• Title/Summary/Keyword: Stiffness curve

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Analysis of restrained steel beams subjected to heating and cooling Part I: Theory

  • Li, Guo-Qiang;Guo, Shi-Xiong
    • Steel and Composite Structures
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    • v.8 no.1
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    • pp.1-18
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    • 2008
  • Observations from experiments and real fire indicate that restrained steel beams have better fire-resistant capability than isolated beams. Due to the effects of restraints, a steel beam in fire condition can undergo very large deflections and the run away damage may be avoided. In addition, axial forces will be induced with temperature increasing and play an important role on the behaviour of the restrained beam. The factors influencing the behavior of a restrained beam subjected to fire include the stiffness of axial and rotational restraints, the load type on the beam and the distribution of temperature in the cross-section of the beam, etc. In this paper, a simplified model is proposed to analyze the performance of restrained steel beams in fire condition. Based on an assumption of the deflection curve of the beam, the axial force, together with the strain and stress distributions in the beam, can be determined. By integrating the stress, the combined moment and force in the cross-section of the beam can be obtained. Then, through substituting the moment and axial force into the equilibrium equation, the behavior of the restrained beam in fire condition can be worked out. Furthermore, for the safety evaluation and repair after a fire, the behaviour of restrained beams during cooling should be understood. For a restrained beam experiencing very high temperatures, the strength of the steel will recover when temperature decreases, but the contraction force, which is produced by thermal contraction, will aggravate the tensile stresses in the beam. In this paper, the behaviour of the restrained beam in cooling phase is analyzed, and the effect of the contraction force is discussed.

Confinement models for high strength short square and rectangular concrete-filled steel tubular columns

  • Aslani, Farhad;Uy, Brian;Wang, Ziwen;Patel, Vipul
    • Steel and Composite Structures
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    • v.22 no.5
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    • pp.937-974
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    • 2016
  • While extensive efforts have been made in the past to develop finite element models (FEMs) for concrete-filled steel tubular columns (CFSTCs), these models may not be suitable to be used in some cases, especially in view of the utilisation of high strength steel and high strength concrete. A method is presented herein to predict the complete stress-strain curve of concrete subjected to tri-axial compressive stresses caused by axial load coupled with lateral pressure due to the confinement action in square and rectangular CFSTCs with normal and high strength materials. To evaluate the lateral pressure exerted on the concrete in square and rectangular shaped columns, an accurately developed FEM which incorporates the effects of initial local imperfections and residual stresses using the commercial program ABAQUS is adopted. Subsequently, an extensive parametric study is conducted herein to propose an empirical equation for the maximum average lateral pressure, which depends on the material and geometric properties of the columns. The analysis parameters include the concrete compressive strength ($f^{\prime}_c=20-110N/mm^2$), steel yield strength ($f_y=220-850N/mm^2$), width-to-thickness (B/t) ratios in the range of 15-52, as well as the length-to-width (L/B) ratios in the range of 2-4. The predictions of the behaviour, ultimate axial strengths, and failure modes are compared with the available experimental results to verify the accuracy of the models developed. Furthermore, a design model is proposed for short square and rectangular CFSTCs. Additionally, comparisons with the prediction of axial load capacity by using the proposed design model, Australian Standard and Eurocode 4 code provisions for box composite columns are carried out.

Dynamic characteristics of multiple inerter-based dampers for suppressing harmonically forced oscillations

  • Chen, Huating;Jia, Shaomin;He, Xuefeng
    • Structural Engineering and Mechanics
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    • v.72 no.6
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    • pp.747-762
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    • 2019
  • Based on the ball-screw mechanism, a tuned viscous mass damper (TVMD) has been proposed, which has functions of amplifying physical mass of the system and frequency tuning. Considering the sensitivity of a single TVMD's effectiveness to frequency mistuning like that of the conventional tuned mass damper (TMD) and according to the concept of the conventional multiple tuned mass damper (MTMD), in the present paper, multiple tuned mass viscous dampers (MTVMD) consisting of many tuned mass dampers (TVMD) with a uniform distribution of natural frequencies are considered for attenuating undesirable vibration of a structure. The MTVMD is manufactured by keeping the stiffness and damping constant and varying the mass associated with the lead of the ball-screw type inerter element in the damper. The structure is represented by its mode-generalized system in a specific vibration mode controlled using the mode reduced-order method. Modal properties and fundamental characteristics of the MTVMD-structure system are investigated analytically with the parameters, i.e., the frequency band, the average damping ratio, the tuning frequency ratio, the total number of TVMD and the total mass ratio. It is found that there exists an optimum set of the parameters that makes the frequency response curve of the structure flattened with smaller amplitudes in a wider input frequency range. The effectiveness and robustness of the MTVMD are also discussed in comparison with those of the usual single TVMD (STVMD) and the results shows that the MTVMD is more effective and robust with the same level of total mass.

