• Title/Summary/Keyword: superposition principle

Search Result 102, Processing Time 0.026 seconds

Numerical Computation of Bearing Capacity Factor $N_{\gamma}$ (지지력 계수 $N_{\gamma}$의 수치적 산정법)

  • Kim, Won-Cheul
    • Proceedings of the Korean Geotechical Society Conference
    • /
    • 2004.03b
    • /
    • pp.565-573
    • /
    • 2004
  • This study is to present explicit analytical expressions for calculating bearing capacity factor $N_{\gamma}$, to provide results of the numerical computation instead of the graphical method. In this study, $N_{\gamma}$ is proposed in the critical failure surface on assumption that the center of log spiral in the radial shear zone can be located at the any points of around footing. The critical failure surface is one which yields minimum passive pressure $P_{\gamma}$ on the radial shear zone from the family of log spirals accoding to change of the center of log spiral. This study adoptes Terzaghi's bearing capacity principle(e.g., Prandtl's mechanism, limit equilibrium equation, superposition principle) but the soil wedge in an elastic zone makes angle $45^{\circ}+{\phi}/2$ with the horizontal and the location of the log spiral's center.

  • PDF

Analysis of Rectangular Plates under Distributed Loads of Various Intensity with Interior Supports at Arbitrary Positions (분포하중(分布荷重)을 받는 구형판(矩形板)의 탄성해석(彈性解析))

  • Suk-Yoon,Chang
    • Bulletin of the Society of Naval Architects of Korea
    • /
    • v.13 no.1
    • /
    • pp.17-23
    • /
    • 1976
  • Some methods of analysis of rectangular plates under distributed load of various intensity with interior supports are presented herein. Analysis of many structures such as bottom, side shell, and deck plate of ship hull and flat slab, with or without internal supports, Floor systems of bridges, included crthotropic bridges is a problem of plate with elastic supports or continuous edges. When the four edges of rectangular plate is simply supported, the double Fourier series solution developed by Navier can represent an exact result of this problem. If two opposite edges are simply supported, Levy's method is available to give an "exact" solution. When the loading condition and supporting condition of a plate does not fall into these cases, no simple analytic method seems to be feasible. Analysis of a simply supported rectangular plate under irregularly distributed loads of various intensity with internal supports is carried out by applying Navier solution well as the "Principle of Superposition." Finite difference technique is used to solve plates under irregularly distributed loads of various intensity with internal supports and with various boundary conditions. When finite difference technique is applied to the Lagrange's plate bending equation, any of fourth order derivative term in this equation produces at least five pivotal points leading to some troubles when the resulting linear algebraic equations are to be solved. This problem was solved by reducing the order of the derivatives to two: the fourth order partial differential equation with one dependent variable, namely deflection, is changed to an equivalent pair of second order partial differential equations with two dependent variables. Finite difference technique is then applied to transform these equations to a set of simultaneous linear algebraic equations. Principle of Superposition is then applied to handle the problems caused by concentrated loads and interior supports. This method can be used for the cases of plates under irregularly distributed loads of various intensity with arbitrary conditions such as elastic supports, or continuous edges with or without interior supports, and this method can also be solve the influence values of deflection, moment and etc. at arbitrary position of plates under the live load.

  • PDF

Elastic solutions for shallow tunnels excavated under non-axisymmetric displacement boundary conditions on a vertical surface

  • Wang, Ling;Zou, Jin-Feng;Yang, Tao;Wang, Feng
    • Geomechanics and Engineering
    • /
    • v.19 no.3
    • /
    • pp.201-215
    • /
    • 2019
  • A new approach of analyzing the displacements and stress of the surrounding rock for shallow tunnels excavated under non-axisymmetric displacement boundary conditions on a vertical surface is investigated in this study. In the proposed approach, by using a virtual image technique, the shear stress of the vertical ground surface is revised to be zero, and elastic solutions of the surrounding rock are obtained before stress revision. To revise the vertical normal stress and shear stress of horizontal ground surface generated by the combined action of the actual and image sinks, the harmonic functions and corresponding stress function solutions were adopted. Based on the Boussinesq's solutions and integral method, the horizontal normal stress of the vertical ground surface is revised to be zero. Based on the linear superposition principle, the final solution of the displacements and stress were proposed by superimposing the solutions obtained by the virtual image technique and the stress revision on the horizontal and vertical ground surfaces. Furthermore, the ground settlements and lateral displacements of the horizontal and vertical ground surfaces are derived by the proposed approach. The proposed approach was well verified by comparing with the numerical method. The discussion based on the proposed approach in the manuscript shows that smaller horizontal ground settlements will be induced by lower tunnel buried depths and smaller limb distances. The proposed approach for the displacement and stress of the surrounding rocks can provide some practical information about the surrounding rock stability analysis of shallow tunnels excavated under non-axisymmetric displacement boundary conditions on a vertical surface.

