• Title/Summary/Keyword: Catenary equation

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Design of Oceanography Buoy - Part II: Mooring System (해양관측용 부이의 설계 건전성 평가 - Part II: 계류시스템 구조건전성 평가)

  • Keum, Dong-Min;Kim, Tae-Woo;Han, Dae-Suk;Lee, Won-Boo;Lee, Jae-Myung
    • Journal of Ocean Engineering and Technology
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    • v.23 no.1
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    • pp.89-95
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    • 2009
  • The purpose of the present study was to evaluate the safety under extreme environmental conditions and the dynamic safety under service environment conditions, of oceanographic buoy mooring systems consisting of a variety of materials, including chain, wire rope, nylon rope, and polypropylene rope. For the static safety assessment of a mooring system, after the calculation of external forces and the division of a mooring system into finite elements, the numerical integral was conducted to yield the elemental static tension until satisfying the geometrical convergence condition. To evaluate the dynamic safety, various processes were considered, including data collection about the anticipated areas for mooring, a determination of the parameters for the interpretation, the interpretation of the dynamic characteristics based on an analytic equation that takes into account the heave motion effect of a buoy hull and a mooring system, and a fatigue analysis of the linear cumulative damage. Based on the analysis results, a supplementary proposal for a wire rope that has a fracture in an actual mooring area was established.

Analysis of restrained steel beams subjected to heating and cooling Part I: Theory

  • Li, Guo-Qiang;Guo, Shi-Xiong
    • Steel and Composite Structures
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    • v.8 no.1
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    • pp.1-18
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    • 2008
  • Observations from experiments and real fire indicate that restrained steel beams have better fire-resistant capability than isolated beams. Due to the effects of restraints, a steel beam in fire condition can undergo very large deflections and the run away damage may be avoided. In addition, axial forces will be induced with temperature increasing and play an important role on the behaviour of the restrained beam. The factors influencing the behavior of a restrained beam subjected to fire include the stiffness of axial and rotational restraints, the load type on the beam and the distribution of temperature in the cross-section of the beam, etc. In this paper, a simplified model is proposed to analyze the performance of restrained steel beams in fire condition. Based on an assumption of the deflection curve of the beam, the axial force, together with the strain and stress distributions in the beam, can be determined. By integrating the stress, the combined moment and force in the cross-section of the beam can be obtained. Then, through substituting the moment and axial force into the equilibrium equation, the behavior of the restrained beam in fire condition can be worked out. Furthermore, for the safety evaluation and repair after a fire, the behaviour of restrained beams during cooling should be understood. For a restrained beam experiencing very high temperatures, the strength of the steel will recover when temperature decreases, but the contraction force, which is produced by thermal contraction, will aggravate the tensile stresses in the beam. In this paper, the behaviour of the restrained beam in cooling phase is analyzed, and the effect of the contraction force is discussed.

Closing Analysis of Symmetric Steel Cable-stayed Bridges and Estimation of Construction Error (대칭형 강 사장교의 폐합해석과 시공오차의 예측)

  • Lee, Min Kwon;Lee, Hae Sung
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.26 no.1A
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    • pp.55-65
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    • 2006
  • This paper presents the closing analysis of a symmetric steel cable-stayed bridge erected by a free cantilever method. Two independent structural systems are formed before the closing procedure of a bridge is performed, and thus the compatibility conditions for vertical displacement and rotational angle are not satisfied at the closing section without the application of proper sectional forces. Since, however, it is usually impossible to apply sectional forces at the closing section, the compatibility conditions should be satisfied by proper external forces that can be actually applicable to a bridge. Unstrained lengths of selected cables and the pull-up force of a derrick crane are adjusted to satisfy nonlinear compatibility conditions, which are solved iteratively by the Newton-Raphson method. Cable members are modeled by the elastic catenary cable elements, and towers and main girders are discretized by linear 3-D frame elements. The sensitivities of displacement with respect to the unstrained lengths of selected cables and the pull-up force of the derrick crane are evaluated by the direct differentiation of the equilibrium equation. A Monte-Carlo simulation approach is proposed to estimate expected construction errors for a given confidence level. The proposed method is applied to the second Jindo Grand Bridge to demonstrate its validity and effectiveness.

