Work Method

Abstract

The equilibrium method described in the preceding chapter can easily be used in the plastic analysis and design of simple frames where the number of redundants is small. As the number of redundants increases, it becomes more difficult to draw the bending moment diagram of the structure, and thus more difficult to use the equilibrium method. For such structures, the work method of plastic analysis is more appropriate and affords a simpler solution. As the name implies, the relation between the strength of a frame and the applied loads in the work method is found by assuming that there is no overall loss of energy as the frame under failure loads undergoes a small change in displacement. Thus, by postulating a valid failure mechanism, an equation can be formed by equating the external work done by the applied loads through the displacements to the internal dissipation of energy at the plastic hinge locations. The interal dissipation of energy is the sum of the products of the plastic moment at each hinge and the corresponding angular change required to effect a small movement of the failure mechanism. The external work is the sum of the products of the component of the small displacement of the failure mechanism in line with the applied load and the corresponding applied load. The equation formed in this way is called the work equation and the corresponding collapse load or the required plastic moment capacity can be determined by solving the work equation [1.8, 5.1–5.5]. The computed load for the particular assumed failure mechanism is exact if a moment check is performed and shows that the plastic moment condition is not violated anywhere in the frame.