Study on the Degradaion Behavior of Acrylonitrile Rubber(NBR) O-ring by Intermittent CSR and Time-Temperature Superposition Principle (간헐 압축응력완화 시험법과 시간-온도 중첩 이론을 이용한 NBR 오링의 노화 거동 분석 연구)

  • Lee, Jin Hyok;Bae, Jong Woo;Choi, Myung Chan;Yun, Yu Mi;Kim, Wonho;Park, Sung Han;Jo, Nam-Ju
    • Journal of the Korean Society of Propulsion Engineers
    • /
    • v.23 no.1
    • /
    • pp.46-51
    • /
    • 2019
  • Intermittent CSR testing was used to investigate the degradation of a NBR O-ring, and also the prediction of its life-time. An intermittent CSR jig was designed taking into consideration the O-ring's environment under use. Degradation of O-rings by thermal aging was observed between $40^{\circ}C$ and $120^{\circ}C$. O-rings showed non-linear degradation behavior under $80^{\circ}C$. At 20% of failure condition, predicted life-times were 32.5 years by Arrhenius plot and 22.6 years by WLF plot.

Dynamic Rheological Properties of Honeys at Low Temperatures as Affected by Moisture Content and Temperature

  • Kang, Kyoung-Mo;Yoo, Byoung-Seung
    • Food Science and Biotechnology
    • /
    • v.17 no.1
    • /
    • pp.90-94
    • /
    • 2008
  • Dynamic rheological properties of honey samples with 3 different moisture contents (17.2, 19.0, and 21.0%) were evaluated at various low temperatures (-15, -10, -5, and $0^{\circ}C$) using a controlled stress rheometer. The honey samples displayed a liquid-like behavior, with loss modulus (G") predominating over storage modulus (G') (G">>G'), showing the high dependence on frequency ($\omega$). The magnitudes of G' and G" decreased with an increase in temperature and water content while a predominant increase of G' was noticed at $-15^{\circ}C$. The time-temperature superposition (TTS) principle was applied to bring G" values for honeys at various temperatures together into a master curve. The G" over the temperature range of -15 to $0^{\circ}C$ obeyed the Arrhenius relationship with a high determination coefficient ($R^2=0.98-0.99$). Activation energy value (Ea=112.4 kJ/mol) of honey with a moisture content of 17.2% was higher than those (Ea=98.8-101.1 kJ/mol) of other honey samples with higher moisture contents.

Pole-pole array electrical resistivity survey and an effective interpretational scheme of its data (2극법 전기비저항 탐사 자료의 효율적인 해석방법)

  • Cho Dong-Heng;Lee Chang Yourl;Jee Sang-Keun
    • 한국지구물리탐사학회:학술대회논문집
    • /
    • 2000.09a
    • /
    • pp.112-131
    • /
    • 2000
  • In spite of its many strong points, pole-pole electrode configuration is not often used for ground electrical resistivity survey except for bore hole survey as normal logging and for archaeological investigation. Above all, poor spatial resolution of pole-pole survey may be responsible for this. But recent experiences so far gained by the present authers lead them to think that pole-pole survey can be at least a viable means of reconnaissance survey in near-surface conductive environment and an effective interpretational scheme may augment its resolution. As well known, a response of any other electrode configuration is a linear combination of pole-pole responses. Based on this principle of linear superposition and the principle of reciprocity, the other 'responses' can be derived with simple additions and subtractions of pole-pole responses. Though such responses are not always correct due to the adverse effects of noises, combined with the potential decay curves, they can be helpful to interprete better pole-pole survey data especially in connection of the resolution. This can be comparable to the use of the first or second derivatives of gravity and magnetic intensity surveys.

