• Title/Summary/Keyword: Secant method

Search Result 115, Processing Time 0.019 seconds

Saw-tooth softening/stiffening - a stable computational procedure for RC structures

  • Rots, Jan G.;Invernizzi, Stefano;Belletti, Beatrice
    • Computers and Concrete
    • /
    • v.3 no.4
    • /
    • pp.213-233
    • /
    • 2006
  • Over the past years techniques for non-linear analysis have been enhanced significantly via improved solution procedures, extended finite element techniques and increased robustness of constitutive models. Nevertheless, problems remain, especially for real world structures of softening materials like concrete. The softening gives negative stiffness and risk of bifurcations due to multiple cracks that compete to survive. Incremental-iterative techniques have difficulties in selecting and handling the local peaks and snap-backs. In this contribution, an alternative method is proposed. The softening diagram of negative slope is replaced by a saw-tooth diagram of positive slopes. The incremental-iterative Newton method is replaced by a series of linear analyses using a special scaling technique with subsequent stiffness/strength reduction per critical element. It is shown that this event-by-event strategy is robust and reliable. First, the model is shown to be objective with respect to mesh refinement. Next, the example of a large-scale dog-bone specimen in direct tension is analyzed using an isotropic version of the saw-tooth model. The model is capable of automatically providing the snap-back response. Subsequently, the saw-tooth model is extended to include anisotropy for fixed crack directions to accommodate both tensile cracking and compression strut action for reinforced concrete. Three different reinforced concrete structures are analyzed, a tension-pull specimen, a slender beam and a slab. In all cases, the model naturally provides the local peaks and snap-backs associated with the subsequent development of primary cracks starting from the rebar. The secant saw-tooth stiffness is always positive and the analysis always 'converges'. Bifurcations are prevented due to the scaling technique.

Fiber Finite Element Mixed Method for Nonlinear Analysis of Steel-Concrete Composite Structures (강-콘크리트 합성구조물의 비선형해석을 위한 화이버 유한요소 혼합법)

  • Park, Jung-Woong;Kim, Seung-Eock
    • KSCE Journal of Civil and Environmental Engineering Research
    • /
    • v.28 no.6A
    • /
    • pp.789-798
    • /
    • 2008
  • The stiffness method provides a framework to calculate the structural deformations directly from solving the equilibrium state. However, to use the displacement shape functions leads to approximate estimation of stiffness matrix and resisting forces, and accordingly results in a low accuracy. The conventional flexibility method uses the relation between sectional forces and nodal forces in which the equilibrium is always satisfied over all sections along the element. However, the determination of the element resisting forces is not so straightforward. In this study, a new fiber finite element mixed method has been developed for nonlinear anaysis of steel-concrete composite structures in the context of a standard finite element analysis program. The proposed method applies the Newton method based on the load control and uses the incremental secant stiffness method which is computationally efficient and stable. Also, the method is employed to analyze the steel-concrete composite structures, and the analysis results are compared with those obtained by ABAQUS. The comparison shows that the proposed method consistently well predicts the nonlinear behavior of the composite structures, and gives good efficiency.

Experimental Study on Development for Separation and Reinforcement Geotextiles with Horizontal Wicking Drain Property (수평방향의 위킹 배수 특성을 지닌 분리·보강용 지오텍스타일 개발을 위한 실험적 연구)

  • Kim, Hong-Kwan;Ahn, Min-Soo
    • Journal of the Korean Geosynthetics Society
    • /
    • v.18 no.4
    • /
    • pp.215-224
    • /
    • 2019
  • According to the recent civil engineering construction work site which is a complex process, development of multi-functional geotextiles is required. In this study, the characteristics of five different modified cross-section fiber yarns for the selection of wicking yarns were analyzed and yarns that can achieve target properties were selected. Experimental prototype geotextiles suitable for horizontal wicking drain property and reinforcement was developed and its tensile strength, 2% secant modulus, vertical water permeability, AOS, friction characteristics by the direct shear method, and vertical/horizontal wicking test were analyzed. These tests are conducted to verify the performance of the geotextiles with horizontal wick drain property, separation and reinforcement developed in this study. As a results of the indoor soil box test, it was confirmed that the geotextiles using the wicking yarn sufficiently exhibited the function of discharging excess pore water in the horizontal direction.

