Minor Principal Axis Research Articles

Experimental and numerical investigations of pin-ended hot-rolled stainless steel angle section columns failing by flexural buckling

A thorough testing and numerical modelling programme has been conducted to investigate the flexural buckling behaviour and strengths of pin-ended hot-rolled stainless steel angle section columns. The testing programme adopted three hot-rolled stainless steel equal-leg angle sections, and included 12 pin-ended column tests about the minor principal axis as well as supplementary initial geometric imperfection measurements on the column specimens. The testing programme was accompanied by a parallel numerical modelling programme, including a validation study, where finite element models were developed and validated against the test results, and a parametric study, where the validated finite element models were employed to generate additional numerical data over a broad spectrum of cross-section dimensions and member effective lengths. The test and numerical data were then adopted to evaluate the accuracy of the relevant design rules, as given in the European code and American design guide, for pin-ended hot-rolled stainless steel angle section columns prone to flexural buckling about the minor principal axis. On the basis of the evaluation results, it can be concluded that (i) the European code results in overall accurate and consistent flexural buckling strength predictions, but many of the predictions for short and intermediate columns with member non-dimensional slendernesses less than around 1.0 are unsafe, and (ii) the American design guide leads to unduly conservative and scattered flexural buckling strength predictions. Finally, a new design approach was developed through modifications to the Eurocode design rules, and shown to offer accurate, consistent and safe-sided flexural buckling strength predictions for pin-ended hot-rolled stainless steel angle section columns over the whole considered range of member non-dimensional slendernesses up to 4.0. The reliability of the new design approach was confirmed by means of statistical analyses according to EN 1990.

Experimental and numerical studies of pin-ended press-braked S960 ultra-high strength steel channel section columns

Grade S960 ultra-high strength steel is receiving increasing attention owing to its excellent strength-to-weight ratio. However, its application in construction engineering is rather limited due to the lack of adequate design rules, as the current established codes in Europe, North America and Australia/New Zealand only cover the design of steel components with material grades up to S700 (or S690). This prompts investigations into different types of S960 UHSS structural components and development of accurate and efficient design rules for them. The present paper focuses on press-braked S960 UHSS channel section columns prone to flexural buckling about the minor principal axes, with their behaviour and resistances thoroughly examined through experiments and numerical modelling. An experimental programme was firstly performed on two non-slender press-braked channel sections, with five column specimens of varying member lengths employed for each cross-section, and included initial global and local geometric imperfection measurements and pin-ended column tests about the minor principal axes. This was followed by a parallel numerical modelling programme, where finite element (FE) models were developed to simulate the experimental results and afterwards adopted to perform a parametric study to generate additional numerical data over a broader spectrum of cross-section dimensions and member lengths. It is worth noting that there were two orientations associated with minor-axis flexural buckling of press-braked S960 UHSS channel section columns, namely ‘C’ orientation (indicating that columns buckled towards the webs) and ‘reverse C’ orientation (indicating that columns buckled towards the flange tips), and both of the two types of failure modes were carefully examined in the present study. It was found that channel section columns failing by flexural buckling in the ‘reverse C’ orientation generally exhibited superior resistances relative to their counterparts with failure in the ‘C’ orientation. The experimental and numerical data were also used to assess the applicability of the codified provisions for press-braked S700 (or S690) channel section columns failing by flexural buckling about the minor principal axes to the design of their S960 counterparts. The assessment results indicated that (i) the existing European code leads to overall conservative and scattered design flexural buckling resistances, especially for those relatively short and intermediate press-braked S960 UHSS channel section columns with failure in the ‘reverse C’ orientation, and (ii) the North American specification and Australian/New Zealand standard result in a higher degree of design accuracy and consistency than the European code, but with many over-predicted flexural buckling resistances for press-braked S960 UHSS channel section short and intermediate columns failing in the ‘C’ orientation.

Numerical Modeling of Stress Disturbance Characteristics during Tunnel Excavation

The stress state and principal stress axis changes of the stress‐field tensor are analyzed during the advancement of a tunnel face on the basis of a given case study of the Jinping II Hydropower Station in China. First, the prevailing pole diagram in geology is used to illustrate the rotation of the stress axes as the tunnel face advances. The results show that the orientation adjustments of principal stresses in different positions near the tunnel boundary share common characteristics. The major and minor principal stress axes ahead of the tunnel face will rotate to intersect with the excavation surface at an angle, with the intermediate principal stress axis being almost parallel to the excavation surface. Furthermore, the stress triaxiality that is commonly used to indicate the deformation and damage of metal materials is introduced to describe the stress state change of the excavation‐induced stress. The stress triaxiality is found to represent the stress state change due to the variation in both the magnitude and orientation of the stress‐field tensor. According to the physical meaning and the change law of the stress triaxiality, stress disturbance during tunnel excavation can be divided into four stages, and the stress disturbance zone is divided into a strong disturbance zone and a weak disturbance zone. The disturbance characteristics of different stages and the distribution patterns of various zones are analyzed, which may be useful for practical application in the design and construction of rock tunnels.

