• Title/Summary/Keyword: Beam equation

Search Result 1,037, Processing Time 0.033 seconds

Stability Design of Steel Frames considering Initial Imperfection based on Second-Order Elastic Analysis (2차 탄성해석을 이용한 강뼈대구조의 초기결함 좌굴설계)

  • Kyung, Yong Soo;Lee, Chang Hwan;Kim, Moon Young
    • KSCE Journal of Civil and Environmental Engineering Research
    • /
    • v.28 no.4A
    • /
    • pp.465-474
    • /
    • 2008
  • Generally design of frame structures composed of beam-column member is accomplished by stability evaluation of each member considering the effective buckling length. This study selects a member of the smallest non-dimension slenderness ratio using the buckling eigenvalue calculated by the elastic buckling eigen-value analysis and axial force of the each member, and decides the initial deflection quantity reflected geometric and material nonlinearities from a suggested equation on the base of standard strength curve of Korea Bridge Design Code. Second-order elastic analysis applying the initial deflection is executed and the stability of each member is evaluated and decides ultimate strength. Through examples of eight-stories and four-stories plane frame structures, the evaluation of the stability is compared with the existing method and ultimate strength of the suggested method is compared with ultimate strength by the nonlinear inelastic analysis. Through these procedures, the increasing of effective buckling length by elastic buckling eigenvalue analysis is prevented from a new design method that considers initial imperfections. And the validity of this method is proved.

Concrete Shear Strength of FRP Reinforced Concrete Beam (FRP 보강근을 사용한 콘크리트 보의 콘크리트 전단강도)

  • Cho, Jae Min;Jang, Hee Suk;Kim, Myung Sik;Kim, Chung Ho
    • KSCE Journal of Civil and Environmental Engineering Research
    • /
    • v.29 no.3A
    • /
    • pp.259-266
    • /
    • 2009
  • This study is to develop equations that consider the elastic modulus ratio of FRP bar and steel reinforcement, shear span to depth ratio, and flexural reinforcement ratio of FRP bar, to determine concrete shear strength of FRP reinforced concrete beams without shear reinforcement. As experimental parameters, 2 types of FRP bar, 3 types of shear span to depth ratio, and 3 types of flexural reinforcement were used. Experimental results for two of shear span to depth ratio were quoted from previous study to evaluate effect of shear span to depth ratio in more detail. Shear strength correction factors needed for evaluating concrete shear strength were proposed from regression analysis using above experimental results. Equations suggested from this study and other codes were examined and compared with 31 experimental results available in the literature. From this comparison, it could be known that the equation suggested from this study gives the most approaching result to experimental results.

Influence of flexoelectricity on bending of piezoelectric perforated FG composite nanobeam rested on elastic foundation

  • Ali Alnujaie;Alaa A. Abdelrahman;Abdulrahman M. Alanasari;Mohamed A. Eltaher
    • Steel and Composite Structures
    • /
    • v.49 no.4
    • /
    • pp.361-380
    • /
    • 2023
  • A size dependent bending behavior of piezoelectrical flexoelectric layered perforated functionally graded (FG) composite nanobeam rested on an elastic foundation is investigated analytically. The composite beam is composed of regularly cutout FG core and two piezoelectric face sheets. The material characteristics is graded through the core thickness by power law function. Regular squared cutout perforation pattern is considered and closed forms of the equivalent stiffness parameters are derived. The modified nonlocal strain gradient elasticity theory is employed to incorporate the microstructure as well as nonlocality effects into governing equations. The Winkler as well as the Pasternak elastic foundation models are employed to simulate the substrate medium. The Hamiltonian approach is adopted to derive the governing equilibrium equation including piezoelectric and flexoelectric effects. Analytical solution methodology is developed to derive closed forms for the size dependent electromechanical as well as mechanical bending profiles. The model is verified by comparing the obtained results with the available corresponding results in the literature. To demonstrate the applicability of the developed procedure, parametric studies are performed to explore influences of gradation index, elastic medium parameters, flexoelectric and piezoelectric parameters, geometrical and peroration parameters, and material parameters on the size dependent bending behavior of piezoelectrically layered PFG nanobeams. Results obtained revealed the significant effects both the flexoelectric and piezoelectric parameters on the bending behavior of the piezoelectric composite nanobeams. These parameters could be controlled to improve the size dependent electromechanical as well as mechanical behaviors. The obtained results and the developed procedure are helpful for design and manufacturing of MEMS and NEMS.

