Straight Column Research Articles

Critical buckling loads of the perfect Hollomon's power-law columns

In this work, we present analytic formulas for calculating the critical buckling states of some plastic axial columns of constant cross-sections. The associated critical buckling loads are calculated by Euler-type analytic formulas and the associated deformed shapes are presented in terms of generalized trigonometric functions. The plasticity of the material is defined by the Hollomon's power-law equation. This is an extension of the Euler critical buckling loads of perfect elastic columns to perfect plastic columns. In particular, critical loads for perfect straight plastic columns with circular and rectangular cross-sections are calculated for a list of commonly used metals. Connections and comparisons to the classical result of the Euler–Engesser reduced-modulus loads are also presented.

Relocation of the Yushu M S7.1 earthquake and its aftershocks in 2010 from HypoDD

After the Yushu MS7.1 earthquake on April 14, 2010, a large number of aftershocks were recorded by the surrounding permanent network and temporary seismic stations. Due to the distribution of stations, knowledge about velocity structure, the reliability of seismic phases, and so on, the location result from conventional method is usually of low precision, from which it is difficult to recognize the spatial and temporal distribution and the trends of aftershock activity. In this paper, by using teleseismic waveforms recorded by permanent station, the seismic velocity structure beneath the vicinity is obtained from receiver function stacking and inversion methods. And the Yushu earthquake sequences are relocated from seismic phase data by HypoDD. The results show that the Yushu MS7.1 earthquake occurred at 13 km depth; the aftershock sequences were distributed mainly in the NWW along the Garze-Yushu fault, and most aftershocks were concentrated in a 100 km length and 5–20 km depth. Combined with the velocity structure, it can be inferred that the earthquake mainly destroys the high-velocity layer of the upper crust. In the west of the seismic fault near (33.3°N, 96.2°E), the aftershock sequences were distributed like a straight column, suggesting there was a comminuted break from 25km depth to the ground.

Characteristics and generation of secondary jets and secondary gigantic jets

Secondary transient luminous events (TLEs) recorded by the ISUAL‐FORMOSAT2 mission can either be secondary jets or secondary gigantic jets (GJs), depending on their terminal altitudes. The secondary jets emerge from the cloud top beneath the preceding sprites and extend upward to the base of the sprites at ∼50 km. The secondary jets likely are negative electric discharges with vertically straight luminous columns, morphologically resembling the trailing jet of the type‐I GJs. The number of luminous columns in a secondary jet seems to be affected by the size of the effective capacitor plate formed near the base of the preceding sprites and the charge distribution left behind by the sprite‐inducing positive cloud‐to‐ground discharges. The secondary GJs originate from the cloud top under the shielding area of the preceding sprites, and develop upward to reach the lower ionosphere at ∼90 km. The observed morphology of the secondary GJs can either be the curvy shifted secondary GJs extending outside the region occupied by the preceding sprites or the straight pop‐through secondary GJs developing through the center of the preceding circular sprites. A key factor in determining the terminal height of the secondary TLEs appears to be the local ionosphere boundary height that established by the preceding sprites. The abundance and the distribution of the negative charge in the thundercloud following the sprite‐inducing positive cloud‐to‐ground discharges may play important role in the generation of the secondary TLEs.

Three-dimensional visual feature representation in the primary visual cortex

In the cat primary visual cortex, it is accepted that neurons optimally responding to similar stimulus orientations are clustered in a column extending from the superficial to deep layers. The cerebral cortex is, however, folded inside a skull, which makes gyri and fundi. The primary visual area of cats, area 17, is located on the fold of the cortex called the lateral gyrus. These facts raise the question of how to reconcile the tangential arrangement of the orientation columns with the curvature of the gyrus. In the present study, we show a possible configuration of feature representation in the visual cortex using a three-dimensional (3D) self-organization model. We took into account preferred orientation, preferred direction, ocular dominance and retinotopy, assuming isotropic interaction. We performed computer simulation only in the middle layer at the beginning and expanded the range of simulation gradually to other layers, which was found to be a unique method in the present model for obtaining orientation columns spanning all the layers in the flat cortex. Vertical columns of preferred orientations were found in the flat parts of the model cortex. On the other hand, in the curved parts, preferred orientations were represented in wedge-like columns rather than straight columns, and preferred directions were frequently reversed in the deeper layers. Singularities associated with orientation representation appeared as warped lines in the 3D model cortex. Direction reversal appeared on the sheets that were delimited by orientation-singularity lines. These structures emerged from the balance between periodic arrangements of preferred orientations and vertical alignment of the same orientations. Our theoretical predictions about orientation representation were confirmed by multi-slice, high-resolution functional MRI in the cat visual cortex. We obtained a close agreement between theoretical predictions and experimental observations. The present study throws a doubt about the conventional columnar view of orientation representation, although more experimental data are needed.