Depth Control and Sweeping Depth Stability of the Midwater Trawl (중층트롤의 깊이바꿈과 소해심도의 안정성)

  • 장지원
    • Journal of the Korean Society of Fisheries and Ocean Technology
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    • v.9 no.1
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    • pp.1-18
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    • 1973
  • For regulating the depth of midwater trawl nets towed at the optimum constant speed, the changes in the shape of warps caused by adding a weight on an arbitrary point of the warp of catenary shape is studied. The shape of a warp may be approximated by a catenary. The resultant inferences under this assumption were experimented. Accordingly feasibilities for the application of the result of this study to the midwater trawl nets were also discussed. A series of experiments for basic midwater trawl gear models in water tank and a couple of experiments of a commercial scale gears at sea which involve the properly designed depth control devices having a variable attitude horizontal wing were carried out. The results are summarized as follows: 1. According to the dimension analysis the depth y of a midwater trawl net is introduced by $$y=kLf(\frac{W_r}{R_r},\;\frac{W_o}{R_o},\;\frac{W_n}{R_n})$$) where k is a constant, L the warp length, f the function, and $W_r,\;W_o$ and $W_n$ the apparent weights of warp, otter board and the net, respectively, 2. When a boat is towing a body of apparent weight $W_n$ and its drag $D_n$ by means of a warp whose length L and apparent weight $W_r$ per unit length, the depth y of the body is given by the following equation, provided that the shape of a warp is a catenary and drag of the warp is neglected in comparison with the drag of the body: $$y=\frac{1}{W_r}\{\sqrt{{D_n^2}+{(W_n+W_rL)^2}}-\sqrt{{D_n^2+W_n}^2\}$$ 3. The changes ${\Delta}y$ of the depth of the midwater trawl net caused by changing the warp length or adding a weight ${\Delta}W_n$_n to the net, are given by the following equations: $${\Delta}y{\approx}\frac{W_n+W_{r}L}{\sqrt{D_n^2+(W_n+W_{r}L)^2}}{\Delta}L$$ $${\Delta}y{\approx}\frac{1}{W_r}\{\frac{W_n+W_rL}{\sqrt{D_n^2+(W_n+W_{r}L)^2}}-{\frac{W_n}{\sqrt{D_n^2+W_n^2}}\}{\Delta}W_n$$ 4. A change ${\Delta}y$ of the depth of the midwater trawl net by adding a weight $W_s$ to an arbitrary point of the warp takes an equation of the form $${\Delta}y=\frac{1}{W_r}\{(T_{ur}'-T_{ur})-T_u'-T_u)\}$$ Where $$T_{ur}^l=\sqrt{T_u^2+(W_s+W_{r}L)^2+2T_u(W_s+W_{r}L)sin{\theta}_u$$ $$T_{ur}=\sqrt{T_u^2+(W_{r}L)^2+2T_uW_{r}L\;sin{\theta}_u$$ $$T_{u}^l=\sqrt{T_u^2+W_s^2+2T_uW_{s}\;sin{\theta}_u$$ and $T_u$ represents the tension at the point on the warp, ${\theta}_u$ the angle between the direction of $T_u$ and horizontal axis, $T_u^2$ the tension at that point when a weights $W_s$ adds to the point where $T_u$ is acted on. 5. If otter boards were constructed lighter and adequate weights were added at their bottom to stabilize them, even they were the same shapes as those of bottom trawls, they were definitely applicable to the midwater trawl gears as the result of the experiments. 6. As the results of water tank tests the relationship between net height of H cm velocity of v m/sec, and that between hydrodynamic resistance of R kg and the velocity of a model net as shown in figure 6 are respectively given by $$H=8+\frac{10}{0.4+v}$$ $$R=3+9v^2$$ 7. It was found that the cross-wing type depth control devices were more stable in operation than that of the H-wing type as the results of the experiments at sea. 8. The hydrodynamic resistance of the net gear in midwater trawling is so large, and regarded as nearly the drag, that sweeping depth of the gear was very stable in spite of types of the depth control devices. 9. An area of the horizontal wing of the H-wing type depth control device was $1.2{\times}2.4m^2$. A midwater trawl net of 2 ton hydrodynamic resistance was connected to the devices and towed with the velocity of 2.3 kts. Under these conditions the depth change of about 20m of the trawl net was obtained by controlling an angle or attack of $30^{\circ}$.

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