• Title/Summary/Keyword: Linear formula

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Chord rotation demand for effective catenary action of RC beams under gravitational loadings

  • Tsai, Meng-Hao
    • Structural Engineering and Mechanics
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    • v.58 no.2
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    • pp.327-345
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    • 2016
  • Many experimental and analytical studies have been conducted with beam-column subassemblages composed of a two-span beam to investigate the progressive collapse resistance of RC frames. Most study results reveal a strength-decreased transition phase in the nonlinear static load-deflection curve, which may induce dynamic snap-through response and increase the chord rotation demand for effective catenary action (ECA). In this study, the nonlinear static response is idealized as a piecewise linear curve and analytical pseudo-static response is derived for each linearized region to investigate the rotation demands for the ECA of the two-span RC beams. With analytical parameters determined from several published test results, numerical analysis results indicate that the rotation demand of 0.20 rad recommended in the design guidelines does not always guarantee the ECA. A higher rotation demand may be induced for the two-span beams designed with smaller span-to-depth ratios and it is better to use their peak arch resistance (PAR) as the collapse strength. A tensile reinforcement ratio not greater than 1.0% and a span-to-depth ratio not less than 7.0 are suggested for the two-span RC beams bridging the removed column if the ECA is expected for the collapse resistance. Also, complementary pseudo-static analysis is advised to verify the ECA under realistic dynamic column loss even though the static PAR is recovered in the nonlinear static response. A practical empirical formula is provided to estimate an approximate rotation demand for the ECA.

Characteristic Analysis of a Small ALIP for the Developing of the Liquid Sodium (액체 소듐 순환 구동용 소형 환단면 선형유도전자펌프의 특성 분석)

  • Kim, Hee-Reyoung;Kim, Jong-Man;Nam, Ho-Yun;Hwang, Jong-Sun;Seo, Jang-Soo
    • Proceedings of the KIEE Conference
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    • 1999.11a
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    • pp.1-3
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    • 1999
  • EM (ElectroMagnetic) pump is used for the purpose of transporting liquid sodium coolant with electrical conductivity in the LMR(Liquid Metal Reactor). (In the present study, pilot EM pump has been designed by using of equivalent circuit method which is commonly employed to analyze linear induction machines for the test of removal of residual heat. The length and diameter of the pump have fixed values of 840 mm and 101.6 mm each by taking account of geometrical size of circulation loop for the installation of EM pump. Flowrate versus developing pressure is related from Laithwaite's standard design formula and the characteristic analyses of developing force and efficiency are carried out according to change of input frequency. From the characteristic curve, input frequency of 13 Hz is determined as the design frequency. On the other hand, The annular air gap size of 6.05 mm is selected not to bring about too much hydraulic loss. Resultantly design analysis makes pump have the electrical input of 604 VA and the hydrodynamical capacity of 1.3 bars and 40 l/min.

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Study of the Scorch/Cure time Relationships (스코치/가황시간의 상관관계에 관한 연구)

  • Ryou, Jin-Ho;Kim, Chang-Hee;Oh, Taeg-Su
    • Elastomers and Composites
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    • v.31 no.1
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    • pp.33-42
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    • 1996
  • NR, NBR, and CR rubber were prepared by mixing filler in various ratios. Their vulcanization characteristics and thermal properties were studied. Vulcanization characteristics were investigated using cure curve that had been obtained from oscillating disk rheometer study. The Arrhenius law is known to describe the relationship between cure time and temperature of most elastomers. Curing could be done by the addition of sulfur, peroxides, and proper acceleratores. The optimum cure time that affects desirable values of modulus and tensile strength of the vulcanizate is taken as t90 as measured by a rheometer. Rubbers were cured in the rheometer at temperatures ranging from $130^{\circ}C\;to\;180^{\circ}C$ in order to check the validity of the curing system used. A linear relationship between ln(ts2) and ln(t90) was found for all elastomers. The term sensitivity has been used to describe the relationship between a change of ts2 to the corresponding change of t90 due to an increment of temperature. This is related to the formula of the compound.