Distortional strength of end-bolted CFS lipped channel columns: Experimental investigation, numerical simulations and DSM design

This paper reports the results of an experimental investigation and numerical simulations concerning the influence of bolted end support conditions on the failure loads of cold-formed steel lipped channel columns buckling and failing in distortional modes, as well as on their prediction by means of the Direct Strength Method (DSM). The end supports consist of pairs of cylindrical high-strength bolts with hexagonal heads and nuts, which are inserted in standard-sized holes located at the intersections of the cross-section flanges with the minor principal centroidal axis (parallel to the web). After selecting the column geometries (cross-section dimensions and lengths) and yield stresses, the test set-up and procedure are described in detail, and the experimental results obtained are presented and discussed. Such results consist of initial imperfection measurements, equilibrium paths relating the applied load to key column displacements, deformed configurations (including the collapse mode) and failure loads. Next, those same experimental results are used to validate a previously developed shell finite model, which is subsequently employed to obtain additional numerical failure load data concerning the end-bolted columns under scrutiny. Then, attention is turned to assessing the merits of the available DSM column distortional design curves. Because it is concluded that these design curves clearly overestimate the failure load data obtained, new/modified strength curves are preliminarily proposed and shown to considerably improve the prediction quality (safety and reliability) of the end-bolted column failure loads, thus providing motivation and encouragement to continue the search for an efficient DSM-based design approach for end-bolted columns failing in distortional modes. • Experimental and numerical investigation on end-bolted lipped channel columns failing distortionally • Procedure and results of test campaign involving 13 column specimens described and discussed. • Validated SFE model employed to perform parametric study and gather distortional failure load data. • Available DSM design curves found to grossly overestimate the experimental and numerical failure loads. • Proposal of DSM-based design approaches that improve considerably the failure load prediction quality.

Simulation of long-term rotational dynamics of large space debris: A TOPEX/Poseidon case study

Accurate knowledge of the rotational dynamics of a large space debris is crucial for space situational awareness (SSA), whether it be for accurate orbital predictions needed for satellite conjunction analyses or for the success of an eventual active debris removal mission charged with stabilization, capture and removal of debris from orbit. In this light, the attitude dynamics of an inoperative satellite of great interest to the space debris community, the joint French and American spacecraft TOPEX/Poseidon, is explored. A comparison of simulation results with observations obtained from high-frequency satellite range measurements is made, showing that the spacecraft is currently spinning about its minor principal axis in a stable manner. Predictions of the evolution of its attitude motion to 2030 are presented, emphasizing the uncertainty on those estimates due to internal energy dissipation, which could cause a change of its spin state in the future. The effect of solar radiation pressure and the eddy-current torque are investigated in detail, and insights into some of the satellite’s missing properties are provided. These results are obtained using a novel, open-source, coupled orbit-attitude propagation software, the Debris SPin/Orbit Simulation Environment (D-SPOSE), whose primary goal is the study of the long-term evolution of the attitude dynamics of large space debris.

Experimental and numerical studies of press-braked S690 high strength steel channel section beams

Abstract The present paper describes an in-depth experimental and numerical investigation into the flexural responses and strengths of press-braked S690 high strength steel channel section beams bent about the minor principal axes in both the ‘u’ and ‘n’ orientations. The experimental study was performed on eight press-braked channel sections, and comprised twenty-four material flat and corner coupon tests, initial local geometric imperfection measurements, and twelve beam tests in the four-point bending configuration. This was followed by a complementary numerical modelling programme, where finite element models were firstly developed and validated against the test results and afterwards adopted for performing parametric studies to obtain an additional numerical data bank over a wide variety of cross-section geometric sizes. The acquired test and numerical data were then employed to evaluate the applicability of the Eurocode slenderness limits for welded and hot-rolled internal webs (in compression) and outstand flanges (in stress gradients) to their press-braked counterparts, revealing that the Eurocode slenderness limits can be safely extended to cover the classifications of plate elements and cross-sections of press-braked S690 high strength steel channel section beams. Evaluation of the accuracy of the cross-section flexural strengths predicted from various design codes established in Europe, North America and Australia/New Zealand was also made, based on the test and numerical data. The results of the quantitative evaluation generally revealed that (i) all the examined design codes lead to overall conservative and scattered predicted cross-section flexural strengths for press-braked S690 high strength steel channel section beams, and (ii) the European code results in more precise design flexural strengths for beams with relatively stocky channel sections, but less accurate strength predictions for beams with relatively slender channel sections, compared to the North American and Australian/New Zealand standards.

