Beam Idealization

For any given bemm with varying cross-section and material properties, it is easy to evaluate a number of parameters Q_i and D_i, by numerical integration, accounting for all generalized forces and displacements. Those parameters can be used directly to set up the flexibility and stiffness matrices and also to determine the fixed-end reactions due to any loading. This method provides great accuracy in short computing time and seems to be much simpler than those in use today. Another method to set up the flexibility and stiffness matrices consists in determining an equivalent idealized beam. For any asymmetric beam, it is possible to determine an idealized beam of three inertias, with the same length and constant elastic properties, that is equivalent to the real beam for the purpose of structural analysis and is defined in terms of the parameters Q_i by a simple method (extended to symmetric beams). A program has been developed and tested on an example problem. It makes any standard program capable of analysing structures including members with varying cross-section and material properties.