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ÖZET Günümüzde bir seferde daha çok yük taşıma problemi, gemilerin büyümesine, dolayısıyla da boylarının uzamasına sebep olmuştur. Bu durumda gemilerin enine mukavemeti kadar boyuna mukavemeti de çok önem kazanmaktadir. Bu çalışmada ilk önce gemilerin boyuna mukavemeti teorik olarak anlatılmıştır. Burada kabul edilen dalga sistemleri, geminin bu dalga sistemindeki konumları ve sonuçları, gemi üzerindeki ağırlık gurupları ve dağılımı, sephiye eğrisinin elde edilmesi, yük, kesme kuvveti ve eğilme momenti eğrilerinin elde edilmesi ve karakterifcikleri, gerilme ve sehim değerleri ve gemi üzerindeki maksimum kesme kuvveti ve eğilme momenti için yaklaşımlar verilmiştir. Daha sonra, sınıflandırma kuruluşlarından Det Norska Veritas, American Bureau of Shiping, Germanisher Lloyd ve Nippon Kaiji Kyokai' nın boyuna mukavemet için vermiş olduğu en son kriterler incelenmiş ve birbirleriyle karşılaştırılmışlardır. Ardından, örnek gemi olarak alınan 18,000 DWT' luk BOLÜ (-B- Sınıfı) gemisinin, seçilen yükleme durumu için, sınıflandırma kuruluşlarının belirlemiş olduğu kriterlere göre boyuna mukavemet değerleri hesaplanmıştır. Boyuna mukavemet hesabı için bir bilgisayar programı yapılmış ve aynı programla seçilen örnek gemiye ait, önceden belirlenmiş olan yükleme durumu için, kesit- lerdeki kesme kuvvetleri, eğilme momentleri ve gerilme değerleri hesaplanmıştır. Program, bu hesap yönteminde kullanılan standart değerlerle sınırlı kalmamış, kullanım sahasını genişletmek amacıyla gemi yapısına ve dalga for¬ muna ait değerlerin girilmesine de imkan vermiştir. Ayrıca, program, çabuk ve yaklaşık değerler elde etmek is¬ teyen kullanıcılara da kolaylık sağlamak amacıyla gemi üzerindeki kesit atalet momenti dağılımı eğrisi ve dalga profili eğrisi gibi değerlerin standart durumlarını da kullanıcıya seçenek olarak sunmaktadır. Sonuç olarak, 18,000 DWT' luk BOLÜ gemisinin sınıflandırma kuruluşlarına ve yapılmış olan boyuna mukavemet programına göre hesaplanan boyuna mukavemet değerleriyle bir arada sunulmuş ve sonuçlar birbirleriyle karşılaştirılmıştır. INVESTIGATION of COMPERATIVE LOHGITODINAL SHIP STRENGTH SÜMMARY Nowadays, the desire of carrying large amounts of cargo at önce, make Bhip owners order bigger ships. The increasing of length of ships brings the problem of lon- gitudinal strength. Although,as a solution, longitudinal framing system is used, the longitudinal stregth is stili the most importent subject för containers and bulk carriers. After having established the principal diraensions, form and general arrangement of the ship, the designer is faced with the problem of providing a struc- ture capable of withstanding the forces which may be im- posed upon it. The hull of a steel ship is a most complex structure. it is unique in the field of engineering struc- tures in that it is primarily a plate structure depending for its majör over-all strength on the plating of the shell, decks and in some cases the inner bottom and the longitudinal bulkheads. The framing members, each of which has its own function to perform, are designed primarily to maintain the plate members to the planned contours and their position relative to each other when subjected to the external forces of water pressure and breaking sea as well as the loads which may be imposed upon it very con- siderably and in many cases are indeterminate. As a result, those responsible for the structural design of ships must be guided by established standarts adopted after many years of every increasing application of scien- tific princples carefully checked from particular ex- periences with ships in service. in general, the problem of the development of a satisfactory structure involves the following considera- tions : (a)it is necessary to establish the sise of and to combine effectively the various component parts so that the structure, with a proper margine of safety, can resist succesfully the majör over-all stresses resulting from longitudinal and traverse bending (ör a combination of both) in stili water and among waves. (b)it is necessary to design each component of part so as to withstand succesfully to the local loads imposed upon it from water pressure, breaking seas, the weight of deck houses, heavy machinary, masts and so on, including such additional margines as somtimes may be required to süit unusually severed conditions encountered in operation.in the consideration of the over-all longitudinal strength, the entire ships hull is considered to be a gir- der having a varying load througout length corresponding to the weight of the structure and its comtents. The sup- porting forces are those resulting from the buoyancy dis- tribution throughout the