• Title/Summary/Keyword: Inelastic Modulus

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Integral Abutment Bridge behavior under uncertain thermal and time-dependent load

  • Kim, WooSeok;Laman, Jeffrey A.
    • Structural Engineering and Mechanics
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    • v.46 no.1
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    • pp.53-73
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    • 2013
  • Prediction of prestressed concrete girder integral abutment bridge (IAB) load effect requires understanding of the inherent uncertainties as it relates to thermal loading, time-dependent effects, bridge material properties and soil properties. In addition, complex inelastic and hysteretic behavior must be considered over an extended, 75-year bridge life. The present study establishes IAB displacement and internal force statistics based on available material property and soil property statistical models and Monte Carlo simulations. Numerical models within the simulation were developed to evaluate the 75-year bridge displacements and internal forces based on 2D numerical models that were calibrated against four field monitored IABs. The considered input uncertainties include both resistance and load variables. Material variables are: (1) concrete elastic modulus; (2) backfill stiffness; and (3) lateral pile soil stiffness. Thermal, time dependent, and soil loading variables are: (1) superstructure temperature fluctuation; (2) superstructure concrete thermal expansion coefficient; (3) superstructure temperature gradient; (4) concrete creep and shrinkage; (5) bridge construction timeline; and (6) backfill pressure on backwall and abutment. IAB displacement and internal force statistics were established for: (1) bridge axial force; (2) bridge bending moment; (3) pile lateral force; (4) pile moment; (5) pile head/abutment displacement; (6) compressive stress at the top fiber at the mid-span of the exterior span; and (7) tensile stress at the bottom fiber at the mid-span of the exterior span. These established IAB displacement and internal force statistics provide a basis for future reliability-based design criteria development.

Elasto-plastic damage modelling of beams and columns with mechanical degradation

  • Erkmen, R. Emre;Gowripalan, Nadarajah;Sirivivatnanon, Vute
    • Computers and Concrete
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    • v.19 no.3
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    • pp.315-323
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    • 2017
  • Within the context of continuum mechanics, inelastic behaviours of constitutive responses are usually modelled by using phenomenological approaches. Elasto-plastic damage modelling is extensively used for concrete material in the case of progressive strength and stiffness deterioration. In this paper, a review of the main features of elasto-plastic damage modelling is presented for uniaxial stress-strain relationship. It has been reported in literature that the influence of Alkali-Silica Reaction (ASR) can lead to severe degradations in the modulus of elasticity and compression strength of the concrete material. In order to incorporate the effects of ASR related degradation, in this paper the constitutive model of concrete is based on the coupled damage-plasticity approach where degradation in concrete properties can be captured by adjusting the yield and damage criteria as well as the hardening moduli related parameters within the model. These parameters are adjusted according to results of concrete behaviour from the literature. The effect of ASR on the dynamic behaviour of a beam and a column are illustrated under moving load and cyclic load cases.

Behavior of Concrete Bridge Deck Using Hybrid Reinforcement System (Hybrid Reinforcement System을 이용한 콘크리트 교량상판 슬래브의 거동)

  • Park Sang-Yeol;Cho Keun-Hee
    • Journal of the Korea Concrete Institute
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    • v.16 no.4 s.82
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    • pp.451-458
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    • 2004
  • This study describes the basic concept and the applicability of Hybrid Reinforcement System using conventional steel reinforcing bars and Fiber Reinforced Polymer bars. The concrete bridge decks are assumed to be supported by beams and reinforced with two layers of reinforcing bars. In concrete bridge deck using HRS, the top tensile force for negative moment zone on beam supports is assumed to be resisted by FRP reinforcing bars, and the bottom tensile force for positive moment zone in the middle of hem supports is assumed to be resisted by conventional steel reinforcing bars, respectively. The FRP reinforcing bars are non-corrosive. Thus, the steel reinforcement is as far away as possible from the top surface of the deck and protected from intrusion of corrosive agent. HRS concrete bridge deck has sufficient ductility at ultimate state as the following reasons; 1) FRP bars have lower elastic modulus and higher ultimate strain than steel re-bars have, 2) FRP bars have lower ultimate strain if provided higher reinforcement ratio, 3) ultimate strain of FRP bars can be reduced if FRP bars are unbonded. Test results showed that FRP and HRS concrete slabs are not failed by FRP bar rupture, but failed by concrete compression in the range of ordinary reinforcement ratio. Therefore, in continuous concrete bridge deck using HRS, steel reinforcing bars for positive moment yield and form plastic hinge first and compressive concrete fail in the bottom of supports or in the top of the middle of supports last. Thus, bridge deck consumes significant inelastic strain energy before its failure.

