• Title/Summary/Keyword: moment equations

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Flexural behaviour of GFRP reinforced concrete beams under cyclic loading

  • Murthy, A. Ramachandra;Gandhi, P.;Pukazhendhi, D.M.;Samuel, F. Giftson;Vishnuvardhan, S.
    • Structural Engineering and Mechanics
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    • v.84 no.3
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    • pp.361-373
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    • 2022
  • This paper examines the flexural performance of concrete beams reinforced with glass fibre-reinforced polymer (GFRP) bars under fatigue loading. Experiments were carried out on concrete beams of size 1500×200×100 mm reinforced with 10 mm and 13 mm diameter GFRP bars under fatigue loading. Experimental investigations revealed that fatigue loading affects both strength and serviceability properties of GFRP reinforced concrete. Experimental results indicated that (i) the concrete beams experienced increase in deflection with increase in number of cycles and failed suddenly due to snapping of rebars and (ii) the fatigue life of concrete beams drastically decreased with increase in stress level. Analytical model presented a procedure for predicting the deflection of concrete beams reinforced with GFRP bars under cyclic loading. Deflection of concrete beams was computed by considering the aspects such as stiffness degradation, force equilibrium equations and effective moment of inertia. Nonlinear finite element (FE) analysis was performed on concrete beams reinforced with GFRP bars. Appropriate constitutive relationships for concrete and GFRP bars were considered in the numerical modelling. Concrete non linearity has been accounted through concrete damage plasticity model available in ABAQUS. Deflection versus number of cycles obtained experimentally for various beams was compared with the analytical and numerical predictions. It was observed that the predicted values are comparable (less than 20% difference) with the corresponding experimental observations.

Bearing capacity of strip footings on unsaturated soils under combined loading using LEM

  • Afsharpour, Siavash;Payan, Meghdad;Chenari, Reza Jamshidi;Ahmadi, Hadi;Fathipour, Hessam
    • Geomechanics and Engineering
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    • v.31 no.2
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    • pp.223-235
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    • 2022
  • Bearing capacity of shallow foundations is often determined for either dry or saturated soils. In some occasions, foundations may be subjected to external loading which is inclined and/or eccentric. In this study, the ultimate bearing capacity of shallow foundations resting on partially saturated coarse-grained cohesionless and fine-grained cohesive soils subjected to a wide range of combined vertical (V) - horizontal (H) - moment (M) loadings is rigorously evaluated using the well-established limit equilibrium method. The unified effective stress approach as well as the suction stress concept is effectively adopted so as to simulate the behaviour of the underlying unsaturated soil medium. In order to obtain the bearing capacity, four equilibrium equations are solved by adopting Coulomb failure mechanism and Bishop effective stress concept and also considering a linear variation of the induced matric suction beneath the foundation. The general failure loci of the shallow foundations resting on unsaturated soils at different hydraulic conditions are presented in V - H - M spaces. The results indicate that the matric suction has a marked influence on the bearing capacity of shallow foundations. In addition, the effect of induced suction on the ultimate bearing capacity of obliquely-loaded foundations is more pronounced than that of the eccentrically-loaded footings.

Guided waves of porous FG nanoplates with four edges clamped

  • Zhao, Jing-Lei;She, Gui-Lin;Wu, Fei;Yuan, Shu-Jin;Bai, Ru-Qing;Pu, Hua-Yan;Wang, Shilong;Luo, Jun
    • Advances in nano research
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    • v.13 no.5
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    • pp.465-474
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    • 2022
  • Based on the nonlocal strain gradient (NSG) theory and considering the influence of moment of inertia, the governing equations of motion of porous functionally graded (FG) nanoplates with four edges clamped are established; The Galerkin method is applied to eliminate the spatial variables of the partial differential equation, and the partial differential governing equation is transformed into an ordinary differential equation with time variables. By satisfying the boundary conditions and solving the characteristic equation, the dispersion relations of the porous FG strain gradient nanoplates with four edges fixed are obtained. It is found that when the wave number is very small, the influences of nonlocal parameters and strain gradient parameters on the dispersion relation is very small. However, when the wave number is large, it has a great influence on the group velocity and phase velocity. The nonlocal parameter represents the effect of stiffness softening, and the strain gradient parameter represents the effect of stiffness strengthening. In addition, we also study the influence of power law index parameter and porosity on guided wave propagation.

