Non-symmetric Loading Research Articles

Linear buckling of quadrangular and kagome gridshells: A comparative assessment

The design of gridshells is subject to strong mechanical and fabrication constraints, which remain largely unexplored for non-regular patterns. The aim of this article is to compare the structural performance of two kind of gridshells. The first one is the kagome gridshell and it is derived from a non-regular pattern constituted of triangles and hexagons. The second one results from a regular pattern of quadrangles unbraced by diagonal elements. A method is proposed to cover kagome gridshells with planar facets, which reduces considerably the cost of fabrication of the cladding.The sensitivity of kagome gridshells to geometrical imperfections is discussed. The linearised buckling load of kagome gridshells is then compared to the one of quadrilateral gridshells. The most relevant design variables are considered in the parametric study. Two building typologies are studied for symmetrical and non-symmetrical load cases: dome and barrel vault. It reveals that the kagome gridshell outperforms quadrilateral gridshell for a very similar construction cost.

An Efficient Method for Topology Optimization of Continuum Structures in the Presence of Uncertainty in Loading Direction

This paper presents a simple yet efficient method for the topology optimization of continuum structures considering interval uncertainties in loading directions. Interval mathematics is employed to equivalently transform the uncertain topology optimization problem into a deterministic one with multiple load cases. An efficient soft-kill bi-directional evolutionary structural optimization (BESO) method is proposed to solve the problem, which only requires two finite element analyses per iteration for each external load with directional uncertainty regardless of the number of the multiple load cases. The presented algorithm leads to significant computational savings when compared with Monte Carlo-based optimization (MCBO) algorithms. A series of numerical examples including symmetric and nonsymmetric loading variations demonstrate the considerable improvement of computational efficiency of the proposed approach as well as the significance of including uncertainties in topology optimization when to design a structure. Optimums obtained from the proposed algorithm are verified by MCBO method.

Longitudinal force on transmission towers due to non-symmetric downburst conductor loads

Many failure incidents for transmission line structures have been observed in various locations around the globe as a result of downburst wind events. The localized nature of such downbursts imposes a load case on transmission towers that does not exist under large-scale events such as hurricanes. This load case happens when the downburst location leads to an uneven and unequal distribution of wind velocity along the conductor spans located at opposite sides of a tower. Hence, a difference in the tension forces will develop between the two spans of the conductors attached to the left and right sides of the tower. This difference in tension forces will lead to a net longitudinal force acting on the tower cross arm, which is believed to be the reason for the failure of a number of towers during downbursts. The estimation of this force requires conducting a nonlinear analysis of the conductors under the variable loading conditions resulting from the most critical downburst location, while taking into account a number of key parameters including the flexibility of the insulators and the conductor’s pretension force. The objective of this paper is to develop a simple procedure that can be used by practitioners to estimate such a force. A study is first conducted to determine the most critical downburst configuration expected to produce the highest values of the longitudinal forces. A parametric study is then conducted to assess the variations in the longitudinal forces with various geometric and material parameters influencing the behaviour of the conductors. Results of this parametric study are then used to develop a set of charts that can be used to estimate the longitudinal forces using three-dimensional linear interpolation. An example is provided to illustrate the application of the developed procedure.

The Effects of Earthquake on the Cylindrical Tanks

This paper deals with a problem of earthquake of the cylindrical tank. During the seismic event, the load acts in one direction only, i.e. in the direction of earthquake. This load imposes a non-symmetrical loading of a structure. At seismic load of structure of cylindrical tank was used accelerogram. In final part of the paper some crucial results are presented both in a graphical and numerical way.