Material Nonlinear Analysis of the RC Shells Considering Tension Stiffening Effects (인장강성 효과를 고려한 RC 쉘의 재료비선형 해석)

  • Jin, Chi Sub;Eom, Jang Sub
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.13 no.5
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    • pp.99-107
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    • 1993
  • In this study, material nonlinear finite element program is developed to analyze reinforced concrete shell of arbitrary geometry considering tension stiffening effects. This study is capable of tracing the load-deformation response and crack propagation, as well as determining the internal concrete and steel stresses through the elastic, inelastic and ultimate ranges in one continuous computer analysis. The cracked shear retention factor is introduced to estimate the effective shear modulus including aggregate interlock and dowel action. The concrete is assumed to be brittle in tension and elasto-plastic in compression. The Drucker-Prager yield criterion and the associated flow rule are adopted to govern the plastic behavior of the concrete. The reinforcing bars are considered as a steel layer of equivalent thickness. A layered isoparametric flat finite element considering the coupling effect between the in-plane and the bending action was developed. Mindlin plate theory taking account of transverse shear deformation was used. An incremental tangential stiffness method is used to obtain a numerical solution. Numerical examples about reinforced concrete shell are presented. Validity of this method is studied by comparing with the experimential results of Hedgren and the numerical analysis of Lin.

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Effects of the Thermal Stress and Water Pressure on the Deformation Behavior of Granite (열응력과 수압이 화강암의 변형 거동에 미치는 영향)

  • Yoon, Yong-Kyun
    • Explosives and Blasting
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    • v.29 no.1
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    • pp.34-40
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    • 2011
  • In this study, effects that thermal stress and water pressure have on the deformation behaviour of granite specimens recovered in Gagok Mine are estimated. To analyze effects of the thermal stress and water pressure on the deformation behaviour, granite specimens were preheated with cycles of predetermined temperatures ranging $200^{\circ}C$ to $700^{\circ}C$ and 500, 600, $700^{\circ}C$ specimens were pressurized to 7.5 MPa. The deformation behaviour of the specimens had been studied by performing uniaxial compressive tests. Axial and lateral strains of specimens were found to increase with increasing temperature, and above $600^{\circ}C$, the increase of strains were more pronounced. The reduction trends of uniaxial compressive strength and Young's modulus with temperature appeared to follow an exponential decay function. Specimens under water pressure showed the more inelastic deformation characteristics, which means that water pressure has an effect on the widening and extending of micro-cracks existed in preheated specimens.

Rate-Dependence of Off-Axis Tensile Behavior of Cross-Ply CFRP Laminates at Elevated Temperature and Its Simulation

  • Takeuchi, Fumi;Kawai, Masamichi;Zhang, Jian-Qi;Matsuda, Tetsuya
    • Advanced Composite Materials
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    • v.17 no.1
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    • pp.57-73
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    • 2008
  • The present paper focuses on experimental verification of the ply-by-ply basis inelastic analysis of multidirectional laminates. First of all, rate dependence of the tensile behavior of balanced symmetric cross-ply T800H/epoxy laminates with a $[0/90]_{3S}$ lay-up under off-axis loading conditions at $100^{\circ}C$ is examined. Uniaxial tension tests are performed on plain coupon specimens with various fiber orientations $[{\theta}/(90-{\theta})]_{3S}$ ($\theta$ = 0, 5, 15, 45 and $90^{\circ}C$) at two different strain rates (1.0 and 0.01%/min). The off-axis stress.strain curves exhibit marked nonlinearity for all the off-axis fiber orientations except for the on-axis fiber orientations $\theta$ = 0 and $90^{\circ}$, regardless of the strain rates. Strain rate has significant influences not only on the off-axis flow stress in the regime of nonlinear response but also on the apparent off-axis elastic modulus in the regime of initial linear response. A macromechanical constitutive model based on a ply viscoplasticity model and the classical laminated plate theory is applied to predictions of the rate-dependent off-axis nonlinear behavior of the cross-ply CFRP laminate. The material constants involved by the ply viscoplasticity model are identified on the basis of the experimental results on the unidirectional laminate of the same carbon/epoxy system. It is demonstrated that good agreements between the predicted and observed results are obtained by taking account of the fiber rotation induced by deformation as well as the rate dependence of the initial Young's moduli.

Characteristics of Static Buckling Load of the Hexagonal Spatial Truss Models using Timber (목재를 이용한 육각형 공간 트러스 모델의 정적좌굴하중 특성)

  • Ha, Hyeonju;Shon, Sudeok;Lee, Seungjae
    • Journal of Korean Association for Spatial Structures
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    • v.22 no.3
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    • pp.25-32
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    • 2022
  • In this paper, the instability of the domed spatial truss structure using wood and the characteristics of the buckling critical load were studied. Hexagonal space truss was adopted as the model to be analyzed, and two boundary conditions were considered. In the first case, the deformation of the inclined member is only considered, and in the second case, the deformation of the horizontal member is also considered. The materials of the model adopted in this paper are steel and timbers, and the considered timbers are spruce, pine, and larch. Here, the inelastic properties of the material are not considered. The instability of the target structure was observed through non-linear incremental analysis, and the buckling critical load was calculated through the singularities and eigenvalues of the tangential stiffness matrix at each incremental step. From the analysis results, in the example of the boundary condition considering only the inclined member, the critical buckling load was lower when using timber than when using steel, and the critical buckling load was determined according to the modulus of elasticity of timber. In the case of boundary conditions considering the effect of the horizontal member, using a mixture of steel and timber case had a lower buckling critical load than the steel case. But, the result showed that it was more effective in structural stability than only timber was used.