Local stability of press-braked stainless steel angle and channel sections: Testing, numerical modelling and design analysis

This paper reports an experimental and numerical investigation into the local stability of press-braked stainless steel angle and channel sections. The experimental programme was performed on two equal-leg angle sections and two plain channel sections, and included material testing, initial local geometric imperfection measurements, eight stub column tests and ten laterally restrained beam tests (about the geometric axes for angle sections and minor principal axes for channel sections). This was supplemented by a numerical simulation programme, where finite element models were firstly established to replicate the test structural responses and then employed to derive further numerical data through parametric studies. The results obtained from the structural testing and numerical modelling were adopted to evaluate the accuracy of the codified local buckling design provisions established in America, Europe and Australia and New Zealand. The evaluation results revealed that all the design codes greatly underestimate the cross-section resistances of press-braked stainless steel equal-leg angle and plain channel section stub columns and laterally restrained beams, mainly attributed to the neglect of the pronounced material strain hardening effect of stainless steel in the design. The continuous strength method (CSM) is an advanced deformation-based design method, allowing for a rational utilisation of material strain hardening in determining cross-section resistances, and its scope of application has been recently extended from doubly-symmetric (I- and tubular) sections to mono-symmetric and asymmetric (angle, channel and T-) sections. Quantitative evaluation of the CSM was conducted through comparing the predicted cross-section resistances against the experimental and numerical results. The CSM was found to yield substantially more accurate and consistent design cross-section resistances for press-braked stainless steel equal-leg angle and plain channel section stub columns and laterally restrained beams than the established design codes.

Flexural behaviour and strengths of press-braked S960 ultra-high strength steel channel section beams

A thorough experimental and numerical study of the flexural behaviour and strengths of press-braked S960 ultra-high strength steel (UHSS) channel section beams bent about the minor principal axes is reported in this paper. The experimental study was conducted on eight different UHSS plain channel sections, and included measurements on the material flat and corner properties and initial local geometric imperfections of the beam specimens as well as 20 four-point bending tests performed about the minor principal axes in both the ‘u’ and ‘n’ orientations. A complementary numerical investigation was then conducted, where finite element (FE) models were firstly developed and validated against the experimental results, followed by parametric studies carried out to acquire further numerical data over a broader range of cross-section dimensions. It is worth noting that the existing design codes for steel structures, as established in Europe, America and Australia/New Zealand, are only applicable to those with material grades up to S690 (or S700 for Eurocode) and cannot be directly used for S960 UHSS structural members. In the present study, the applicability of the codified design provisions and formulations for flexural members to the examined S960 UHSS channel section beams was evaluated, based on the ultimate moments derived from structural testing and numerical modelling. The quantitative evaluation results generally revealed that the current European code provides overall consistent and precise flexural strength predictions for Class 1 and Class 2 S960 UHSS channel sections in minor-axis bending, but leads to a high level of inaccuracy (scatter and conservatism) for the design of their Class 3 and Class 4 counterparts, whilst the American specification and Australian/New Zealand standard result in scattered and excessively underestimated design flexural strengths, except for the cases of slender S960 UHSS channel section beams in ‘u’-orientation bending.

In-plane bending behaviour and capacities of S690 high strength steel welded I-section beams