Non linear soil structure interaction of space frame-pile foundation-soil system

  • Chore, H.S.;Ingle, R.K.;Sawant, V.A.
    • Structural Engineering and Mechanics
    • /
    • v.49 no.1
    • /
    • pp.95-110
    • /
    • 2014
  • The study deals with physical modeling of space frame-pile foundation and soil system using finite element models. The superstructure frame is analyzed using complete three-dimensional finite element method where the component of the frame such as slab, beam and columns are descretized using 20 node isoparametric continuum elements. Initially, the frame is analyzed assuming the fixed column bases. Later the pile foundation is worked out separately wherein the simplified models of finite elements such as beam and plate element are used for pile and pile cap, respectively. The non-linear behaviour of soil mass is incorporated by idealizing the soil as non-linear springs using p-y curve along the lines similar to that by Georgiadis et al. (1992). For analysis of pile foundation, the non-linearity of soil via p-y curve approach is incorporated using the incremental approach. The interaction analysis is conducted for the parametric study. The non-linearity of soil is further incorporated using iterative approach, i.e., secant modulus approach, in the interaction analysis. The effect the various parameters of the pile foundation such as spacing in a group and configuration of the pile group is evaluated on the response of superstructure owing to non-linearity of the soil. The response included the displacement at the top of the frame and bending moment in columns. The non-linearity of soil increases the top displacement in the range of 7.8%-16.7%. However, its effect is found very marginal on the absolute maximum moment in columns. The hogging moment decreases by 0.005% while sagging moment increases by 0.02%.

Application of direct tension force transfer model with modified fixed-angle softened-truss model to finite element analysis of steel fiber-reinforced concrete members subjected to Shear

  • Lee, Deuck Hang;Hwang, Jin-Ha;Ju, Hyunjin;Kim, Kang Su
    • Computers and Concrete
    • /
    • v.13 no.1
    • /
    • pp.49-70
    • /
    • 2014
  • Steel fiber-reinforced concrete (SFRC) is known as one of the efficient modern composites that can greatly enhance the material performance of cracked concrete in tension. Such improved tensile resistance mechanism at crack interfaces in SFRC members can be heavily influenced by methodologies of treatments of crack direction. While most existing studies have focused on developing the numerical analysis model with the rotating-angle theory, there are only few studies on finite element analysis models with the fixed-angle model approach. According to many existing experimental studies, the direction of principal stress rotated after the formation of initial fixed-cracks, but it was also observed that new cracks with completely different angles relative to the initial crack direction very rarely occurred. Therefore, this study introduced the direct tension force transfer model (DTFTM), in which tensile resistance of the fibers at the crack interface can be easily estimated, to the nonlinear finite element analysis algorithm with the fixed-angle theory, and the proposed model was also verified by comparing the analysis results to the SFRC shear panel test results. The secant modulus method adopted in this study for iterative calculations in nonlinear finite element analysis showed highly stable and fast convergence capability when it was applied to the fixed-angle theory. The deviation angle between the principal stress direction and the fixed-crack direction significantly increased as the tensile stresses in the steel fibers at crack interfaces increased, which implies that the deviation angle is very important in the estimation of the shear behavior of SFRC members.

Retrofit Design of RC Column by Displacement-Based-Design Method (변위기반설계법에 의한 철근콘크리트 기둥의 보강설계)

  • Lim, Cheong-Kweon;Kwon, Min-Ho;Ha, Keum-Hee;Kim, Jin-Sup
    • Journal of the Korea Academia-Industrial cooperation Society
    • /
    • v.13 no.6
    • /
    • pp.2804-2811
    • /
    • 2012
  • In this study, It is developed a retrofitting procedure of RC column with rectangular section to archive the target displacement at failure. Nonlinear behavior of the column is considered as the equivalent linear system. First, target displacement is determined, and then elastic displacement spectrum is constructed to estimate the equivalent natural vibration period of the SDOF system. After natural vibration period is determined, required strength is calculated using secant stiffness based on the mass of system. In accordance with, obtained force-displacement relationship through non-linear fiber based section analysis, retrofit design was carried out to meet required strength. As a result, retrofitted RC column can confirm that the improved seismic performance. It is observed that the proposed design procedure can be applicable to seismic retrofitting design of columns.

