• Title/Summary/Keyword: Calculation methods and principles

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Stress-Strain Responses of Concrete Confined by FRP Composites (FRP 합성재료에 의하여 구속된 콘크리트의 응력-변형률 응답 예측)

  • Cho, Soon-Ho
    • Journal of the Korea Concrete Institute
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    • v.19 no.6
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    • pp.803-810
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    • 2007
  • An analytical method capable of predicting various stress-strain responses in axially loaded concrete confined with FRP (fiber reinforced polymers) composites in a rational manner is presented. Its underlying idea is that the volumetric expansion due to progressive microcracking in mechanically loaded concrete is an important measure of the extent of damage in the material microstructure, and can be utilized to estimate the load-carrying capacity of concrete by considering the corresponding accumulated damage. Following from this, an elastic modulus expressed as a function of area strain and concrete porosity, the energy-balance equation relating the dilating concrete to the confining device interactively, the varying confining pressure, and an incremental calculation algorithm are included in the solution procedure. The proposed method enables the evaluation of lateral strains consecutively according to the related mechanical model and the energy-balance equation, rather than using an empirically derived equation for Poisson's ratio or dilation rate as in other analytical methods. Several existing analytical methods that can predict the overall response were also examined and discussed, particularly focusing on the way of considering the volumetric expansion. The results predicted by the proposed and Samaan's bilinear equation models correlated with observed results with a reasonable degree, however it can be judged that the latter is not capable of predicting the response of lateral strains correctly due to incorporating the initial Poisson's ratio and the final converged dilation rate only. Further, the proposed method seems to have greater benefits in other applications by the use of the fundamental principles of mechanics.

An Analysis on Processes of Justifying the Standard Fraction Division Algorithms in Korean Elementary Mathematics Textbooks (우리나라 초등학교 수학 교과서에서의 분수 나눗셈 알고리즘 정당화 과정 분석)

  • Park, Kyo Sik
    • Journal of Elementary Mathematics Education in Korea
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    • v.18 no.1
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    • pp.105-122
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    • 2014
  • In this paper, fraction division algorithms in Korean elementary mathematics textbooks are analyzed as a part of the groundwork to improve teaching methods for fraction division algorithms. There are seemingly six fraction division algorithms in ${\ll}Math\;5-2{\gg}$, ${\ll}Math\;6-1{\gg}$ textbooks according to the 2006 curriculum. Four of them are standard algorithms which show the multiplication by the reciprocal of the divisors modally. Two non-standard algorithms are independent algorithms, and they have weakness in that the integration to the algorithms 8 is not easy. There is a need to reconsider the introduction of the algorithm 4 in that it is difficult to think algorithm 4 is more efficient than algorithm 3. Because (natural number)${\div}$(natural number)=(natural number)${\times}$(the reciprocal of a natural number) is dealt with in algorithm 2, it can be considered to change algorithm 7 to algorithm 2 alike. In textbooks, by converting fraction division expressions into fraction multiplication expressions through indirect methods, the principles of calculation which guarantee the algorithms are explained. Method of using the transitivity, method of using the models such as number bars or rectangles, method of using the equivalence are those. Direct conversion from fraction division expression to fraction multiplication expression by handling the expression is possible, too, but this is beyond the scope of the curriculum. In textbook, when dealing with (natural number)${\div}$(proper fraction) and converting natural numbers to improper fractions, converting natural numbers to proper fractions is used, but it has been never treated officially.

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An Analysis of the Addition and Subtraction of Fractions in Elementary Mathematics Instructional Materials (분수의 덧셈과 뺄셈에 관한 초등학교 수학과 교과용 도서 분석)

  • Pang, Jeong-Suk;Lee, Ji-Young
    • Journal of Elementary Mathematics Education in Korea
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    • v.13 no.2
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    • pp.285-304
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    • 2009
  • The operations of fractions are the main contents of number and operations in the elementary mathematics curriculum. They are also difficult for students to understand conceptually. Nevertheless, there has been little study on the addition and subtraction of fractions. Given this, this paper explored the connection between the national mathematics curriculum and its concomitant textbooks, the adequacy of when to teach, and the method of constructing each unit to teach addition and subtraction of fractions. This paper then analyzed elementary mathematics textbooks and workbooks by three parts aligned with the general instructional flow: 'introduction', 'activity', and, 'exercise'. First, it was analyzed with regard to the introduction part whether the word problems of textbooks might reflect on students' daily lives as intended, how different meanings of operations would be expected to be taught, and how the subsequent activities were connected with the original word problems. Second, the main analysis of activity part of the textbooks dealt with how to use concrete or iconic models to promote students' conceptual understanding of operations and how to formalize the calculation methods and principles with regard to addition and subtraction of fractions. Third, the analysis of the part of exercise in the textbooks and workbooks was conducted with regard to problem types and meanings of operations. It is expected that the issues and suggestions stemming from this analysis of current textbooks and workbooks are informative in developing new instructional materials aligned to the recently revised mathematics curriculum.