displacement length. When there is a balance between the total downward forces of weight and total upward forces of buoyancy and the centers of ac- tion of these two forces coincide longitudinally, the ship is in equilibrium; even so there normally will result an excess of buoyancy över weight througout certain portions of the length, counterbalanced by an excess of weight över buoyancy throughout the remaining portions. These excesses of upward and downward forces creat conditions of shear forces and bending moments in the same manner as in ordi- nary beams. it is quite possible, by means of simple approximations, to establish with a reasonable degree of accuracy, the general characteristics of the weight curve and in the case of ships operating in smooth water exclusively, the buoyacy curve can be determined easily, so that the shearing forces and bending moments under any condition of load can be estimated accurately. For ocean going ship, there is dearth of information, as to just what are the most sever conditions that a ship might reasonably be expected to encounter, so that för the purpose of assessing för the longitudinal strength requirements on a comperative basis betveen structures of the same general type there has been adopted what is termed a standart wave in association with which buoyancy curves ör curves of supporting forces can be developed. The standart wave is assumed to have a length from crest to crest equal to the length of the ship. Its contour formes to that of a trochoid, having a depth from crest to trough can easily be defined with the help of rules of different classifisation societies. it is cus- tomary to consider the vessel either poised on a wave, with a crest at the middle of the length and a trough at each end ör as bridging two crests, with öne at each end and a trough at amidship. The former condition induces what is termed a `hogging moment` (öne which tends to depress the ends of the ship inducing tension in the deck and compression in the bottom) and the later condition in¬ duces what is designated as the `sagging moment` (öne which tends to depress the ship at amidship inducing com¬ pression in the deck and tension in the bottom). in some investigations, calculations are made with crest of a standart wave, located at regular inter- vals along the length of the vessel and the peaks of the bending moment curves, so obtaine för both hogging and sagging, are then connected into two curves called the `envelope curves` for the maximum hogging and saggingconditions. However, it has been found that, the standart calculations with either a crest ör hollow at the middle of the lenth, are sufficient to indicate whether ör not there are present any abnormal conditions of form of weight distribution, as to make it desirable to provide the margines in the over-all longitudinal strength över and above the established standarts. in this thessis, both hogging and sagging conditions are tried to be applied to the same ship in order to compare the results. When the srength of a ship is investigated, the first thing to be done is to work out the total weight ör displacement of the ship and longitudinal position of its centre of gravity for the particular condition of loading being considered. At the begining we have to determine ali the hydrostatic values of the body form and draw the Bon- Jean curves of area. The problem is then to find the dis¬ tribution of buoyancy which will give these values of dis¬ placement and centre of gravity so that the ship shall be in static equilibrium either in stili water ör on the wave. in the stili water from the total weight of the ship the draught of which the ship afloats can be easily determined from the Bon-Jean curves of area. But this is a very dificult task to find the accurate position of ship on a wave. Because of the wave form and the adjustment of wave on the ship, the displacement and the centre of gravity values might not be equal to the values determined from the load distribution. For the approximate position of the wave we need some approximations to correct the wave position. After getting the buoyancy distribution, we need to determine the weight distribution on the ship. For this, we divide the weight of deadwight and lightweight items in groups as tanks, cargo holds, machinery, ete. and calculate the weight distribution over-all the ship. The load on the structure at any point in the length of the ship is the dlfference between the weightper unit length and the buoyancy per unit length. By taking the difference between buoyancy curve and weight curve forms a curve of which usually called the load curve. The total area enclosed by the load curve should be zero this means equivalancy