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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 systems, he hoped that structurally stable systems would be typical. This would have been consistent with the situation in low dimensions