  • PDF

Step-up and Step-down Asymmetrical 24-Pulse Autotransformer Rectifier

  • Zhang, Lu;Ge, Hong-juan;Jiang, Fan;Yang, Guang;Lin, Yi
    • Journal of Power Electronics
    • /
    • v.18 no.5
    • /
    • pp.1536-1544
    • /
    • 2018
  • The existing 24-pulse autotransformer rectifier unit (ATRU) needs interphase reactors for parallel work of the rectifier bridges, and its output voltage cannot be regulated. Aiming at these problems, a step-up and step-down asymmetrical 24-pulse ATRU is proposed in this paper. The connections and turns ratios among transformer windings are well designed. In addition, a 15-degree phase difference is formed between two of the 24 voltage vectors produced by the transformer, which makes the four rectifier bridge groups produce a 24-pulse DC voltage without interphase reactors. Meanwhile, by adding extended winding to each phase of the transformer, wide-range regulation of the ATRU output voltage can be realized, and the reasonable voltage regulation range is between 0.2 and 1.6. The superposition of the voltage vectors and the principle of the voltage regulation are analyzed in detail. Furthermore, the turns ratio of the windings, winding current, output voltage, and kilovolt-ampere rating are all derived. Finally, the simulations and experiments are carried out, and the correctness of the principle and theoretical analysis of the new 24-pulse ATRU are verified.

A Study on the Formation of a Style - Focusing on the Style of Iris Van Herpen - (스타일 형성에 관한 연구 - Iris Van Herpen의 스타일을 중심으로 -)

  • Kim, Yon-Son
    • Journal of Fashion Business
    • /
    • v.16 no.2
    • /
    • pp.124-137
    • /
    • 2012
  • This study aims to identify the meaning and formation cause of a style, and the essential elements of style formation, through psychobiological research as well as an analysis of the designs of Iris Van Herpen, a fashion designer, who in just 6 years has developed into a world-renowned new designer. As a result, it has been found that the psychobiological causes to form a style stem from the action of 'long-term memory', which is consolidated by 'selective attention', 'perceptional subjectivity', the principle of the 'neuron's connection specificity and invariance', and the principle of a 'neuronal signal's unilateral flow'. With such action, Herpen could develop her own original composition techniques. The formative shapes created by such composition techniques are characterized by enumeration, superposition, and hanging. The study has also found that the essential elements for a designer to be able to form his/her own style include 'aesthetic originality' in which the designer views the property of a thing from his/her inherent perspective, and finds the uniqueness from the thing that only he/she can express, 'technical differences' that are creative and original, and 'formative specificity' that is summarized into one property through an impressive shape.

Life-time Prediction of a FKM O-ring using Intermittent Compression Stress Relaxation (CSR) and Time-temperature Superposition (TTS) Principle (간헐 압축응력 완화와 시간-온도 중첩 원리를 이용한 FKM 오링의 수명 예측 연구)

  • Lee, Jin-Hyok;Bae, Jong-Woo;Kim, Jung-Su;Hwang, Tae-Jun;Park, Sung-Doo;Park, Sung-Han;Min, Yeo-Tae;Kim, Won-Ho;Jo, Nam-Ju
    • Elastomers and Composites
    • /
    • v.45 no.4
    • /
    • pp.263-271
    • /
    • 2010
  • Intermittent CSR testing was used to investigate the degradation of an FKM O-ring, also the prediction of its life-time. An intermittent CSR jig was designed taking into consideration the O-ring's environment under use. The testing allowed observation of the effects of friction, heat loss, and stress relaxation by the Mullins effect. Degradation of O-rings by thermal aging was observed between 60 and $160^{\circ}C$. In the high temperature of range ($100-160^{\circ}C$) O-rings showed linear degradation behavior and satisfied the Arrhenius relationship. The activation energy was about 60.2 kJ/mol. From Arrhenius plots, predicted life-times were 43.3 years and 69.9 years for 50% and 40% failure conditions, respectively. Based on TTS (time-temperature superposition) principle, degradation was observed at $60^{\circ}C$, and could save testing time. Between 60 and $100^{\circ}C$ the activation energy decreased to 48.3 kJ/mol. WLF(William-Landel-Ferry) plot confirmed that O-rings show non-linear degradation behavior under $80^{\circ}C$. The life-time of O-rings predicted by TTS principle was 19.1 years and 25.2 years for each failure condition. The life-time predicted by TTS principle is more conservative than that from the Arrhenius relationship.

The Stress Field in the Body by Tangential Loading of a Rectangular Patch on a Semi-Infinite Solid (반 무한체 위의 사각조각 표면에 작용하는 접선하중에 의한 반 무한체내의 응력 해석)

  • Lee, Mun-Ju;Gu, Yeong-Pil;Jo, Yong-Ju
    • Transactions of the Korean Society of Mechanical Engineers A
    • /
    • v.24 no.4 s.175
    • /
    • pp.1032-1038
    • /
    • 2000
  • The stress field in the body by tangential loading of a rectangular patch on a semi-infinite solid has been solved analytically using potential function. The validity of result of this study was proved by Saint-Venant's principle in the remote region and in the vicinity of the surface with superposition of point loads.