Laboratory Study on Pore Pressure Generation and Liquefaction of Low-Plasticity Silty Sandy Soils during the 2012 Earthquake in Italy

AbstractThis paper describes the results of a laboratory investigation performed on clean sand and low-plasticity silty sands, recovered at different locations of the bank stretch at Scortichino, which was affected by serious damages following the 2012 Emilia Romagna earthquake in Italy. A comprehensive cyclic simple shear (CSS) testing program was undertaken to evaluate the liquefaction potential and pore pressure response of silty sand layers, which form the subsoil at the site. A series of undrained CSS tests were carried out on undisturbed samples by applying an initial static driving shear stress before cyclic loading (nonsymmetrical tests), with the aim of gaining a better understanding of the role played by a static preshearing on the observed liquefaction phenomena. The results obtained prove that, in nonsymmetrical cyclic loading tests, low-plasticity silty sands tend to be more susceptible to liquefaction than in symmetrical cyclic loading tests. The onset of liquefaction occurs by large shear s...

Analysis of Cylindrical Tanks under the Seismic Load

The paper deals with cylindrical tanks. Structures of this type have been used in hydraulic engineering, e.g. water towers, sewerage plant tanks. In recent years, cylindrical tanks have been also used in biogas management as fermentation and storage tanks.While the standard hydrostatic load acts symmetrically, it evokes the rotary symmetric load. During the seismic event, the load acts in one direction only, i.e. in the direction of earthquake. This load imposes a non-symmetrical loading of a structure. By a combination of individual loads the resulting forces are slightly non-symmetrical.Specific tank has been modeled. In one model, the solution is made using the quasi-static load induced by the hydrodynamic pressure according to the standard EC1998, part 4 [12]. The other model is presented as a calculation using the modal and spectral analyses under the seismic load. At the conclusion, these two solutions have been compared.

The optimum shape of an arch under non-symmetric loading conditions

An arch is a structural element that aims to reduce flexural moments while also spanning an open space. For this reason, the shapes of loaded arches have always attracted scientists and engineers. The analytical expression of a loaded arch under different loading conditions advances knowledge and precision. This paper presents the analytical expression of an arch under different gravitational loading conditions, including non-symmetrically distributed and punctual loadings. Several numerical examples and one experiment are shown in detail.

Concrete beams stiffened by polymer-based mortar layers: Experimental investigation and modeling

In the present work, the main results provided by an experimental investigation, assessing the mechanical performances of concrete elements stiffened by a single or more layers of different kinds of polymer-modified cementitious repair mortar, are presented. The study aims to investigate the failure mechanism occurring in the samples under bending loading. In particular, the experimental investigation allows checking if the collapse mechanism is driven by delamination occurring along the interface among the overlays or by cracks propagating from the tensile region to the compressive zone, as it occurs in a typical failure mechanism driven by flexure. Thirty-eight precast and pre-stressed concrete samples were realized and cured to simulate load-bearing concrete ceiling beams widely employed as floor systems for residential buildings. After curing, the samples were subjected to three-point loading bending tests in order to evaluate the mechanical response of the specimens in terms of load vs. mid-span transverse displacement. Through the experimental tests, the crack initiation and propagation during the bending loading have been investigated also. Simplified finite element (FE) simulations were performed to properly reproduce the actual response of ceiling beams under non-symmetric loading bending. It is shown that the proposed FE model can be straightforwardly used to predict the behavior of concrete beams stiffened by polymer-based repair mortar layers.

An experimental study on out-of-plane inelastic buckling strength of fixed steel arches

This paper presents an experimental study on the out-of-plane inelastic buckling strength of fixed circular steel arches under symmetric and non-symmetric loading. A test loading arrangement that allows for lateral deflections to develop freely under vertical loading is described. A finite element (FE) model consisting of the tested steel arch and the loading system is established for carrying out supplementary numerical investigation on the inelastic out-of-plane buckling strength of the fixed steel arches. The FE numerical model is validated by the experimental results. From the experimental results and supplementary FE investigation, it is found that the out-of-plane inelastic buckling strength of fixed steel arches is influenced significantly by the magnitude and distribution of initial out-of-plane geometric imperfections, as well as the out-of-plane elastic buckling modes and the in-plane loading patterns. It is also found that the out-of-plane buckling strength of a fixed steel arch under non-symmetric loading is lower than that under symmetric loading. Based on the experimental and FE results, a lower bound interaction equation is developed for predicting the out-of-plane inelastic buckling strength in the design of fixed circular steel arches against their out-of-plane failure.

