• Title/Summary/Keyword: Secant method

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Lateral stiffness of corner-supported steel modular frame with splice connection

  • Yi-Fan Lyu;Guo-Qiang Li;Ke Cao;Si-Yuan Zhai;De-Yang Kong;Xuan-Yi Xue;Heng Li
    • Steel and Composite Structures
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    • v.48 no.3
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    • pp.321-333
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    • 2023
  • This paper proposes a comprehensive investigation on lateral stiffness of corner-supported steel modular frame using splice connection. A full-scale modular frame with two stacked steel modules under lateral load is tested. Ductile pattern in the transfer of lateral load is found in the final failure mode. Two types of lateral stiffness, including tangent stiffness and secant stiffness, are defined from the load-displacement due to the observed nonlinearity. The difference between these two types of stiffness is found around 20%. The comparisons between the experimental lateral stiffness and the predictions of classical methods are also conducted. The D-value method using hypothesis of independent case is a conservative option for predicting lateral stiffness, which is more recommended than method of contraflexural bending moment. Analyses on two classical short-rod models, including fix-rod model and pin-rod model, are further conducted. Results indicate that fix-rod model is more recommended than pin-rod model to simplify splice connection for simulation on lateral stiffness of modular frame in elastic design stage.

Experimental study and calculation of laterally-prestressed confined concrete columns

  • Nematzadeh, Mahdi;Fazli, Saeed;Hajirasouliha, Iman
    • Steel and Composite Structures
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    • v.23 no.5
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    • pp.517-527
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    • 2017
  • In this paper, the effect of active confinement on the compressive behaviour of circular steel tube-confined concrete (STCC) and concrete-filled steel tube (CFST) columns is investigated. In STCC columns the axial load is only applied to the concrete core, while in CFST columns the load is carried by the whole composite section. A new method is introduced to apply confining pressure on fresh concrete by laterally prestressing steel tubes. In order to achieve different prestressing levels, short-term and long-term pressures are applied to the fresh concrete. Three groups of STCC and CFST specimens (passive, S-active and L-active groups) are tested under axial loads. The results including stress-strain relationships of composite column components, secant modulus of elasticity, and volumetric strain are presented and discussed. Based on the elastic-plastic theory, the behaviour of the steel tube is also analyzed during elastic, yielding, and strain hardening stages. The results show that using the proposed prestressing method can considerably improve the compressive behaviour of both STCC and CFST specimens, while increasing the prestressing level has insignificant effects. By applying prestressing, the linear range in the stress-strain curve of STCC specimens increases by almost twice as much, while the improvement is negligible in CFST specimens.

Extension of Direct Displacement-Based Design to Include Higher-Mode Effects in Planar Reinforced Concrete Frame Buildings

  • Abebe, Beka Hailu;Lee, Jong Seh
    • Journal of the Earthquake Engineering Society of Korea
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    • v.22 no.5
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    • pp.299-309
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    • 2018
  • Now that problems with force-based seismic design have been clearly identified, design is inclined toward displacement-based methods. One such widely used method is Direct-Displacement-Based Design (DDBD). Yet, one of the shortcomings of DDBD is considering higher-mode amplification of story shear, moments, and displacements using equations obtained from limited parametric studies of regular planar frames. In this paper, a different approach to account for higher-mode effects is proposed. This approach determines the lateral secant stiffness of the building frames that fulfill the allowable inter-story drift without exceeding the desired story displacements. Using the stiffness, an elastic response spectrum analysis is carried out to determine elastic higher-mode force effects. These force effects are then combined with DDBD-obtained first-mode force effects using the appropriate modal superposition method so that design can be performed. The proposed design procedure is verified using Nonlinear Time History Analysis (NTHA) of twelve planar frames in four categories accounting for mass and stiffness irregularity along the height. In general, the NTHA response outputs compared well with the allowable limits of the performance objective. Thus, it fulfills the aim of minimizing the use of NTHA for planar frame buildings, thereby saving computational resources and effort.