that the total verticle force on the ship is zero. This is, öne of the conditions of the static eguilibrium. Similarly, the total moment of the area of the load curve about any point shoul be aero to satify the other condition of static equilibrium. The tabular method of integration, for integrat- ing the load curve, is öne which is used very frequently nowadays.lt is particularly suited where the stepped type of weight curve has been employed. The sum of load curve for each section multiplied by length of section l, will give us the shearing force at any point. Second summation will be made for determinig the bending moment. xiFor the two conditions, as the ship on a wave either with crests at the perpendicular ör with a crest amidships, it is possible to state some general charac- teristics of shearing force and bending moment curves. Since the ship is freely supported, both the shearing force and bending moment must be zero at each ends. The bending moment curve rises to maximum value at ör about amidships, although in some instances of very un- symetrical loading the maximum bending moment may be some distance from amidships. Because of the relation of shear¬ ing force and bending moment, it follows that where the bending moment is maximum the shearing force is zero, so that in general the shearing force will be zero at amidships. The greatest values of the shearing force occur towards the end of the half length amidships. The position of the wave relative to the ship has an influence on the position of the maximum bending moment. If the wave is assumed to be in some position in- termediate between the two conditions which have been dicussed, it will be found that the position of the maxi- mum bending moment moves from amidships but the value of the maximum will be less. it will be seen that the two basic conditions assumed, as sagging and hogging, will yield the greatest bending moments and for ali purposes these greatest bending moments occur at amidships. in addition to wave form weight distribution has a great influence on the bending moments over-all the length of the ship. Generally, it may bee stated that con- centration of weight near the points of support will result in smaller bending moments than if weight vere con- centrated away from the points of support. This means that the sagging condition concentration of loads near amid¬ ships will result in high bending moments, and in the hog¬ ging condition weights concentrated towards the ends of the ship will lead to high bending moments. To obtain a weight distribution which give the minimum wave bending moment for a given displacement of the ship, the wave bending moment in both sagging and hogging conditions should be worked out. For the calculation of longitudinal ship strength, a computer programe is formed for any load and buoyancy distributions chosen by the user. in addition to this, programe is able to give the chance of choosing some standart values used in the calculations, as the height of the wave form and the distribution of moment of inertia över the entire length of the ship, for getting quick and approximate results of load distribution shear forces and bending moments on the sections choosen and the hydros- tatic values of the vessel, if required. in the other part of this thessis, the rules of some clasification societies, mostly prefered in our country, were subjected and the requirements, as the load distribution, maximum shear forces and bending moments, xiisection modules and moment of inertia of the chosen sec- tions about the transverse neuteral axis were compared. in the final part, a bulkcarier, of 18,000 DWT, named BOLU, was chosen as an example and the requirements of clasification societies vere utilized for the chosen load distribution which is reguired in the rules. Later the results, calculated by the computer programe of lon- gitudinal ship strength, for the same load distribution and results determined from rules were compared in order to recognize the accuray of the rules. 246

Cutting stock problems rank among the first applications ofoperations research and they have been implemented in a wide range ofopepations for optimization of cutting and allocation problems.In this study, a cutting stock procedure is developed for theslitting operation of sheet metal rolls for a multi-plant firm whichproduces durable household goods. The objective is set as minimizationof work-in-prbcess accumulation of sheet-metal parts and also avoidingshortages of these parts. This is the main difference of this procedurefrom the existing ones which seek the solution with minimum wastage.Theprocedul'e has been implemented in the firm and the resultsha ve been encouraging . 74