Generalized Theory of the Thru-Reflect-Match Calibration Technique

The thru-reflect-match (TRM) calibration technique uses as standards a through connection of ports 1 and 2 of the vector network analyzer, two symmetrical highly reflecting loads, and two broadband loads (match) of impedance close to the measuring system impedance ( <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$ { Z} _{0}$</tex></formula> ). The classical theory of the TRM calibration refers the calibration to the impedance of the load used as the match standard ( <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${ Z} _{M}$</tex></formula> ), which is assumed as symmetrical. In practice, <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${ Z} _{M}$</tex></formula> may be frequency dependent. Moreover, as the frequency increases, the symmetry condition of the load used as match standard may become difficult to preserve, thus affecting the reference impedance definition and reducing the accuracy of the calibration. In this paper, the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${ ABCD}$</tex></formula> -parameters matrix formalism is used to introduce for the first time a generalized TRM calibration theory, allowing the use of either symmetrical or nonsymmetrical loads of arbitrary impedance as the match standard.

Slanted connection at elevated temperature under various loadings

This paper presents a detailed comparison of two types of slanted end-plate connections, under symmetric and non-symmetric gravity loads, in terms of friction factors and angles of slanted end-plate connections. This study contributes to better understanding of roll of slanted end-plate connections under non-symmetric gravity loads on the value of the induced initial axial force due to elevated temperature in steel beams, and a comparison of the effect of symmetric gravity loads on the behaviour of such connections, before and after elevated temperature. The results imply that, before any thermal effects, a non-symmetric gravity load can be more critical than a symmetric load; the average ratio of axial force of a non-symmetric load to a symmetric load was found to be 1·49–1·57. This value was determined to be 1·64–1·90 when friction bolts instead of normal bolts were used. On the other hand, when a steel beam is subjected to a temperature increase, the amount of reaction and initial axial forces in the steel beam are not related to the type of loading. This can be considered an advantage of the slanted end-plate connection compared with a conventional vertical end-plate connection, and it could be developed in structures exposed to longitudinal movement due to expansion. The optimum angle of the slanted end-plate connection in both cases ranged from 17° to 60°.

Direct stiffness model of slant connection under thermal and non-symmetric gravity load

Conventional steel beams exhibit lower structural performance when subjected to thermally induced axial expansion. In this regard, the design of a connection plays an utmost essential role in restrained beams. Most existing studies on the thermal behaviour of connections have so far focused only on vertical end-plate (conventional) type. This paper describes therefore the elastic mechanical behaviour of a newly proposed beam with a slant bolted end-plate connection under non-symmetric gravity load in the presence of an elevated temperature by means of direct stiffness finite element modelling. The presented direct stiffness method is relatively easy and useful to evaluate the behaviour of a steel beam with slant end-plate connection of various dimensions due to temperature increase. The performance of slant end-plate connections, with a proposed capability of damping additional thermally induced axial force, is determined under two resisting mechanisms. First, by friction force dissipation between two faces of slant end-plate connection and second, by small upward crawling on inclined plane. The applicability of the current model is ensured through a satisfactory verification with the results from the experimental test. Departing from the good agreement, a series of design charts in terms of axial force and temperature that initiates end-plate crawling has been produced for various friction factors and slanting angles.

Strengthening of Reinforced Concrete Arches with Externally Bonded Composite Materials: Testing and Analysis

