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1、Graduate Course WorkSteel Structure Stability DesignSchool: China University of MiningName: Liu FeiStudent ID: TSP130604088Grade: 2013Finish Date: 2014.1.1AbstractSteel structure has advantages of light weight, high strength and high degree of industryalization, which has been widely used in the con
2、struction engineering. We often hear this the accident case caused by its instability and failure of structure 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 th
3、rough the summary of the stability of steel structure design of the concept, principle, analysis method and combination with engineering practice.Key words: steel structure; stability design; detail structureSteel Structure Stability DesignStructurally stable systems were introduced by Aleksandr And
4、ronov and Lev Pontryagin in 1937 under the name systmes grossires, or rough systems. They announced a characterization 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 endow
5、ed with appropriate topology. In higher dimensions, this is no longer true, indicating that typical dynamics 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 s
6、tability is a fundamental property of a dynamical system which means that the qualitative behavior of the 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,
7、which considers perturbations of initial conditions for a fixed system, structural stability deals with 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.
8、The stability is one of the content which needs to be addressed in the design of steel structure engineering. 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 s
9、tructure, suddenly fell on the ground in 1978. The reason is the compressive bar buckling instability;13.2 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
10、across suddenly collapsed, killing seven people, 8 people seriously injured, 26 people slightly injured.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 a
11、nd failure of steel structure is the unreasonable structural design, structural design defects.To fundamentally 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
12、to analysis of concrete physical systems. The idea of such qualitative analysis goes back to the work of 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 pract
13、ice, the evolution law of the system (i.e. the differential equations) is never known exactly, due to the 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 gove
14、rned by a certain known physical law. Qualitative analysis was further developed by George Birkhoff in 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 oscillatio
15、ns by Andronov, Witt, and Khaikin. The term structural stability is due to Solomon Lefschetz, who oversaw 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 Mors
16、e and Hassler Whitney initiated and Ren Thom developed a parallel theory of stability for differentiable 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 develo
17、ped 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: dimension two for flows and dimension one for diffeomorph
18、isms. However, he soon found examples of vector fields on higher-dimensional manifolds that cannot be made 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 s
19、ystems are not dense. In addition, a structurally stable system may have transversal homoclinic trajectories 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 consider
20、ed by Andronov and Pontryagin is given by the MorseSmale systems.Structure theory of stability study was 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 t
21、he compressive rods, load could not have absolute alignment section center; There will always be some initial 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
22、residual stress, etc. So, in addition to the modulus of elasticity and geometry size of bar, all the above-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 m
23、athematical model to study the stability of the theory is called buckling theory, based on the actual bar 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 oc
24、curred during use or as the loading test of the buckling load is called crushing load and ultimate bearing 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
25、vector degrees for the rod length of 1/1000. About tissue defects, in the national standard formula is 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 in
26、tensity and stabilityThe intensity refers to that the structure or a single component maximum stress (or 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 acc
27、ording to the characteristics of the material varies. for steel ,it is the yield point. The research of 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 st
28、ructure entering the state, so it is a question of deformation. For example, for an axial compression columns, 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 compressio
29、n strength. At this point, the instability is the main reason of the pillar fracture .1.2. The classification 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
30、 compression buckling all belong to this category.3) The stability of the equilibrium bifurcation problem(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 c
31、ategory.5) Jumping instability6) Jumping instability is a kind of different from the above two types of 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, th
32、e whole system and the stability of the part requirements must be considered ,and most of the current steel 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
33、 increasing the necessary supporting artifacts, etc. A planar structures of plane stability calculation 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
34、multilayer frame structure, we usually do not make analysis of the framework stability but the frame column 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 wh
35、ich results in the equivalent between frame column stability calculation and stability calculation. For 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. Includ
36、ing:all the pillars in the framework is the loss of stability at the same time, that is ,the critical load 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 t
37、ypical.Designers need to make sure that the design of structure must be in accordance with these assumptions.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
38、conforms to the stability of the calculation is a problem that needs high attention in the design of steel 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
39、it comes to stability, a structure often have different in strength or special consideration. But requirement 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
40、 beam end section to conform to the stability analysis of boundary conditions.3. The analysis method of 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 de
41、formation of the structure or buckling. Deformation between load and structure is nonlinear relationship , 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 calculatio
42、n of the stability bearing capacity of the structure or component.In the elastic stability theory, the 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 a
43、s the calculation of the stability bearing capacity of the structure or component. Follow the basic assumptions 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 accord
44、ance with hookes law, namely the linear relationship between the stress and strain.4) Component accords 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 c
45、urvature can be approximately represented by the second derivative of the deflection function.Based on 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. E
46、nergy methodEnergy method is an approximate method for solving stability bearing capacity, through the 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
47、 is in equilibrium state, the strain energy storaged in the structure is equal to the work that the external 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 equati
48、on can be established by the principle of conservation of energy.2) The principle of potential energy in 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 r
49、emains unchanged,that is, the total potential energy with in value, the structure is in a state of balance. 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