The present paper describes an in-depth experimental and numerical investigation into the in-plane flexural behaviour and bending moment capacities of S690 high strength steel welded I-section beams. The experimental investigation was conducted on six different welded I-sections fabricated from the same batch of 5 mm thick S700MC high strength steel hot-rolled plates by means of gas metal arc welding, and involved initial local geometric imperfection measurements and twelve in-plane four-point bending tests, with six performed about the cross-section major principal axes and another six conducted about the cross-section minor principal axes. Following the experimental study, a numerical investigation was performed, where the developed finite element models were firstly validated against the test results and then used to perform parametric studies to generate further structural performance data over a broader range of cross-section sizes. The obtained experimental and numerical results were carefully analysed and then adopted to evaluate the accuracy of the existing slenderness limits (for classifications of plate elements and cross-sections) and local buckling design rules for S690 high strength steel welded I-sections in bending, as set out in the European, Australian and American standards. The results of the evaluation revealed that the codified slenderness limits are generally safe when used for the classification of the constituent plate elements of the examined S690 high strength steel welded I-section beams, except for that given in the American specification for slender/non-slender outstand elements in compression. All of the three considered design standards were shown to yield accurate cross-section bending moment capacity predictions for compact (Class 1 and 2) S690 high strength steel welded I-section beams bent about both the principal axes and non-compact (Class 3) S690 high strength steel welded I-section beams bent about the major principal axes, but resulted in a rather high level of conservatism in predicting the cross-section bending moment capacities for non-compact (Class 3) S690 high strength steel welded I-sections in bending about the minor principal axes and slender (Class 4) S690 high strength steel welded I-sections subjected to both major-axis bending and minor-axis bending.

Finite Element Modeling and Design of Single Angle Member Under Bi-axial Bending

Practical single angle members are mostly subjected to eccentric forces due to the end connections to their legs. Plastic Class 1 and compact Class 2 angle cross-sections are allowed for using their plastic reserves. However, most of the interaction equations in the current design codes are linear whereas the nonlinear equations associated with plastic surface are provided in the literature. In this study, a new design method for single angle member to address the plastic failure as well as stability checks is proposed. The first yield moments at different critical points due to the interaction between the normal forces and the biaxial bending are provided. Moreover, the elastic flexural and flexural-torsional buckling loads for single angle member are calculated using a simplified equation rather than the complex design charts or series of equations in literature or design codes. New buckling curves, taking the Eurocode 3 design rules into account, are presented for single angle member subjected to eccentric load about both major and minor principal axes. A reliable and efficient finite element model is provided to verify the proposed equations and to investigate the different parameters affecting the buckling behavior. Finally, various initial geometric imperfections together with a residual stress distribution pattern are studied and provided in this paper.

Non-linear biaxial bending of steel Z-beams

Confusion as to the way in which the bending of Z-section beams has been described has led to misleading descriptions of the limiting moments of beams which undergo non-linear biaxial bending and twisting as being elastic buckling moments. Further difficulties arise from the use of the same symbols to describe both the principal and the rectangular axes of Z-sections.A constrained beam with restraints which prevent lateral displacement of the compression region does not buckle laterally, and only needs to be designed against in-plane failure. A beam with restraints which prevent lateral displacement of the tension region should be designed against lateral-distortional buckling, which may be approximated by lateral buckling with an enforced centre of rotation.An unconstrained beam bent about its minor principal axis does not buckle laterally, and should be designed against in-plane failure. An unconstrained beam bent about its major principal axis may buckle laterally.An unconstrained beam under biaxial bending deflects and twists as soon as loading commences and reaches very large deformations as a limiting moment is approached. The large deformations cause premature yielding before the limiting moment is reached. Pre-buckling effects reduce these large deformations somewhat, but not sufficiently that the limiting moment can be safely used in first yield design. Instead, interaction equations may be used. The linear interaction equation is unnecessarily conservative, and may be replaced by a parabolic interaction equation.

Imperfection sensitivity analysis of steel columns at ultimate limit state

The present paper applies Sobol's variance-based global sensitivity analysis (SSA) to quantify the contribution of input imperfections to the load-carrying capacity (LCC) of an IPN 200 steel compressed member. LCC is evaluated using the geometrically and materially non-linear finite element solution with regard to the effects of initial random imperfections including residual stresses. Comparison of results of SSA for (i) buckling about the minor principal axis, (ii) buckling about the major principal axis and (iii) lateral–torsional buckling due to bending moment is performed on the non-dimensional slenderness interval of 0–2. SSA for (i) and (ii) is performed for steel grade (a) S235 and (b) S355, SSA for (iii) is performed only for steel grade S235. SSA found similarities in results (ia) and (ib), (iia) and (iib) and identified significant differences between results (ia) and (iiia), (iia) and (iiia), where sensitivity to the initial axial curvature is more than two times higher in (ia) than in (iiia). The relationships between the effects of initial imperfections on LCC and the design criteria of reliability of Eurocode 3 are discussed.

