Betonarme köprülerin hareketli trafik yükü altında davranışı

Abstract

İnşaat Mühendisliğinin geniş çalışma alanlarından bir tanesi köprü tasarımıdır. Ağır lokomotif ve katar yükleri için tasarlanan demiryolu köprüleri günümüzde karayolu ağlarının hışla artması ile yerlerini karayolu köprülerine bırakmaktadır. Bu köprülerin tasarımında değişik özellikleri göz önüne alınmalıdır. Betonarme köprülerin trafik yüküne verdiği yanıt bu çalışmanın esas konusudur. Betonarme bir köprü üzerinde hareket halindeki araçlar kütleleri, yayları ve amortisörleri ile birer dinamik sistemdirler. Bu çalışmada tek bir araç, tek serbestlik dereceli dinamik bir sistem olarak modelleştirilmiş ve sabit hızla ilerleyen bu araca köprü tarafından verilen yanıt incelenmiştir. Bu davranışın incelenmesi için bazı basitleştirici kabuller yapılmış, başlangıç ve sınır koşulları belirlenerek, hareketin diferansiyel denklemle ri çıkarılmıştır. Bu denklemler Eunge Kutta Gill yöntemi ve bir bilgisayar programı yardımı ile çözülerek, açıklık orta kesitine ait düşey yerdegiştirmeler ve eğilme momen ti değerleri bulunmuştur. Hesaplarda kullanılan köprü eğilme rljltligi El, araç kütlesi M gibi bazı parametre ler değiştirilerek hesaplar tekrarlanmış ve sonuçlara ait diyagramlar çizilmiştir. Tüm sonuçlar kütlesiz hareketli tekil düşey bir yüke verilen yanıtlarla karşılaştırılarak değerlendirmeler yapılmıştır.

This study is concerned with the aspect of the problem of highway bridge response to moving traffic loads. It is obvious that both deflections and stresses in a bridge subjected to a dynamic moving load will differ from- the deflections and stresses which would be caused by a load applied statically. Each vehicle passing the bridge is actually a dynamic system with its mass, mechanical springs and schock absorbers. This dynamic character constitutes a time-varying load. Highway bridge designers have acknowledged the effect of this dynamic load by adding an impact factor to the static live load. This factor is related to the length of the span. It is only in recent years that numerical results in quantity have been attainable by the use of electronic computations. Presently considerable ^interest in highway bridge vibration is concerned with two needs: namely, a means to predict vibration to a given design, so as to avoid designs which would vibrate excessively and a means to predict dynamic live load stresses", so that material of construction can be used safely but with economy. Engineering has long recognized that, apart from the safety of bridges, which may be handled in terms of stresses, it is desirable to avoid excessive dynamic deflections because of the discomfort and apprehension which these may cause the public, particularly the pedestrain public. The number of highway bridges continues to increase at a rapid rate. It is worthy of note that a large percentage of these bridges have grade seperations, joints, humps, cracks and other forms of roughnesses, which may cause vibrations. Although real bridges may experience the effects of several vehicles concurrently. At this study the consideration is limited to a single vehicle. vi To solve the problem and to compute the responses of the bridge under the dynamic load effect, some assumptions had to be made. Such as: The bridge is accepted as a simply supported beam. The vehicle is idealized as a single degree of freedom system. The entire vehicle weight is applied to the bridge at the center of the vehicle mass. Considering the assuptions and initial conditions, the modal equations have been written. It is possible to obtain infinite equations for infinite modes. This study considers only three modes. The differential equations have been solved by using the Kunge Kutta Gill method and a computer program. The inputs of the computer program are the geometrical and mechanical characteristics of the bridge and the vehichle. Following values have been obtained as computer outputs. 1) Dynamic deflections of each mode and dynamic deflections at midspan. 2) Bending moments. Some parameters like the flexural rigidity of the bridge EI, vehicle mass M have been varied by the inputs and various solutions have been obtained. The graphics of the different results have been drawin. All these results are examined and compared with the results of the effect of moving massless single vertical force P. The context of this study submitted as a M. Sc thesis is composed of the following chapters. Chapter 1- Introduction: General information is given about the subject. Chapter 2- The purpose of the study and the methods and the principles to be used by the calculations have been explained by this chapter. Chapter 3- The idealised bridge and vehicle. The parameters and values to be used by the computation. The assumptions. vii The differential equations for the response to the dynamic moving load. The differential equations for the response to the moving massless single vertical force P. Chapter 4- General Informations about the Runge Kutta Gill method and the computer program. Input values for the computer program. Runge Kutta Gill method has been used to solve system of the differential equations. Runge Kutta Gill method is a numerical technique to approximate initial value problems. In this study, the problem is to solve differential equations like; y' = f At one side of the equation there is the derivative of the dependent variable, at the other side a function of this variable and other variables. The expressions to be used are as follows. K = fn, where o>n is the frequency for the n'th mode, which do not safisfy above obtain diverging solutions. bridge natural For values of At conditions, we The computer inputs are the geometrical and the mechanical parameters of the vehicle and the bridge. The computer outputs are the vertical dynamic deflections at midspan and the bending moments. Chapter 5- Drawings according the computer output values. Comparisons and conclusions about the results. CONCLUSIONS In view of the comparisons of the drawings conclusions have been done. following The responses to the dynamic definitely from the responses to single vertical force P. moving loads differ the moving massless The bending moments, particularly the midspan deflection diagrams show quite different characters. These differences indicate clearly, that the effect of the dynamic character of the load is not a matter to be neglected. Bridge elastic rigidity EI and vehicle mass M are major parameters for the response to the dynamic moving load and for the response to the moving massless single vertical force P. The magnitude of dynamic deflection is seen to depend upon parameters os vehicle natural frequency, M vehicle mass, EI bridge flexural rigidity m bridge mass per mode, o> bridqe natural frequencies for each mode. m " The bending moment diagrams have also similar characters as deflection diagrams. Both deflections and bending moments of the response to the dynamic load differ from the deflections and bending moments which are coused by the load applied staticaly. Responses to dynamic load show many variations depending on many parameters like vehicle mass, bridge flexural rigidity, frequencies of bridge and vehicle. For this reason the dynamic effects of traffic loads have to be accounted considering those parameters. To define the dynamic effects by increasing the static live load by an empirical factor which depends only upon bridge span length, seems to may cause an under or overestimation.