Hareketli yükler altındaki köprülü kren kirişlerinin dinamik davranışı
Bu çalışmada, üzerinde hareketli yükler bulunan köprülü kren kirişlerinin dinamik davranışını be-lirlemek amacıyla bir Berneuolli-Euler esnek kiriş sistemi incelenmiştir. Bilgisayar analizi SAP 2000 programında modelleme yapılarak gerçekleştirilmiştir. Dinamik analizlerde Newmark doğru-dan zaman integrasyonu metodu ve oransal sönümleme tercih edilmiştir. Yükün hareket hızının ve kiriş kütlesine olan oranının farklı değerleri için kirişin dinamik davranışı diyagramlarda verilmiş-tir. Kren kirişlerinin dinamik davranışı, üzerindeki hareket eden yükün hareket hızına ve kütlesine bağlı olarak değişmektedir. Hareket eden yük, kiriş sisteminin tabii titreşim frekansını değiştirmekte ve yük kiriş üzerinde ilerlerken kiriş sistemi farklı titreşim yapmaktadır. Yükün hızı arttıkça maksi-mum yer değiştirmenin oluştuğu yer, kiriş orta noktasından ileriye gitmektedir. Bazı hız değerleri için maksimum nokta orta noktanın gerisinde de olabilmektedir. Kirişin hareketi dinamik olduğun-dan bazı durumlarda, yük statik olarak maksimum yer değiştirme oluşturacak orta noktada iken, kirişin hareketinin zıt yönde olabilmesiyle orta noktada maksimum yer değiştirme oluşmamaktadır. Kren kirişlerinin tasarımında verilen kiriş uzunluğuna göre kiriş orta noktasının yer değiştirme miktarının tasarım açısından yeterli olamadığı gösterilmiştir. Maksimum noktanın kiriş üzerinde sabit bir yerde oluşmamasından dolayı kiriş üzerinde hafif konstrüksiyon veya diğer nedenlerle oluşturulan kesit süreksizlikleri yüksek hızlarda çalışması düşünülen krenlerde risk oluşturmakta-dır. Ağır şartlarda hızlı çalışacak krenlerin hizmet ömrünün belirlenmesi için tasarım aşamasında kren kiriş sisteminin dinamik davranışının hassas olarak belirlenmesi zorunludur. Kaldırılacak yü-kün miktarı ve arabanın hızı, taşıyıcı kiriş sisteminin dinamik özellikleri dikkate alınarak yapılacak hesapların daha doğru olacağı gösterilmiştir.
Dynamic analysis of overhead crane beams under moving loads
In this study dynamic behavior of Overhead Crane beams is investigated. A Bernoulli-Euler thin beam under moving (carriage) load is studied. Computerized analysis was carried out in SAP 2000. Moving load or loads are applied to the system by lanes which can be determined on the geometry of beam structure. For frame finite elements this lane is placed on the axis of the beam and goes parallel to throughout whole length of the beam. For shell, area and solid elements lane or lanes can be determined on the upper plates of the beam structure. The computer program allows obtaining time history analysis for very short time interval. In the dynamic analyses linear transient direct integration method called Newmark method was used. Structures under moving loads have been studied for more than a hundred years. Early studies were made by some scientist who studied on dynamic behavior of railway bridges and motorway bridges. The need of high speed transportation, aviation and sky stud-ies and high speed precision machining studies in-creases the importance of the subject. Beside deflec-tions due to self weight of the beam and the static effect of moving load on it, it is obvious that dynamic deflections occur due to interaction of moving load and the beam vibration. The total deflection may be much higher than static deflection. Analysis carried out the mass ratios (mass of the load/mass of the beam m/M) 0.2, 0.5, 0.8 and for load velocities of 0.01, 0.5, 1.25, 2.5, 4, 5 and 6.25 m/s. Dynamic response of the beam was obtained depending on the mass ratio of the load to the mass of the beam and the velocity of the load. Dynamic response of crane beams depends on velocity and mass of moving load. Since the position of the mov-ing mass on the crane beam changes, it causes changes in the natural frequency of the system. While the load moving, depending on the position of the mass of load the vibration of the system varies. Generally, if the velocity of the load increases, the position of the maximum response on the beam oc-curs far from the midpoint. At very high speeds the maximum deflection of the beam occurs close to the end of the beam. For some values of the velocity the maximum response may occur before the middle of the beam. Dynamic response of very slow carriage velocity of 0.01m/s is, with an error in a thousand, very near to static deflection of the beam when the carriage is at the middle of the beam. At very slow speeds maximum deflection of the beam occurs near the middle of the beam because the system reduces to a quasi-static solution. For same mass ratio when the velocity of the load increases, the deflection of the beam goes higher. The dynamic behavior of the beam is more affected from the velocity of load than mass ratio of the sys-tem. Since the maximum point is not at a definite point throughout the beam length, every section on the whole length of the beam may be under high stress. For light construction or other needs in the design of the crane beams there can be desired sec-tion discontinuities. But, if an overhead crane will run at high speeds, the section discontinuities of the beams may cause risk of destruction. It is very im-portant to determine dynamic behavior of beam sys-tem of overhead cranes which is desired to use at heavy condition. Generally, today to avoid uncontrollable vibration, overhead cranes work at very low speeds and the design of these cranes is made due to FEM (Federa-tion Europenne de la Manutention) and DIN (Deutsches Institut für Normung) standards. To eliminate dynamic effects some magnification con-stants are used. Usage of above mentioned stand-ards in designing of high speed crane beams will be insufficient. Global competition and serial service needs will direct manufacturers to build high speed cranes and it is necessary to define dynamic effects of high speed motion of carriage on the crane beams. This work aims to study dynamic behavior of over-head crane beams under moving loads and to give engineers some idea in the design of crane beams. It is showed that carrying analysis in terms of only the midpoint deflection or midpoint stresses in engineer-ing calculations of the beam systems is insufficient. Taking into account the mass and velocity of the moving load and dynamic properties of carrying system in dynamic analysis brings out more accurate results.
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