Development of Preliminary Quality Assurance Software for $GafChromic^{(R)}$ EBT2 Film Dosimetry ($GafChromic^{(R)}$ EBT2 Film Dosimetry를 위한 품질 관리용 초기 프로그램 개발)

  • Park, Ji-Yeon;Lee, Jeong-Woo;Choi, Kyoung-Sik;Hong, Semie;Park, Byung-Moon;Bae, Yong-Ki;Jung, Won-Gyun;Suh, Tae-Suk
    • Progress in Medical Physics
    • /
    • v.21 no.1
    • /
    • pp.113-119
    • /
    • 2010
  • Software for GafChromic EBT2 film dosimetry was developed in this study. The software provides film calibration functions based on color channels, which are categorized depending on the colors red, green, blue, and gray. Evaluations of the correction effects for light scattering of a flat-bed scanner and thickness differences of the active layer are available. Dosimetric results from EBT2 films can be compared with those from the treatment planning system ECLIPSE or the two-dimensional ionization chamber array MatriXX. Dose verification using EBT2 films is implemented by carrying out the following procedures: file import, noise filtering, background correction and active layer correction, dose calculation, and evaluation. The relative and absolute background corrections are selectively applied. The calibration results and fitting equation for the sensitometric curve are exported to files. After two different types of dose matrixes are aligned through the interpolation of spatial pixel spacing, interactive translation, and rotation, profiles and isodose curves are compared. In addition, the gamma index and gamma histogram are analyzed according to the determined criteria of distance-to-agreement and dose difference. The performance evaluations were achieved by dose verification in the $60^{\circ}$-enhanced dynamic wedged field and intensity-modulated (IM) beams for prostate cancer. All pass ratios for the two types of tests showed more than 99% in the evaluation, and a gamma histogram with 3 mm and 3% criteria was used. The software was developed for use in routine periodic quality assurance and complex IM beam verification. It can also be used as a dedicated radiochromic film software tool for analyzing dose distribution.

Ambient Vibration Testing and System Identification for Tall Buildings (고층건물의 자연 진동실험 및 시스템판별)

  • Cho, Soon-Ho
    • Journal of the Earthquake Engineering Society of Korea
    • /
    • v.16 no.3
    • /
    • pp.23-33
    • /
    • 2012
  • Dynamic response measurements from natural excitation were carried out for three 18-story office buildings to determine their inherent properties. The beam-column frame system was adopted as a typical structural form, but a core wall was added to resist the lateral force more effectively, resulting in a mixed configuration. To extract modal parameters such as natural frequencies, mode shapes and damping ratios from a series of vibration records at each floor, the most advanced operational system identification methods based on frequency- and time-domain like FDD, pLSCF and SSI were applied. Extracted frequencies and mode shapes from the different identification methods showed a greater consistency for three buildings, however the three lower frequencies extracted were 1.2 to 1.7 times as stiff as those obtained using the initial FE models. Comparing the extracted fundamental periods with those estimated from the code equations and FE analysis, the FE analysis results showed the most flexible behavior, and the most simple equation that considers the building height as the only parameter correlated fairly well with test results. It is recognized that such a discrepancy arises from the fact that the present tests exclude the stiffness decreasing factors like concrete cracking, while the FE models ignore the stiffness increasing factors, such as the contribution of non-structural elements and the actual material properties used.

