Gemi Kirişlerinin Eğilme Ve Burulması

Abstract

Konteyner gemilerinin son yıllarda kazandığı yaygınlık sebebiyle, gemilerin dış yüklere maruz kaldığında genel davranışını incelemek için, ince çeperli gemi kirişi modelleri kullanılmaya başlanmıştır. Ambar ağız açıklıkları bugüne değin inşaa edilmiş gemilerden çok fazla olan bu tür gemilerin yüklemelere karşı lokal zorlamalarım incelemek için çok boyutlu ve karmaşık modeller gerekmektedir. Ancak ince çeperli gemi kirişleri genel davranış hakkında bir fikir vermekte, ve dizayn aşamasında daha fazla seçeneği ekonomik bir şekilde incelemeye olanak tanımaktadır. Bu tür bir modellemenin yapılabilmesi için çalışmada öncelikle kullanılacak fiziksel özelliklerin tamım yapılmış, daha sonra inceleme konusu olan eğilmeli burulma zorlaması için hareket denklemleri çıkartılmıştır. Sayısal örnek olarak en kesiti parabol olan prizmatik bir dubanın davranışı Galericin yöntemi ile incelenmiştir. Bu inceleme bilgisayar teknolojisi ve teorik matematiği bir araya getiren MATHEMATICA programı ile yapılmıştır. Yapılan çalışmada kullanılan formülasyondan yola çıkılarak, gerekli eklemler ve uygunluk şartlarının da modele katılmasıyla duba problemleri dışında, kesit özellikleri farklılık gösteren gemilere de uygulamak mümkündür.

Bending and Torsion of Ship Beams During the last decade the importance of torsion of thin walled cross sections has grown significantly. Earlier it was unusual to check the influence of torsion on load carrying structural elements, but today it is quite often that stresses and defor mations caused by torsion will determine the scantlings of the structures. There are two important factors that have contributed to that development: continuously grow ing accuracy of calculations and therefore reduction of the factor of uncertainties; and the development toward use of thin walled cross sections instead of solid beams and columns to obtain optimal weight strength ratio. In the field of ship structures this development is very clear. As an example one could mention the hull of a modern container ship. Here a complicated torsional situation will decide over the structural design of the cross section of the hull. But also in the field of bridge constructions and advanced building constructions thin walled cross sections are widely used as load carrying elements, where torsion is a decisive factor. In most cases cross sections of thin walled prismatic beam will warp when tor sion loads act on the beam. Because the supports and connections will resist such a warping, stresses, in many cases significant, will arise in the beam. There exist ad vanced numerical methods, like the finite element method, that can be used to ana lyze the stresses that are caused by restraint warping. But the cost of such a calcula tion is very high, and will just in few cases be economical. Therefore, it is of great interest if one could use a beam theory, which includes the stresses and strains, caused by warping. In this study the behavior of a prismatic thin walled beam thin walled beam under torsion load is investigated. The basic assumptions for the study are as fol lows.. The material is elastic, isotropic and obeys Hooke's law.. The beam is straight before loading and there is no local buckling or other deformation of the cross section.. The longitudinal normal stresses and in-plane shear stress are the only sig nificant stresses.. The loads are conservative.. The deformations are sufficiently small that the usual assumption about curvature can be made. In the first chapter basic definitions are given, which are important to under stand the problem. The literature on applications to ship structure is listed. In the second and third chapters, the governing equations of the problem are derived. The numerical part of the study deals with the solution of the behavior of a prismatic thin walled pontoon with parabolic cross section under horizontal moment, vertical moment, and torsional moment loads caused by the waves. The magnitudes and the distribution of the loads are determined from the experimental and statistical solutions. Figure 1 The cross section of the pontoon Figure 2 Pontoon with parabolic cross section The equations of motion derived in chapter three are rewritten for the problem. The system of equations are coupled and take the symetry of the cross section into account. XI EAu"2+p2=0 (1) GIpp(u:-Q'y)+GIpM-Vhpx =0 (2) GIqM-Q'*)+Py=° 0) -EIxe:+GIqil(u'y-ex)-mx=0 (4) ^e;+G//7p(w;-e,)+G//!r(e;-e)+^ =0 (5) GI^l-Q^+GKQ' + GT, (ul-Q'y )+mT = 0 (6) G/^+G^e-eO+G/^e; -e)+G/pr(< +e,)-,^ =o (7) The closed cross section of the beam consists of only one cell. As a first step, cross sectional properties are determined analytically. The unknown functions are, {ux,uy,uz,Qx,Qy,Qz,Ql (8) The boundary conditions and the load terms are such, that the displacement along the pontoon's longitudinal axis uz (Eq. 1) vanishes. Thus the system is reduced to six equations. The numerical method used to solve these equations is the Galerkin method, which is a member of the weighted residual methods. The weighing func tions are chosen as polynomial functions which satisy the boundary conditions of the "free-free" beam problem. xn ux=Y,aiXM ^=2v+1 ;'=1 /=1./+!.?-tiff °-P(i, S/+1 ' x ] Y+1 (9) The MATHEMATICA system is chosen to solve the problem.The reasons why MATHEMATICA was chosen and a brief introduction to the MATHEMATICA system are given in the APPENDIX section.