Search results for: Buckling instability

Authors: Chayanon Hansapinyo

Abstract:

This paper presents experimental investigation and finite element analysis on buckling behavior of irregular section coldformed steel columns under axially concentric loading. For the experimental study, four different sections of columns were tested to investigate effect of stiffening and width-to-thickness ratio on buckling behavior. For each of the section, three lengths of 230, 950 and 1900 mm. were studied representing short, intermediate long and long columns, respectively. Then, nonlinear finite element analyses of the tested columns were performed. The comparisons in terms of load-deformation response and buckling mode show good agreement and hence the FEM models were validated. Parametric study of stiffening element and thickness of 1.0, 1.15, 1.2, 1.5, 1.6 and 2.0 mm. was analyzed. The test results showed that stiffening effect pays a large contribution to prevent distortional mode. The increase in wall thickness enhanced buckling stress beyond the yielding strength in short and intermediate columns, but not for the long columns.

Keywords: Buckling behavior, Irregular section, Cold-formed steel, Concentric loading.

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Authors: Cemil Tunc

Abstract:

In this paper, we study the instability of the zero solution to a nonlinear differential equation with variable delay. By using the Lyapunov functional approach, some sufficient conditions for instability of the zero solution are obtained.

Keywords: Instability, Lyapunov-Krasovskii functional, delay differential equation, fifth order.

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Authors: Viriyavudh Sim, Jung Kyu Choi, Yong Ju Kwak, Oh Hyeon Jeon, Woo Young Jung

Abstract:

In this study, we investigated the buckling performance of basalt fiber reinforced polymer (BFRP) sandwich infill panels. Fiber Reinforced Polymer (FRP) is a major evolution for energy dissipation when used as infill material of frame structure, a basic Polymer Matrix Composite (PMC) infill wall system consists of two FRP laminates surrounding an infill of foam core. Furthermore, this type of component is for retrofitting and strengthening frame structure to withstand the seismic disaster. In-plane compression was considered in the numerical analysis with ABAQUS platform to determine the buckling failure load of BFRP infill panel system. The present result shows that the sandwich BFRP infill panel system has higher resistance to buckling failure than those of glass fiber reinforced polymer (GFRP) infill panel system, i.e. 16% increase in buckling resistance capacity.

Keywords: Basalt fiber reinforced polymer, buckling performance, FEM analysis, sandwich infill panel.

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Authors: M. Lashgari

Abstract:

Steel plate shear walls (SPSWs) in buildings are known to be an effective means for resisting lateral forces. By using un-stiffened walls and allowing them to buckle, their energy absorption capacity will increase significantly due to the postbuckling capacity. The post-buckling tension field action of SPSWs can provide substantial strength, stiffness and ductility. This paper presents the Finite Element Analysis of low yield point (LYP) steel shear walls. In this shear wall system, the LYP steel plate is used for the steel panel and conventional structural steel is used for boundary frames. A series of nonlinear cyclic analyses were carried out to obtain the stiffness, strength, deformation capacity, and energy dissipation capacity of the LYP steel shear wall. The effect of widthto- thickness ratio of steel plate on buckling behavior, and energy dissipation capacities were studied. Good energy dissipation and deformation capacities were obtained for all models.

Keywords: low yield point steel, steel plate shear wall, thin plates, elastic buckling, inelastic buckling, post-buckling.

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Authors: N. Wang, Y. Pan, J. Zhou, J. Lei, X. Z. Yang

Abstract:

Experimental investigations were made on the instability of supercritical kerosene flowing in active cooling channels. Two approaches were used to control the pressure in the channel. One is the back-pressure valve while the other is the venturi. In both conditions, a kind of low-frequency oscillation of pressure and temperature is observed. And the oscillation periods are calculated. By comparison with the flow time, it is concluded that the instability occurred in active cooling channels is probably one kind of density wave instability. And its period has no relationship with the cooling channel geometry, nor the pressure, but only depends on the flow time of kerosene in active cooling channels. When the mass flow rate, density and pressure drop couple with each other, the density wave instability will appear.

Keywords: scramjets, active cooling, instability, density wave

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Authors: T. H. Young, Y. J. Tsai

Abstract:

A method for determining the stress distribution of a rectangular plate subjected to two pairs of arbitrarily distributed in-plane edge shear loads is proposed, and the free vibration and buckling of such a rectangular plate are investigated in this work.  The method utilizes two stress functions to synthesize the stress-resultant field of the plate with each of the stress functions satisfying the biharmonic compatibility equation. The sum of stress-resultant fields due to these two stress functions satisfies the boundary conditions at the edges of the plate, from which these two stress functions are determined. Then, the free vibration and buckling of the rectangular plate are investigated by the Galerkin method. Numerical results obtained by this work are compared with those appeared in the literature, and good agreements are observed.

