Büyük depolama tanklarının cidar hesabı ve arayüz tasarımı
Calculating the large storage tank shell thickness and designing of user interface
Yazar: OKAN KARABUĞA
Danışman: ÖĞR. GÖR. ALİ İMRE AYDENİZ
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Makine Mühendisliği Ana Bilim Dalı / Konstrüksiyon Bilim Dalı
Derece: Yüksek Lisans, 2017
Konu: Makine Mühendisliği = Mechanical Engineering

Özet:
Endüstriyel tesislerde kullanılan en yaygın ekipmanlardan olan dikey silindirik tankların cidar kalınlıkları; konstrüksiyonun emniyeti, malzeme maliyetleri, işçilik maliyetleri, ömür açısından değerlendirilerek tasarlanmalıdır. Kalınlık artışı konstrüksiyonun ağırlığını arttırdığı gibi burkulma açısından da tasarımı zayıflatmaktadır. Bu nedenle mümkün olduğunca ince tank cidar kalınlıkları elde edilmelidir. 
Tank cidar hesabında yaygın olarak kullanılan iki yöntem bulunmaktadır. API 650 standardında önerilen bir adım yöntemi(1FM) ve değişken nokta tasarım yöntemi(VDPM) endüstriyel depolama tanklarında cidar kalınlığı hesabı için kullanılmaktadır. Tanktaki çevresel gerilmenin maksimum olduğu yer, tankın taban plakasına kaynak edildiği noktanın üzerinde gerçekleşmesi nedeniyle kalınlık hesaplarında bu yüksekliğin dikkate alınmasıyla daha ince cidar hesapları elde edilir. 1FM yöntemi taban plakasından 1 ft başka bir değişle 0,304m yukarıdan alınarak hesaplanır. Bu yöntem her zaman emniyetli sonuçlar vermektedir. Tank kalınlıkları taşıyabilecekleri yükten daha kalındır. İkinci yöntem olan VDPM ise, bir adım yönteminde alınan mesafeyi amprik bir ifadeyle hesaplayarak alır. Genellikle 0,304m'den yüksek çıkan bu değeri, daha ince cidar kalınlıklarının elde edilmesini sağlar. VDPM ile yapılan tanklar zaman zaman aşırı gerilmelere maruz kalmaktadır. Bu nedenle tasarımların sonlu elemanlar analizleri ile kontrolleri gerçekleştirilmelidir.1FM ve VDPM yöntemleri, ağır tasarımlara ya da emniyetiz tasarımlara neden olabilmektedir.
Bu tez çalışmasında Timoshenko'nun hidrostatik basınç altındaki dikey silindirik depolama tankları için yazmış olduğu denklemin sonlu farklar yöntemi(SFY) ile çözümü yapılmıştır. Deformasyon ve gerilme değerleri incelenerek hali hazırda kullanılan yöntemler ile karşılaştırılması yapılmıştır. Elde edilen çözüm koduna arayüz oluşturularak kullanışlı bir yerli tasarım programı haline getirilmiştir.
Sonuç olarak elde edilen arayüz programı ile on sekiz adet tank 1FM, VDPM ve SFY yöntemlerine göre tank cidar kalınlıkları hesaplanmıştır. Cidar kalınlıkları birinci donamda SFY ile 1FM ilk donamlarda ve ara donamlarda oldukça birbirine yakın değerler vermektedir. Farklar %1 ile %4 arasında değişmektedir. SFY sonuçları daha incedir. SFY ile VDPM ilk ve ara donamlarda %6 ile %8 farklar ile birbirine yakındır. Tank çapı 100m'den büyük olan tanklarda yüksekliklerin de artmasıyla VDPM ile SFY çözümleri arası sapmalar bir karakterin dışına çıkmaktadır. Bir sapma genellemesi yapılamamaktadır. SFY ile yapılan çözümleme bazı istisnalar dışında literatürde bulunan diğer tank kalınlığı hesaplama yöntemlerinden olan 1FM'den daha ince donam kalınlıkları vermektedir. Bu durumda burkulma riskinin azaltılması için daha ince donam kalınlıkları elde edilmiştir. Tank donam kalınlıklarının daha ince çıkması sonucunda, malzeme tasarrufu, saha işleri, işçilik maliyetleri lojistik gibi tasarım, imalat ve inşaat süreçlerinde daha ekonomik ve güvenilir bir çözüm elde edilmiştir. Yapılan çalışma program haline getirilerek, yerli sürekli kullanılabilir program haline getirilmiştir.

Abstract:
Shell thicknesses of vertical cylindrical tanks from the most common equipment used in industrial installations has great importance according to safety of construction, material costs, labor costs, life expectancy, etc.. The increase in thickness increases the weight of the construction as well as weakens the design in terms of buckling. For this reason thin shell thicknesses should be obtained as thin as possible.
