Su Depolarında Rijitlik Frekans İlişkisi

Abstract

Yapılan bu tez çalışmamızda bir su deposunun rijitlik, frekans ilişkisini incelemek amacıyla üç farklı grupta modellemeler yapılmış ve sonuçları gözlemlenmiştir. Rijitlik, bir yapının yükler karşısında stabil kalabilme yeteneğine verilen isimdir yani, elastik cisimlerin ve yapıların ötelenme ve yer değiştirme tesirlerine karşı koyma derecesini ifade eder. Frekans veya titreşim sayısı bir olayın birim zaman (genel olarak 1 saniye) içinde hangi sıklıkla, kaç defa tekrarlandığının ölçümüdür, matematiksel ifadeyle periyodun çarpmaya göre tersidir birimi s-1 veya Hertzdir. Bir olayın frekansının ölçmek için o olayın belirli bir zaman aralığında kaç kere tekrar ettiği sayılır, sonra bu sayı zaman aralığına bölünerek frekans elde edilir. Yapılan bütün çalışmalar, (modelleme, analiz, sonuç tabloları), SAP2000 isimli bilgisayar programında sonlu elemanlar yöntemi kullanılarak yapıldı. İlk model gurubunda yapının aks bilgileri değiştirilmeden içerisinde bulunan su miktarı değiştirilmiş ve analiz yapılmıştır. İkinci gurupta ise yapı içerisinde su bulunmayacak şekilde değiştirilmiş ve yapının yüksekliği kademeli olarak artırılmıştır. Üçüncü ve son gurupta ise benzer şekilde yapının içerisinde su bulunmadan, perde kalınlıkları değiştirilerek analizler yapılmıştır. Yapılan bütün modellemelerin analiz sonuçları karşılaştırıldığında yapının rijitliğinde görülen değişmenin frekans ve periyot değerlerine etkisi görülmüştür. İlk model gurubunu incelediğimizde üstü tamamen açık olan su depomuzun (3 metre yüksekliğinde 5 metre genişliğinde ve 10 metre uzunluğunda) içerisinde bulunan su yüksekliği 0, 1,5 ve 3 metre olacak şekilde üç farklı model tasarlanmıştır. Yapılan bu modellemelerin analiz sonuçları karşılaştırıldığında frekans değerlerinde herhangi bir değişiklik gözlemlenmemiştir. Aynı modellemeler bu defa üstü kapalı olacak şekilde tasarlanıp analiz sonuçları gözlemlenmiştir. Bu modellemelerde de değişen su miktarı frekansa etki etmemiştir. Üstü kaplı model açık modele göre daha rijit olduğundan dolayı frekans değerleri daha düşük çıkmıştır. İkinci model gurubumuzda yapı içerisinde su bulunmamaktadır, yapının yüksekliği 2,4,6,8,10 ve 12 metre olarak değişitirilmiş olup altı farklı model tasarlanmış ve analiz sonuçları kayıt altına alınmıştır. Sonuçlar göstermiştir ki yapının yüksekliği arttıkça, yapının kütlesi artıp rijitliği azalacağından dolayı, beklenen şekilde frekans değerlerinde düşüş gözlemlenmiştir. Aynı gurubunda ikinci kısmında aynı modeller yapının üstü kapalı olacak şekilde tekrar tasarlanıp analizler yapılmıştır. Bu analiz sonuçlarına baktığımızda, üstü açık benzer şekilde frekans değerlerinde, yükseklik arttıkça, düşüş gözlenmiştir. Ayrıca bu modellemeler, üstü açık modellere göre, kütlesi daha fazla olduğundan dolayı frekans değerleri daha küçük gözlemlenmiştir. Üçüncü ve son model gurubunda ise yapının içerisinde su bulunmamaktadır yapının perde duvarları 5,10,15 ve 20 cm olacak şekilde dört farklı model tasarlanmış ve analiz sonuçları incelenmiştir. Yapıda bulunan taşıyıcı perde duvar kalınlığı artması dolayısıyla yapının rijitliği artmış ve beklendiği üzere frekans değerleri artmıştır. Gurubun ikinci kısmında aynı yapılar üzeri tamamen kapalı olacak şekilde tekrar tasarlanıp analiz sonuçları kayıt altına alınmıştır. Sonuçlar da benzer şekilde olup, perde kalınlığı arttıkça frekansta artış gözlenmiştir. İki kısım modelleri karşılaştırdığımızda, beklenen şekilde üstü kapalı gurubun frekans değerleri daha yüksek gözlenmiştir. Sonuç olarak yapılan bu çalışma göstermiştir ki rijitliği artan yapının frekansı her şart altında artmamaktadır. Bazı durumlarda kütledeki artış daha baskın olabilmektedir.