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Damage identification of 2D and 3D trusses by using complete and incomplete noisy measurements

  • Rezaiee-Pajand, M.;Kazemiyan, M.S.
    • Structural Engineering and Mechanics
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    • v.52 no.1
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    • pp.149-172
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    • 2014
  • Four algorithms for damage detection of trusses are presented in this paper. These approaches can detect damage by using both complete and incomplete measurements. The suggested methods are based on the minimization of the difference between the measured and analytical static responses of structures. A non-linear constrained optimization problem is established to estimate the severity and location of damage. To reach the responses, the successive quadratic method is used. Based on the objective function, the stiffness matrix of the truss should be estimated and inverted in the optimization procedure. The differences of the proposed techniques are rooted in the strategy utilized for inverting the stiffness matrix of the damaged structure. Additionally, for separating the probable damaged members, a new formulation is proposed. This scheme is employed prior to the outset of the optimization process. Furthermore, a new tactic is presented to select the appropriate load pattern. To investigate the robustness and efficiency of the authors' method, several numerical tests are performed. Moreover, Monte Carlo simulation is carried out to assess the effect of noisy measurements on the estimated parameters.

Frequency Tracking Error Analysis of LQG Based Vector Tracking Loop for Robust Signal Tracking

  • Park, Minhuck;Kee, Changdon
    • Journal of Positioning, Navigation, and Timing
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    • v.9 no.3
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    • pp.207-214
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    • 2020
  • In this paper, we implement linear-quadratic-Gaussian based vector tracking loop (LQG-VTL) instead of conventional extended Kalman filter based vector tracking loop (EKF-VTL). The LQG-VTL can improve the performance compared to the EKF-VTL by generating optimal control input at a specific performance index. Performance analysis is conducted through two factors, frequency thermal noise and frequency dynamic stress error, which determine total frequency tracking error. We derive the thermal noise and the dynamic stress error formula in the LQG-VTL. From frequency tracking error analysis, we can determine control gain matrix in the LQG controller and show that the frequency tracking error of the LQG-VTL is lower than that of the EKF-VTL in all C/N0 ranges. The simulation results show that the LQG-VTL improves performance by 30% in Doppler tracking, so the LQG-VTL can extend pre-integration time longer and track weaker signals than the EKF-VTL. Therefore, the LQG-VTL algorithm is more robust than the EKF-VTL in weak signal environments.

A study on assessment of bone mass from aluminum-equivalent image by digital imaging system (디지털 영상 시스템을 이용한 알루미늄 당량화상에 의한 골량 측정에 관한 연구)

  • Kim Jin-Soo;Choi Eui-Hwan;Kim Jae-Duk
    • Journal of Korean Academy of Oral and Maxillofacial Radiology
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    • v.27 no.1
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    • pp.87-97
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    • 1997
  • The purpose of this study was to evaluate the method for quantitative assessment of bone mass from aluminum-equivalent value of hydroxyapatite by using digital imaging system consisted of Power Macintosh 7200/120, 15-inch color monitor, and GT-9000 scanner with transparency unit. After aluminum-equivalent image made from correlation between aluminum thickness and grey scale, the accuracy of conversion to mass from aluminum-equivalent value was evaluated. Measured bone mass was compared with converted bone mass from aluminum-equivalent value of hydroxyapatite block by correlation formula between aluminum-equivalent value of hydroxyapatite block and hydroxyapatite mass. The results of this study were as follow; 1. Correlation between aluminum thickness and grey level for obtaining aluminum-equivalent image was high positively associated(r²=0.99). Converted masses from aluminum-equivalent value were very similar to measured masses. There was, statistically, no significant difference(P<0.05) between them 2. Correlation between hydroxyapatite aluminum-equivalent and hydroxyapatite mass was shown to linear relation (r²=0.95). 3. Converted masses from aluminum-equivalent value of 3 dry mandible segments were similar to measured masses. The difference between the exposure directions was not significantly different(P<0.05).

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Development of Curve Fitted Equation for the Dynamic Response of a Buried Concrete Pipelines with Various End Boundary Conditions (여러 단부경계조건을 가진 콘크리트 매설관의 동적응답에 대한 곡선적합식의 개발)

  • Jeong, Jin-Ho;Kim, Sung-Ban;Joeng, Du-Hwoe
    • Proceedings of the Korean Geotechical Society Conference
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    • 2006.03a
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    • pp.572-581
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    • 2006
  • This study is to investigate dynamic response of concrete buried pipelines with various end boundary conditions and develop a curve fitted equation to ensure practicality and convenience for the use at the actual field for the test of resistance of earthquake. Dynamic response under the various end boundary conditions is calculated with analysis on values and computing programs. However, such a method of analysis requires skillfulness in using computing programs for dynamic movement of buried pipelines with dynamic analysis formula and has lower efficiency and practicality because, in the nature of analysis program of values, it needs much time to conduct repeated calculations. Therefore, the study is intended to develop a curve fitted equation to ensure more efficient and practical analysis. This paper tests various degrees of equation with non-linear least square method and developments a curve fitted equation based on the transmission speed with the best results. In the use of curve fitted equation, degree of polynomial and determining coefficient are influenced by the speed of transmission.