Keywords: Stress analysis, free vibration, plate buckling, nonuniform in-plane edge shear.

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Authors: R. Pilafkan, M. Kaffash Irzarahimi, S. F. Asbaghian Namin

Abstract:

The biaxial buckling behavior of single-layered graphene sheets (SLGSs) is studied in the present work. To consider the size-effects in the analysis, Eringen’s nonlocal elasticity equations are incorporated into classical plate theory (CLPT). A Generalized Differential Quadrature Method (GDQM) approach is utilized and numerical solutions for the critical buckling loads are obtained. Then, molecular dynamics (MD) simulations are performed for a series of zigzag SLGSs with different side-lengths and with various boundary conditions, the results of which are matched with those obtained by the nonlocal plate model to numerical the appropriate values of nonlocal parameter relevant to each type of boundary conditions.

Keywords: Biaxial buckling, single-layered graphene sheets, nonlocal elasticity, molecular dynamics simulation, classical plate theory.

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Authors: E.Talebi, F.Zahmatkesh

Abstract:

Buckling-Restrained Braced Frame system(BRBFs) are a new type of steel seismic-load-resisting system that has found use in several countries because of its efficiency and its promise of seismic performance far superior to that of conventional braced frames. The system is addressed in the 2005 edition of the AISC Seismic Provisions for Structural Steel Buildings, also a set of design provisions has been developed by NEHRP. This report illustrates the seismic design of buckling restrained braced frames and compares the result of design in the application of earthquake load for ordinary bracing systems and buckling restrained bracing systems to see the advantage and disadvantages of this new type of seismic resisting system in comparison with the old Ordinary Concentric Braced Frame systems (OCBFs); they are defined by the provisions governing their design.

Keywords: Buckling Restrained Braced Frame system (BRBFs), Ordinary Concentric Braced Frame systems (OCBFs).

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Authors: S. A. Faizi, S. Yoshitomi

Abstract:

The optimal design procedure of buckling restrained braces (BRBs) in reinforced concrete (RC) building structures can provide the distribution of horizontal stiffness of BRBs at each story, which minimizes story drift response of the structure under the constraint of specified total stiffness of BRBs. In this paper, a simple rule is proposed to convert continuous horizontal stiffness of BRBs into sectional sizes of BRB which are available from standardized section list assuming realistic structural design stage.

Keywords: Buckling restrained brace, building engineering, optimal damper placement, structural engineering.

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Authors: Ruoyang Tang, Jianguo Nie

Abstract:

Lateral-torsional bracing members are critical to the stability of girder systems during the construction phase of steel-concrete composite bridges, and the interaction effect of multiple girders plays an essential role in the determination of buckling load. In this paper, an investigation is conducted on the lateral-torsional buckling behavior of the steel girder system which is composed of three or four I-shaped girders and braced by solid web crossbeams. The buckling load for such girder system is comprehensively analyzed and an analytical solution is developed for uniform pressure loading conditions. Furthermore, post-buckling analysis including initial geometric imperfections is performed and parametric studies in terms of bracing density, stiffness ratio as well as the number and spacing of girders are presented in order to find the optimal bracing plans for an arbitrary girder layout. The theoretical solution of critical load on account of local buckling mode shows good agreement with the numerical results in eigenvalue analysis. In addition, parametric analysis results show that both bracing density and stiffness ratio have a significant impact on the initial stiffness, global stability and failure mode of such girder system. Taking into consideration the effect of initial geometric imperfections, an increase in bracing density between adjacent girders can effectively improve the bearing capacity of the structure, and higher beam-girder stiffness ratio can result in a more ductile failure mode.

Keywords: Bracing member, construction stage, lateral-torsional buckling, steel girder system.

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Authors: Shuenn-Yih Chang, Chiu-Li Huang

Abstract:

Three structure-dependent integration methods have been developed for solving equations of motion, which are second-order ordinary differential equations, for structural dynamics and earthquake engineering applications. Although they generally have the same numerical properties, such as explicit formulation, unconditional stability and second-order accuracy, a different performance is found in solving the free vibration response to either linear elastic or nonlinear systems with high frequency modes. The root cause of this different performance in the free vibration responses is analytically explored herein. As a result, it is verified that a weak instability is responsible for the different performance of the integration methods. In general, a weak instability will result in an inaccurate solution or even numerical instability in the free vibration responses of high frequency modes. As a result, a weak instability must be prohibited for time integration methods.

