结构力学英文课件chapter-2

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
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: (1) 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; (2) To discuss geometric construction rules of stable systems.
(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
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
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
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.
Geometric construction analysis 2.1purpose of analyzing geometric construction of structures, of structure
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 Hale Waihona Puke Baidumall that their effect on the geometric construction analysis of the structures can be neglected.
n=0
n=1
(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
n=2
②The 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 ③Restrict in vertical and horizontal directions and the rotation about A three restraints
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 ①The 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