• Title, Summary, Keyword: Foundations of Geometry

Search Result 27, Processing Time 0.042 seconds

Nonlinear vibration analysis of laminated plates resting on nonlinear two-parameters elastic foundations

  • Akgoz, Bekir;Civalek, Omer
    • Steel and Composite Structures
    • /
    • v.11 no.5
    • /
    • pp.403-421
    • /
    • 2011
  • In the present manuscript, geometrically nonlinear free vibration analysis of thin laminated plates resting on non-linear elastic foundations is investigated. Winkler-Pasternak type foundation model is used. Governing equations of motions are obtained using the von Karman type nonlinear theory. The method of discrete singular convolution is used to obtain the discretised equations of motion of plates. The effects of plate geometry, boundary conditions, material properties and foundation parameters on nonlinear vibration behavior of plates are presented.

Ultimate bearing capacity of conical shell foundations

  • Colmenares, J.E.;Kang, So-Ra;Shin, Young-Jin;Shin, Jong-Ho
    • Structural Engineering and Mechanics
    • /
    • v.52 no.3
    • /
    • pp.507-523
    • /
    • 2014
  • Shell foundations have been employed as an alternative for the conventional flat shallow foundations and have proven to provide economical advantage. They have shown considerably improved performance in terms of ultimate capacity and settlement characteristics. However, despite conical shell foundations are frequently used in industry, the theoretical solutions for bearing capacity of these footings are available for only triangular shell strip foundations. The benefits in design aspects can be achieved through theoretical solutions considering shell geometry. The engineering behavior of a conical shell foundation on mixed soils was investigated experimentally and theoretically in this study. The failure mechanism was obtained by conducting laboratory model tests. Based on that, the theoretical solution of bearing capacity was developed and validated with experimental results, in terms of the internal angle of the cone. In comparison to the circular flat foundation, the results show 15% increase of ultimate load and 51% decrease of settlement at an angle of intersection of $120^{\circ}$. Based on the results, the design chart of modified bearing capacity coefficients for conical shell foundation is proposed.

A study of the types of students' justification and the use of dynamic software (학생들의 정당화 유형과 탐구형 소프트웨어의 활용에 관한 연구)

  • 류희찬;조완영
    • Journal of Educational Research in Mathematics
    • /
    • v.9 no.1
    • /
    • pp.245-261
    • /
    • 1999
  • Proof is an essential characteristic of mathematics and as such should be a key component in mathematics education. But, teaching proof in school mathematics have been unsuccessful for many students. The traditional approach to proofs stresses formal logic and rigorous proof. Thus, most students have difficulties of the concept of proof and students' experiences with proof do not seem meaningful to them. However, different views of proof were asserted in the reassessment of the foundations of mathematics and the nature of mathematical truth. These different views of justification need to be reflected in demonstrative geometry classes. The purpose of this study is to characterize the types of students' justification in demonstrative geometry classes taught using dynamic software. The types of justification can be organized into three categories : empirical justification, deductive justification, and authoritarian justification. Empirical justification are based on evidence from examples, whereas deductive justification are based logical reasoning. If we assume that a strong understanding of demonstrative geometry is shown when empirical justification and deductive justification coexist and benefit from each other, then students' justification should not only some empirical basis but also use chains of deductive reasoning. Thus, interaction between empirical and deductive justification is important. Dynamic geometry software can be used to design the approach to justification that can be successful in moving students toward meaningful justification of ideas. Interactive geometry software can connect visual and empirical justification to higher levels of geometric justification with logical arguments in formal proof.

  • PDF

Development of Elementary Mathematics Teaching-Learning Programs for pre-Service Elementary Teacher (초등교사 양성 대학의 초등수학교육에 대한 교수-학습 프로그램 개발)

  • 신준식
    • The Mathematical Education
    • /
    • v.42 no.4
    • /
    • pp.453-463
    • /
    • 2003
  • The main purpose of this paper is to develope elementary mathematics teaching-learning programs for pre-service elementary teachers. The elementary mathematics education program developed in this work is divided into two parts: One is the theory, the other is the practice. The theory deals with the foundations of mathematics, the objectives of mathematics education, the history of mathematics education in Korea, the psychology of mathematics learning, the theories of mathematics teaching and learning, and the methods of assessment. With respect to the practice, this study examines the background knowledge and activities of numbers and their operation, geometry, measurement, statistics and probability, pattern and function.

  • PDF

GENERALIZED AFFINE DEVELOPMENTS

  • Park, Joon-Sik
    • Journal of the Chungcheong Mathematical Society
    • /
    • v.28 no.1
    • /
    • pp.65-72
    • /
    • 2015
  • The (affine) development of a smooth curve in a smooth manifold M with respect to an arbitrarily given affine connection in the bundle of affine frames over M is well known (cf. S.Kobayashi and K.Nomizu, Foundations of Differential Geometry, Vol.1). In this paper, we get the generalized affine development of a smooth curve $x_t$ ($t{\in}[0,1]$) in M into the affine tangent space at $x_0$ (${\in}M$) with respect to a given generalized affine connection in the bundle of affine frames over M.

