• Title/Summary/Keyword: Secant method

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A modified shear strength reduction finite element method for soil slope under wetting-drying cycles

  • Tu, Yiliang;Zhong, Zuliang;Luo, Weikun;Liu, Xinrong;Wang, Sui
    • Geomechanics and Engineering
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    • v.11 no.6
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    • pp.739-756
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    • 2016
  • The shear strength reduction finite element method (SSRFEM) is a powerful tool for slope stability analysis. The factor of safety (FOS) of the slope can be easily calculated only through reducing effective cohesion (c′) and tangent of effective friction angle ($tan{\varphi}^{\prime}$) in equal proportion. However, this method may not be applicable to soil slope under wetting-drying cycles (WDCs), because the influence of WDCs on c′ and $tan{\varphi}^{\prime}$ may be different. To research the method of estimating FOS of soil slopes under WDCs, this paper presents an experimental study firstly to investigate the effects of WDCs on the parameters of shear strength and stiffness. Twelve silty clay samples were subjected to different number of WDCs and then tested with triaxial test equipment. The test results show that WDCs have a degradation effect on shear strength (${\sigma}_1-{\sigma}_3)_f$, secant modulus of elasticity ($E_s$) and c′ while little influence on ${\varphi}^{\prime}$. Hence, conventional SSRFEM which reduces c′ and $tan{\varphi}^{\prime}$ in equal proportion cannot be adopted to compute the FOS of slope under conditions of WDCs. The SSRFEM should be modified. In detail, c′ is merely reduced among shear strength parameters, and elasticity modulus is reduced correspondingly. Besides, a new approach based on sudden substantial changes in the displacement of marked nodes is proposed to identify the slope failure in SSRFEM. Finally, the modified SSRFEM is applied to compute the FOS of a slope example.

The Fatigue Cumulative Damage and Life Prediction of GFRP under Random Loading (랜덤하중하의 GFRP의 피로누적손상거동과 피로수명예측)

  • Kim, Jeong-Gyu;Sim, Dong-Seok
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.20 no.12
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    • pp.3892-3898
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    • 1996
  • In this study, the prediction of the fatigue life as well as the extimation of the characteristics of fatigue cumulative damage on GFRP under random loading were performed. The constant amplitude tests and the ramdom loading test were carried on notched GFRP specimens with a circular hole. Random waves were generated with a micro-computer and had wide band spectra. Since it is useful that the prediction of fatigue life ot the given load sequences is based on S-N curves under constant amplitude loading, the estimation of equivalent stress is done on every random waves. The equivalent stress wasat first estimated by Miner's rule and then by the proposed model which was based on Hashin-Rotem's comulative damage theory regarding nonlinear fatigue cumulative damage behavior. The fatigue lives were predicted from each equivalent stress evaluated. And each predicted fatigue llife was compared with experimental results. The number of cycles of random loads were counted by mean-cross counting method. The reuslts showed that the fatigue life predicted by proposed model was correlated well with the experimental results in comparison with Miner's model.

Influence of dual layer confinement on lateral load capacity of stone columns: An experimental investigation

  • Akash Jaiswal;Rakesh Kumar
    • Geomechanics and Engineering
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    • v.32 no.6
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    • pp.567-581
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    • 2023
  • Enhanced vertical load capacity of the ground reinforced with the stone columns drew great attention by the researchers as it deals with many of the geotechnical difficulties associated with the weak ground. Recently, it has been found that the stone columns are also prone to fail under the shear load when employed beneath the embankments or the foundations susceptible to lateral loads. In this study, the effect of various encasement conditions on the lateral deflection of stone columns is investigated. A method of dual layers of encasement has been introduced and its the effect on lateral load capacity of the stone columns has been compared with those of the single encased stone column and the un-encased stone columns. Large shear box tests were utilised to generate the shear deformation on the soil system under various normal pressure conditions. The stiffness of the soil-stone column combined system has been compared for various cases of encasement conditions with different diameters. When subjected to lateral deformation, the encased columns outperformed the un-encased stone columns installed in loose sand. Shear stress resistance is up to 1.7 times greater in dual-layered, encased columns than in unencased columns. Similarly, the secant modulus increases as the condition changes from an unencased stone column to single-layer encasement and then to dual-layer encasement, indicating an improvement in the overall soil-stone column system.