Generalized Analysis of RC and PT Flat Plates Using Limit State Model (한계상태모델을 이용한 철근콘크리트와 포스트텐션 무량판의 통합해석)

  • Kang, Thomas H.K.;Rha, Chang-Soon
    • Journal of the Korea Concrete Institute
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    • v.21 no.5
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    • pp.599-609
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    • 2009
  • This paper discusses generalized modeling schemes for both reinforced concrete (RC) and post-tensioned (PT) flat plate buildings. In this modeling approach, nonlinear behavior due to slab flexure, moment and shear transfer at slab-column connections, and punching shear was included along with linear secant stiffness of each member or connection that accounts for concrete cracking. This generalized model was capable of simulating all different scenarios of slab-column connection failures such as brittle punching, flexure-shear interactive failure, and flexural failure followed by drift-induced punching. Furthermore, automatic detection of drift-induced punching shear and subsequent backbone curve modifications were realistically modelled by incorporating the limit state model, in which gravity shear versus drift capacity relations were adopted. The validation of the model was conducted using one-third scale two-story by two-bay RC and PT flat plate frames. The comparisons revealed that the model was robust and effective.

Seismic Rehabilitation of Nonductile Reidorced Concrete Gravity Frame (비연성 철근 콘크리트 중력 프레임에 의한 지진 보강)

  • Dong Choon Choi;Javeed A. Munsh;Kwang W. Kim
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.43 no.5
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    • pp.116-123
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    • 2001
  • This paper represents results of an effort to seismically rehabilitate a 12-story nonductile reinforced concrete frame building. The frame located in the most severe seismic area, zone 4, is assumed to be designed and detailed for gravity load requirements only. Both pushover and nonlinear time-history analyses are carried out to determine strength, deformation capacity and the vulnerability of the building. The analysis indicates a drift concentration at the $1^{st}$ floor level due to inadequate strength and ductility capacity of the ground floor columns. The capacity curve of the structure, when superimposed on the average demand response spectrum for the ensemble of scaled earthquakes indicates that the structure is extremely weak and requires a major retrofit. The retrofit of the building is attempted using viscoelastic (VE) dampers. The dampers at each floor level are sized in order to reduce the elastic story drift ratios to within 1%. It is found that this requires substantially large dampers that are not practically feasible. With practical size dampers, the analyses of the viscoelastically damped building indicates that the damper sizes provided are not sufficient enough to remove the biased response and drift concentration of the building. The results indicate that VE-dampers alone are not sufficient to rehabilitate such a concrete frame. Concrete buildings, in general, being stiffer require larger dampers. The second rehabilitation strategy uses concrete shearwalls. Shearwalls increased stiffness and strength of the building, which resulted in reducing the drift significantly. The effectiveness of VE-dampers in conjunction with stiff shearwalls was also studied. Considering the economy and effectiveness, it is concluded that shearwalls were the most feasible solution for seismic rehabilitation of such buildings.

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Fatigue Cumulative Damage and Life Prediction of Uncovered Freight Car Under Service Load using Rainflow Counting Method (운전하중하의 레인플로집계법을 이용한 철도차량 무개화차의 피로누적손상과 수명예측)

  • Baek, Seok-Heum;Lee, Kyoung-Young;Mun, Sung-Jun;Cho, Seok-Swoo;Joo, Won-Sik
    • Transactions of the Korean Society of Automotive Engineers
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    • v.13 no.2
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    • pp.1-9
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    • 2005
  • An end beam is one of the most important structural members supporting uncovered freight under in-service loading. In general, it needs to endure over 25 years. However fatigue fracture has occurred at dynamic stress concentration location of the end beam because user's specifications demanded high speed and vehicle manufacturer made the uncovered freight car with comparatively low strength and stiffness. For durability analysis, finite element analysis is performed to evaluate the problem of uncovered freight structure and local strain. The uncovered freight car was operated on actual problematic railroad line to measure dynamic stress versus time history on the critical part from which a crack is initiated often. Rainflow cycle counting method was used to estimate fatigue damage at dangerous area under operating condition. Therefore, this study shows that analytical fatigue life at the end beam can be predicted on the basis of S-N curve and structure analysis and has a fairly good correlation with experimental fatigue life.

