Instability and Complete Failure of Steel Columns Subjected to Cyclic Loading

In a testing system design for large deformations, structural columns were loaded to complete failure, defined as either complete separation of the column or inability to sustain the prescribed axial load. The test system consists of very large stroke quasistatic jacks, digital displacement transducers that can ensure accurate measurement of large deformations, hydraulic pump units capable of controlling the oil flow, controllers that control the jack motion, and separate personal computers for operating the jack controllers and for supervising and measuring data. These components are connected on-line for data and signal operations, which enables automatic and accurate load control for tests that lead specimens to complete failure. Six columns having a square tube cross section are tested in cyclic loading condition, with the axial load and column length as major parameters. The load–deformation relationships obtained from the tests are presented in detail, and relationships among the deformation capacity, failure mode, slenderness, and axial load are discussed. Intermediate axial load (30% of the yield axial load) is effective in retarding the occurrence and growth of cracks, resulting in larger deformation capacity to complete failure. Finite element analysis accurately duplicates the experimental behavior up to a large inelastic range including material yielding, strain hardening, and local buckling. It fails to simulate the experimental behavior in a very large deformation range where the column surfaces crashed and contacted each other. More experimental data is strongly needed for the behavior of structural systems and elements at and near complete failure.     

Buckling Mode Interaction in Fixed-End Column with Central Brace

The postbuckling behavior of an elastic fixed-end column with an elastic brace at the center is investigated. Attention is focused on those of brace stiffness near its threshold value at which, under axial load, the column becomes critical with respect to two buckling modes simultaneously. We show that, for the brace stiffness greater than the threshold value, there are precisely two secondary bifurcation points on each primary postbuckling path bifurcating from one of the least two classical buckling loads, and the corresponding secondary postbuckling paths connect all of these secondary bifurcation points in a loop. For the brace stiffness less than the threshold value, no secondary bifurcation occurs. The asymptotic expansions of the primary and secondary postbuckling paths are constructed. The stability analysis indicates that, when the brace stiffness goes beyond its threshold value, the primary postbuckling path with a node in the center becomes unstable from stable by means of the secondary bifurcation (i.e., secondary buckling occurs).     

Control of Suspension Bridge Nonlinear Vibrations due to Moving Loads

The flexibility and low damping of the long-span suspended cables in the suspension bridges make them prone to vibrations due to wind and moving loads, which affect the dynamic response of the suspended cables and the bridge deck. This paper shows the design of two control schemes to control the nonlinear vibrations in the suspended cable and the bridge deck due to a vertical load moving on the bridge deck with a constant speed. The first control scheme is an optimal state feedback controller. The second control scheme is a robust state feedback controller, whose design is based on the design of optimal controllers. The proposed controllers, whose design is based on Lyapunov theory, guarantee the asymptotic stability of the system. A vertical cable between the bridge deck and the suspended cable is used to install a hydraulic actuator able to generate the active control force on the bridge deck. The MATLAB software is used to simulate the performance of the system with the designed controllers. The simulation results indicate that the proposed controllers are capable of significantly reducing the nonlinear oscillations of the system. In addition, the performance of the system with the proposed controllers is compared to the performance of the system controlled with a velocity feedback controller. It is found that the system with the proposed controllers can provide better performance than the system with the velocity feedback controller.     

Design and Fabrication of CFRP Interstage Attach Fitting for Launch Vehicles

Lattice structures that are made of carbon-fiber-reinforced plastics (CFRP) have been commonly used for interstage structures in launch vehicles because of their high axial compressive strength-to-weight ratio. The purpose of this research is to investigate the failure behavior of filament wound lattice structures to demonstrate that these structures can be fabricated and formed precisely and automatically. For the failure modes, the general buckling as a shell and excessive stress are considered. Various types of lattice shells under axial compressive loads are presented, and the optimal constraint with the highest compressive failure load is found. The main emphasis is placed on the effects of geometrical configuration of the structure and the manufacturing process. The main geometrical characteristics that affect failure are the winding pattern, winding angle, and the slenderness of the members. The primary advantage of a filament wound lattice structure is that fibers are wound continuously and aligned with the load direction. The manufacturing process includes automated winding, winding path control, bridging effects, and the winding tension force. It is shown that these structures can be constructed by filament winding, that the process can be automated, and that the manufacturing cost can be reduced.     