Analysis and design of eccentrically loaded lightweight aggregate concrete-encased steel slender columns

  • Mostafa M.A. Mostafa
    • Structural Engineering and Mechanics
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    • v.88 no.1
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    • pp.25-42
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    • 2023
  • This paper presents a finite element (FE) simulation of eccentrically loaded lightweight aggregate concrete-encased steel (LACES) columns with H-shaped steel sections, analytical equations are also established to estimate the columns' axial and bending moment interaction capacities. The validity of the proposed models is checked by comparing the results with experimental data. Good agreements between the test and proposed models' results are found with acceptable agreements. Moreover, design parameters, including the lightweight aggregate concrete (LWAC) strength, eccentricity, column slenderness ratio, and confinement, are studied using the FE analysis, and their efficiency factors are discussed. The results show that the ultimate axial capacity of the LACES composite columns subjected to eccentric loading is negatively affected by the increase in the columns' height, but it is positively affected by the increase of the confinement. Increasing the eccentricity and columns' height reduced the columns'stiffness. In addition, the ultimate capacity of the LACES column is significantly influenced by the LWAC strength and eccentricity, where the ultimate capacity of the LACES column is significantly increased by increasing LWAC strength, and it is remarkably decreased by increasing the eccentricity. When the eccentricity changed from zero to 70 mm, the ultimate axial capacity and stiffness decreased by 67.97% and 63.56%, respectively.

Experiment and Nonlinear Analysis of DH Beams with Steel Form (외부철판이 사용된 DH Beam의 휨거동에 대한 실험 및 비선형해석)

  • Moon, Jeong-Ho;Oh, Young-Hun
    • Journal of the Korea Concrete Institute
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    • v.26 no.2
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    • pp.171-179
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    • 2014
  • The purpose of this study is to evaluate the structural performance of DH beams. DH beam construction method uses thin steel plates as form-works and structural elements. The prefabricated plates and rebars of DH beams were transported to a construction site and erected for casting concrete at the site. In this study, the contribution of steel plates to the flexural strength was evaluated since the plates were expected to play a role as reinforcements. Five test specimens were made for experimental and analytical studies. They consisted of two DH beams for the positive moment test and two DH beams for the negative moment test and a RC beam for the comparison purpose. Test results on DH beams were compared with design equations and the RC beam test result. It was proven that DH beams demonstrated the good flexural behavior showing sufficient strengths and deformation capacities. Flexural strengths, principal strains of concrete, and rebar stresses were evaluated through nonlinear finite element analyses for two test beams. The analyses also showed that steel plates can contribute to the enhancement of flexural strength of DH beams. Based on experimental and analytical studies, it was concluded that steel plates of DH beams can be used as good flexural reinforcements.

Theoretical Evaluation of the Post Tensioning Effect in Continuous Slabs (연속 슬래브의 포스트 텐셔닝 보강에 대한 이론적 분석)

  • Kim, Chang-Hyuk;Kim, Kang-Su;Kim, Sang-Sik
    • Journal of the Korea Concrete Institute
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    • v.21 no.1
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    • pp.105-116
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    • 2009
  • Reinforced concrete (RC) structures have been most widely used because of their good economic efficiency. However, it is very weak in tensile stresses and difficult to control deflection due to the heavy self-weight of concrete. On the other hand, it is generally known that prestressed concrete structures can be the most effective to overcome the demerits of RC structures by using various tendon lay-out and its amount. In the prestressed concrete members, the inflection points of tendons should be placed effectively for the deflection control and the moment reduction. Therefore, in this study, the equations of tendon profiles are derived in terms of polynomials that satisfy essential conditions of tendon geometries such as inflection points and natural curved shapes of tendons placed in continuous members, from which vertical components of prestressing forces can be also calculated. The derived high order polynomial expression for the distributed shape of the upward and downward forces was transformed to an simplified equivalent uniform vertical force in order to improve the applicability in the calculation of member deflection. The influences of vertical forces by tendons to deflection and moment in a continuous slab were also considered depending on the distance from column face to the location of tendons. The applicability of the proposed method was examined by an example of deflection calculation for the cases of slabs with and without tendons, and the efficiency of deflection control by tendons was also quantitatively estimated.

Assessment of System Reliability and Capacity-Rating of Composite Steel Box-Girder Highway Bridges (합성 강 상자형 도로교의 체계신뢰성 해석 및 안전도평가)

  • Cho, Hyo Nam;Lee, Seung Jae;Kang, Kyoung Koo
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.13 no.2
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    • pp.51-59
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    • 1993
  • This paper develops practical and realistic reliability models and methods for the evaluation of system-reliability and system reliability-based rating of various types of box-girder bridge superstructures. The strength limit state model for box-girder bridges suggested in the paper are based on not only the basic flexural strength but also the strength interaction equations which simultaneously take into account flexure, shear and torsion. And the system reliability problem of box-girder superstructure is formulated as parallel-series models obtained from the FMA(Failure Mode Approach) based on major failure mechanisms or critical failure states of each girder. In the paper, an improved IST(Importance Sampling Technique) simulation algorithm is used for the system reliability analysis of the proposed models. This paper proposes a practical but rational approach for the evaluation of capacity rating in terms of the equivalent system-capacity rating corresponding to the estimated system-reliability index which is derived based on the concept of the equivalent FOSM(First Order Second Moment) form of system reliability index. The results of the reliability evaluation and rating of existing bridges indicate that the reserved reliability and capacity rating at system level are significantly different from those of element reliability or conventional methods especially in the case of highly redundant box-girder bridges.

