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1、Graduate Course WorkSteel Structure Stability DesignAbstractSteel structure has advantages of light weight, high strength and high degree of industryalization, which has been widely used in the construction engineering. We often hear this the accident case caused by its instability and failure of st
2、ructure of casualties and property losses, and the cause of the failure is usually caused by structure design flaws. This paper says the experiences in the design of stability of steel structure through the summary of the stability of steel structure design of the concept, principle, analysis method
3、 and combination with engineering practice.Key words: steel structure; stability design; detail structureSteel Structure Stability DesignStructurally stable systems were introduced by Aleksandr Andronov and Lev Pontryagin in 1937 under the name systmes grossires, or rough systems. They announced a c
4、haracterization of rough systems in the plane, the AndronovPontryagin criterion. In this case, structurally stable systems are typical, they form an open dense set in the space of all systems endowed with appropriate topology. In higher dimensions, this is no longer true, indicating that typical dyn
5、amics can be very complex (cf strange attractor). An important class of structurally stable systems in arbitrary dimensions is given by Anosov diffeomorphisms and flows.In mathematics, structural stability is a fundamental property of a dynamical system which means that the qualitative behavior of t
6、he trajectories is unaffected by C1-small perturbations. Examples of such qualitative properties are numbers of fixed points and periodic orbits (but not their periods). Unlike Lyapunov stability, which considers perturbations of initial conditions for a fixed system, structural stability deals with
7、 perturbations of the system itself. Variants of this notion apply to systems of ordinary differential equations, vector fields on smooth manifolds and flows generated by them, and diffeomorphisms.The stability is one of the content which needs to be addressed in the design of steel structure engine
8、ering. Three are more engineering accident case due to the steel structure instability in the real life. For example,the stadium, in the city of Hartford 92 m by 110 m to the plane of space truss structure, suddenly fell on the ground in 1978. The reason is the compressive bar buckling instability;1
9、3.2 m by 18.0 m steel truss, in 1988,lack of stability of the web member collapsed in construction process in China; On January 3, 2010 in the afternoon, 38 m steel structure bridge in Kunming New across suddenly collapsed, killing seven people, 8 people seriously injured, 26 people slightly injured
10、.The reason is that the bridge steel structure supporting system is out of stability, suddenly a bridge collapsing down to 8 m tall. We can see from the above case, the usual cause of instability and failure of steel structure is the unreasonable structural design, structural design defects.To funda
11、mentally prevent such accidents, stability of steel structure design is the key.Structural stability of the system provides a justification for applying the qualitative theory of dynamical systems to analysis of concrete physical systems. The idea of such qualitative analysis goes back to the work o
12、f Henri Poincar on the three-body problem in celestial mechanics. Around the same time, Aleksandr Lyapunov rigorously investigated stability of small perturbations of an individual system. In practice, the evolution law of the system (i.e. the differential equations) is never known exactly, due to t
13、he presence of various small interactions. It is, therefore, crucial to know that basic features of the dynamics are the same for any small perturbation of the model system, whose evolution is governed by a certain known physical law. Qualitative analysis was further developed by George Birkhoff in
14、the 1920s, but was first formalized with introduction of the concept of rough system by Andronov and Pontryagin in 1937. This was immediately applied to analysis of physical systems with oscillations by Andronov, Witt, and Khaikin. The term structural stability is due to Solomon Lefschetz, who overs
15、aw translation of their monograph into English. Ideas of structural stability were taken up by Stephen Smale and his school in the 1960s in the context of hyperbolic dynamics. Earlier, Marston Morse and Hassler Whitney initiated and Ren Thom developed a parallel theory of stability for differentiabl
16、e maps, which forms a key part of singularity theory. Thom envisaged applications of this theory to biological systems. Both Smale and Thom worked in direct contact with Maurcio Peixoto, who developed Peixotos theorem in the late 1950s.When Smale started to develop the theory of hyperbolic dynamical
17、 systems, he hoped that structurally stable systems would be typical. This would have been consistent with the situation in low dimensions: dimension two for flows and dimension one for diffeomorphisms. However, he soon found examples of vector fields on higher-dimensional manifolds that cannot be m
18、ade structurally stable by an arbitrarily small perturbation (such examples have been later constructed on manifolds of dimension three). This means that in higher dimensions, structurally stable systems are not dense. In addition, a structurally stable system may have transversal homoclinic traject
19、ories of hyperbolic saddle closed orbits and infinitely many periodic orbits, even though the phase space is compact. The closest higher-dimensional analogue of structurally stable systems considered by Andronov and Pontryagin is given by the MorseSmale systems.Structure theory of stability study wa
20、s conducted on the mathematical model of the ideal, and the actual structure is not as ideal as mathematical model, in fact ,we need to consider the influence of various factors. For example ,for the compressive rods, load could not have absolute alignment section center; There will always be some i
21、nitial bending bar itself, the so-called geometric defects; Material itself inevitably has some kind of defect, such as the discreteness of yield stress and bar manufacturing methods caused by the residual stress, etc. So, in addition to the modulus of elasticity and geometry size of bar, all the ab
22、ove-mentioned factors affecting the bearing capacity of the push rod in different degrees, in the structure design of this influence often should be considered. Usually will be based on the ideal mathematical model to study the stability of the theory is called buckling theory, based on the actual b
23、ar study consider the various factors related to the stability of the stability of the ultimate bearing capacity theory called the theory of crushing.Practical bar, component or structure damage occurred during use or as the loading test of the buckling load is called crushing load and ultimate bear
24、ing capacity. For simplicity, commonly used buckling load. About geometric defects, according to a large number of experimental results, it is generally believed to assume a meniscus curve and its vector degrees for the rod length of 1/1000. About tissue defects, in the national standard formula is
25、not the same, allow the buckling stress curve given by the very different also, some problems remain to be further research.1. Steel structure stability design concept1.1. The difference between intensity and stabilityThe intensity refers to that the structure or a single component maximum stress (o