Ultrasonic Pulses Characteristics in Lightweight Fine Aggregate Concrete under Various Load Histories (하중 이력에 따른 경량 잔골재 콘크리트의 초음파 특성)

  • Yoo, Kyung-Suk;Kim, Jee-Sang;Kim, Ik-Beam
    • Journal of the Korean Recycled Construction Resources Institute
    • /
    • v.2 no.3
    • /
    • pp.209-216
    • /
    • 2014
  • One of the widely used NDT(Non-destructive techniques) is the ultrasonic pulse velocity (USPV) method, which determines the travel time of the ultrasonic pulse through the tested materials and most studies were focused on the results expressed in time domain. However, the signal of ultrasonic pulse in time domain can be transformed into frequency domain, through Fast fourier transform(FFT) to give more useful informations. This paper shows a comparison of changes in the pulse velocity and frequency domain signals of concrete for various load histories using lightweight fine aggregates. The strength prediction equation for normal concrete using USPV cannot be used to estimate lightweight fine aggregate concrete strength. The signals in frequency domain of ultrasonic pulse of lightweight fine aggregate concrete does not show any significant difference comparing with those of normal concrete. The increases in stress levels of concrete change the pulse velocities and maximum frequencies, however the apparent relationship between themselves can not be found in this experiment.

Behavior of 550MPa 43mm Hooked Bars Embedded in Beam-Column Joints (보-기둥 접합부에 정착된 550 MPa 43 mm 갈고리철근의 거동)

  • Bae, Min-Seo;Chun, Sung-chul;Kim, Mun-Gil
    • Journal of the Korea Concrete Institute
    • /
    • v.28 no.5
    • /
    • pp.611-620
    • /
    • 2016
  • In the construction of nuclear power plants, only 420 MPa reinforcing bars are allowed and, therefore, so many large-diameter bars are placed, which results in steel congestion. Consequently, re-bar works are difficult and the quality of RC structures may be deteriorated. To solve the steel congestion, 550 MPa bars are necessary. Among many items for verifying structural performance of reinforced concrete with 550 MPa bars, the 43 mm hooked bars are examined in this study. All specimens failed by side-face blowout and the side cover explosively spalled at maximum loads. The bar force was initially transferred to the concrete primarily by bond along a straight portion. At the one third of maximum load, the bond reached a peak capacity and began to decline, while the hook bearing component rose rapidly. At failure, most load was resisted by the hook bearing. For confined specimens with hoops, the average value of test-to-prediction ratios by KCI code is 1.45. The modification factor of confining reinforcement which was not allowed for larger than 35 mm bars can be applied to 43 mm hooked bars. For specimens with 70 MPa concrete, the average value of test-to-prediction ratios by KCI code is 1.0 which is less than the values of the other specimens. The effects of concrete compressive strength should be reduced. An equation to predict anchorage capacity of hooked bars was developed from regression analysis including the effects of compressive strength of concrete, embedment length, side cover thickness, and transverse reinforcement index.

The Forced Motion Analyses by Using Two Dimensional 6-Node and Three Dimensional 16-Node Isoparametric Elements with Modification of Gauss Sampling Point (6절점 2차원 및 16절점 3차원 등매개변수 요소의 가우스 적분점 수정을 이용한 강제진동 해석)