The Effect of Stress Ratio on the Surface Crack Growth Behavior in 7075-T651 Aluminum Alloy (7075-T651 Al合金의 表面균열進展에 미치는 應力比의 影響)

  • 박영조;김정규;신용승;김성민
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.10 no.1
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    • pp.62-69
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    • 1986
  • Fatigue surface crack growth was studied in 7075-T651 aluminum alloy plates subjected largely to bending loads. The surface crack length and its depth were measurement by the unloading elastic compliance method. The surface crack growth rate dc/dN, on the surface and da/dN, in the depth direction were obtained by the secant method. The stress intensity factor range .DELTA.K was computed by means of Newman and Raju equation. The aspect ratio a/c was presented in form of a/c=0.815-0.853(a/T). The effect of the stress ratio on the stable surface crack growth rates under increasing .DELTA.T is larger in lower .DELTA.K, while the relation between dc/dN, da/dN and the effective stress intensity factor range .DELTA.K$_{eff}$ is weakly dependent on the stress ratio.o.

The effect of active and passive confining pressure on compressive behavior of STCC and CFST

  • Nematzadeh, Mahdi;Fazli, Saeed
    • Advances in concrete construction
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    • v.9 no.2
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    • pp.161-171
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    • 2020
  • In this paper, an experimental study was conducted on the compressive behavior of steel tube confined concrete (STCC) and concrete-filled steel tube (CFST) columns with active and passive confinement. To create active confinement in the STCC and CFST specimens, an innovative method was used in this study, in which by applying pressure on the fresh concrete, the steel tube was laterally pretensioned and the concrete core was compressed simultaneously. Of the benefits of this technique are improving the composite column behavior, without the use of additives and without the need for vibration, and achieving high prestressing levels. To achieve lower and higher prestressing levels, short and long term pressures were applied to the specimens, respectively. Nineteen STCC and CFST specimens in three groups of passive, short-term active, and long-term active confinement were subjected to axial compression, and their mechanical properties including the compressive strength, modulus of elasticity and axial strain were evaluated. The results showed that the proposed method of prestressing the STCC columns led to a significant increase in the compressive strength (about 60%), initial modulus of elasticity (about 130%) as well as a significant reduction in the axial strain (about 45%). In the CFST columns, the prestressing led to a considerable increase in the compressive strength, a small effect on the initial and secant modulus of elasticity and an increase in the axial strain (about 55%). Moreover, increased prestressing levels negligibly affected the compressive strength of STCCs and CFSTs but slightly increased the elastic modulus of STCCs and significantly decreased that of CFSTs.

Nonlinear analysis of cable-stayed spatial latticed structures

  • Zhou, Dai;Liu, Hongyu;Jin, Bo
    • Structural Engineering and Mechanics
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    • v.15 no.4
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    • pp.415-436
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    • 2003
  • The combination of spatial latticed structures (hereafter SLS) and flexible cables, the cable-stayed spatial latticed structures (hereafter CSLS) can cross longer span. According to variation principle, a novel geometric nonlinear formulation for 3-D bar elements considering large displacement and infinitesimal rotation increments with second-order precision is developed. The cable nonlinearity is investigated and it is taken that the secant modulus method can be considered as an exact method for a cable member. The tower column with which the cables link is regarded as a special kind of beam element, and, a new simplified stiffness formulation is presented. The computational strategies for the nonlinear dynamic response of structures are given, and the ultimate load carrying capacities and seismic responses are analyzed numerically. It is noted that, compared with corresponding spatial latticed shells, the cable-stayed spatial latticed shells have more strength and more stiffness, and that the verical seismic responses of both CSLS and CLS are remarkably greater than the horizontal ones. In addition, the computation shows that the stiffness of tower column influences the performance of CSLS to a certain extent and the improvement of structural strength and stiffness of CSLS is relevant not only to cables but also to tower columns.

Curved-quartic-function elements with end-springs in series for direct analysis of steel frames

  • Liu, Si-Wei;Chan, Jake Lok Yan;Bai, Rui;Chan, Siu-Lai
    • Steel and Composite Structures
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    • v.29 no.5
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    • pp.623-633
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    • 2018
  • A robust element is essential for successful design of steel frames with Direct analysis (DA) method. To this end, an innovative and efficient curved-quartic-function (CQF) beam-column element using the fourth-order polynomial shape function with end-springs in series is proposed for practical applications of DA. The member initial imperfection is explicitly integrated into the element formulation, and, therefore, the P-${\delta}$ effect can be directly captured in the analysis. The series of zero-length springs are placed at the element ends to model the effects of semi-rigid joints and material yielding. One-element-per-member model is adopted for design bringing considerable savings in computer expense. The incremental secant stiffness method allowing for large deflections is used to describe the kinematic motion. Finally, several problems are studied in this paper for examining and validating the accuracy of the present formulations. The proposed element is believed to make DA simpler to use than existing elements, which is essential for its successful and widespread adoption by engineers.