Keywords: Dynamic analysis, high frequency, integration method, overshoot, weak instability.

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Authors: Babak Safaei, A. M. Fattahi

Abstract:

In the present study we have investigated axial buckling characteristics of nanocomposite beams reinforced by single-walled carbon nanotubes (SWCNTs). Various types of beam theories including Euler-Bernoulli beam theory, Timoshenko beam theory and Reddy beam theory were used to analyze the buckling behavior of carbon nanotube-reinforced composite beams. Generalized differential quadrature (GDQ) method was utilized to discretize the governing differential equations along with four commonly used boundary conditions. The material properties of the nanocomposite beams were obtained using molecular dynamic (MD) simulation corresponding to both short-(10,10) SWCNT and long- (10,10) SWCNT composites which were embedded by amorphous polyethylene matrix. Then the results obtained directly from MD simulations were matched with those calculated by the mixture rule to extract appropriate values of carbon nanotube efficiency parameters accounting for the scale-dependent material properties. The selected numerical results were presented to indicate the influences of nanotube volume fractions and end supports on the critical axial buckling loads of nanocomposite beams relevant to long- and short-nanotube composites.

Keywords: Nanocomposites, molecular dynamics simulation, axial buckling, generalized differential quadrature (GDQ).

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Authors: O. Miraliyari, M.M. Najafizadeh, A.R. Rahmani, A. Momeni Hezaveh

Abstract:

This paper presents the buckling analysis of short and long functionally graded cylindrical shells under thermal and mechanical loads. The shell properties are assumed to vary continuously from the inner surface to the outer surface of the shell. The equilibrium and stability equations are derived using the total potential energy equations, Euler equations and first order shear deformation theory assumptions. The resulting equations are solved for simply supported boundary conditions. The critical temperature and pressure loads are calculated for both short and long cylindrical shells. Comparison studies show the effects of functionally graded index, loading type and shell geometry on critical buckling loads of short and long functionally graded cylindrical shells.

Keywords: Buckling, Functionally graded materials, Short and long cylindrical shell, Thermal and mechanical loads.

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Authors: B. S. Jayashankarbabu, Karisiddappa

Abstract:

The finite element method is used to obtain the elastic buckling load factor for square isotropic plate containing circular, square and rectangular cutouts. ANSYS commercial finite element software had been used in the study. The applied inplane loads considered are uniaxial and biaxial compressions. In all the cases the load is distributed uniformly along the plate outer edges. The effects of the size and shape of concentric cutouts with different plate thickness ratios and the influence of plate edge conditions, such as SSSS, CCCC and mixed boundary condition SCSC on the plate buckling strength have been considered in the analysis.

Keywords: Concentric cutout, Elastic buckling, Finite element method, Inplane loads, Thickness ratio.

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Authors: T. Cornelius

Abstract:

Masonry cavity walls are loaded by wind pressure and vertical load from upper floors. These loads results in bending moments and compression forces in the ties connecting the outer and the inner wall in a cavity wall. Large cavity walls are furthermore loaded by differential movements from the temperature gradient between the outer and the inner wall, which results in critical increase of the bending moments in the ties. Since the ties are loaded by combined compression and moment forces, the loadbearing capacity is derived from instability equilibrium equations. Most of them are iterative, since exact instability solutions are complex to derive, not to mention the extra complexity introducing dimensional instability from the temperature gradients. Using an inverse variable substitution and comparing an exact theory with an analytical instability solution a method to design tie-connectors in cavity walls was developed. The method takes into account constraint conditions limiting the free length of the wall tie, and the instability in case of pure compression which gives an optimal load bearing capacity. The model is illustrated with examples from praxis.

Keywords: Masonry, tie connectors, cavity wall, instability, differential movements, combined bending and compression.

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Authors: Ali N. Suri, Ahmad A. Al-Makhlufi

Abstract:

Sandwich construction is widely accepted as a method of construction especially in the aircraft industry. It is a type of stressed skin construction formed by bonding two thin faces to a thick core, the faces resist all of the applied edge loads and provide all or nearly all of the required rigidities, the core spaces the faces to increase cross section moment of inertia about common neutral axis and transmit shear between them provides a perfect bond between core and faces is made.

