Dissertation
Dissertation > Industrial Technology > Building Science > Building structure > The system structure of the rod > Rod structure > Frame

Study on the New Methods for Dynamic Stability of Frame Structures

Author WangXiaoFeng
Tutor QinRong
School Guangxi University
Course Structural Engineering
Keywords frame structure spline function QR-method spline weighted residualmethod dynamic stability critical load
CLC TU323.5
Type PhD thesis
Year 2012
Downloads 637
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The stability of structure is one of the most important problems in structure analysis. Nolinear static stability problem has solved and the results has applied in the static design of structure.The dynamic stability problems of structure have not solved and can not be applied in structure design. One of the most difficult problems of dynamic stability is the dynamic stability criterion, which is different with static stability. The criteria of dynamic stability of structure include the judgements of both the positive definiteness of effective stiffness matrix and the dynamic response of structure. To study the dynamic stability of structure, the time history analysis must be done, and the stability of structure can be judged during time history analysis. Generally the time history analysis must be done at every level of dynamic load and the rough range of critical dynamic load can obtained by several times of the time history analysis. Then the exact critical load of structure under dynamic loads can be got by minishing the increment of dynamic loads.The dynamic stability analysis involve large numbers of nonlinear time history analyses, and in every analysis massive calculation and multiple iterative computations must be done for convergence. The number of times for iterative computations increases substantially when the dynamic loads are close to the critical load. Even simple frame structure, the time spent in dynamic stability analysis is lengthy. If complex structure is minor complex, the computational time will much lengthy, and the Increased iteration error accumulation may lead to wrong results. So, it is necessary to study the more efficient methods of dynamic stability analysis of frame structural.Although its very difficult to study dynamic stability of structure, the dynamic stability must be thoroughly studied because of its practical significance. The most feasible way is to study the problem step by step, and begin with a simple subject. So in this paper frame structure is selected as the subject investigated, and the calculation model of QR-method of dynamic stability is established by spline function. The non-linear time history analysis is used in the dynamic stability of frame structure as the main principal method.Spline function is the basis of QR-method, so the basic property and concept of Spline function are studied at first. The fundamental of conception that may be used in this paper on QR-method is discussed as emphasis, so that the QR discretization model of calculation and the spline weighted residual method in time history analysis of dynamic stability can be obtain from it. In order to establish the model and calculation method of dynamic stability, the static stability model and calculation method is established at first which can also be used for contrast of dynamic stability and static stability to show differences. An example of static stability of frame structure is studied by QR-method and finite element method respectively, and the critical loads of the frame is obtained. The results reveal that the critical loads of the frame structure by QR-method differ litter from that by finite element method, but QR-method shows higher efficiency in calculation speed and accuracy than finite element method. In view of above reasons and the huge amount of calculation in dynamic stability analysis, QR-method is adopted in the establishmet of analysis model to increase of calculation efficiency and coped with the problems in nonlinear analysis.The nonlinear dynamic stability of frame structure is studied after the nonlinear static stability of frame is solved by QR-method. Nonlinear dynamic time history analysis is the basis of nonlinear dynamic stability problems, so it is emphasized and the high efficiency method in nonlinear dynamic time history analysis must be established. The time history analysis model and calculation method is established by spline weighted residual method, then the calculation program is designed. An example revealed that nonlinear dynamic time history analysis methods established by spline weighted residual method have more accurate and efficient comparing with of other time history analysis methods of finite element method. The calculation model established by QR-method which has less number of unknown variables can accelerate the speed of iterative calculation and increase the efficiency of nonlinear dynamic time history analysis greatly.The dynamic stability analysis model is accomplished by QR method and spline weighted residual method afer the nonlinear dynamic time history analysis method was settled. The criterion for dynamic instability criteria and the concrete methods to judge dynamic instability of frame structure are presented detailedly. As the dynamic loads is increased step by step, nonlinear dynamic time history analysis is done at every level of dynamic loads. During every time history analysis, the positive definiteness of effective stiffness matrix and the convergence property of dynamic response are investigated at every time history step to judge if the frame structure is in state of dynamic instability. When the effective stiffness matrix becomes nonpositive definite and the dynamic response becomes misconvergence, the frame structure has lose dynamic stability and becomes unstable. In order to get the critical load of dynamic stability, load increment is minish and time history analysis is repeated. The above course proceeds if the load increment which induces structure unstable is in the range of acceptable precision. The calculation program is designed for above method to solve dynamic stability problems of frame structure on the basis of static dynamic program of QR method. Large numbers of calculation examples for different frames with different conditions are studied by using the dynamic stability program, and the critical load of dynamic stability of frame structure is obtained. The results of these examples reveal some of the rules of dynamic stability of frame structures:1. The new method presented in this paper can be used to analyze the stability of frame structure with satisfactory accuracy and speed, and the high efficiency of the new method makes it possible to study the dynamic stability of frame structure and reduces the difficulty of dynamic stability of frame structure using finite element method. The new method of this paper can complete dynamic stability analysis of frame structure and obtain the critical load, which is the key reason for that many calculating examples can be accomplished during the degree thesis stage.2. The critical dynamic loads of frame structure under step load in horizontal direction have a great reduction compared with the static critical loads. The examples reveal that there is A30~40%drop when the critical loads of dynamic and static contrast. So, the critical load of dynamic stability can be estimated through multiplying the value of static critical load by a parameter about0.6to0.7. When the ccuracy is not required too high, the complex dynamic stability analysis can be avoided in the design of frame structure by reducing the value of static critical load30~40%. If the high precision of dynamic critical loads is required, the efficiency of dynamic stability analysis can be improved considering the estimated dynamic critical load stability, and the blindness in searching dynamic critical loads can be avoided.3. The relationship between dynamic critical loads and the duration of dynamic loads for frame structure under step dynamic load in horizontal direction can be summarized as follows. When load acting time is short, usually less than half of fundamental period of the frame structure, the critical loads of frame structure under step load decrease obviously as the load acting time increases. The critical loads of frame structure under step loads vary scarcely when load acting time is greater than half of fundamental period of the structure. That is to say, the critical loads of frame structure are always remains the same. So in the practice, we can analysis the dynamic stability of frame structure at a long load acting time (offten larger than half of fundamental period) and have not to calculate critical loads at every load acting time, and the critical loads from that can be used in frame structure design with great confidence.4. The vertical loads, usually self weight of walls and floor slab, has great influence on the critical load of frame structure, and the critical load decreases substantially when the vertical loads increase. So it is emphasized that the vertical loads must be considered in calculating dynamic stability of frame structure for actual engineering design. Of course, in the dynamic stability analysis for actual frame structure, in addition to the vertical load, considering the influence of the vertical load (especially for vertical constant load) on the dynamic characteristics of frame structure in the calculation of the seismic critical load of frame structure is very necessary, because the mass of the beams, slabs, and other elements can substantially influence both the dynamic characteristics of frame structures and the dynamic stability analysis of the structure. The dynamic critical load of frame structure considering the vertical load and the mass of the vertical laod elements have more practical significance for practical engineering because it more close to reality.5. The influence of the stories of frame structure on the critical loads of dynamic stability can be be summarized as follows. The ratio of dynamic critical loads and static critical loads for frame structure decreases slightly as the floors of frame increase, and that ratio is between0.67and0.72when the floors of frame belows15. The total dynamic loads in horizontal direction decrease when the floors of frame increases, so frame structure tends to be more easily unstable when the foors increase and it is necessary to analysis the dynamic stability of high frame structure.

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