Axial-Bundle Phases − New Modes of 2D, 3D, and Helical Columnar Self-Assembly in Liquid Crystalline Phases of Bolaamphiphiles with Swallow Tail Lateral Chains

Two series of polyphilic molecules composed of a rigid and linear p-terphenyl core, terminated at both ends with polar glycerol groups capable of hydrogen bonding, and two branched swallow tail-type lateral chains, composed of a fluorinated and a nonfluorinated branch or two fluorinated branches, were synthesized and investigated by differential scanning calorimetry, polarizing microscopy, and X-ray diffraction (XRD) with respect to their self-assembly in thermotropic liquid crystalline (LC) phases. Hexagonal columnar phases were formed by all molecules, at least at the highest temperature. In these phases the columns are composed of a core of aromatic rods and an aliphatic shell. The aromatic rods form bundles which are rotationally averaged and lie parallel to the column long axis. This unique organization is proven by different optical and XRD methods. The aromatic and glycerol groups inside the rod bundles are segregated into alternating segments. Depending on temperature and molecular structure, long-range intercolumnar correlation of this periodicity could take place, leading to a 3D-ordered LC phase with rhombohedral R ̄3m symmetry. The bundles are embedded in the matrix of the lateral chains, which is divided into fluoroalkyl- and aliphatic-rich regions. In the 2D columnar phase the fluorinated regions take the form of either straight columns running along the edges of the hexagonal Voronoi cells or, for compounds with a higher degree of fluorination, fuse to a hexagonal honeycomb enclosing the aromatic cores. In the R ̄3m phase the fluorine-rich chains are preferentially found along right- and left-handed helices wound around the 3(1) screw axes between the main aromatic columns.

Stochastic stability of a viscoelastic column axially loaded by a white noise force

This paper deals with the analysis of stability of a hinged-hinged viscoelastic column subjected to a non-zero mean stochastic axial force. The randomly variable part of this is described by a stationary Gaussian white noise process. The viscosity affects the curvature of the column, for which the classic Euler–Bernoulli's model is adopted. The viscosity is described by the linear Kelvin–Voigt's model. A dynamic stability analysis is performed. Normal modes are introduced in the integro-differential equation of motion so that uncoupled modal equations are retrieved. With reference to the first mode, by using an additional state variable, three Itô’s ODE are obtained, from which the differential equations ruling the response statistical moment evolution are written by means of Itô’s differential rule. The zero solution, that is undeformed straight column, corresponds to zero moments. If the column is perturbed, it is stable when the response moments tend to zero. A necessary and sufficient condition of stability in the moments of order r is that the matrix A r of the coefficients of the ODE system ruling them has negative real eigenvalues and complex eigenvalues with negative real parts. Because of the linearity of the system the stability of the first two moments is the strongest condition of stability. If the mean axial force μ P or the white noise intensity w P are increased, there exist critical values μ Pcr , w P c r for which almost an eigenvalue is positive. The critical mean axial force is found to be inversely proportional to the parameter φ ∞ , which measures the amount of viscous deformation. The search for the critical values of w P is made numerically, and several graphs are presented for a representative column.

