• Title/Summary/Keyword: stiffness EI

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Analytical, experimental and numerical study of timber-concrete composite beams for bridges

  • Molina, Julio C.;Calil, Carlito Junior;de Oliveira, Diego R.;Gomes, Nadia B.
    • Computers and Concrete
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    • v.24 no.2
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    • pp.103-115
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    • 2019
  • In this study, the strength and stiffness (EI) of wood-concrete composite beams for bridges with T-shaped cross section were evaluated. Two types of connectors were used: connectors bonded with epoxy adhesive and connectors attached to the wood just by pre-drilling (without adhesive). The connectors consisted of common steel bars with a diameter of 12.5 mm. Initially, the strength and stiffness (EI) of the beams were analyzed by bending tests with the load applied at the third point of the beam. Subsequently, the composite beams were evaluated by numerical simulation using ANSYS software with focus on the connection system. To make the composite beams, Eucalyptus citriodora wood and medium strength concrete were used. The slip modulus K and the ultimate strength values of each type of connector were obtained by direct shear tests performed on composite specimens. The results showed that the connector glued with epoxy adhesive resulted in better strength and stiffness (EI) for the composite beams when compared to the connector fixed by pre-drilling. The differences observed were up to 10%. The strength and stiffness (EI) values obtained analytically by $M{\ddot{o}}hler^{\prime}$ model were lower than the values obtained experimentally from the bending tests, and the differences were up to 25%. The numerical simulations allowed, with reasonable approximation, the evaluation of stress distributions in the composite beams tested experimentally.

The Convergence of Accuracy Ratio in Finite Element Method (유한요소법의 정도수렴)

  • Cho, Soon-Bo
    • Journal of Korean Association for Spatial Structures
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    • v.3 no.2 s.8
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    • pp.85-90
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    • 2003
  • If we use a third order approximation for the displacement function of beam element in finite element methods, finite element solutions of beams yield nodal displacement values matching to beam theory results to have no connection with the number increasing of elements of beams. It is assumed that, as the member displacement value at beam nodes are correct, the calculation procedure of beam element stiffness matrix have no numerical errors. A the member forces are calculated by the equations of $\frac{-M}{EI}=\frac{{d^2}{\omega}}{dx^2}\;and\;\frac{dM}{dx}=V$, the member forces at nodes of beams have errors in a moment and a shear magnitudes in the case of smaller number of element. The nodal displacement value of plate subject to the lateral load converge to the exact values according to the increase of the number of the element. So it is assumed that the procedures of plate element stiffness matrix calculations has a error in the fundamental assumptions. The beam methods for the high accuracy ratio solution Is also applied to the plate analysis. The method of reducing a error ratio of member forces and element stiffness matrix in the finite element methods is studied. Results of study were as follows. 1. The matrixes of EI[B] and [K] in the equations of M(x)=EI[B]{q} and M(x) = [K]{q}+{Q} of beams are same. 2. The equations of $\frac{-M}{EI}=\frac{{d^2}{\omega}}{dx^2}\;and\;\frac{dM}{dx}=V$ for the member forces have a error ratio in a finite element method of uniformly loaded structures, so equilibrium node loads {Q} must be substituted in the equation of member forces as the numerical examples of this paper revealed.

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Effective Length of Reinforced Concrete Columns in Braced Frames

  • Tikka, Timo K.;Mirza, S. Ali
    • International Journal of Concrete Structures and Materials
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    • v.8 no.2
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    • pp.99-116
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    • 2014
  • The American Concrete Institute (ACI) 318-11 permits the use of the moment magnifier method for computing the design ultimate strength of slender reinforced concrete columns that are part of braced frames. This computed strength is influenced by the column effective length factor K, the equivalent uniform bending moment diagram factor $C_m$ and the effective flexural stiffness EI among other factors. For this study, 2,960 simple braced frames subjected to short-term loads were simulated to investigate the effect of using different methods of calculating the effective length factor K when computing the strength of columns in these frames. The theoretically computed column ultimate strengths were compared to the ultimate strengths of the same columns computed from the ACI moment magnifier method using different combinations of equations for K and EI. This study shows that for computing the column ultimate strength, the current practice of using the Jackson-Moreland Alignment Chart is the most accurate method for determining the effective length factor. The study also shows that for computing the column ultimate strength, the accuracy of the moment magnifier method can be further improved by replacing the current ACI equation for EI with a nonlinear equation for EI that includes variables affecting the column stiffness and proposed in an earlier investigation.

