CONTINUUM MODELING METHODOLOGY FOR DYNAMIC BEHAVIOR OF TOWERS

A very common problem in Civil Engineering is the analysis and design of lattice structures. These types of structures generally consist of repetitive sections and have been utilized in the erection of transmission and communication towers, space roof trusses, solar energy collectors, and space platforms. Since lattice structures consist of a significantly large number of members and subsequently a large number of nodes, the classical discrete technique of analysis can be very expensive even on today's modern computers. This study applies a rational approach which capitalizes on the repetitive nature of towers to develop the equivalent continuum model for the lattice structure. The continuum approach is based on equivalencing the strain and kinetic energies of the actual latticed tower with that of the equivalent continuum model. Introducing the kinematic assumption that the strain components of the lattice structure have linear variations in the plane of the tower cross section is the key step in obtaining correct expressions for the equivalent properties of the continuum model. Procedures for developing continuum models are presented along with the constitutive equations and strain expressions. The procedures are demonstrated by applying the continuum modeling approach to planar trusses, triangular towers with constant cross sections, triangular towers with variable cross sections, and towers with rectangular cross sections. Numerical results for static deflections and free vibration analysis of planar trusses and towers with triangular cross sections are presented, and they indicate the high accuracy of the continuum model solution. In addition, a numerical technique is developed to obtain member forces of the actual lattice structure from the continuum model results. Moreover, a comparison of computer times using the SAP IV finite element program to analyze the actual lattice structures versus the equivalent continuum model is presented. In general, the continuum approach when applied to the analysis of lattice structures demonstrates a significant savings in computer cost with a relatively insignificant loss in accuracy.