The Estimation of Initial Elastic Modulus of Clay by Standard Consolidation Test (표준압밀시험에 의한 점토의 초기탄성계수 산정)

  • Kwon, Byenghae;Eam, Sunghoon
    • Journal of The Korean Society of Agricultural Engineers
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    • v.66 no.1
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    • pp.15-24
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    • 2024
  • Unlike artificially created homogeneous materials, the process of calculating the elastic modulus of natural soil involves the possibility of errors. Because the stress-strain behavior of soil is nonlinear, the secant modulus of elasticity is often used based on 1/2 of the stress at failure. Since soil has the property of changing its elastic modulus depending on the confining pressure, numerical analysis models that analyze its behavior inevitably include complex elements. The hyperbolic model, which relatively accurately simulates the behavior immediately after loading in soft ground, assumes that the stress-strain curve of the consolidated undrained triaxial test is hyperbolic and requires the slope of the tangent line at the starting point. However, the slope of the initial tangent in the stress-strain curve obtained from an actual triaxial test is difficult to have regularity according to changes in confining pressure. Additionally, due to the characteristics of a hyperbola, even small changes in related factors cause large changes in the hyperbola. Therefore, there is a lot of randomness in the process of calculating model parameters from the triaxial test results, which causes large differences in the results. Therefore, the method of calculating the initial elastic modulus by the consolidation test presented in this study is also used to verify the method by the triaxial test. It can be applied. However, since this study was applied to only one sample showing typical consolidation characteristics, it is necessary to check samples with various physical properties in the future.

The Proposition of Efficient Nonlinear Solution Technique for Space Truss (공간 트러스에 대한 효율적인 비선형 해석 기법 제안)

  • 석창목;권영환
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.15 no.3
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    • pp.481-490
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    • 2002
  • The purpose of this paper is to evaluate the efficiency of various solution techniques and propose new efficient solution techniques for space trusses. Solution techniques used in this study are three load control methods (Newton-Raphson Method, modified Newton-Raphson Method, Secant-Newton Method), two load-displacement control methods(Arc-length Method, Work Increment Control Method) and three combined load-displacement control methods(Combined Arc-length Method I , Combined Arc-length MethodⅡ, Combined Work Increment Control Method). To evaluate the efficiency of these solution techniques, we must examine accuracy of their solutions, convergences and computing times of numerical examples. The combined load-displacement control methods are the most efficient in the geometric nonlinear solution techniques and in tracing post-buckling behavior of space truss. The combined work increment control method is the most efficient in tracing the buckling load of spate trusses with high degrees of freedom.

A Study on the Characteristics of Member Force, Horizontal Displacement and Concrete Strength by Design Elements of SPW Retaining Walls (SPW 흙막이 벽체의 설계요소별 부재력과 수평변위 및 콘크리트강도 특성 연구)

  • Wan-Ho Kim;Yu-Seok Shin;Yeong-Jin Lee;Yong-Chai Chang;Kang-Il Lee
    • Journal of the Korean Geosynthetics Society
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    • v.22 no.1
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    • pp.75-85
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    • 2023
  • In areas where excavation works are carried out, it is very important to select a retaining wall method to minimize ground water level and ground subsidence changes. In this regard, the use of Secant Pile Wall(SPW) method, which can complement the disadvantages of the CIP method, is gradually domestic increasing for the construction of retaining wall method. This study investigated the design elements of the SPW method and the interrelationship between the structural stability factors of the wall. The design elements for the retaining method are the overlap length between piles, pile diameter, and the specifications of the H-Beam specifications, while the structural stability factors of the wall are the bending stress, shear stress, horizontal displacement, and concrete strength. The study results showed that the pile diameter and H-Beam specifications have a significant impact on the capacity of the H-Beam, the overlap length and pile diameter have a significant impact on the horizontal displacement, and the pile diameter and H-Beam specifications have a significant impact on the required strength of the concrete.