An experimental and analytical study that includes testing to failure of fiber-reinforced polymer (FRP) strengthened medium-scaled reinforced concrete shallow arches and the application of a specially tailored high-order finite element for their analysis is presented. Three arches are tested. One is used as a control arch, whereas the other two are strengthened with externally bonded FRP strips in different patterns. The loading system includes six nonsymmetric vertical point loads equally spaced along the arch. The theoretical study is based on a multilayered finite-element approach, which accounts for the deformability of the adhesive layer and its shear and radial normal (through the thickness) stiffness. The arch is modeled as a polygon that consists of inclined specially tailored high-order finite elements. The results show that applying the FRP strips leads to an increase of about 40% in the failure load of the arch, changes to the cracking pattern, and a significant increase in deflection capacity. Edge debonding of the FRP strip is observed during the test but without causing total failure of the arch. The ability of the theoretical model to describe the overall structural response, the stress transfer mechanism in the strengthened arch, and the interfacial stresses and the local stress concentrations near irregular points are also demonstrated. Together they throw light on the behavior of the FRP-strengthened arch and on the evolution of its failure mechanism.

Thermal Behaviour of Beams with Slant End-Plate Connection Subjected to Nonsymmetric Gravity Load

Research on the steel structures with confining of axial expansion in fixed beams has been quite intensive in the past decade. It is well established that the thermal behaviour has a key influence on steel structural behaviours. This paper describes mechanical behaviour of beams with bolted slant end-plate connection with nonsymmetric gravity load, subjected to temperature increase. Furthermore, the performance of slant connections of beams in steel moment frame structures in the elastic field is investigated. The proposed model proved that this flexible connection system could successfully decrease the extra thermal induced axial force by both of the friction force dissipation among two faces of slant connection and a small upward movement on the slant plane. The applicability of primary assumption is illustrated. The results from the proposed model are examined within various slant angles, thermal and friction factors. It can be concluded that higher thermal conditions are tolerable when slanting connection is used.

Full-field analysis of three dimensional piezoelectric layered half-space with point loading

Abstract In this study, a three dimensional transversely isotropic piezoelectric layered half-space subjected to concentrated loading and electric charge was analyzed. This paper provides an effective analytical methodology to obtain the explicit full-field solutions for this problem. Due to the dissimilar structures of the solutions, the applied loadings are separated into axis-symmetric loadings and non-symmetric loadings. By using the double Fourier transformation technique in conjunction with series expansion, the explicit closed-from solutions for displacements, stresses, and the electric field in the layered half-space are obtained. The analytical solutions are valid for loadings applied either in the interior or at the surface of the structure. It can be seen that the complete solutions obtained by the method used in this study comprise only the fundamental solutions of an infinite space with a concentrated loading. One of the fundamental solutions is the Green's function of an infinite space and the others are solutions induced to satisfy the boundary and interface conditions. The mathematical meaning of the method used in the study is in fact the image method or Mindlin's superposition method. Instead of finding image singularities manually, the intensity and locations of the image singularities are determined automatically from the mathematical technique used in this paper. Taking PZT materials as an example, the numerical computation for the full-field distributions of the displacement and electric field in the layered half-space medium subjected to a point force and a point charge was discussed.

Platform switching on wide-diameter external hex implants: a finite element analysis.

Objectives: The objective of this work was to use finite element analysis to compare the effect of forces coming to bear on abutments 4.1 or 5.0 mm in diameter connected to a 5.0 mm implant (i.e. with or without platform switching). Study design: A 3D CAD model of a 5 x 11.5 mm external hex implant was developed, complete with a connection screw and either of two abutments, one 4.1 and the other 5 mm in diameter, to assess the influence of two loading conditions, i.e. 200 N loaded either axially or off center on the top of the abutment. Results and conclusions: In the symmetrically loaded models, greater stresses were transmitted to the bone in the area below the neck of the implant in the case of the wider-diameter abutment. When the narrower abutment was considered, the stress lines remained confined to the metal and were transferred to the bone in a more distal position. When the stresses in the bone where compared under non-symmetrical loading of the larger- and smaller-diameter abutments, the stresses reached lower values in the latter case. These findings indicate that platform switching (i.e. coupling a 4.1 mm abutment with a 5 mm implant) achieves a better, more even distribution of the peri-implant stresses deriving from simulated occlusal loads on the bone margins. Key words:Platform switching, finite element analysis, implant.