EVOLUTION AND STATE‐OF‐THE‐ART OF COLUMN STABILITY CRITERIA

The strength and stability of steel columns have been the subjects of a great many studies since the original work of Leonhard Euler in 1744 and 1759. Numerous examinations of elastic buckling of perfectly straight columns were conducted during the 19th century, the most famous being the studies of Engesser and Considère, with several series of column tests attempting to find agreement between theory and physical behavior. The research work continued in the 20th century, examining the influence of material and member imperfections, including the famous tangent modulus work of Shanley, and the resolution of the effects of material non‐linearity, residual stress and column out‐of‐straightness. The definitive solutions were only obtained in the 1970‐s, when modeling and numerical solutions allowed for the incorporation of all nonlinear effects. Since that time reliability and probabilistic solutions have provided state‐of‐the‐art criteria for limit state treatment of the column problem. These principles are now the bases of the design standards for columns in all of the countries in the world. The paper focuses on the major evolutions that have taken place, but especially the work over the past 40 years. Realistic treatment and representation of the strength of columns in actual structures have now been achieved by the engineering profession. Santrauka Plieniniu kolonu stiprumas ir pastovumas buvo daugelio tyrinejimu objektas, pradedant nuo originaliu Leonhardo Eulerio 1744 ir 1759 m. darbu. XIX a. buvo atlikta daugelis idealiai tiesiu kolonu tampriojo klupumo tyrimu, iš kuriu žymiausi buvo Engesero (Engesser) ir Konsideres (Considere) tyrimai, apeme kelias kolonu bandymu serijas. Jais siekta rasti derme tarp teorijos ir fizines elgsenos. Darbai buvo tesiami ir XX a., nagrinejant medžiagu ir elementu nuokrypiu poveiki, iskai‐tant gerai žinoma Šenlio (Shanley) liestines modulio darba, ir medžiagu netiesiškumo, liekamuju itempiu bei kolonu išklupimo poveikius. Galutiniai sprendiniai buvo gauti tik 1970 m., kai modeliavimas ir skaitiniai eksperimentai leido atsižvelgti i visus netiesinius poveikius. Nuo to laiko patikimumo ir tikimybiniai sprendiniai suteike šiuolaikinius kriterijus kolonu problemos ribiniu būviu traktuotei. Dabar šie principai yra visu pasaulio šaliu kolonu projektavimo normu pagrindas. Straipsnyje pristatytos pagrindines raidos kryptys, apžvelgiamas darbas, nuveiktas per pastaruosius 40 metu. Statybos profesionalai pasieke tikroviška dabartiniu statiniu kolonu stiprumo traktuote ir pateikima.

2210 構想設計段階における車両衝突安全性評価法(OS3-2 設計・デザイン論II,OS3 設計・デザイン論)

This paper proposes a crashworthiness evaluation and optimization method for straight thin-walled columns using simplified models, to alleviate massive computational cost due to a large number of shell elements, required for accurate prediction of nonlinear collapse behavior. The simplified crashworthiness analysis model, developed in this research, is composed of beam and non-linear spring elements. The properties of non-linear spring elements are derived from analytical calculation results of crush mechanism of thin-walled beam. This paper also clarify the design criteria for crashworthiness design optimization problems, and genetic algorithms are used to solve this optimization problem. The proposed optimization method is applied to a numerical example problem and the optimal solution obtained using the simplified analysis model is compared with the result when using a detailed analysis employing shell elements. The optimal solution provided by the simplified analysis model agrees well with the solution based on detailed analysis results.

Phase diagram of the La–Si binary system under high pressure and the structures of superconducting LaSi 5 and LaSi 10

The La–Si binary phase diagram under a high pressure of 13.5 GPa was experimentally constructed. New superconducting silicides LaSi 5 and LaSi 10 were found, which have peritectic decomposition temperatures at 1000 and 750 °C, respectively. The single crystal X-ray structural analysis revealed that there are two polymorphs in LaSi 5. The α-form obtained by heating a molar mixture of LaSi 2 and 3 Si at about 700 °C or by a rapid cooling from 1000 °C under pressure crystallizes with the space group C2 /m and the lattice parameters a=15.11(3), b=4.032(6), c=8.26(1) Å, and β=109.11(1)°. The β-form obtained by a slow cooling from 800–950 °C to 600 °C under pressure has the same space group but with slightly different lattice parameters, a=14.922(7), b=3.906(2), c=8.807(4) Å, and β=107.19(1)°. The β-form is formed during the incomplete transformation of the α-form on cooling, and has always been obtained as a mixture with the α-form. The compound can be characterized as a Zintl phase with a polyanionic framework ∞ 3 [ Si 5 ] 3 - with large tunnels running along the b axis hosting lanthanum ions. In the β-form, three of the five Si sites are disordered. The two polymorphs contain one dimensional sila-polyacene ribbons, Si ladder polymer, running along the b axis. The α-form showed superconductivity with the transition temperature T c of 11.5 K. LaSi 10 crystallizes with the space group 6 3/ mmc and the lattice parameters a=9.623(4), c=4.723(3) Å. It is composed of La containing Si 18 polyhedra (La@Si 18) of hexagonal beer-barrel shape, which form straight columns by stacking along the c-axis via face sharing. One-dimensional columns of La@Si 18 barrels are edge-shared, and bundled with infinite Si trigonal bipyramid chains via corner sharing. The Si atoms in the straight chains have a five-fold coordination. LaSi 10 became a superconductor with T c =6.7 K. The ab initio calculation of the electric band structures showed that α-LaSi 5 and LaSi 10 are metallic, and the conduction electrons mainly come from Si-3 p orbitals.