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Model Tests on the Lateral Behavior of Steel Pipe Piles(I) in the Nak -dong River Sand (강관말뚝의 수평거동에 대한 모형실험 연구(I) -대구지역 낙동강 모래에 대하여)

  • 김영수;허노영
    • Geotechnical Engineering
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    • v.13 no.5
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    • pp.59-74
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    • 1997
  • This paper shows the results of a series of model bests on the behavior of single steel pipe pile which is subjected to lateral load in Nak-dong river sand. The purpose of the present paper is to estimate the effect of Non -homogeneous soil, constraint condition of pile head, lateral load velocity, relative density of soil, embedded pile length, and flexural stiffness of pile on the behavior of single pile which is embedded in Nak-dong river strand. These effects can be quantined only by the results of model tests. The nonlinear responses of lateral loadieflection relationships are fitted to 2nd polynomial equations by model tests results. Also, the lateral load of a deflection, yield and ultimate lateral load max. bending moment, and yield bending moment can be expressed as exponential function in terms of relative density and deflection ratio. By comparing Brom's results with model results on the lateral ultimate load, it is found that short and long pile show the contrary results with each other. The contrary results are due to the smaller assumed soil reaction than the soil reaction of the Nakiong river sand at deep point. By comparing lateral behavior on the homogeneous soil with non-homogeneous soil, it is shown that lateral loadieflection relationship is very dependent on the upper relative density. This phenomenon is shown remarkably as the difference between upper and lower relative density increases.

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Characteristics of Structural Behavior of Steel Fiber Reinforced Ultra High Performance Concrete Beams Subjected to Torsion (강섬유 보강 초고성능 콘크리트 보의 비틀림 거동 특성)

  • Yang, In-Hwan;Joh, Changbin;Lee, Jung-Woo;Kim, Byung-Suk
    • Journal of the Korea Concrete Institute
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    • v.26 no.1
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    • pp.87-95
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    • 2014
  • Experimental investigation on the structural behavior of steel fiber-reinforced ultra high performance concrete (UHPC) beams subjected to torsion are presented. Six tests carried out on square beams under torsional moment are presented. The experimental parameters were the volume fraction of the fibers and closed-stirrup ratio. The volume fraction of the fibers was 1.0% and 2.0%. The closed-stirrup ratio was 0, 0.35%, and 0.70%. The test results indicated that ultimate torsional strength increased with increasing fiber volume, and that ultimate torsional strength also increased with increasing the closed-stirrup ratio. In addition, predictive equations for evaluating the ultimate torsional strength of UHPC beams were proposed. The comparison between computed values and the experimentally observed values was shown to validate the proposed analytical equations. It was found that predictions by using proposed equation provides good agreement with test results of UHPC beams.

Nonlinear Flexural Modeling of Prestressed Concrete Beams with Composite Materials (복합소재 프리스트레스트 콘크리트보의 비선형 휨 모델링)

  • ;;Naaman, Antoine
    • Magazine of the Korea Concrete Institute
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    • v.10 no.6
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    • pp.269-280
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    • 1998
  • Recently, application of composite materials such as fiber reinforced concretes(FRCs) and fiber reinforced plastics(FRPs) in conjunction with conventional structural components has become one of the main research areas. A proper use of advanced composite materials requires understanding their resistance mechanism and failure mode when they are applied to structures or their components. Particular considerations are given in this research to develop an analytical model which can predict the nonlinear flexural responses of bonded and unbonded prestressed concrete beams possibly having layers of different cementitious composite matrices in a section and/or FRP tendons. The block concept is used, which can be regarded as an intermediate modeling method between the couple method with one block and the layered method with multiply sliced layers in a section. In order to find a particular deflection point of a beam under load, solutions to the 2N-variables are found numerically by using approximate N-force equilibrium equations and N-moment equilibirum equations. The model is shown to successfully predict the flexual behavior of variously reinforced bonded and unbonded prestressed concrete beams. The model is also successful in simulating a gradually increasing load after sudden drop inload resistance due to fracture of one or more FRP tendons. This feature is useful in tracing the overall load-deflection response of a beam prestressed with brittle FRP tendons.