Application of Direct Inelastic Design for Steel Structures (철골조를 위한 직접비탄성설계법의 적용)

  • Eom, Tae Sung;Park, Hong Gun
    • Journal of Korean Society of Steel Construction
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    • v.17 no.1 s.74
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    • pp.103-113
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    • 2005
  • In the present study, the Direct Inelastic Design (DID) for steel structures developed in the previous study was improved to expand it applicability. The proposed design method can perform inelastic designs that address the design characteristics of steel structures: Group member design, discrete member sizes, variation of moment-carrying capacity according to axial force, connection types, and multiple design criteria and load conditions. The design procedure for the proposed method was established, and a computer program incorporating the design procedure was developed. The design results from the conventional elastic method and the DID were compared and verified by the existing computer program for nonlinear analysis. Compared with the conventional elastic design, the DID addressing the inelastic behavior reduced the total weight of steel members and enhanced the deformability of the structure. The proposed design method is convenient because it can directly perform inelastic design by using linear analysis for secant stiffness. Also, it can achieve structural safety and economical design by controlling deformations of the plastic hinges.

A Study on Flying Height of Head Slider in Rotary Type Actuator (회전 구동용 헤드 슬라이더의 부상높이에 관한 연구)

  • 이재헌;최동훈;윤상준;김광식
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.15 no.6
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    • pp.1886-1896
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    • 1991
  • This paper presents a method to predict the flying height of the head slider in a hard disk drive. Quantitative predicts of the flying height according to the variations of the external load and the disk velocity have been done by numerical computation. In addition, the magnitude of the external load to keep flying height constant were also suggested. The Modified Reynolds' equation driven from hydrodynamic lubrication theory under slip flow condition was used to describe air-bearing system under the slider. To solve the equation, a Finite Volume Method (FVM) has been applied. To determine the final minimum flying height and pitch angle of the head slider, the Secant iteration method is used which update initial guess of the minimum flying height and pitch angle of the slider. In this study, the model head slider has been selected from a real hard disk drive which is equipped in many commercial personal computers. As a result, as the disk velocity increases at constant external load, the minimum flying height and the pitch angle increase due to the in crease of the air-bearing force at the bottom of slider.

Comparison of Limit Strength of Steel Cable-Stayed Bridges using Nonlinear Inelastic Displacement and Buckling Analyses (비선헝 비탄성 유한변위 해석 및 좌굴해석에 의한 강사장교의 극한강도 비교)

  • Kim Sung-Eock;Choi Dong-Ho;Ma Sang-Soo;Song Weon-Keun
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.18 no.3
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    • pp.277-289
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    • 2005
  • The study examines the limit strength for steel cable-stayed bridges. A case studies have been performed in order to evaluate the limit strength lot steel cable-stayed bridges using nonlinear inelastic analysis approach and bifurcation point instability analysis approach, effective tangent modulus $(E_f)$ method. To realize it, a practical nonlinear inelastic analysis condoling the initial shape is developed. In the initial shape analysis, updated structural configuration is introduced instead of initial member forces for beam-column members at every iterative step. Geometric and material nonlinearities of beam-column members are accounted by using stability function, and by using CRC tangent modulus and parabolic function, respectively Besides, geometric nonlinearity of cable members is accounted by using secant value of equivalent modulus of elasticity. The load-displacement relationships obtained by the proposed method are compared well with those given by other approaches. The limit strengths evaluated by the proposed nonlinear inelastic analysis for the proposed cable-stayed bridges with tee dimensional configuration compared with those by the inelastic bifurcation point instability analyses.

