending moment values from the proposed equation are compared to values from finite element method buckling analyses. The new equation is sufficiently accurate for use in design and in the evaluation of existing bridges.     

Derivative of Buckling Load with Respect to Support Locations

This paper formulates the derivative of buckling load with respect to intermediate constraint locations. These intermediate constraints include intermediate spring supports and pinned supports. The analysis is based on the generalized energy functional, which includes the product of Lagrange multipliers and boundary conditions. The results show that the derivative of buckling load with respect to the constraint position is proportional to the force between the constraint and the structure as well as to the spatial slope of the associated buckling mode at the constraint position. With the combination of this derivative formula and the Courant maximum-minimum principle, an interesting theorem on the optimal constraint position is proposed.     

Ritz Buckling Analysis of Rectangular Plates with Internal Hinge

This paper presents the Ritz method for buckling analysis of rectangular plates with an internal line hinge. The Ritz method involves the domain decomposition method to cater for the discontinuity of slope at the hinge line. The correctness of the Ritz formulation and solutions is confirmed by the exact solutions derived using the Levy method for plates with two opposite sides simply supported. Based on the Ritz method, buckling factors are generated for rectangular plates of various aspect ratios, hinge locations, and support and loading conditions.     

Buckling of Delaminated Composite Beams with Shear Deformation Effect

A general 1D model of composite delaminated beams with shear deformation effect is derived for buckling behavior. The constitutive models of composite laminated beams are derived from the classical 2D laminate theory. The present cylindrical bending models can be used—with much greater accuracy than their well-known plane-strain and plane-stress counterparts—as upper and lower bounds toward one of which the behavior tends, depending on the width-to-length ratio. The analysis is based on the first-order Timoshenko-Mindlin kinematic approach. The differential equations are solved with the aid of a specially developed, very efficient interlaced finite-difference scheme eliminating the “shear locking” phenomenon. A parametric study of the shear deformation effect associated with various constitutive models is carried out for angle-ply delaminated laminate. It was found that the most significant difference between the models is associated with the mix of local and global modes.     

Tension Buckling in Multilayer Elastomeric Bearings

The compression buckling of mutilayer elastomeric bearings which are widely used as vibration mounts, bridge bearings, and seismic isolators for buildings is well understood and is governed by theoretical analysis and confirmed by extensive experimental work. What is not well known is that the theoretical analysis that predicts the compression buckling behavior also predicts that a bearing could be subject to buckling in tension with a tension buckling load that is of the same order as the compressive buckling load and a buckled shape that is the same as that in compression. The tensile buckling load will not be achievable in practice in most bearings since it will generally be much larger than the load that will induce cavitation in the elastomer, but the analysis can be very valuable in explaining the behavior of seismic isolators when loaded in tension while laterally displaced. This can occur when extreme seismic loading on an isolated building induces global overturning. Isolators at the periphery of the building can be in a state of combined tension and shear. The analysis shows that the elastomer can sustain the tension load without cavitation since rotation of the central portion converts tension to rotated shear.     

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.     

Flexural-Torsional Buckling of Cantilever Strip Beam-Columns with Linearly Varying Depth

In this paper, one investigates the elastic flexural-torsional buckling of linearly tapered cantilever strip beam-columns acted by axial and transversal point loads applied at the tip. For prismatic and wedge-shaped members, the governing differential equation is integrated in closed form by means of confluent hypergeometric functions. For general tapered members (0<(hmax?hmin)/hmax<1), the solution to the boundary value problem is obtained in the form of a Frobenius’ series, which is shown to converge in the interior of the domain and at the boundary if and only if 0<(hmax?hmin)/hmax<1/2. Therefore, for 1/2?(hmax?hmin)/hmax<1 the Frobenius’ series solution cannot be used to establish the characteristic equation for the cantilever beam-columns; the problem is then solved numerically by means of a collocation procedure. Some of the analytical solutions (buckling loads) were compared with the results of shell finite-element analyses and an excellent agreement was found in all cases, thus validating the mathematical model and confirming the correctness of the analytical results. The paper closes with a discussion on the convexity of the stability domain (in the load parameter space) and the accuracy of approximations based on Dunkerley-type theorems.