Furthermore, structures must be stable to be able to serve their desirable functions. An indeterminate structure is one whose unknown forces cannot be determined by the conditions of static equilibrium alone and will require, in addition, a consideration of the compatibility conditions of different parts of the structure for its complete analysis. A determinate structure is one whose unknown external reaction or internal members can be determined using only the conditions of equilibrium. Prior to the choice of an analytical method, it is important to establish the determinacy and stability of a structure. In other words, the reaction force of a link is in the direction of the link, along its longitudinal axis.Ī fixed support offers a constraint against rotation in any direction, and it prevents movement in both horizontal and vertical directions.ģ.3 Determinacy and Stability of Beams and Frames It permits movement in all direction, except in a direction parallel to its longitudinal axis, which passes through the two hinges. Its idealized form is depicted in Table 3.1.Ī link has two hinges, one at each end. ![]() The characteristics of a rocker support are like those of the roller support. The idealized representation of a roller and its reaction are also shown in Table 3.1. It restrains the structure from movement in a vertical direction. Its idealized representation and reactions are shown in Table 3.1.Ī roller support allows rotation about any axis and translation (horizontal movement) in any direction parallel to the surface on which it rests. ![]() However, the characteristics of some of the supports are described below and shown in Table 3.1.Ī pin support allows rotation about any axis but prevents movement in the horizontal and vertical directions. It is assumed that the student is already familiar with several types of supports for rigid bodies, as this was introduced in the statics course. ![]() Supports connect the member to the ground or to some other parts of the structure. The type of support provided for a structure is important in ensuring its stability. ∑ F x and ∑ F y are the summation of the x and y components of all the forces acting on the structure, and ∑ M z is the summation of the couple moments and the moments of all the forces about an axis z, perpendicular to the plane xy of the action of the forces.Ī structure in three dimensions, that is, in a space, must satisfy the following six requirements to remain in equilibrium when acted upon by external forces:ģ.2 Types of Supports and Their Characteristics The above three conditions are commonly referred to as the equations of equilibrium for planar structures. The equilibrium requirements for structures in two and three dimensions are stated below.įor a structure subjected to a system of forces and couples which are lying in the xy plane to remain at rest, it must satisfy the following three equilibrium conditions: \)Įquilibrium Structures, Support Reactions, Determinacy and Stability of Beams and FramesĮngineering structures must remain in equilibrium both externally and internally when subjected to a system of forces.
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