CALCULATION OF ROD FORCE OF THE TRUSS CONSTRUCTION

Abstract

The calculation of the forces of truss construction can be determined by graphical method, known as Cremona method and analytical method, known as Ritter method.  Calculations in both ways can take much time and is dependent on the number of connecting points and considerable loading simulations. This paper describes an alternative analytical calculation method, which combines the two methods, namely the connection balance method and the optimization calculation method.  And the last method is available in Microsoft Excel Solver (MES). The connection balance method is the fulfillment of the balance equation of SFx = 0 and SFy = 0 at each joint of the truss. The way of the balance fulfillment in this paper is different from the way of Ritter. In the way of Ritter, the balance fulfillment is applied to each connection point, one by one point. The connection point can be calculated if at the point there are maximum two unknown rod force and minimum one known rod force. While by using the MES program, the balance of connecting point is simultaneously computed for the entire construction. MES program works by simulating/finding the value of variables, and at the same time fulfilling the defined objective function and constraint functions. In this case, the variables are all the rod forces, while the constraint functions are the balance equation at all connecting point. An objective function can be taken from one of the SFx = 0 or SFy = 0 from one connecting point only. This paper has recorded 10 different types of geometric shapes of certain truss construction (statically determined) which can be considered to represent the ones in the field (including the form of Howe, Pratt, and Warren for the roof truss and bridge truss). Then the mathematical models that were adjusted to the MES program were created for each of the ten truss constructions. Based on the created mathematical models, the forces of the rods were then calculated using the MES program. For validation purposes, the calculation results are compared with the calculations result using the analytical Ritter method. It can be concluded that the presented calculation method is highly satisfactory, especially for the analysis of statically determined   truss construction.