Improved concept models for straight thin-walled columns with box cross section

This paper focuses on developing improved concept models for straight thin-walled box sectional columns which can better predict the peak crushing force that occurs during crashworthiness analyses. We develop a nonlinear translational spring based on previous research and apply such a spring element to build the enhanced concept models. The work presented in this article is developed on the basis of the publication of the author (Liu and Day, 2006b) and has been applied in a crashworthiness design issue, which is presented by the author in another paper (Liu, 2008).

Application 0f Draft Tube in the Reduction of Backmixing Rate in Oscillatory Flow in a Baffled Column

Oscillatory flow in a baffled tube/column is an efficient way to enhance mixing in a straight smooth column. However, liquid oscillation moving back and forth across the baffle causes backmixing which is a disadvantage when plug flow is desired. This paper presents results from a study conducted to reduce the backmixing rate in oscillatory flow in a baffled column with the use of a draft tube. Results of this study showed that backmixing increases with oscillation velocity and decreases with liquid flow rate. The use of a draft tube reduces backmixing. The backmixing reduction is proportional to the ratio of L/Do However, the draft tube can not be extended too long because it disrupts the flow behavior in the column and creates dead zones near the baffle region. The draft tube length is maximized by extending it to both sides of the baffle, provided that the L/De on each side of the baffle is at 0.67 or less.

Crashworthiness design of multi-corner thin-walled columns

This paper presents a crashworthiness design of regular multi-corner thin-walled columns with different types of cross-sections and different profiles, including straight octagonal columns and curved hexagonal columns. In this paper, the straight octagonal section columns are first optimized, which mainly take axial crash loads during crashes. Next, the curved hexagonal section columns are optimized following the same approach, which are subject to bending moment when impact occurs. During the design optimizations, specific energy absorption ( SEA) is set as the design objective, side length of the cross-sections and wall thickness are selected as design variables, and maximum crushing force ( P m) is set as the design constraint. Both the objective and constraint are formulated using the response surface method (RSM) based on sets of finite element (FE) results obtained from FE analyses (FEA). After obtaining the optimal designs, parametric studies are performed to investigate the influences of the design variables on the crash performance of such multi-corner thin-walled columns.

Column buckling with shear deformations—A hyperelastic formulation

Column constitutive relationships and buckling equations are derived using a consistent hyperelastic neo-Hookean formulation. It is shown that the Mandel stress tensor provides the most concise representation for stress components. The analogous definitions for uniaxial beam plane stress and plane strain for large deformations are established by examining the virtual work equations. Anticlastic transverse curvature of the beam cross-section is incorporated when plane stress or thick beam dimensions are assumed. Column buckling equations which allow for shear and axial deformations are derived using the positive definiteness of the second order work. The buckling equations agree with the equation derived by Haringx and are extended to incorporate anticlastic transverse curvature which is important for low slenderness, high buckling modes and with increasing width to thickness ratio. The work in this paper does not support the existence of a shear buckling mode for straight prismatic columns made of an isotropic material.

Morphology and thermal conductivity of yttria-stabilized zirconia coatings

An electron beam directed vapor deposition method was used to grow 7 wt.% Y 2O 3–ZrO 2 (7YSZ) coatings and the effects of substrate rotation upon the coating porosity, morphology, texture, and thermal conductivity were explored. As the rotation rate was increased, the texture changed from 〈1 1 1〉 to 〈1 0 0〉. Under stationary deposition, the coatings were composed of straight columns, while low-frequency rotation resulted in wavy columns. Increases in rotation rate resulted in a gradual straightening and narrowing of the growth columns. The pore fraction slowly decreased as the rotation rate increased. The thermal conductivity was found to be inversely related to the pore fraction. The structural and thermal conductivity alterations are a result of changes to flux shadowing associated with specimen rotation in a gas jet-entrained vapor plume. The minimum thermal conductivity at a low rotation rate is 0.8 W/(m K), well below that of conventionally deposited coatings.