The calculation of shell thicknesses in pressure and non-pressure tanks is based on the calculation of the shell thickness at which the internal pressure can carry the load. If liquid is stored in the tank, the effect of liquid static height must also be considered. Internal pressure, liquid static pressure and safety factors must be considered together to make calculations. The tank has a cylindrical, spherical or a different geometry.
There are two methods used for common in tank shell thickness calculations. One foot method (1FM) and variable design point method (VDPM) recommended by API 650 standard are used for shell thickness calculation in industrial storage tanks. 
In the industrial applications of storage tanks, tank shell thickness calculations differ in the above mentioned baselines and thicknesses in terms of tank manufacturing and material cost. Thicknesses are the largest at the bottom of the cylindrical storage tanks and the thickness at the top should be the smallest since there is no load. This makes the tank manufacturing impossible. For this reason, it is necessary to use graded thicknesses. Every step is called a course. The thickness of the course is calculated so that it will bear the liquid pressure which affects it. Each course has different thicknesses so that welded construction could be manufactured. In such a design, it seems that there will be excesses in thickness. In this case, the upper part of the lower unit could carry some amount of the upper unit's load. Thus, the fluid height could be reduced somewhat in the calculation of the course thickness. This value is obtained empirically and used as 1 ft (0,304 m). The value of the liquid height is subtracted by one foot (1 ft) from the value of the course thickness. Thus, the thicknesses calculated are thinner and the total cost is reduced. The second method, VDPM, takes the distance taken in one foot method by calculating it with an empirical expression. This value, which is generally higher than 0,304m, enables thinner shell thicknesses to be obtained. Tanks constructed with VDPM are subject to occasional extreme stresses. For this reason, designs should be inspected with finite element analysis. 1FM and VDPM methods could cause heavy designs or unsafe designs.
In this thesis study, the equation that Timoshenko wrote for storage tanks under hydrostatic pressure of vertical cylindrical tanks was solved with finite difference method (FDM). Deformation and stress values were examined and compared with the currently used two methods. By creating an interface for the obtained solution code, it has become a useful in house design program. 
In cases where the functions are given analytically, it is easy to calculate the function values at the desired points, to find the derivatives of the desired order at certain points of the function, or to calculate the integrals at certain intervals of the function. While some discrete values of the functions are known, such calculations could be approximated using finite difference method (FDM). Even where analytical solutions are evident, higher-order differential equations could be preferred in terms of ease of solution by use of finite differences. Finite difference method, solution of heat propagation equations, electromagnetic force equations, and preferred method with ease of use in nonlinear systems and solution of high order differential equations in places where structural analysis is performed. If the general equation for vertical cylindrical storage tanks is applied to the finite difference method, the fourth-order differential equation is transformed into a set of linear equations. 
In order to be able to control the accuracy of this solution by means of an experiment, it is necessary to adapt the thickness of a certain tank to a numerical method. The numerical solution of the design of the tank designed for the solution and the stress values on the tank courses must be found by numerical method. It is seen that the maximum deviation of the calculated error between the model and the experiment is -6,23%. The model we construct by the finite difference method characteristically overlaps with the experimental results although there are deviations.
The solution algorithm which was validated with the experimental results was compared with the other methods used in the literature on eighteen tanks. 
The first six tanks are recommended diameter values in the API 650 standard. The next six tanks are the tanks previously examined in the literature. The last six tanks are the tanks that are outside the standard used dimensions. 2.8m was selected for the tank course height. The stored liquid water is considered as open tanks to the atmosphere. The thicknesses obtained are shown in charts and graphs. Corrosion allowance is not included. Welding efficiency (JE) is assumed as 1,0.
As a result of the obtained interface program, tank shell thicknesses were calculated according to eighteen tanks 1FM, VDPM and FDM methods. 
FDM and 1FM are very close to each other in the first course and intermediate courses. The differences of thicknesses are range from 1% to 4%. The FDM results are thinner than 1FM. In the top course, the deviation between the thicknesses is large because the thicknesses that are too small. In other words, if the top course is close to the lower courses' heights, the deviations will be in the same order again. It is possible to make economic designs by changing the heights of the courses. FDM and VDPM are close to each other with 6% to 8% difference in initial and intermediate courses. However, there is still a big deviation as it is in the 1FM. In tanks which tank diameters greater than 100 m, the differences between the VDPM and FDM solutions are out of character by increasing tanks' heights. A deviation generalization is not possible. As a result, the analysis with FDM gives thinner courses' thicknesses result than 1FM methods in the literature. In this case, a more economical solution has been obtained for the risk of buckling in design, manufacturing and construction processes, such as thinner shell thickness, less material use, field work, labor costs, logistics. The work done is turned into a program and made available continuously.
As a result, in this study, to calculate the shell thicknesses of large storage tanks, the shell deformation equation for vertical cylindrical tanks under hydrostatic pressure of Timoshenko is solved using the finite difference method. The resulting solution code, interface and program have been prepared. Thus, a useful in house design program has been obtained.