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An Efficient Dynamic Response Optimization Using the Design Sensitivities Approximated Within the Estimate Confidence Radius

  • Park, Dong-Hoon;Kim, Min-Soo
    • Journal of Mechanical Science and Technology
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    • v.15 no.8
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    • pp.1143-1155
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    • 2001
  • In order to reduce the expensive CPU time for design sensitivity analysis in dynamic response optimization, this study introduces the design sensitivities approximated within estimated confidence radius in dynamic response optimization with ALM method. The confidence radius is estimated by the linear approximation with Hessian of quasi-Newton formula and qualifies the approximate gradient to be validly used during optimization process. In this study, if the design changes between consecutive iterations are within the estimated confidence radius, then the approximate gradients are accepted. Otherwise, the exact gradients are used such as analytical or finite differenced gradients. This hybrid design sensitivity analysis method is embedded in an in-house ALM based dynamic response optimizer, which solves three typical dynamic response optimization problems and one practical design problem for a tracked vehicle suspension system. The optimization results are compared with those of the conventional method that uses only exact gradients throughout optimization process. These comparisons show that the hybrid method is more efficient than the conventional method. Especially, in the tracked vehicle suspension system design, the proposed method yields 14 percent reduction of the total CPU time and the number of analyses than the conventional method, while giving similar optimum values.

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Progressive Quadratic Approximation Method for Effective Constructing the Second-Order Response Surface Models in the Large Scaled System Design (대형 설계 시스템의 효율적 반응표면 근사화를 위한 점진적 이차 근사화 기법)

  • Hong, Gyeong-Jin;Kim, Min-Su;Choe, Dong-Hun
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.24 no.12
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    • pp.3040-3052
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    • 2000
  • For effective construction of second-order response surface models, an efficient quad ratic approximation method is proposed in the context of trust region model management strategy. In the proposed method, although only the linear and quadratic terms are uniquely determined using 2n+1 design points, the two-factor interaction terms are mathematically updated by normalized quasi-Newton formula. In order to show the numerical performance of the proposed approximation method, a sequential approximate optimizer is developed and solves a typical unconstrained optimization problem having 2, 6, 10, 15, 30 and 50 design variables, a gear reducer system design problem and two dynamic response optimization problems with multiple objectives, five objectives for one and two objectives for the other. Finally, their optimization results are compared with those of the CCD or the 50% over-determined D-optimal design combined with the same trust region sequential approximate optimizer. These comparisons show that the proposed method gives more efficient than others.

Minimum life-cycle cost design of ice-resistant offshore platforms

  • Li, Gang;Zhang, Da-Yong;Yue, Qian-Jin
    • Structural Engineering and Mechanics
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    • v.31 no.1
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    • pp.11-24
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    • 2009
  • In China, the oil and natural gas resources of Bohai Bay are mainly marginal oil fields. It is necessary to build both ice-resistant and economical offshore platforms. However, risk is involved in the design, construction, utilization, maintenance of offshore platforms as uncertain events may occur within the life-cycle of a platform under the extreme ice load. In this study, the optimum design model of the expected life-cycle cost for ice-resistant platforms based on cost-effectiveness criterion is proposed. Multiple performance demands of the structure, facilities and crew members, associated with the failure assessment criteria and evaluation functions of costs of construction, consequences of structural failure modes including damage, revenue loss, death and injury as well as discounting cost over time are considered. An efficient approximate method of the global reliability analysis for the offshore platforms is provided, which converts the implicit nonlinear performance function in the conventional reliability analysis to linear explicit one. The proposed life-cycle optimum design formula are applied to a typical ice-resistant platform in Bohai Bay, and the results demonstrate that the life-cycle cost-effective optimum design model is more rational compared to the conventional design.