  • 김정운;권영두
    • Computational Structural Engineering
    • /
    • v.8 no.4
    • /
    • pp.87-97
    • /
    • 1995
  • For the same configuration of two-dimensional finite element models, 6-node element exhibits stiffer bending stiffness than 8-node element. This is true in the relation between 16-node element and 20-node element for three-dimensional model. This stiffening phenomenon comes from the elimination of several mid nodes from full-node elements. Therefore, this may be called 'relative stiffness stiffening phenomenon'. It seems that there are a couple of ways to correct the stiffening effect, however, we could find only one effective method-the method of modification of Gauss sampling points-which passes the patch test and does not alter other kinds of stiffness, such as extensional stiffness. The quantity of modification is a function of Poisson's ratios of the constituent materials. We could obtain two modification equations, one for plane stress case and the other for plane strain case. This method can be extended to 3-dimensional solid elements. Except the exact plane strain cases, most 3-dimensional plates could be modeled successfully with 16-node element modified by the equation for the plane stress case. The effectiveness of the modification method is checked by applying it to several examples with excellent improvements. In numerical examples, beams with various boundary conditions are subjected to static and time-dependent loads. Free and forced motion analyses of beams and plates are also tested. The beam and plate may be composed of isotropic multilayers as well as a single layer.

  • PDF

Investigation on the Effective Moment of Inertia of Reinforced Concrete Flexural Members Under Service Load (사용하중 상태에서 철근콘크리트 휨부재의 유효 단면2차모멘트에 대한 고찰)

  • Lee, Seung-Bea;Park, Mi-Young;Jang, Su-Youn;Kim, Kang-Su;Kim, Sang-Sik
    • Journal of the Korea Concrete Institute
    • /
    • v.20 no.3
    • /
    • pp.393-404
    • /
    • 2008
  • The approaches in many design codes for the estimation of the deflection of flexural reinforced concrete (RC) members utilize the concept of the effective moment of inertia which considers the reduction of flexural rigidity of RC beams after cracking. However, the effective moment of inertia in design codes are primarily based on the ratio of maximum moment and cracking moment of beam subjected to loading without proper consideration on many other possible influencing factors such as span length, member end condition, sectional size, loading geometry, materials, sectional properties, amount of cracks and its distribution, and etc. In this study, therefore, an experimental investigation was conducted to provide fundamental test data on the effective moment of inertia of RC beams for the evaluation of flexural deflection, and to develop a modified method on the estimation of the effective moment of inertia based on test results. 14 specimens were fabricated with the primary test parameters of concrete strength, cover thickness, reinforcement ratio, and bar diameters, and the effective moments of inertia obtained from the test results were compared with those by design codes, existing equations, and the modified equation proposed in this study. The proposed method considered the effect of the length of cracking region, reinforcement ratio, and the effective concrete area per bar on the effective moment of inertia, which estimated the effective moment of inertia more close to the test results compared to other approaches.

A Study on the Dynamic Response of Steel Highway Bridges Using 3-D Vehicle Model (3차원(次元) 차량(車輛)모델을 사용(使用)한 강도로교(鋼道路橋)의 동적응답(動的應答) 관(關)한 연구(硏究))

  • Chung, Tae Ju;Park, Young Suk
    • KSCE Journal of Civil and Environmental Engineering Research
    • /
    • v.14 no.5
    • /
    • pp.1055-1067
    • /
    • 1994
  • This paper is presented to perform linear dynamic analysis of bridges due to vehicle moving on bridges. The road surface roughness and bridge/vehicle interaction are also considered. The bridge and vehicle are modeled as 3-D bridge and vehicle model, respectively. The road surface roughness of the roadway and bridge decks are generated from power spectral density(PSD) function for good road. The PSD function proposed by C.J. Dodds and J.D. Robson is used to describe the road surface roughness for good road condition. The vehicles are modeled as two nonlinear vehicle model with 7-D.O.F of truck and 12-D.O.F of tractor-trailer and the equations of motion of the vehicles are derived using Lagrange's equation. The main girder and concrete deck are modeled as beam and shell element, respectively and rigid link is used between main girder and concrete deck. The equations of motion of the vehicles are solved by Newmark ${\beta}$ method and the equations of the motion of the bridges are solved by mode-superposition procedures. The validity of the proposed procedure is demonstrated by comparing the results with the experimental data reported by the AASHO Road Test. The comparison shows that the agreement between experiment and theory is quite satisfactory.

  • PDF