26、r internal force)caused by load in stable equilibrium state is more than the ultimate strength of building materials, so it is a question of the stress. The ultimate strength value is different according to the characteristics of the material varies. for steel ,it is the yield point. The research of
27、 stability is mainly is to find the external load and structure unstable equilibrium between internal resistance. That is to say, deformation began to rapid growth and we should try to avoid the structure entering the state, so it is a question of deformation. For example, for an axial compression c
28、olumns, in the condition column instability, the lateral deflection of the column add a lot of additional bending moment, thus the fracture load of pillars can be far less than its axial compression strength. At this point, the instability is the main reason of the pillar fracture .1.2. The classifi
29、cation of the steel structure instability1) The stability problem with the equilibrium bifurcation(Branch point instability).2) The axial compression buckling of the perfect straight rod and tablet compression buckling all belong to this category.3) The stability of the equilibrium bifurcation probl
30、em(Extreme value point instability). 4) The ability of the loss of stability of eccentric compression member made of construction steel in plastic development to a certain degree , fall into this category.5) Jumping instability6) Jumping instability is a kind of different from the above two types of
31、 stability problem. It is a jump to another stable equilibrium state after loss of stability balance.2. The principle of steel structure stability design2.1. For the steel structure arrangement, the whole system and the stability of the part requirements must be considered ,and most of the current s
32、teel structure is designed according to plane system, such as truss and frame. The overall layout of structure can guarantee that the flat structure does not appear out-of-plane instability,such as increasing the necessary supporting artifacts, etc. A planar structures of plane stability calculation
33、 is consistent with the structure arrangement.2.2. Structure calculation diagram should be consistent with a diagram of a practical calculation method is based on. When designing a single layer or multilayer frame structure, we usually do not make analysis of the framework stability but the frame co
34、lumn stability calculation. When we use this method to calculate the column frame column stability , the length factor should be concluded through the framework of the overall stability analysis which results in the equivalent between frame column stability calculation and stability calculation. For
35、 a single layer or multilayer framework, the column length coefficient of computation presented by Specification for design of steel structures (GB50017-2003) base on five basic assumptions. Including:all the pillars in the framework is the loss of stability at the same time, that is ,the critical l
36、oad of the column reach at the same time. According to this assumes, each column stability parameters of the frame and bar stability calculation method, is based on some simplified assumptions or typical.Designers need to make sure that the design of structure must be in accordance with these assump
37、tions.2.3. The detail structure design of steel structure and the stable calculation of component should be consistent. The guarantee that the steel structure detail structure design and component conforms to the stability of the calculation is a problem that needs high attention in the design of st
38、eel structure. Bending moment to non-transmission bending moment node connection should be assigned to their enough rigidity and the flexibility.Truss node should minimize the rods bias. But, when it comes to stability, a structure often have different in strength or special consideration. But requi
39、rement above in solving the beam overall stability is not enough.Bearing need to stop beam around the longitudinal axis to reverse,meanwhile allowing the beam in the in-plane rotation and free warp beam end section to conform to the stability analysis of boundary conditions.3. The analysis method of
40、 the steel structure stabilitySteel structure stability analysis is directed at the outer loads under conditions of the deformation of structure.The deformation should be relative to unstability deformation of the structure or buckling. Deformation between load and structure is nonlinear relationshi
41、p , which belongs to nonlinear geometric stability calculation and uses a second order analysis method. Stability calculated, both buckling load and ultimate load, can be regarded as the calculation of the stability bearing capacity of the structure or component.In the elastic stability theory, the
42、calculation method of critical force can be mainly divided into two kinds of static method and energy method.3.1. Static methodStatic method, both buckling load and ultimate load, can be regarded as the calculation of the stability bearing capacity of the structure or component. Follow the basic ass
43、umptions in establishing balance differential equation:1) Components such as cross section is a straight rod.2) Pressure function is always along the original axis component3) Material is in accordance with hookes law, namely the linear relationship between the stress and strain.4) Component accords
44、 with flat section assumption, namely the component deformation in front of the flat cross-section is still flat section after deformation.5) Component of the bending deformation is small ant the curvature can be approximately represented by the second derivative of the deflection function.Based on
45、the above assumptions, we can balance differential equation,substitude into the corresponding boundary conditions and solve both ends hinged the critical load of axial compression component .3.2. Energy methodEnergy method is an approximate method for solving stability bearing capacity, through the
46、principle of conservation of energy and potential energy in principle to solve the critical load values.1) The principle of conservation of energy to solve the critical loadWhen conservative system is in equilibrium state, the strain energy storaged in the structure is equal to the work that the ext
47、ernal force do, namely, the principle of conservation of energy. As the critical state of energy relations:U =WUThe increment of strain energyWThe increment of work forceBalance differential equation can be established by the principle of conservation of energy.2) The principle of potential energy i
48、n value to solve the critical load valueThe principle of potential energy in value refers to: For the structure by external force, when there are small displacement but the total potential energy remains unchanged,that is, the total potential energy with in value, the structure is in a state of bala
49、nce. The expression is:d=dU-dW =0dUThe change of the structure strain energy caused by virtual displacement , it is always positive;dWThe work the external force do on the virtual displacement;3.3. Power dynamics methodMany parts of the qualitative theory of differential equations and dynamical systems deal with asymptotic properties of solutions and the trajectorieswhat happens with the system after a long period of t