结构力学英文课件cha.ppt

Geometric construction analysis of structure,2.1purpose of analyzing geometric construction of structures, stable and unstable structural systems in order to withstand and transmit load, the geometric shape of a structure system is variable under loads, the structural system cannot be used as a structure. it should be realized that all physical bodies deform when subjected to loads; the deformation in most engineering structures under service conditions are so small that their effect on the geometric construction analysis of the structures can be neglected.,For simplicity we call a structure as a system, For instance, framed structures are named framed systems. According to the shape and location of their members, framed systems can be classified into two categories: (1)Geometrically stable system Under the action of the loads, the system still maintains its shape and remains its location if the small deformations of the members are neglected as shown in Fig.2.1,(2)Geometrically unstable system Under the action of the loads, the system will change its shape and its location if the small deformations of the members are neglected as shown in fig,2.2 Corresponding to geometrically stable and unstable system, there are internally stable and unstable systems as well. A structure is considered to be internally stable, or rigid, if it maintains its shape and remains a rigid body when detached from the supports,Conversely , a structure is termed internally unstable if it cannot maintain its shape and may undergo large displacements under small disturbances when not supported externally. Purpose of analyzing geometric construction of structures is as following: To estimate whether or not a system is geometrically stable, so as to determine whether the system can be used as a structure or not; To discuss geometric construction rules of stable systems.,2.2 the concept of degrees of freedom and restraints,In the analyzing geometric construction of structures, it is very feasible to consider one part of the members or joints of a system as an object which possesses degrees of freedom, whereas other part of the members or joints of the system as restraints which restricts the movement of the object. The relationship of these two parts are then analyzed and whether or not the system will be determined. Accordingly, the concept of degrees of freedom and restraints of a system is discussed first of all,2.2.1the degrees of freedom The degrees of freedom of a system are the numbers of independent movements which are required to locate the system fully.obviously, arigid body has three degrees of freedom in a planar coordinate system(six degrees of freedom in a three dimensional coordinate system),e.g., the position of member AB may be determined by three parameters Xa, Ya and (1)The degrees of freedom of a joint The movement of a point in a planar coordinate system can decomposed into two translations in any different directions i.e., a point possesses two independent moving styles or two independent coordinates are needed to locate its position in a planar coordinate system. So a joint has two degrees of freedom in a planar coordinate system .in fig the parameters Xa, Ya will locate joint A.,n=2,(2)The degrees of freedom of freedom of a rigid body The movement of a rigid body in planar coordinate system can be decomposed to two translations in any different directions and a rotation about some point in the system ,i.e.,a rigid body possesses three independent moving styles or three independent coordinates are needed to locate its position in a planar coordinate system. Therefore, a rigid body has three degrees of freedom in a planar coordinate system .the position of member AB may be determined by three parameters Xa, Ya and,n=3,2.2.2 Restraints the devices or connections which can reduce the degrees of freedom of a system are defined as restraints. The number of the degrees of freedom of a system reduced by the device or connection is named the number of its restraints. There are two kinds of restraints, support restraints and connecting restraints between rigid bodies. (1)Support restraints The roller support can restrict the translation of joint A in the direction perpendicular to its moving surface but cannot prevent its translation along its moving surface and rotation about joint A, i.e., one roller support reduces one degree of freedom and is equivalent to one restraint,n=2,The hinged support can restrict the translation of joint A in verticar and horizontal directions but cannot prevent the rotation about joint A, i.e., one hinged support reduces two degrees of freedom and is equivalent to two restraints Restrict in vertical and horizontal directions and the rotation about A three restraints (2 )Connecting restraints between rigid bodies we will pay more attention to connecting restraints between two rigid bodies. One rigid body has three degrees of freedom and two independent rigid bodies have six degrees of freedom in a planar coordinate system, when connecting them together, their degrees of freedom would be reduced. Now we will discuss the equivalent restraints of a few kinds of commonly used connections.,n=1,n=0,Link, the two independent rigid bodies AB and DC have three relative degrees of freedom with respect to each other, when they are connected by link EF which is a bar with hinges at its ends, the relative between the two rigid bodies in the direction of the link is restricted , i.e., one of the degree of freedom between them is removed. Therefore, one link is equivalent to one restraint. Simple hinge Only one relative degree of freedom Between them is existed, i.e., the relative rotation about A, there ,one simple hinge = 2 restraint Simple rigid joint There exist no relative degree of freedom Between them in the plane, three of degree So , one simple rigid joint=3 restraints,By similar analysis, a hinge connecting three rigid bodies makes the system remove four degrees of freedom; the hinge is thusly equivalent to two simple hinges. while a rigid joint connecting three rigid bodies set the system remove six degrees of freedom; the rigid joint is then equivalent to two simple rigid rigid joints. Therefore ,if a hinge or a rigid joint is used to connect more than two rigid bodies,it is called a multiple hinge or multiple rigid joint. A multiple hinge rigid connecting N bars is equivalent to N-1 simple hinges or 2(N-1) restraints, while a multiple rigid joint connecting N bars is equivalent to N-1 simple rigid joints or 3(N-1)restraints,2.2.3 Restraint substitution and virtual hinges Foregoing discussion tells us that one hinge is equivalent to two restraints and two links are also equivalent to two restraints; whereas restraints can be substitute. In order to extend the concept of restraint substitution, the concept of virtual or instantaneous hinge are introduced. Two noncollinear links which connects two rigid bodies are equivalent to one hinge. If two noncollinear links AB and AC intersect at point A which lies on the rigid body , the point A will be an actual simple hinge. If the intersectional point A does not lie on the two rigid bodies, i.e., the intersecting point lies outside of the two rigid bodies, the intersection is referred to as a virtual or instantaneous hinge, which has a variable position.,2.2.4Necessary restraints and redundant restraints In a framed system, the restraints which can restrict the degrees of freedom of the system are named as necessary restraints; whereas the restraints which are not able to restrict the degree of freedom of the system are referred to as redundant restraints. A free joint A has two degrees of freedom; if it was attached to the ground with two noncollinear links ,its position would be determined and its two degrees of freedom would be restricted. Therefore ,the links are all necessary restraints in order to locate th