The aim of this study is to find a connection between stiffness and frequency at a water tank. Stiffness is the rigidity of an object the extent to which it resists deformation in response to an applied force. The complementary concept is flexibility or pliability; the more flexible an object is the less stiff it is. The stiffness of a structure is very important in many engineering applications, so the modulus of elasticity is usually one of the primary properties when selecting a material. For example, less modulus of elasticity is needed when flexibility is required. The stiffness, k, of a body measure of the resistance offered by an elastic body to deformation. For an elastic body with a single degree of freedom (DOF) is proportion of force applied on the body and displacement produced by the force along the same degree of freedom. Period is the time needed for one complete cycle of vibration to pass a known point. Period and frequenc are in an inverse proportion. For example, while the period increasing frequency will decrease. Period eqals to total time divided by the number of cycles. Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency, which emphasizes the contrast to spatial frequency and angular frequency. Calculating the frequency of a repeating event is accomplished by counting the number of times that event occurs within a specific time period, then dividing the count by the length of the time period. The period is the duration of time of one cycle in a repeating event, so the period is the reciprocal of the frequency. Frequency is an important parameter used in science and engineering to specify the rate of vibration phenomena, such as earthquakes. The unit of frequency is the Hertz (Hz) and also s-1. Mass is a speciality of a physical body. It is a measure of a object's resistance to accelerationwhen a force is applied. Mass is not the same as weight, even though we often calculate an object's mass by measuring its weight with a spring scale, rather than comparing it directly with known masses. An object on the moon would weight less than on the earth. But mass never changes. A water tank is a container for storing liquid. The need for a water tank is as old as civilization, to provide storage of water for use in many applications, drinking water, irrigation agriculture, food preparation, etc. during history wood, ceramic and stone have been used as water tanks. These containers were all naturally occuring and some man made and a few of these tanks are still in use. Various materials are used for making a water tank; plastics, fiberglass, concrete, stone, steel. Water tanks are an efficient way to help developing countries to store clean water. By design a water tank must not harm to the water. Water is susceptible to a number of amount negative influences, viruses, changes in pH and accumulated gas. In this study we analyzed a concrete water tank in three groups. At the first group of the structure has same measurements, (3 meters height, 5 meters width and 10 meters length), but the water level changes from 0 to 3 meters. This group has two sections. Firstly, the top of structure totally open and secondly, the top of structure totally closed. The second group of the structure has no water and the height is being changed from 2 to 12 meters. This group has two sections. Firstly, the top of structure totally open and secondly, the top of structure totally closed. The third group of the structure has no water and the thickness of the concrete wall is changed from 5 to 20 centimeters. This group has two sections. Firstly, the top of structure totally open and secondly, the top of structure totally closed. All models analyzed with SAP2000 with finite element method. At the first group there are two sections and six different models. The top surface of first section is totally open, there is a completely contact between water and air. The first model of this group has no water. The second model of this group has 1,5 meters depth of water. The third and last model this group is totally full of water (3 meters of water depth). The top surface of second section is totally closed. The fourth model of this group has no water. The fifth model of this group has 1,5 meters depth of water. The sixth and last model this group is totally full of water (3 meters of water depth) All of this models are analyzed and observed theirs frequency. It is seen obviously the change of water depth has no effect to structures frequency. If we compare two section of this group, with same water level, the closed section is much more rigid than open section and the frequency of closed sections are smaller. For example, the first model is totally open and there is no water inside it and the frequency is 0,061217. The second model is also totally open and there is 1.5 meters water level and its frequency is 0,061217. The fourth model is totally closed and there is water level and its frequency is 0,049517. The fifth model is also totally closed and there is 1.5 meters water level and its frequency is 0,049517. At the second group there are two sections also but twelve models. Both sections have no water. The top surface of first section is totally open. The first model's height is 2 meters. The second model's height is 4 meters. The third model's height is 6 meters. The fourth model's height is 8 meters. The fifth model's height is 10 meters. The sixth and the last models height is 12 meters. The top surface of second section is totally closed. The seventh model's height is 2 meters. The eighth model's height is 4 meters. The ninth model's height is 6 meters. The tenth model's height is 8 meters. The eleventh model's height is 10 meters. The twelfth and the last models height is 12 meters. All of these models are analyzed and observed their frequency. The result of analyses are as expected, while the height of structure is increased the stiffness of the model is decreased. Therefore, the frequency is increasing. If we compare two section of this group generally the closed section is much more rigid than open section and the frequency of closed sections are bigger. But the first model of two sections which have 2 meters height, the change of the frequency different. The first model of this groups frequency is, which has 2 meters height and totally open, 0,031833. The first model of the second group's frequency is, which has 2 meters height and totally closed, 0,047303. It means the increasing of mass has much more effect on the frequency than the increasing of stiffness at these two models. At the third and the last group there are two sections and eight models. Both sections have no water. The top surface of first section is totally open. The thickness of concrete wall of structure is 5 cm at the first model. The thickness of concrete wall of structure is 10 cm at the second model. The thickness of concrete wall of structure is 15 cm at the third model. The thickness of concrete wall of structure is 20 cm at the fourth model. The top surface of second section is totally closed has same thickness. The thickness of concrete wall of structure is 5 cm at the fifth model. The thickness of concrete wall of structure is 10 cm at the sixth model. The thickness of concrete wall of structure is 15 cm at the seventh model. The thickness of concrete wall of structure is 20 cm at the eighth model. The result of analyses are as expected, while the thickness of concrete wall of structure is increased the stiffness of the model is increased. Therefore, the frequency is increasing. If we compare two section of this group the closed section is much more rigid than open section and the frequency of closed sections are bigger. For example, the first model of this group, the thickness of concrete wall is 5 cm and totally open, its frequency is 4.0878. The second model of this group, the thickness of concrete wall is 10 cm and also totally open, its frequency is 8.1739. The fifth model of this group, the thickness of concrete wall is 5 cm and totally closed, its frequency is 12,247. After all the results above increasing of the stiffness (decreasing of structure height, increasing the thickness of concrete wall, changing top surface condition open or closed, etc.) does not increase the frequency allways. If we look the second group of study we can realize that at some conditions increasing of mass has much more effect on the frequency