Resistance of cold-formed built-up stainless steel columns – Part I: Experiment

Nowadays, the codified procedure for design of centrically compressed cold-formed stainless steel (CFSS) built-up members is absent in Europe. Besides, there are no published research information and experimental data in this structural area. This paper focuses on a comprehensive experimental investigation of closely spaced CFSS built-up columns and addresses their flexural buckling capacity about the minor principal axis. Two series with a total of 36 built-up members were assembled, each formed by two discontinuously and directly connected channel chords oriented back-to-back to form an I-section. The chords were press-braked from flat strips of austenitic stainless steel EN 1.4301 as non-slender channel sections. The chords were uniformly interconnected by bolts or by welds. To identify the effects of interconnection spacing on chords' composite action, the overall and chord slenderness ratios were varied. Material properties, cross-section response and initial imperfections were quantified before testing. As a result, the overall flexural buckling without any local-overall interactions was observed as the dominant failure mode. All findings were used in the accompanying paper [1] to establish qualitative data base through numerical simulations of flexural buckling tests. Additionally, a quantitative accuracy assessment of the design methods for carbon steel built-up columns provided in Eurocode and American Specification was reported on the basis of their ability to predict flexural buckling resistances of the tested columns. This enabled numerical parametric studies and proposing design rules for CFSS built-up columns with non-slender sections that capture interconnection shear stiffness, overall and chord slenderness ratio and strain hardening effects.

Generating spiral tool paths based on spiral enter assistant line

In order to increase cutting width, decrease tool path length, and improve machining efficiency, the spiral enter assistant line (SEAL) is embedded into a convex pocket to plan a spiral tool path. First, the inner offset curve of the pocket boundary undergoes equidistant division to acquire the external equidistant points. Subsequently, principal component analysis (PCA) and length factors optimization are employed to obtain SEAL. Next, vector operation is performed on the external equidistant points and SEAL to calculate the corresponding internal points. After connecting the external equidistant points and the corresponding internal points, a B-spline spiral tool path is planned based on linear interpolation and B-spline curve fitting. In addition, the length factors can be adjusted to modify the distribution and length of the tool path. Theoretical analysis and machining experiments demonstrate that compared to other conventional algorithms, the spiral tool path presented in this study has obvious advantages on cutting width, tool path length, and machining efficiency. These advantages are especially pronounced when the major principal axis is much longer than the minor principal axis.

Beam-Column In-Plane Resistance Based on the Concept of Equivalent Geometric Imperfections

AbstractAssessment of the flexural buckling resistance of bisymmetrical I-section beam-columns using FEM is widely discussed in the paper with regard to their imperfect model. The concept of equivalent geometric imperfections is applied in compliance with the so-called Eurocode’s general method. Various imperfection profiles are considered. The global effect of imperfections on the real compression members behaviour is illustrated by the comparison of imperfect beam-columns resistance and the resistance of their perfect counterparts. Numerous FEM simulations with regard to the stability behaviour of laterally and torsionally restrained steel structural elements of hot-rolled wide flange HEB section subjected to both compression and bending about the major or minor principal axes were performed. Geometrically and materially nonlinear analyses, GMNA for perfect structural elements and GMNIA for imperfect ones, preceded by LBA for the initial curvature evaluation of imperfect member configuration prior to loading were carried out. Numerical modelling and simulations were conducted with use of ABAQUS/Standard program. FEM results are compared with those obtained using the Eurocode’s interaction criteria of Method 1 and 2. Concluding remarks with regard to a necessity of equivalent imperfection profiles inclusion in modelling of the in-plane resistance of compression members are presented.

The Elastic Critical Load of Single Angle Columns

The design of single angle columns requires the ability to predict their flexural-torsional buckling strengths and flexural buckling strengths about the minor principal axis. Present design code provisions are quite different. This paper presents close approximations for the elastic critical load of equal angle section columns. It is found that the member capacities are less than the minor axis capacity at low slenderness and almost remain constant. A formula of the balance point is proposed which is simpler and better understanding.