Nonlinear Seismic Response Analysis for Shallow Soft Soil Deposits (낮은 심도의 연약지반에 대한 비선형 지진응답해석)

  • Park, Hong-Gun;Kim, Dong-Kwan;Lee, Kyung-Koo;Kim, Dong-Soo
    • Journal of the Earthquake Engineering Society of Korea
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    • v.14 no.5
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    • pp.1-12
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    • 2010
  • This study presents a finite element analysis method that can accurately evaluate the nonlinear behaviour of structures affected by shallow soft subsoils and the soil-structure interaction. A two-dimensional finite element model that consists of a structure and shallow soft subsoil was used. The finite element model was used for a nonlinear time domain analysis of the OpenSees program. A parametric study was performed to investigate the effects of soil shear velocities, earthquake input motions, soft soil depth, and soil-structure interaction. The result of the proposed nonlinear finite element analysis method was compared with the result of an existing frequency domain analysis method, which is frequently used for addressing nonlinear soil behavior. The result showed that the frequency domain analysis, which uses equivalent secant soil stiffness and does not address the soil-structure interaction, significantly overestimated the response of the structures with short dynamic periods. The effect of the soil-structure interaction on the response spectrum did not significantly vary with the foundation dimensions and structure mass.

Effect of stud corrosion on stiffness in negative bending moment region of steel-concrete composite beams

  • Yulin Zhan;Wenfeng Huang;Shuoshuo Zhao;Junhu Shao;Dong Shen;Guoqiang Jin
    • Steel and Composite Structures
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    • v.48 no.1
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    • pp.59-71
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    • 2023
  • Corrosion of the headed studs shear connectors is an important factor in the reduction of the durability and mechanical properties of the steel-concrete composite structure. In order to study the effect of stud corrosion on the mechanical properties in the negative moment region of steel-concrete composite beams, the corrosion of stud was carried out by accelerating corrosion method with constant current. Static monotonic loading was adopted to evaluate the cracking load, interface slip, mid-span deflection, and ultimate bearing capacity of four composite beams with varying corrosion rates of headed studs. The effect of stud corrosion on the stiffness of the composite beam's hogging moment zone during normal service stage was thoroughly examined. The results indicate that the cracking load decreased by 50% as the corrosion rate of headed studs increase to 10%. Meanwhile, due to the increase of interface slip and mid-span deflection, the bending stiffness dropped significantly with the same load. In comparison to uncorroded specimens, the secant stiffness of specimens with 0.5 times ultimate load was reduced by 25.9%. However, corrosion of shear studs had no obvious effect on ultimate bending capacity. Based on the experimental results and the theory of steel-concrete interface slip, a method was developed to calculate the bending stiffness in the negative bending moment region of composite beams during normal service stage while taking corrosion of headed studs into account. The validity of the calculation method was demonstrated by data analysis.

Development of Performance-Based Seismic Design of RC Column Retrofitted By FRP Jacket using Direct Displacement-Based Design (직접변위기반설계법에 의한 철근콘크리트 기둥의 FRP 피복보강 내진성능설계법의 개발)

  • Cho, Chang-Geun
    • Journal of the Earthquake Engineering Society of Korea
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    • v.11 no.2 s.54
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    • pp.105-113
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    • 2007
  • In the current research, an algorithm of performance-based seismic retrofit design of reinforced concrete columns using FRP jacket has been proposed. For exact prediction of the nonlinear flexural analysis or FRP composite RC members, multiaxial constitutive laws of concrete and composite materials have been presented. For seismic retrofit design, an algorithm of direct displacement-based design method (DDM) proposed by Chopra and Goel (2001) has been newly applied to determine the design thickness of FRP jacket in seismic retrofit of reinforced concrete columns. To compare with the displacement coefficient method (DCM), the DDM gives an accurate prediction of the target displacement in highly nonlinear region, since the DCM uses the elastic stiffness before reaching the yield load as the effective stiffness but the DDM uses the secant stiffness.

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

  • Rots, Jan G.;Invernizzi, Stefano;Belletti, Beatrice
    • Computers and Concrete
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    • v.3 no.4
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    • pp.213-233
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    • 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.