Material for face sheets can be of metal or reinforced plastics laminates, core material can be metallic cores of thin sheets forming corrugation or honeycomb, or non metallic core of Balsa wood, plastic foams, or honeycomb made of reinforced plastics.

For in plane axial loading web core and web-foam core Sandwich panels can fail by local buckling of plates forming the cross section with buckling wave length of the order of length of spacing between webs.

In this study local buckling of web core and web-foam core Sandwich panels is carried out for given materials of facing and core, and given panel overall dimension for different combinations of cross section geometries.

The Finite Strip Method is used for the analysis, and Fortran based computer program is developed and used.

Keywords: Local Buckling, Finite Strip, Sandwich panels, Web and foam core.

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Authors: V. Polenta, S. D. Garvey, D. Chronopoulos, A. C. Long, H. P. Morvan

Abstract:

A parametric study on circular thin-walled pipes subjected to pure bending is performed. Both straight and curved pipes are considered. Ratio D/t, initial pipe curvature and internal pressure are the parameters varying in the analyses. The study is mainly FEA-based. It is found that negative curvatures (opposite to bending moment) considerably increase stiffness and buckling limit of the pipe when no internal pressure is acting and, similarly, positive curvatures decrease the stiffness and buckling limit. For internal pressurised pipes the effects of initial pipe curvature are less relevant. Results show that this phenomenon is in relationship with the cross-section deformation due to bending moment, which undergoes relevant ovalisation for no pressurised pipes and little ovalisation for pressurised pipes.

Keywords: Buckling, curved pipes, internal pressure, ovalisation, pure bending, thin-walled pipes.

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Authors: Daniel Y. Abebe, Jaehyouk Choi

Abstract:

There are several types of metal-based devices conceived as dampers for the seismic energy absorber whereby damages to the major structural components could be minimized for both new and existing structures. This paper aimed to develop and evaluate structural performance of slit circular shear panel damper for passive seismic energy protection by inelastic deformation. Structural evaluation was done using commercially available nonlinear FE simulation program. The main parameters considered are: diameter-to-thickness (D/t) ratio and slit length-to-width ratio (l/w). Depending on these parameters three different buckling mode and hysteretic behavior was found: yielding prior to buckling without strength degradation, yielding prior to buckling with strength degradation and yielding with buckling and strength degradation which forms pinching at initial displacement. The susceptible location at which the possible crack is initiated is also identified for selected specimens using rupture index.

Keywords: Slit circular shear panel damper, Hysteresis Characteristics, Slip length-to-width ratio, D/t ratio, FE analysis.

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Authors: Yadan Mao, Chengwang Lei, John C. Patterson

Abstract:

The mixing of pollutions and sediments in near shore regions of natural water bodies depends heavily on the characteristics such as the strength and frequency of flow instability. In the present paper, the instability of natural convection induced by absorption of solar radiation in littoral regions is considered. Spectral analysis is conducted on the quasi-steady state flow to reveal the power and frequency modes of the instability at various positions. Results indicate that the power of instability, the number of frequency modes, the prominence of higher frequency modes, and the highest frequency mode increase with the offshore distance and/or Rayleigh number. Harmonic modes are present at relatively low Rayleigh numbers. For a given offshore distance, the position with the strongest power of instability is located adjacent to the sloping bottom while the frequency modes are the same over the local depth. As the Rayleigh number increases, the unstable region extends toward the shore.

Keywords: Instability, Littoral waters, natural convection, Spectral analysis

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Authors: R. Leelaruji, V. Knazkins

Abstract:

This paper proposes a methodology for mitigating the occurrence of cascading failure in stressed power systems. The methodology is essentially based on predicting voltage instability in the power system using a voltage stability index and then devising a corrective action in order to increase the voltage stability margin. The paper starts with a brief description of the cascading failure mechanism which is probable root cause of severe blackouts. Then, the voltage instability indices are introduced in order to evaluate stability limit. The aim of the analysis is to assure that the coordination of protection, by adopting load shedding scheme, capable of enhancing performance of the system after the major location of instability is determined. Finally, the proposed method to generate instability prediction is introduced.

Keywords: Blackouts, cascading failure, voltage stability indices, singular value decomposition, load shedding.