Approximate Derivation of Critical Buckling Load

This paper proposes an approximate derivation for the critical buckling load of a column, based on the application of a uniformly loaded beam's midspan moment and deflection to the buckled column's rotational equilibrium. The curvature of a pin-ended member, when it buckles under axial load, is similar to the curvature assumed by the same member when it deflects under a uniformly distributed load applied transversely along its entire length. Euler's famous equation for critical buckling load is based, of course, on the former assumption, in which the deflected column assumes the shape of a sine curve. However, dividing a uniformly loaded beam's midspan moment by its deflection provides a conservative result for the critical buckling load, within 3% of Euler's value, that can be derived solely on the basis of these commonly used beam equations.     

薄铺层复合材料薄壁管轴压屈曲行为研究

在薄壁结构的应用中,屈曲稳定性是影响其承载性能的关键因素,为研究减薄铺层厚度对复合材料薄壁结构局部屈曲行为的影响,本文采用不同厚度(0.125、0.055和0.020 mm)的预浸料制备复合材料薄壁管,实验测试了其在轴压下的局部屈曲行为.实验结果表明,随着铺层厚度减薄,实验采用的正交和均衡两种铺层方式的复合材料薄壁管局部屈曲载荷均随之提高,而屈曲失效模式没有发生改变.力学分析表明,铺层厚度减薄后,管壁弯曲刚度的改变和层间剪切应力分布对薄壁管局部屈曲载荷提高有重要影响.采用薄铺层制备复合材料薄壁结构件能够有效提高其局部屈曲能力.      

Static Stability of Beam-Columns under Combined Conservative and Nonconservative End Forces: Effects of Semirigid Connections

Stability criteria that evaluate the effects of combined conservative and nonconservative end axial forces on the elastic divergence buckling load of prismatic beam-columns with semirigid connections is presented using the classic static equilibrium method. The proposed method and stability equations follow the same format and classification of ideal beam-columns under gravity loads presented previously by Aristizabal-Ochoa in 1996 and 1997. Criterion is also given to determine the minimum lateral bracing required by beam-columns with semirigid connections to achieve “braced” buckling (i.e., with sidesway inhibited). Analytical results obtained from three cases of cantilever columns presented in this paper indicate that: (1) the proposed method captures the limit on the range of applicability of the Euler’s method in the stability analysis of beam-columns subjected to simultaneous combinations of conservative and nonconservative loads. The static method as proposed herein can give the correct solution to the stability of beam-columns within a wide range of combinations of conservative and nonconservative axial loads without the need to investigate their small oscillation behavior about the equilibrium position; and (2) dynamic instability or flutter starts to take place when the static critical loads corresponding to the first and second mode of buckling of the column become identical to each other. “Flutter” in these examples is caused by the presence of nonconservative axial forces (tension or compression) and the softening of both the flexural restraints and the lateral bracing. In addition, the “transition” from static instability (with sidesway and critical zero frequency) to dynamic instability (with no sidesway or purely imaginary sidesway frequencies) was determined using static equilibrium. It was found also that the static critical load under braced conditions (i.e., with sidesway inhibited) is the upper bound of the dynamic buckling load of a cantilever column under nonconservative compressive forces. Analytical studies indicate the buckling load of a beam-column is not only a function of the degrees of fixity (ρa and ρb), but also of the types and relative intensities of the applied end forces (Pci and Pfj), their application parameters (ci, ηj, and ξj), and the lateral bracing provided by other members (SΔ).     

Dynamic Buckling of Simply Supported Columns under Axial Slamming

Dynamic buckling properties of simply supported columns under axial fluid-solid slamming are experimentally investigated in this study. By observing the elastic-plastic responses of columns, the dynamic buckling criterion and the dynamic plasticity criterion of columns are defined and the relevant critical impulses are determined. The effect of the slenderness ratio of the column on the elastic-plastic dynamic buckling properties is also examined. The dynamic buckling characteristics of fluid-solid slammed columns are compared and discussed with respect to those of columns under solid-solid impact. It is found that they are different from those of columns subjected to either impulsive impact or impact owing to suddenly applied load.     