Influence of end fixity on post-yield behaviors of a tubular member

  • Cho, Kyu Nam
    • Structural Engineering and Mechanics
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    • v.13 no.5
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    • pp.557-568
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    • 2002
  • For the evaluation of the capability of a tubular member of an offshore structure to absorb the collision energy, a simple method can be employed for the collision analysis without performing the detailed analysis. The most common simple method is the rigid-plastic method. However, in this method any characteristics for horizontal movement and rotation at the ends of the corresponding tubular member are not included. In a real structural system of an offshore structure, tubular members sustain a certain degree of elastic support from the adjacent structure. End fixity has influences in the behaviors of a tubular member. Three-dimensional FEM analysis can include the effect of end fixity fully, however in viewpoints of the inherent computational complexities of the 3-D approach, this is not the recommendable analysis at the initial design stage. In this paper, influence of end fixity on the behaviors of a tubular member is investigated, through a new approach and other approaches. A new analysis approach that includes the flexibility of the boundary points of the member is developed here. The flexibility at the ends of a tubular element is extracted using the rational reduction of the modeling characteristics. The property reduction is based on the static condensation of the related global stiffness matrix of a model to end nodal points of the tubular element. The load-displacement relation at the collision point of the tubular member with and without the end flexibility is obtained and compared. The new method lies between the rigid-plastic method and the 3-demensional analysis. It is self-evident that the rigid-plastic method gives high strengthening membrane effect of the member during global deformation, resulting in a steeper slope than the present method. On the while, full 3-D analysis gives less strengthening membrane effect on the member, resulting in a slow going load-displacement curve. Comparison of the load-displacement curves by the new approach with those by conventional methods gives the figures of the influence of end fixity on post-yielding behaviors of the relevant tubular member. One of the main contributions of this investigation is the development of an analytical rational procedure to figure out the post-yielding behaviors of a tubular member in offshore structures.

A Method for Calculation of Compressive Strength of a One-Sided Stiffened Plate (편면 보강판의 압축강도 해석을 위한 한 방법)

  • C.D. Jang;S.I. Seo
    • Journal of the Society of Naval Architects of Korea
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    • v.28 no.1
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    • pp.117-124
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    • 1991
  • In this paper, a method to overcome inefficiency of the finite element method in the calculation of compressive strength of one-sided stiffened plates, is proposed. In this method the collapse modes of stiffened plates are assumed as follows. a) Overall buckling $\rightarrow$ Overall collapse b) Local buckling $\rightarrow$ Overall collapse c) Local buckling $\rightarrow$ Local collapse In each collapse mode, shape of deflection is assumed, and then elastic large deformation analysis based on the Rayleigh-Ritz method is carried out. One-sided stiffening effect is considered by taking into account of the moment due to eccentricity. Plastic analysis by assuming hinge lines is also carried out. The ultimate strength of a stiffened plate is obtained as the point of intersection of the elastic analysis curve and the plastic one. From this study, it is concluded that the angles between the plastic hinge lines in plastic collapse mode are determined as the ones which give the minimum collapse load, and these angles are different from the ones assumed in the previous studies. Minimum stiffness ratios can also be calculated. Calculated results according to this method show good agreements with the results by the finite element method.

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Experimental study on the Behavior CFT Column to H-Beam Endplate Connections with Penetrated High Strength Bolts (II) (관통형 고력볼트를 사용한 엔드플레이트형식 콘크리트 충전 각형강관 기둥.H형강 보 접합부의 거동에 관한 실험적 연구 (II))

  • Kim, Jae Keon;Moon, Tae Sup
    • Journal of Korean Society of Steel Construction
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    • v.11 no.2 s.39
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    • pp.109-116
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    • 1999
  • This paper presents an experimental study on the behavior of CFT Column to H-Beam Endplate Connections with penetrated H/T bolts under monotonic loading. The object of this study is to estimate accurately the effect about the thickness of endplate and the arrangement of H/T bolts which was not got a grip on the results reported in the previous paper. Main parameters are the thickness of endplates (12mm, 16mm) and the arrangemement of H/T bolts (EP1, EP2, EP3 Type). The experimental results compared and analysed. 1) The specimens were classified by Bjorhovde's and EC3's method. 2) A formula to predict the ultimate moment of connection was derived based on the T-stub model, and theoretical value $(_tM_u)$ computed by the formula corresponded to the experimental value $(_eM_u)$.

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Field Test on the Rigidities of Substructures of High Speed Railway Bridges (고속철도교량 하부구조 강성도에 관한 현장실험)

  • Chin Won-Jong;Choi Eun-Suk;Kwark Jong-Won;Kang Jae-Yoon;Cho Jeong-Rae;Kim Byung-Suk
    • Journal of the Korean Society for Railway
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    • v.9 no.1 s.32
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    • pp.118-124
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    • 2006
  • SThe rigidities of bridge substructures are the important data in the rail-bridge interaction analysis in Korean High -Speed Railway. This experimental study is being performed because of followings. 1) More correct longitudinal stiffness of the structure including substructure should be considered in the calculation of stresses in rails. 2) There are many uncertainties in the design and construction of the piers and foundations. 3) Actual guideline for the rigidities of piers and foundations in the design is necessary. 4) Measurement on the rigidity of pier according to the types of piers, foundations and soil-conditions is needed. Curve for estimating the total rigidity of substructure will be obtained through this and further experimental studies. It may be used in the analysis of Korean High-Speed Railway bridge and then, longitudinal stresses in the rails can be estimated more accurately. One pair of piers, which consist of pot-bearing for fixed support and pad-bearing for movable support, are loaded by steel frame devices with steel wire ropes and hydraulic jack. The responses which are measured at each loading stages in those field tests are displacements and tilted angles on the top and bottom of piers. This study is being performed testing and analysis about several piers in the construction field.