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Calculation of Unit Hydrograph from Discharge Curve, Determination of Sluice Dimension and Tidal Computation for Determination of the Closure curve (단위유량도와 비수갑문 단면 및 방조제 축조곡선 결정을 위한 조속계산)

  • 최귀열
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.7 no.1
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    • pp.861-876
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    • 1965
  • During my stay in the Netherlands, I have studied the following, primarily in relation to the Mokpo Yong-san project which had been studied by the NEDECO for a feasibility report. 1. Unit hydrograph at Naju There are many ways to make unit hydrograph, but I want explain here to make unit hydrograph from the- actual run of curve at Naju. A discharge curve made from one rain storm depends on rainfall intensity per houre After finriing hydrograph every two hours, we will get two-hour unit hydrograph to devide each ordinate of the two-hour hydrograph by the rainfall intensity. I have used one storm from June 24 to June 26, 1963, recording a rainfall intensity of average 9. 4 mm per hour for 12 hours. If several rain gage stations had already been established in the catchment area. above Naju prior to this storm, I could have gathered accurate data on rainfall intensity throughout the catchment area. As it was, I used I the automatic rain gage record of the Mokpo I moteorological station to determine the rainfall lntensity. In order. to develop the unit ~Ydrograph at Naju, I subtracted the basic flow from the total runoff flow. I also tried to keed the difference between the calculated discharge amount and the measured discharge less than 1O~ The discharge period. of an unit graph depends on the length of the catchment area. 2. Determination of sluice dimension Acoording to principles of design presently used in our country, a one-day storm with a frequency of 20 years must be discharged in 8 hours. These design criteria are not adequate, and several dams have washed out in the past years. The design of the spillway and sluice dimensions must be based on the maximun peak discharge flowing into the reservoir to avoid crop and structure damages. The total flow into the reservoir is the summation of flow described by the Mokpo hydrograph, the basic flow from all the catchment areas and the rainfall on the reservoir area. To calculate the amount of water discharged through the sluiceCper half hour), the average head during that interval must be known. This can be calculated from the known water level outside the sluiceCdetermined by the tide) and from an estimated water level inside the reservoir at the end of each time interval. The total amount of water discharged through the sluice can be calculated from this average head, the time interval and the cross-sectional area of' the sluice. From the inflow into the .reservoir and the outflow through the sluice gates I calculated the change in the volume of water stored in the reservoir at half-hour intervals. From the stored volume of water and the known storage capacity of the reservoir, I was able to calculate the water level in the reservoir. The Calculated water level in the reservoir must be the same as the estimated water level. Mean stand tide will be adequate to use for determining the sluice dimension because spring tide is worse case and neap tide is best condition for the I result of the calculatio 3. Tidal computation for determination of the closure curve. During the construction of a dam, whether by building up of a succession of horizontael layers or by building in from both sides, the velocity of the water flowinii through the closing gapwill increase, because of the gradual decrease in the cross sectional area of the gap. 1 calculated the . velocities in the closing gap during flood and ebb for the first mentioned method of construction until the cross-sectional area has been reduced to about 25% of the original area, the change in tidal movement within the reservoir being negligible. Up to that point, the increase of the velocity is more or less hyperbolic. During the closing of the last 25 % of the gap, less water can flow out of the reservoir. This causes a rise of the mean water level of the reservoir. The difference in hydraulic head is then no longer negligible and must be taken into account. When, during the course of construction. the submerged weir become a free weir the critical flow occurs. The critical flow is that point, during either ebb or flood, at which the velocity reaches a maximum. When the dam is raised further. the velocity decreases because of the decrease\ulcorner in the height of the water above the weir. The calculation of the currents and velocities for a stage in the closure of the final gap is done in the following manner; Using an average tide with a neglible daily quantity, I estimated the water level on the pustream side of. the dam (inner water level). I determined the current through the gap for each hour by multiplying the storage area by the increment of the rise in water level. The velocity at a given moment can be determined from the calcalated current in m3/sec, and the cross-sectional area at that moment. At the same time from the difference between inner water level and tidal level (outer water level) the velocity can be calculated with the formula $h= \frac{V^2}{2g}$ and must be equal to the velocity detertnined from the current. If there is a difference in velocity, a new estimate of the inner water level must be made and entire procedure should be repeated. When the higher water level is equal to or more than 2/3 times the difference between the lower water level and the crest of the dam, we speak of a "free weir." The flow over the weir is then dependent upon the higher water level and not on the difference between high and low water levels. When the weir is "submerged", that is, the higher water level is less than 2/3 times the difference between the lower water and the crest of the dam, the difference between the high and low levels being decisive. The free weir normally occurs first during ebb, and is due to. the fact that mean level in the estuary is higher than the mean level of . the tide in building dams with barges the maximum velocity in the closing gap may not be more than 3m/sec. As the maximum velocities are higher than this limit we must use other construction methods in closing the gap. This can be done by dump-cars from each side or by using a cable way.e or by using a cable way.