Automatic Downstream Water-Level Feedback Control of Branching Canal Networks: Theory

Most of the research on the design of feedback controllers for irrigation canals has been concentrated on single, in-line canals with no branches. Because the branches in a network are hydraulically coupled with each other, it may be difficult to automatically control a branching canal network by designing separate feedback controllers for each branch and then letting them run simultaneously. Thus feedback control of an entire branching canal system may be more efficient if the branching flow dynamics are explicitly taken into account during the feedback controller design process. This paper develops two different feedback controllers for branching canal networks. The first feedback controller was developed using linear quadratic regulator theory and the second using model predictive control. Both algorithms were able to effectively control a simple branching canal network example with relatively small flow changes.     

Nonlinear Analysis of Uniform Pantographic Columns in Compression

The linear analysis of a uniform pantographic deployable column shows that, in bending, its behavior is very similar to that of an equivalent solid column, whereas under axial loading the two columns display distinct differences in their force and deformation distributions. The total change in the height of a particular pantographic unit in the deployable structure consists of two parts, one due to relative rotation of bars in the unit, the other to their bending. To account for configuration changes, the internal forces must satisfy the equilibrium of each unit “after rotation.” The additional pantographic unit deformation due to bending of bars is found to be based on these forces. The set of equilibrium and nonlinear deformation equations is solved iteratively. The “deformation-controlled” approach for solving this system of equations shows the load maximum in the equilibrium paths that corresponds to the snap-through buckling of the top pantographic unit. It is found that the change in the number of units in the column introduces only minor differences in the equilibrium paths as long as the column height and degree of deployment are kept constant. The axial stiffness of the pantographic column is greatly increased and the snap-through buckling considerably postponed if just one additional constraint is introduced, namely the horizontal link between the two nodes at a particular unit interface. The optimal location of the link is found.     

Stability Analysis of Box-Girder Cable-Stayed Bridges

The objective of this study is to investigate the stability characteristics of box-girder cable-stayed bridges by three-dimensional finite-element methods. Cable-stayed bridges have many design parameters, because they have a lot of redundancies, especially for long-span bridges. Cable-stayed bridges exhibit several nonlinear behaviors concurrently under normal design loads because of large displacements; the interaction among the pylons, the stayed cables, and the bridge deck; the strong axial and lateral forces acting on the bridge deck and pylons; and cable nonlinearity. A typical two-lane, three-span, steel box-girder cable-stayed bridge superstructure was selected for this paper. The numerical results indicate that, if the ratio of the main span length with respect to the total span length, L1∕L, is small, the structure usually has a higher critical load. If the ratio Ip∕Ib increases, the critical load of the bridge decreases, in which Ip is the moment of inertia of the pylon and Ib is the moment of inertia of the bridge deck. When the ratio Ip∕Ib is greater than 10.0, the decrement becomes insignificant. For cable arrangements, bridges supported by a harp-type cable arrangement are the better design than bridges supported by a fan-type cable arrangement on buckling analysis. The numerical results also indicate that use of either A-type or H-type pylons does not significantly affect the critical load of this type of structure. In order to make the numerical results useful, the buckling loads have been nondimensionalized and presented in both tabular and graphical forms.     

Simple Optimal Downstream Feedback Canal Controllers: Theory

A new class of downstream water-level feedback controllers is proposed that can vary from a series of individual proportional-integral (PI) controllers (each gate adjusted based on one water level) to fully centralized controllers (each gate adjusted based on all water levels) that include the effects of lag time. The controller design method uses discrete-time state-feedback control with a quadratic penalty function, physically based states, and no state estimation. A simple, linear model of canal pool response, the integrator-delay model, is used to define the state transitions. All controllers within this class are tuned for the entire canal using optimization techniques. This avoids the tedious task of manually tuning simple controllers. The relative performance of the various controllers within this class can be directly compared without simulation, since the same objective function is used to tune each controller. An example is provided which suggests that the fully centralized controller will perform better than a series of local controllers. However, reasonably good performance can be obtained for some intermediate PI controllers that pass information to one additional check structure upstream and downstream. This should limit some of the difficulties reported for full optimal controllers where all check structures respond to water-level errors in all pools (e.g., saturation of inputs). The results of simulation studies of these controllers are provided in a companion paper.     