A new model for T-shaped combined footings part I: Optimal dimensioning

  • Luevanos-Rojas, Arnulfo;Lopez-Chavarria, Sandra;Medina-Elizondo, Manuel
    • Geomechanics and Engineering
    • /
    • v.14 no.1
    • /
    • pp.51-60
    • /
    • 2018
  • The foundations are classified into shallow and deep, which have important differences: in terms of geometry, the behavior of the soil, its structural functionality, and its constructive systems. The shallow foundations may be of various types according to their function; isolated footings, combined footings, strip footings, and slabs foundation. The isolated footings are of the type rectangular, square and circular. The combined footing may be rectangular, trapezoidal or T-shaped in plan. This paper presents a new model for T-shaped combined footings to obtain the most economical contact surface on the soil (optimal dimensioning) to support an axial load and moment in two directions to each column. The new model considers the soil real pressure, i.e., the pressure varies linearly. The classical model uses the technique of test and error, i.e., a dimension is proposed, and subsequently, the equation of the biaxial bending is used to obtain the stresses acting on each vertex of the T-shaped combined footing, which must meet the conditions following: The minimum stress should be equal or greater than zero, and maximum stress must be equal or less than the allowable capacity that can withstand the soil. To illustrate the validity of the new model, numerical examples are presented to obtain the minimum area of the contact surface on the soil for T-shaped combined footings subjected to an axial load and moments in two directions applied to each column.

Experimental Evaluation of the Moment Capacity of a Railway Electric Pole Foundation Adjacent to a Fill Slope (실물 재하시험을 통한 성토사면에 근접한 철도 전철주기초의 저항모멘트 평가)

  • Lee, Su-Hyung;Lee, Sung-Jin;Lee, Il-Wha
    • Journal of the Korean Geotechnical Society
    • /
    • v.28 no.6
    • /
    • pp.5-17
    • /
    • 2012
  • The moment responses of electric pole foundations for a railway were investigated using real-scale load tests. Large overturning moments were applied to two circular rigid piles with a 0.75 m diameter and a 2.5 m embedded depth; the circular rigid piles were installed in an actual railway embankment fill. Two different loading directions-toward the fill slope and toward the track -were applied to evaluate the influence of the fill slope on the moment capacities of the foundations. It was found that the failure of the foundations that were constructed according to Korean railway practices exhibited a sudden overturning pattern without any significant pre-failure displacement. The moment capacity toward the fill slope was less than the moment capacity toward the track by 30%. From the test results, the geometry factor (K), which accounted for the reduction of the moment capacity, due to the fill slope, was 0.7. Moment capacities determined from the load tests were compared with those predicted from three existing design methods, and their applicability was discussed.

The UndrainBd Behavir or of Drilled Shaft Foundations Subjected to Static Inclined Loading (정적 경사하중을 받는 현장타설 말뚝기초의 비배수 거동)

  • ;Kulhawy, Fred H.
    • Geotechnical Engineering
    • /
    • v.11 no.3
    • /
    • pp.91-112
    • /
    • 1995
  • Drilled shafts are used increasingly as the foundations for many types of structures. However, very little knowledge of drilled shaft behavior under inclined load is available. In this study, a systematic experimental testing program was conducted to understand the undrained behavior of drilled shaft foundations under inclined loads. A semi-theoretical method of predicting the inclined capacity was developed through a parametric study of the variables such as shaft geometry and load inclination. Test parameters were chosen to be representative of those most frequently used in the electric utility industry. Short, rigid shafts with varying depth/diameter(D/B) ratios were addressed, and loading modes were investigated that includes exial uplift, inclined uplift, and inclined compression loads. Capacities were evaluated using the structural interaction formula and an equation developed from this experimental study. This new equation models the laboratory data well and is applicable for the limites field data.

  • PDF

특정 사례터널 해석 결과 및 평가

  • Lee, Seung-Rae;O, Se-Bung;Baek, Gyu-Ho
    • Proceedings of the Korean Geotechical Society Conference
    • /
    • /
    • pp.123-132
    • /
    • 1991
  • The GEOKST program was used to solve the tunnel example problem. The package can solve such geotechnical problem as excavation, embankment, foundations, etc., in which the soil can be modeled by various elastoplastic geomaterial models. The main objective was to consider the effects of excavation depth to the face of the tunnel on the stability of the ground and support system. Depended on the strength of the ground materials, the limit excavation depth without any support system could be established by analyzing three-dimensional excavation problem. In this given example problem, the strengths of the ground materials were enough for the stability of the tunnel without any support system up to fairly deep excavation and the maximum tunnel section displacement was stabilized as the excavation proceed. The asymptotic value was approximately the same as that of the plane strain analysis. Thus, assuming the plain strain condition and simulation the actual excavation procedure, the maximum tunnel section displacement was caculated after final step. The maximum calculated displacement occured at the top section of the tunnel geometry and was about 8mm.

  • PDF

Analysis of elastic foundation plates with internal and perimetric stiffening beams on elastic foundations by using Finite Differences Method

  • Orbanich, C.J.;Ortega, N.F.
    • Structural Engineering and Mechanics
    • /
    • v.45 no.2
    • /
    • pp.169-182
    • /
    • 2013
  • The mechanical behavior of rectangular foundation plates with perimetric beams and internal stiffening beams of the plate is herein analyzed, taking the foundation design into account. A series of dimensionless parameters related to the geometry of the studied elements were defined. In order to generalize the problem statement, an initial settlements was considered. A numeric procedure was developed for the resolution by means of the Finite Differences Method that takes into account the stiffness of the plate, the perimetric and internal plate beams and the soil reaction module. Iterative algorithms were employed which, for each of the analyzed cases, made it possible to find displacements and reaction percentages taken by the plate and those that discharge directly into the perimetric beams, practically without affecting the plate. To enhance its mechanical behavior the internal stiffening beams were prestressed and the results obtained with and without prestressing were compared. This analysis was made considering the load conditions and the soil reaction module constant.