Evaluation on Fire Test for the Concrete Filled Steel Tube Column -Fire Damage Evaluation on Steel Tube and Concrete after a Fire Test- (콘크리트충전 강관기둥의 내화실험에 대한 고찰 -재하가열실험후의 강관 및 콘크리트 화재손상평가를 중심으로-)

  • Park, Ki-Chang;Choi, Sung-Mo;Kim, Dong-Kyu
    • Journal of Korean Society of Steel Construction
    • /
    • v.12 no.6
    • /
    • pp.759-767
    • /
    • 2000
  • In this study, the time dependent internal stress changes of a Concrete Filled Steel Tube(CFT) column during a fire test were quantitatively analyzed. The strain ratio of a CFT column on the different loads was measured by tensile strength tests in terms of yield strength, tensile strength average extensibility and elasticity modulus. To understand the internal material properties change of concrete in CFT column damaged due to a fire, the compressive strength and elastic modulus tests were measured on a core sample from the center of the steel tube after the fire test. The elastic modulus test measured the strain from the stress. To determine the fire temperature of the test material, a differential thermal analysis was done. From the tested result, the gained data were conducted and an analysis method was suggested. The purpose of this work is to suggest a basic data for structure regulation enactments of the internal fire design of CFT.

  • PDF

Finite Element Method for Structural Concrete Based on the Compression Field Theory (압축응력장 이론을 적용한 콘크리트 유한요소법 개발)

  • 조순호
    • Computational Structural Engineering
    • /
    • v.9 no.1
    • /
    • pp.151-159
    • /
    • 1996
  • A finite element formulation based on the CFT(Compression Field Theory) concept such as the effect of compression softening in cracked concrete, and macroscopic and rotating crack models etc. was presented for the nonlinear behaviour of structural concrete. In this category, tangential or secant material stiffnesses for cracked concrete were also defined and discussed in view of the iterative solution schemes for nonlinear equations. Considering the computational efficiency and the ability of modelling the post-ultimate behaviour as major concerns, the incremental displacement solution algorithm involving initial material stiffnesses and the relaxation procedure for fast convergence was adopted and formulated in a type of 8-noded quadrilateral isoparametric elements. The analysis program NASCOM(Nonlinear Analysis of structrual Concrete by FEM : Monotonic Loading) developed baed on the CFT constitutive relationships and the incremetal solution strategy described enables the predictions of strength and deformation capacities in a full range. crack patterns and their corresponding widths, and yield extents of reinforcement. As the verfication purpose of NASCOM, the prediction of Cervenka's panel test results including the load resistance and the deformation history was made. A limited number of predictions indicate a good correlation in a general sense.

  • PDF

Relationship between shear behavior characteristics and mechanical parameters of fractures (절리면에서의 전단거동 특성과 역학적 파라미터들 간의 상관성)

  • 이종욱;이찬구;황신일;장천중;최원학
    • The Journal of Engineering Geology
    • /
    • v.3 no.1
    • /
    • pp.1-20
    • /
    • 1993
  • In this study, laboratory direct shear tests on 37 core specimens of gneiss were performed to examine the characteristics of shear behavior on fractures by using a portable direct shear box. The multi-stage shear testing method was used and normal stress applied to specimens ranges from 5.60 to $25.67kg/\textrm{cm}^2$. On the basis of test results, the empirical equations for the shear strength on fractures were suggested. The methanical parameters that can influence the shear behavior were derived and compared between each parameter. The values of shear stiffness have a trend showing rapid increase with the increase of normal stress and joint roughness coeffident, and the average value of secant shear stiffness for all specimens is about $110.68kg/\textrm{cm}^3$ under the range of normal stress applied in this test In addition, the relationship between the length of specimen and shear stiffness is inversely correlated due to the size effect. Therefore, even the specimens with the same joint roughness coeffident show the trend of decreasing shear stiffness in case of the specimens being the longer length.

  • PDF

Lateral Stiffness and Natural Period Evaluation of Flat Plate Tall Buildings for Wind Design (내풍설계를 위한 초고층 무량판 건축물의 횡강성 및 고유주기 산정)

  • Park, Je-Woo;Kim, Hong-Jin;Jo, Ji-Seong
    • Journal of the Computational Structural Engineering Institute of Korea
    • /
    • v.23 no.1
    • /
    • pp.73-80
    • /
    • 2010
  • Wind-induced vibration is one of the important structural design factors for serviceability of tall buildings. In order to evaluate the reliable wind-loads and wind induced-vibration, it is necessary to obtain the exact natural period of buildings. The discrepancy in the natural period estimation often results in the overestimation of wind loads. In this study, the effectiveness of lateral stiffness estimation method for tall buildings with flat plate system is evaluated. For this purposed, the results of finite element analysis of three recently constructed buildings are compared with those obtained from field measurement. For the analysis, factors affecting on the lateral resistance such as cracked stiffness of vertical members, elastic modulus of concrete, effective slab width, and cracked stiffness of link beam are considered. Form the results, it is found that the use of non-cracked stiffness and application of dynamic modulus of elasticity rather than initial secant modulus yields closer analysis result to the as-built period.