Acceleration Feedback-Based Active and Passive Vibration Control of Landing Gear Components

In this paper, a novel methodology is developed to absorb the vibrations of relatively large-scale aircraft structures such as landing gear components. This is accomplished using a combination of active and passive controls. A system equivalent to a Boeing 747 landing gear break rod is selected as a test bed. The expected goal of this study is to dissipate the fundamental vibration mode of the tube. A beam-type dynamic absorber and a constrained layer damping treatment are used for passive vibration control. Simulations and experimental results are provided for the dynamic absorber case. In addition, full-state feedback along with state estimation based on the “reciprocal state space” method is presented. The plant responses and estimates for both the open loop and closed loop systems are shown in simulations. An optimal controller based on acceleration measurements using piezoelectric actuators is implemented using a hardware in the loop protocol for the active vibration control of the system. The integrated controller with passive and active components absorbs the fundamental mode of the system, according to the experimental results.     

Design∕Control Optimization of Cross‐Ply Laminates Under Buckling and Vibration

The optimal layer thicknesses and optimal feedback control function are determined for a symmetric, cross‐ply laminate. The objectives of the optimization are to maximize the biaxial buckling load (design objective) and to minimize the dynamic response to external disturbances (control objective) subject to a constraint on the expenditure of control energy. The design∕control problem is formulated as a multiobjective optimization problem by employing a performance index that combines the design and control objectives in a weighted sum. Numerical results are given for a laminate made of an advanced composite material. Comparisons of controlled and uncontrolled laminates as well as optimally designed and nonoptimal laminates indicate the benefits of treating the design and control problems in unified formulation. The implications of solving these two problems are discussed. The values of optimal design and control variables are given for a number of problem parameters.     

Euler Critical Force Calculation for Laced Columns

The paper presents a method of solving the buckling problem of laced column as a statically indeterminate structure without analyzing determinants of high order. The flexural and torsional buckling problems of laced column are reduced to the two-point boundary value problem for a difference equation system. The value of Euler critical load is determined as a result of analyzing the fourth order determinant for column with any degree of static indeterminacy. The solution is based on the method of initial values. Stability of columns with any types of lattice (crosswise, serpentine, with batten struts); with any number of lattice panels and with variable lattice spacing can be examined by this manner. The analogy between the flexural and torsional buckling of the laced column is established. It enables one to use the same relations for consideration of both kinds of buckling. The obtained numerical results show that the Euler critical loads calculated by this method can be substantially differed from those based on the approximated Engesser’s approach. A PC program for checking stability of laced column by designer can be developed on the basis of the present method.     

Slender Steel Columns Strengthened Using High-Modulus CFRP Plates for Buckling Control

This paper presents the results of an experimental investigation into the behavior of slender steel columns strengthened using high-modulus (313?GPa), carbon fiber-reinforced polymer (CFRP) plates. Eighteen slender hollow structural section square column specimens, 44×44×3.2?mm, were concentrically loaded to failure. The effectiveness of CFRP was evaluated for different slenderness ratios (kL/r), namely, 46, 70, and 93. The maximum increases in ultimate load ranged from 6 to 71% and axial stiffness ranged from 10 to 17%, respectively, depending on kL/r. As kL/r reduced, the effectiveness of CFRP plates also reduced, and failure mode changed from CFRP plate crushing after occurrence of overall buckling, to debonding prior to, or just at, buckling. A simplified analytical model is proposed to predict the ultimate axial load of FRP-strengthened slender steel columns, based on the ANSI/AISC 360-05 provisions, which were modified to account for the transformed section properties and a failure criteria of FRP derived from the experimental results. It was shown that for a given FRP reinforcement ratio, there is a critical kL/r at the low end, below which FRP may not enhance the strength of the column.     