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A Study on the Ordering Status of Traditional Landscape Design Service in Cultural Heritage (문화재의 전통조경설계용역 발주실태 연구)

  • Kim, Min-Seon;Kim, Choong-Sik;Lee, Jae-Yong
    • Journal of the Korean Institute of Traditional Landscape Architecture
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    • v.39 no.3
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    • pp.33-41
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    • 2021
  • This study identified the scale that traditional landscape design has taken up by analyzing a total of 1037 services for design of cultural heritage that had been ordered by the government agencies from 2018 to 2020, and has drawn characteristics of traditional landscape design focusing on major cases. The results are as follows. First, the number of order cases for traditional landscape design has shown differences annually in the services of design of cultural heritage, but the design amount has been found to have the similar average annually, which confirmed that the same level has been maintained each year. It was found that the number of cases of traditional landscape design requiring responsibilities or participations of landscape engineers for 3 years in the entire design had a high proportion of approximately 26%. Second, the traditional landscape design has required professional knowledge and experiences of landscape engineers that could not be replaced by the business operator for design of cultural heritage consisting of architects. The expertise has been shown differently depending on types of construction. First, the topographical design for the work to build a foundation has required understanding of ground shapes and its elevations and professional knowledge on calculation of the amount of the earth work and the remains maintenance technique etc. The plantation design has required basic knowledge on growth characteristics of trees and the environment for growth and understanding of the vegetation landscape of the past. Meanwhile, the design for traditional pavement and traditional landscape structures and facilities has required the expertise on traditional materials that are different from the modern ones and their processing and construction methods. The understanding of changes to water paths and ecosystem, the principles of fluids, and characteristics of each type of fluid was essential for the design for the ecological landscape work including the maintenance of a water system such as rivers etc. As such, the traditional landscape design has a scale accounting for approximately one fourth of the entire cultural heritage design and requires the expertise differentiated from other fields. This improves the provisions of the current law on limiting the actual design, suggesting the need for the establishment of a traditional landscape design company so that all traditional landscape designs can be carried out by landscape engineers.

Correction of positional change of frontal cephalometric landmarks caused by vertical head rotation (두부의 수직회전 시 정모두부방사선사진상의 계측점 변화와 이의 보정)

  • Kim, Mi-Young;Lee, Kyung-Min;Cho, Jin-Hyoung;Hwang, Hyeon-Shik
    • The korean journal of orthodontics
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    • v.41 no.2
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    • pp.98-111
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    • 2011
  • Objective: Superimposition of frontal cephalograms cannot be performed when the cephalograms are taken with different vertical head rotations. The purpose of the present study was to evaluate the validity of correcting the positional change of frontal cephalometric landmarks caused by vertical head rotation. Methods: In 30 adult individuals, frontal and lateral cephalograms were taken at a $90^{\circ}$ angle. Geometric principles of radiography were used to calculate the possible vertical and horizontal landmark changes if the head should be rotated down $5^{\circ}$ about an ear rod axis. The calculated changes were then compared with cephalometric changes measured on frontal cephalogram actually taken with the head rotated down $5^{\circ}$. Results: When the frontal cephalograms were taken with the head rotated down $5^{\circ}$ about an ear rod axis, significant changes in the vertical position of the landmarks occurred, particularly in the landmarks located farther anteriorly from the ear rod axis. The comparison of calculated changes and real cephalometric changes showed that the differences were less than 0.4 mm in the vertical direction and less than 0.2 mm in the horizontal direction. The differences between calculated and real changes were smaller in the landmarks less affected by vertical head rotation. Conclusions: Even when frontal cephalograms are taken at different vertical head rotations, the concomitant changes in the position of the landmarks can be corrected through calculation using the geometric principle of radiography as long as frontal and lateral cephalograms are taken perpendicular to each other.