Dual Linearly-Polarized Unit-Cells With Nearly 2-Bit Resolution For Reflectarray Applications In X-Band

A fully reconfigurable dual linearly-polarized phase-shifting unit-cell for reflectarrays is proposed in X-band. It consists of two orthogonal and symmetrical cross-type printed triangular dipoles loaded by 2 × 4 pin diodes. To keep independent phase responses both in vertical and horizontal polarizations and to minimize cross-polarization (by preserving the cell symmetry), the diodes are driven by pairs, leading to a maximum possible phase resolution of 2 bits per polarization. Two alternative solutions are described to bias the diode pairs. The corresponding phase responses of the unit-cell are compared for symmetrical and non-symmetrical diode loading of the dipole arms. The numerical results show that the biasing solution with no central via is more robust. They are validated experimentally around 8 GHz. The measured average loss and equivalent bit resolution at the central frequency equal 1.25 dB and 1.8 bit respectively.

DECREASING DISPLACEMENTS OF PRESTRESSED SUSPENSION BRIDGE

A suspension bridge is the most suitable type for a long-span bridge due to rational use of structural materials. Increased deformability, which is conditioned by the appearance of the elastic and kinematic displacements, is the major disadvantage of suspension bridges. The problem of increased kinematic displacements under the action of symmetrical and non-symmetrical load can be solved by the prestressing. A prestressed suspension bridge with span of 200 m was considered as an object of investigations. The cable truss with the cross web was considered as the main load carrying structure of prestressed suspension bridges and was compared with the single cable. The considered prestressed suspension bridge was investigated by the FEM program ANSYS 12 and by the small scale physical model. Rational, from the point of view of minimal vertical kinematic displacements, main load-carrying structure of prestressed suspension bridge was developed. The obtained results shows, that usage of cable truss with the cross web as the main load carrying structures of prestressed suspension bridge in comparison with the single cable, reduces vertical displacements upwards by 63.1%, downwards by 1.8% and total displacements by 29.6% under the action of worth situated load.

Linkage between static and cyclic liquefaction of loose sand with a range of fines contents

The underlying mechanism of static and cyclic liquefaction of loose contractant sandy soil is unstable behaviour associated with deviatoric strain-softening. Such unstable (strain-softening) behaviour has been referred to as static or cyclic instability depending on whether the loading condition is monotonic or cyclic. Past research into linkage between static instability and cyclic instability of sand with fines is based largely on comparing monotonic and one-way cyclic loading behaviour of specimens of the same void ratio and fines content. In this article, the authors attempt to link the condition that defines triggering of cyclic instability to that of static instability of specimens of different void ratios and fines contents. This is achieved by the proposed concept of equivalent granular state parameter. Two specimens are considered as equivalent if they have the same equivalent granular state parameters at the start of undrained shearing. The effective stress ratio at triggering of static instability can be used to predict impending cyclic instability of an equivalent specimen of different fines content and void ratio. This linkage between static and cyclic instability was evaluated for a wide range of fines contents, initial mean effective stresses, and types of cyclic loading. The last factor includes symmetrical and nonsymmetrical two-way cyclic loading.

Design of Thick Concrete Plates Using Strut-and-Tie Model

A strut-and-tie model is developed to model the punching shear behavior of thick concrete plates. This model provides a quick and simple approach to punching shear behavior. It is applicable to both normal- and high-strength concrete under symmetric and nonsymmetric loading with and without shear reinforcement. The strut-and-tie model for symmetric punching consists of a bottle-shaped compressive zone in the upper section of the slab depth, leading to a rectangular-stress compressive zone in the lower section depth. An equation based on failure criteria for the strut-and-tie method is used to model the behavior in the lower compressive stress zone. Another strut-and-tie model is also developed to rationally model nonsymmetric punching shear behavior due to unbalanced moment transfer and symmetric punching behavior of concrete slabs with shear reinforcement. The results of the strut-and-tie models for symmetric and nonsymmetric loading with and without shear reinforcement were compared to experimental test results performed and published by others. The results of the strut-and-tie models showed excellent agreement with available test results.