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Authors: A.R.Nezamabadi, M.Mansouri Gavari, S.Mansouri, M.Mansouri Gavari

Abstract:

This article considers the positional buckling of composite thick plates under thermal loading . For this purpose , the complex finite strip method is used . In analysis of complex finite strip, harmonic complex function in longitudinal direction , cubic functions in transversal direction and parabola distribution of transverse shear strain in thickness of thick plate based on higherorder shear deformation theory are used . In given examples , the effect of angles of stratification , number of layers , dimensions ratio and length – to – thick ratio across critical temperature are considered.

Keywords: Thermal buckling , Thick plate , Complex finite strip , Higher – order shear deformation theory.

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Authors: Muzaffer Borekci, Murat S. Kirçil

Abstract:

Predicting the collapse potential of a structure during earthquakes is an important issue in earthquake engineering. Many researchers proposed different methods to assess the collapse potential of structures under the effect of strong ground motions. However most of them did not consider degradation and softening effect in hysteretic behavior. In this study, collapse potential of SDOF systems caused by dynamic instability with stiffness and strength degradation has been investigated. An equation was proposed for the estimation of collapse period of SDOF system which is a limit value of period for dynamic instability. If period of the considered SDOF system is shorter than the collapse period then the relevant system exhibits dynamic instability and collapse occurs.

Keywords: Collapse, degradation, dynamic instability, seismic response.

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Authors: L. Dahmani, S. Drizi, M. Djemai, A. Boudjemia, M. O. Mechiche

Abstract:

Channel sections are widely used in practice as beams. However, design rules for eccentrically loaded (not through shear center) beams with channel cross- sections are not available in Eurocode 3. This paper compares the ultimate loads based on the adjusted design rules for lateral torsional buckling of eccentrically loaded channel beams in bending to the ultimate loads obtained with Finite Element (FE) simulations on the basis of a parameter study. Based on the proposed design rule, this study has led to a new design rule which conforms to Eurocode 3.

Keywords: ANSYS, Eurocode 3, finite element method, lateral torsional buckling, steel channel beam.

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Authors: Mohammed I. Ali, Feng Fan, Peter N. Khakina, Ma H.H

Abstract:

In construction of any structure, the aesthetic and utility values should be considered in such a way as to make the structure cost-effective. Most structures are composed of elements and joints which are very critical in any skeletal space structure because they majorly determine the performance of the structure. In early times, most space structures were constructed using rigid joints which had the advantage of better performing structures as compared to pin-jointed structures but with the disadvantage of requiring all the construction work to be done on site. The discovery of semi-rigid joints now enables connections to be prefabricated and quickly assembled on site while maintaining good performance. In this paper, cost-effective is discussed basing on strength of connectors at the joints, buckling of joints and overall structure, and the effect of initial geometrical imperfections. Several existing joints are reviewed by classifying them into categories and discussing where they are most suited and how they perform structurally. Also, finite element modeling using ABAQUS is done to determine the buckling behavior. It is observed that some joints are more economical than others. The rise to span ratio and imperfections are also found to affect the buckling of the structures. Based on these, general principles that guide the design of cost-effective joints and structures are discussed.

Keywords: Buckling, Connectors, Joint stiffness, Eccentricity, Second moment of area, Semi-rigid joints.

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Authors: M. Reza Bagerzadeh Karimi, M. Ali Lotfollahi Yaghin, R. Mehdi Nezhad, V. Sadeghi, M. Aghabalaie

Abstract:

One of the main purposes of designing bucklingrestrained braces is the fact that the entire lateral load is wasted by the braces, the entire gravitational load is moved to the foundation through the beams, and the columns can be moved to the foundation. In other words, braces are designed for bearing lateral load. In the implementation of the structure, it should be noted that the implementation of various parts of the structure must be conducted in such a way that the buckling-restrained braces would not bear the gravitational load. Moreover, this type of brace has been investigated under impact loading, and the design goals of designing method (direct motion) are controlled under impact loading. The results of dynamic analysis are shown as the relocation charts of the floors and switch between the floors. Finally, the results are compared with each other.

Keywords: Buckling-Restrained Braced Frame (BRBF), energydissipating, ABAQUS, SAP2000, impact load.

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Authors: Viriyavudh Sim, Woo Young Jung

Abstract:

Performance of Basalt Fiber Reinforced Polymer (BFRP) sandwich infill panel system under diagonal compression was studied by means of numerical analysis. Furthermore, the variation of temperature was considered to affect the mechanical properties of BFRP, since their composition was based on polymeric material. Moreover, commercial finite element analysis platform ABAQUS was used to model and analyze this infill panel system. Consequently, results of the analyses show that the overall performance of BFRP panel had a 15% increase compared to that of GFRP infill panel system. However, the variation of buckling load in terms of temperature for the BFRP system showed a more sensitive nature compared to those of GFRP system.