Electromagnetically induced transparency for guided light in an atomic array outside an optical nanofiber

We study the propagation of guided light along an array of three-level atoms in the vicinity of an optical nanofiber under the condition of electromagnetically induced transparency. We examine two schemes of atomic levels and field polarizations where the guided probe field is quasilinearly polarized along the major or minor principal axis, which is parallel or perpendicular, respectively, to the radial direction of the atomic position. Our numerical calculations indicate that 200 cesium atoms in a linear array with a length of 100 $\ensuremath{\mu}\mathrm{m}$ at a distance of 200 nm from the surface of a nanofiber with a radius of 250 nm can slow down the speed of guided probe light by a factor of about $3.5\ifmmode\times\else\texttimes\fi{}{10}^{6}$ (the corresponding group delay is about 1.17 $\ensuremath{\mu}\mathrm{s})$. In the neighborhood of the Bragg resonance, a significant fraction of the guided probe light can be reflected back with a negative group delay. The reflectivity and the group delay of the reflected field do not depend on the propagation direction of the probe field. However, when the input guided light is quasilinearly polarized along the major principal axis, the transmittivity and the group delay of the transmitted field substantially depend on the propagation direction of the probe field. Under the Bragg resonance condition, an array of atoms prepared in an appropriate internal state can transmit guided light polarized along the major principal in one specific direction even in the limit of infinitely large atom numbers. The directionality of transmission of guided light through the array of atoms is a consequence of the existence of a longitudinal component of the guided light field as well as the ellipticity of both the field polarization and the atomic dipole vector.

DETECTION OF THE VELOCITY SHEAR EFFECT ON THE SPATIAL DISTRIBUTIONS OF THE GALACTIC SATELLITES IN ISOLATED SYSTEMS

We report a detection of the effect of the large-scale velocity shear on the spatial distributions of the galactic satellites around the isolated hosts. Identifying the isolated galactic systems each of which consists of a single host galaxy and its satellites from the Seventh Data Release of the Sloan Digital Sky Survey and reconstructing linearly the velocity shear field in the local universe, we measure the alignments between the relative positions of the satellites from their isolated hosts and the principal axes of the local velocity shear tensors projected on to the plane of sky. We find a clear signal that the galactic satellites in isolated systems are located preferentially along the directions of the minor principal axes of the large-scale velocity shear field. Those galactic satellites which are spirals, brighter, located at distances larger than the projected virial radii of the hosts and belonging to the spiral hosts yield stronger alignment signals, which implies that the alignment strength depends on the formation and accretion epochs of the galactic satellites. It is also shown that the alignment strength is quite insensitive to the cosmic web environment as well as the size and luminosity of the isolated hosts. Although this result is consistent with the numerical finding of Libeskind et al. based on a N-body experiment, due to the very low significance of the observed signals it remains inconclusive whether or not the velocity shear effect on the satellite distribution is truly universal.

Assessment of Coherency for Bidirectional Horizontal Ground Motions and Its Application for Simulating Records at Multiple Stations

Estimation of the coherency of ground‐motion records in two horizontal orthogonal directions at single or multiple stations is carried out using records from SMART‐1 array for several seismic events in Taiwan. Empirical coherency function is suggested for the components of records in two horizontal orthogonal directions at single‐ and multiple‐recording stations. It was also found that the coherency for the records along the major and minor principal axes at a recording station is similar to that for two randomly oriented orthogonal directions. The spatial coherency and the spatial correlation of the records are used to establish a procedure for simulating bidirectional horizontal ground motions at multiple stations, considering that the stochastic point‐source method or the stochastic finite‐fault method can be used to define the reference Fourier amplitude spectra for scenario events. Use of the proposed procedure to simulate records is illustrated for a scenario seismic event; the adequacy of the simulated records in approximating the target spatial correlation and coherency is presented.

ALIGNMENTS OF THE GALAXIES IN AND AROUND THE VIRGO CLUSTER WITH THE LOCAL VELOCITY SHEAR

An observational evidence is presented for the alignment between the cosmic sheet and the principal axis of the velocity shear field at the position of the Virgo cluster. The galaxies in and around the Virgo cluster from the Extended Virgo Cluster Catalog recently constructed by Kim et al. are used to determine the direction of the local sheet. The peculiar velocity field reconstructed from the Sloan Digital Sky Survey Data Release 7 is analyzed to estimate the local velocity shear tensor at the Virgo center. Showing first that the minor principal axis of the local velocity shear tensor is almost parallel to the line of sight direction, we detect a clear signal of alignment between the positions of the Virgo satellites and the intermediate principal axis of the local velocity shear projected onto the plane of the sky. Furthermore, the dwarf satellites are found to appear more strongly aligned than the normal counterparts, which is interpreted as indication of the following: (i) The normal and the dwarf satellites fall in the Virgo cluster preferentially along the local filament and the local sheet, respectively. (ii) The local filament is aligned with the minor principal axis of the local velocity shear while the local sheet is in parallel to the plane spanned by the minor and the intermediate principal axes. Our result is consistent with the recent numerical claim that the velocity shear is a good tracer of the cosmic web.