Vulnerability Screening and Capacity Assessment of Reinforced Concrete Columns Subjected to Blast

In this study, a nonlinear model is developed to study the response of blast-loaded reinforced concrete (RC) columns. The strain rate dependency and the axial load and P?Δ effects on the flexural rigidity variation along the column heights were implemented in the model. Strain rate and axial load effects on a typical RC column cross section were investigated by developing strain-rate-dependent moment-curvature relationships and force-moment interaction diagrams. Analysis results showed that the column cross section strength and deformation capacity are highly dependent on the level of strain rates. Pressure-impulse diagrams were developed for two different column heights with two different end connection details (ductile and nonductile) and the effects of the axial load on the column midheight deflection and end rotation at failure were evaluated for both connection types. Based on the results of this study, a pressure-impulse band (PIB) technique is proposed. The PIB technique presents a useful tool that covers practical uncertainties associated with RC column reinforcement details as well as possible increase of column axial loads resulting from different blast-induced progressive collapse scenarios. Finally, the uses of the PIB technique for vulnerability screening of critical infrastructure or postblast capacity assessment of RC columns of target structures are presented.     

Closed-Form Solutions for Buckling of Long Anisotropic Plates with Various Boundary Conditions under Axial Compression

Closed-form solutions for buckling of long plates with flexural/twist anisotropy with the short edges simply supported and with the longitudinal edges simply supported, clamped, or elastically restrained in rotation under axial compression are presented. An energy method (Rayleigh–Ritz) is employed to obtain the critical buckling loads. The critical buckling loads are expressed in terms of minimum nondimensional buckling coefficients and stiffness parameters. The new closed-form solutions show an excellent agreement when compared to existing solutions and finite-element analysis. Due to their simplicity and accuracy, the new closed-form solutions can be confidently used as an alternative to computationally expensive structural analysis to assess buckling in the preliminary design phase of composite structures.     

Static Stability Formulas of a Weakened Timoshenko Column: Effects of Shear Deformations

The static stability analysis of two-dimensional Timoshenko columns weakened at an arbitrary section is derived in a classic manner. The effects of shear deformations along the column, influenced by the additional shear force induced by the applied axial load as the member deforms according to the modified shear equation proposed by Haringx, are presented and studied in detail. The proposed model also captures: (1) the influence on the buckling load capacity of the column when an arbitrary weakened section is formed at any location; (2) the tension buckling phenomenon due to the low shear stiffness of columns made of composite materials or elastomeric rubbers; and (3) the beneficial effects of an additional lateral bracing located at the weakened section to alleviate the buckling load reduction of the column. Seven classical and nonclassical cases of columns mostly used in civil and mechanical engineering are summarized in condensed formulas which allow the straightforward determination of buckling loads and shapes.     

Tension and Compression Stability and Second-Order Analyses of Three-Dimensional Multicolumn Systems: Effects of Shear Deformations

The stability and second-order analyses of three-dimensional (3D) multicolumn systems including the effects of shear deformations along the span of each column are presented in a condensed manner. This formulation is an extension to an algorithm presented recently by the writer in 2002 and 2003 by which the critical load of each column, the total critical load, and the second-order response of a 3D multicolumn system with semirigid connections can be determined directly. The proposed solution includes not only the combined effects of flexural deformations and shear distortions along the columns in their two principal transverse axes, but also the effect of the shear forces along each member induced by the applied end axial force as the columns deform and deflect (as suggested by Haringx in 1947 and explained by Timoshenko and Gere in 1961) in their two principal transverse axes. The extended characteristic transcendental equations (corresponding to multicolumn systems with sidesway and twist uninhibited, partially inhibited, and totally inhibited) that are derived and discussed in this publication find great applications in the stability and second-order analyses of 3D multicolumn systems made of materials with relatively low shear stiffness such as orthotropic composite materials (fiber reinforced plastic) and multilayer elastomeric bearings used for seismic isolation of buildings. The phenomenon of buckling under axial tension in members with relatively low shear stiffness (observed by Kelly in 2003 in multilayer elastomeric bearings, and recently discussed by the writer in 2005) is captured by the proposed method. Tension buckling must not be ignored in the stability analysis of multicolumn systems made of columns in which the shear stiffness GAs is of the same order of magnitude as π2EI/h2.