The Use Of Kirchoff's Current Law (Kcl) And Cut Set Equations In The Analysis Of Bridges And Trusses

Abstract

The purpose of this paper is to show that the analysis of trusses (and hence that of bridges) can be effectively carried out using the three concepts of Basic Electric Circuit Analysis, namely, the Superposition Theorem, Kirchhoff’s Current Law and the Cut-set method. The curricular effect of this study is the improvement of multidisciplinary engineering education by relating the sophomore courses of Statics and Circuits and putting the courses under one common analysis framework. Introduction In any engineering curriculum, it is common practice to teach Statics and Basic Circuit Analysis in the sophomore year as separate subjects. In the subject of Statics [1], the analysis of bridges and trusses is taught using the two concepts based on equilibrium equations, namely (i) the algebraic sum of moments taken at a point is zero, and (ii) the algebraic sum of the various forces at any joint in each of the vertical and horizontal directions will be equal to zero. In Basic Circuit Analysis [2], the subject matter starts with Kirchoff’s Current Law (KCL). For any network, KCL states that “the vectorial sum of the various currents incident at any node is always equal to zero”. Kirchhoff’s Voltage Law (KVL) is not considered in this paper. In addition, when sinusoidal excitation is considered, such a current can be represented as a phasor. Also, since linear networks are considered, the principle of Superposition holds. The Superposition theorem states that “the total response in a branch is the vectorial sum of the various responses, each response being obtained when only source is considered, with all other independent sources being made equal to zero”. In addition to the above, the cut-set concept is also discussed. The cut-set concept is the generalization of the KCL at a node in that the KCL holds for a surface also [3]. It is the purpose of this paper to show that the above-mentioned concepts of basic circuit analysis can be effectively used in the analysis of bridges and trusses. This common framework in the analysis of structures and circuits should be shown to the students to provide a better comprehension of the relationship between the two subjects of Statics and Circuits. For purposes of illustration, the example in [1, pp.284] will be considered in this paper with the difference that the length of each arm is arbitrary and the forces acting at junctions are independent of one another. This is as shown in Figure1.