IN-PLANE NONLINEAR BEHAVIOUR OF CIRCULAR PINNED ARCHES WITH ELASTIC RESTRAINTS UNDER THERMAL LOADING

This paper considers the nonlinear in-plane behaviour of a circular arch subjected to thermal loading only. The arch is pinned at its ends, with the pins being on roller supports attached to longitudinal elastic springs that model an elastic foundation, or the restraint provided by adjacent members in a structural assemblage. By using a nonlinear formulation of the strain-displacement relationship, the principle of virtual work is used to produce the differential equations of in-plane equilibrium, as well as the statical boundary conditions that govern the structural behaviour under thermal loading. These equations are solved to produce the equilibrium equations in closed form. The possibility of thermal buckling of the arch is addressed by considering an adjacent buckled equilibrium configuration, and the differential equilibrium equations for this buckled state are also derived from the principle of virtual work. It is shown that unless the arch is flat, in which case it replicates a straight column, thermal buckling of the arch in the plane of its curvature cannot occur, and the arch deflects transversely without bound in the elastic range as the temperature increases. The nonlinear behaviour of a flat arch (with a small included angle) is similar to that of a column with a small initial geometric imperfection under axial loading, while the nonlinearity and magnitude of the deflections decrease with an increase of the included angle at a given temperature. By using the closed form solutions for the problem, the influence of the stiffness of the elastic spring supports is considered, as is the attainment of temperature-dependent first yielding of a steel arch.

Stability of a slender beam-column with locally varying Young's modulus

A locally varying temperature field or a mixture of two or more different materials can cause local variation of elasticity properties of a beam. In this paper, a new Euler-Bernoulli beam element with varying Young`s modulus along its longitudinal axis is presented. The influence of axial forces according to the linearized 2nd order beam theory is considered, as well. The stiffness matrix of this element contains the transfer constants which depend on Young`s modulus variation and on axial forces. Occurrence of the polynomial variation of Young`s modulus has been assumed. Such approach can be also used for smooth local variation of Young`s modulus. The critical loads of the straight slender columns were studied using the new beam element. The influence of position of the local Young`s modulus variation and its type (such as linear, quadratic, etc.) on the critical load value and rate of convergence was investigated. The obtained results based on the new beam element were compared with ANSYS solutions, where the number of elements gradually increased. Our results show significant influence of the locally varying Young`s modulus on the critical load value and the convergence rate.

High sensitive determination of sufentanil in human plasma of parturients and neonates following patient-controlled epidural analgesia (PCEA)

A validated method for the determination of sufentanil in human plasma using liquid chromatography-tandem mass spectrometry (LC-MS/MS) is described. Sufentanil was extracted from human plasma with solid-phase-extraction using deuterated sufentanil, [(2)H(5)]-sufentanil, as internal standard. Sufentanil and the internal standard were determined with an API 4000 tandem mass spectrometer equipped with a Turbo-V-Source operating in positive ESI mode on an Alltima HP HILIC straight phase column. The method showed a lower limit of quantification of 0.25 pg/ml (12.5 fg on column). The applicability of the method is shown in a clinical study, in which levels of sufentanil in plasma of parturients and arterial umbilical plasma of their neonates following patient-controlled epidural analgesia (PCEA) under several regimen treatments was analyzed.

Caustics and Buckling of Cracked Columns

The experimental method of caustics is applied to buckling behaviour of straight cracked columns. Two major parameters of the problem may be defined through the caustics method: the SIF and the high strain internal region. The knowledge of these parameters may be used to improve predictions of the buckling behaviour of cracked columns.

Flexural–torsional buckling of fixed steel arches under uniform bending

This paper develops a closed-form solution for the elastic flexural–torsional buckling of a laterally fixed steel circular arch that is subjected to uniform bending. The formulation makes recourse to an orthogonal rotations matrix in order to derive the finite strains and the energy equation for buckling. Whilst the flexural–torsional buckling of pinned arches has received some degree of treatment in the literature, it appears that the flexural–torsional buckling of fixed arches has not been reported openly. The buckling solutions are very different from those of pinned arches, and significantly they illustrate that the concept of an ‘effective length’ approach, that is often useful for determining the buckling response of straight beams or columns, is not applicable for the flexural–torsional buckling of arches. The ramifications of this observation are that design procedures for the out-of-plane buckling of pinned arches cannot be used as a basis for design procedures for fixed arches.

Microstructure of nanoporous yttria-stabilized zirconia films fabricated by EB-PVD

Microstructures of ZrO 2–4 mol% Y 2O 3 coating layers fabricated by EB-PVD are characterized. Coating layers are found to consist of porous columnar grains with a feather-like structure containing evenly dispersed nano-sized gaps. Nanopores less than 50 nm in diameter could also be observed within columnar grains. The columnar grain size and column width of the coating layers increased with increasing coating thickness and substrate rotation speed. The porosity of the coating layers also shows increases with increasing substrate rotation speed. Specimens rotated at 1 rpm are found to contain wavy or scalloped columnar grains. Specimens rotated at higher speeds are found to consist of straight columns with a banded structure.