Statistical calibration of safety factors for flexural stiffness of composite columns

  • Aslani, Farhad;Lloyd, Ryan;Uy, Brian;Kang, Won-Hee;Hicks, Stephen
    • Steel and Composite Structures
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    • v.20 no.1
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    • pp.127-145
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    • 2016
  • Composite column design is strongly influenced by the computation of the critical buckling load, which is very sensitive to the effective flexural stiffness (EI) of the column. Because of this, the behaviour of a composite column under lateral loading and its response to deflection is largely determined by the EI of the member. Thus, prediction models used for composite member design should accurately mirror this behaviour. However, EI varies due to several design parameters, and the implementation of high-strength materials, which are not considered by the current composite design codes of practice. The reliability of the design methods from six codes of practice (i.e., AS 5100, AS/NZS 2327, Eurocode 4, AISC 2010, ACI 318, and AIJ) for composite columns is studied in this paper. Also, the reliability of these codes of practice against a serviceability limit state criterion are estimated based on the combined use of the test-based statistical procedure proposed by Johnson and Huang (1997) and Monte Carlo simulations. The composite columns database includes 100 tests of circular concrete-filled tubes, rectangular concrete-filled tubes, and concrete-encased steel composite columns. A summary of the reliability analysis procedure and the evaluated reliability indices are provided. The reasons for the reliability analysis results are discussed to provide useful insight and supporting information for a possible revision of available codes of practice.

Exploring Reliability of Oriented Strand Board's Tensile and Stiffness Strengths

  • Wang, Y.;Young, T.M.;Guess, F.M.;Leon, R.V.
    • International Journal of Reliability and Applications
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    • v.8 no.1
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    • pp.111-124
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    • 2007
  • In this paper, we apply insightful statistical reliability tools to manage and seek improvements in the strengths of Oriented Strand Board (OSB). As a part of the OSB manufacturing process, the product undergoes destructive testing at various intervals to determine compliance with customers' specifications. Workers perform these tests on sampled cross sections of the OSB panel to measure the tensile strength, also called internal bond (IB), in pounds per square inches until failure. Additional stiffness strength tests include parallel and perpendicular elasticity indices (EI), which are taken from cross sectional samples of the OSB panel in the parallel and perpendicular directions with respect to the orientation of the wood strands. We explore both graphically and statistically these "pressure-to-failures" of OSB. Also, we briefly comment on reducing sources of variability in the IB and EI of OSB.

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Bending characteristics of Prestressed High Strength Concrete (PHC) spun pile measured using distributed optical fibre strain sensor

  • Mohamad, Hisham;Tee, Bun Pin;Chong, Mun Fai;Lee, Siew Cheng;Chaiyasarn, Krisada
    • Smart Structures and Systems
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    • v.29 no.2
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    • pp.267-278
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    • 2022
  • Pre-stressed concrete circular spun piles are widely used in various infrastructure projects around the world and offer an economical deep foundation system with consistent and superior quality compared to cast in-situ and other concrete piles. Conventional methods for measuring the lateral response of piles have been limited to conventional instrumentation, such as electrical based gauges and pressure transducers. The problem with existing technology is that the sensors are not able to assist in recording the lateral stiffness changes of the pile which varies along the length depending on the distribution of the flexural moments and appearance of tensile cracks. This paper describes a full-scale bending test of a 1-m diameter spun pile of 30 m long and instrumented using advanced fibre optic distributed sensor, known as Brillouin Optical Time Domain Analysis (BOTDA). Optical fibre sensors were embedded inside the concrete during the manufacturing stage and attached on the concrete surface in order to measure the pile's full-length flexural behaviour under the prescribed serviceability and ultimate limit state. The relationship between moments-deflections and bending moments-curvatures are examined with respect to the lateral forces. Tensile cracks were measured and compared with the peak strains observed from BOTDA data which corroborated very well. By analysing the moment-curvature response of the pile, the structure can be represented by two bending stiffness parameters, namely the pre-yield (EI) and post-yield (EIcr), where the cracks reduce the stiffness property by 89%. The pile deflection profile can be attained from optical fibre data through closed-form solutions, which generally matched with the displacements recorded by Linear Voltage Displacement Transducers (LVDTs).

Effect of Initial Uniform Moment on Lateral Free Vibration of Arches (등분포 모멘트를 받는 아치의 횡 자유진동)

  • 염응준;한택희;임남형;강영종
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2002.10a
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    • pp.3-10
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    • 2002
  • Recently, arches are used structurally because of their high in-plane stiffness and strength, which result from their ability to transmit most of the applied loading by axial forces actions, so that the bending actions are reduced. On the other hand, the resistances of arches to (out-of-plane,) flexural-torsional behavior depend on the rigidities EI/sub y/, for lateral bending, GJ for Uniform torsion, and EI/sub w/ for warping torsion which are related to axial stress for flexural-torsional behavior. The resistance of an arch to out-of-plane behavior may be reduced by its in-plane curvature, and so it may require significant lateral bracing. Thus. it is supposed that In-plane preloading which cause an axial stress, have an effect on out-of-plane free vibration behavior of arches. Because axial stresses caused increase or decrease out-of-plane stiffness. But study about this substance is insufficient. In this thesis, We will study an effect of preloading on lateral free vibration of arches, using finite element method based on Kang and Yoo's curved beam theory (about curved beam element have 7 degree of freedom including warping) with FORTRAN programming.