Keywords: Basalt Fiber Reinforced Polymer, Buckling performance, numerical simulation, temperature dependent materials.

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Authors: Daniel Y. Abebe, Jaehyouk Choi

Abstract:

The idea of adding metallic energy dissipaters to a structure to absorb a large part of the seismic energy began four decades ago. There are several types of metal-based devices conceived as dampers for the seismic energy absorber whereby damages to the major structural components could be minimized for both new and existing structures. This paper aimed to develop and evaluate structural performance of both stiffened and non stiffened circular shear panel damper for passive seismic energy protection by inelastic deformation. Structural evaluation was done using commercially available nonlinear FE simulation program. Diameter-to-thickness ratio is employed as main parameter to investigate the hysteresis performance of stiffened and unstiffened circular shear panel. Depending on these parameters three different buckling mode and hysteretic behavior was found: yielding prior to buckling without strength degradation, yielding prior to buckling with strength degradation and yielding with buckling and strength degradation which forms pinching at initial displacement. Hence, the hysteresis behavior is identified, specimens which deform without strength degradation so it will be used as passive energy dissipating device in civil engineering structures.

Keywords: Circular shear panel damper, FE analysis, Hysteretic behavior, Large deformation.

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Authors: Win Ko Ko, A. N. Temnov

Abstract:

The problem of nonlinear oscillations of a two-layer liquid completely filling a limited volume is considered. Using two basic asymmetric harmonics excited in two mutually perpendicular planes, ordinary differential equations of nonlinear oscillations of the interface of a two-layer liquid are investigated. In this paper, hydrodynamic coefficients of linear and nonlinear problems in integral relations were determined. As a result, the instability regions of forced oscillations of a two-layered liquid in a cylindrical tank occurring in the plane of action of the disturbing force are constructed, as well as the dynamic instability regions of the parametric resonance for different ratios of densities of the upper and lower liquids depending on the amplitudes of liquids from the excitations frequencies. Steady-state regimes of fluid motion were found in the regions of dynamic instability of the initial oscillation form. The Bubnov-Galerkin method is used to construct instability regions for approximate solution of nonlinear differential equations.

Keywords: Hydrodynamic coefficients, instability region, nonlinear oscillations, resonance frequency, two-layered liquid.

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Authors: Amir Ayazi, Hamde Ahmadi, Soheil Shafaei

Abstract:

Composite steel shear wall is a lateral load resisting system which consists of a steel plate with concrete wall attached to one or both sides to prevent it from elastic buckling. The composite behavior is ensured by utilizing high-strength bolts. This paper investigates the effect of distance between bolts, and for this purpose 14 one-story one-bay specimens with various bolts spacing were modeled by finite element code which is developed by the authors. To verify the model, numerical results were compared with a valid experiment which illustrate proper agreement. Results depict increasing the distance between bolts would improve the seismic ever, this increase must be limited, because of large distances will cause widespread buckling of the steel plate in free subpanels between bolts and would result in no improvement. By comparing the results in elastic region, it was observed initial stiffness is not affected by changing the distance.

Keywords: Composite steel shear wall, bolt, buckling, finite element.

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Authors: H. R. Kazemi Nia, A. Yeganeh Fallah

Abstract:

Without uncertainty by applying external loads on beams, bending is created. The created bending in I-beams, puts one of the flanges in tension and the other one in compression. With increasing of bending, compression flange buckled and beam in out of its plane direction twisted, this twisting well-known as Lateral Torsional Buckling. Providing bending moment varieties along the beam, the critical moment is greater than the case its under pure bending. In other words, the value of bending gradient coefficient is always greater than unite. In this article by the use of " ANSYS 10.0" software near 80 3-D finite element models developed for the propose of analyzing beams` lateral torsional buckling and surveying influence of slenderness on beams' bending gradient coefficient. Results show that, presented Cb coefficient via AISC is not correct for some of beams and value of this coefficient is smaller than what proposed by AISC. Therefore instead of using a constant Cb for each case of loading , a function with two criterion for calculation of Cb coefficient for some cases is proposed.

Keywords: Beams critical moment, Bending Gradient Coefficient, finite element, Lateral Torsional Buckling

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