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A Study on a Repair Technique for a Reinforced Concrete Frame Subjected to Seismic Damage Using Prestressing Cable Bracing

  • Lee, Jin Ho;EI-Ganzory, Hisham
    • Architectural research
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    • v.3 no.1
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    • pp.53-60
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    • 2001
  • The proposed building upgrading technique employs prestressing cables to function as bracing to improve the seismic performance during future events. A four-story reinforced concrete moment resisting frame damaged from an ultimate limit state earthquake is assessed and upgraded using the proposed technique. Both existing and upgraded buildings are evaluated in regard of seismic performance parameters performing static lateral load to collapse analysis and dynamic nonlinear time history analysis as well. To obtain realistic comparison of seismic performance between existing and upgraded frames, each frame is subjected to its critical ground motion that has strength demand exceeding the building strength supply. Furthermore, reliability of static lateral load to collapse analysis as a substitute to time history analysis is evaluated. The results reveal that the proposed upgrading technique improves the stiffness distribution compared to the ideal distribution that gives equal inter-story drift. As a result, the upgraded building retains more stories that contribute to energy dissipation. The overall behavior of upgraded building beyond yield is also enhanced due to the gradual change of building stiffness as the lateral load increases.

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Finite Element Analysis of the Reinforced Concrete Circular (탄성적으로 지지된 철근콘크리트 선형판의 유한요소 해석)

  • 조진구
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.35 no.1
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    • pp.59-66
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    • 1993
  • Ring Sector Plate Supported by Elastic Beam Although all the reinforced concrete circular ring sector plates are elastically supported, it is conventional to simplify their supporting conditions as fixed or simply-supported ones assuming that their supporting beam has infinite stiffness. However, in order to obtain a precise solution, it should be required to consider the stiffness of their supporting beam. As a methodological improvement to the precise analysis, "Reinforced Concrete Model" previously developed by the author was applied to the structural analysis of the reinforced concrete circular ring sector plates with elastically supported beam. The results of analysis in the cases under various conditions of open angle, steel ratio, relative stiffness(EI/DL) between plate and supporting beam were summarized as follows ; 1.Although the effect of relative stiffness between plate and supporting beam varies depending on the magnitude of open angle, in general, it shows the largest when not more than 5.0 and negligible when not less than 10.0. Therefore, it would be considered as fixed supporting condition :in the case of its open angle of 0$^{\circ}$rectangular plates), its stiffness ratio being not less than 10.0 and in the other case of its open angle of 30$^{\circ}$, its stiffness ratio being not less than 5.0. 2.In the rectangular plates, the effect of steel ratio is considerable in no supporting condition, but neglible in the supporting condition. So, the effect of steel ratio should be negligible in the case of the elastically supported circular ring sector plates. 3.However, the effect of steel ratio is much more considerable in the case of the fixed supported circular plates, especially, when steel ratio being not more than 1.0% and stiffness ratio being smaller. So, the effect of steel ratio should be considered in the analysis of reinforced concreate circular ring sector plates with fixed conditions. 4.The effect of open angle is greater in the case of without-supporting beam conditions. However, in the other case of with-supporting beam conditions, the effect is a little bit when open angle of not more than 300 and negligible when open angle of not more than 30$^{\circ}$.

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Buckling Analysis of Curved Stiffened Web Plate using Eight and Nine-Node Flat Shell Element with Substitute Shear Strain Field (대체전단변형률 장을 갖는 8, 9절점 평면 쉘요소를 이용한 곡선 보강 복부판의 좌굴해석)

  • Ji, Hyo-Seon
    • Journal of Korean Society of Steel Construction
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    • v.23 no.4
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    • pp.455-464
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    • 2011
  • In this study, the buckling analysis of the vertically curved stiffened web plate was conducted through finite-element analysis, using an eight- and nine-node flat shell element with a substitute shear strain field. To investigate the buckling behavior of the vertically curved web plate with a longitudinal or vertical stiffener under in-plane moment loading, parametric studies were conducted for the variation of the width (b) and ratio of the bending stiffness of the stiffener to that of the plate (${\gamma}=EI/bD$). The static behavior of the vertically curved web plate without a stiffener was also investigated, and then the buckling abilities of the longitudinal and vertical stiffeners were compared under moment loading.