Research Progress Report 321 October, 1967
A Generalized Stiffness Analysis of Space Frames
Stanley K. Suddarth
Department of Forestry and Conservation

This paper presents a method for the analysis of any framed structure in three space or a plane containing any number of prismatic members oriented in any desired way and having any number of reactions of the fixed, pin, or roller type. Any number of loads having any desired orientation can be applied to each member. Concentrated and uniform loads only are discussed in detail but the incorporation of other load types follows the same pattern. Non-prismatic members can be treated by breaking them into an equivalent series of approximating prismatic members, assembling the stiffness matrix of this equivalent structure, and then applying known relationships to obtain the necessary stiffness matrix for the member as a whole. By this device, the system can be made to generate its own input information sufficient to overcome its original restriction to prismatic members.

A single master computer program based on this system is limited only by the degree of sophistication built into it and the storage and peripheral facilities of the computer used. Degree of sophistication means here that a plane program might represent one degree while a three-space program might represent another. Internal features might be added to automatically treat non-prismatic
members while others might be added to accommodate pins to create higher degrees of sophistication.

The ordinarily difficult input data for structural analysis deal with the preparation and recording of member dimensions, slopes and related geometric information. This system uses coordinates of points in space, an assembly matrix consisting of zeros and ones and simple vector descriptions of reactions to enter these geometric data. Devices for automatic reduction of graphic data can be used with drawings of the proposed structure to eliminate the only difficult part of the process - the determination of the point coordinates.

Ordinary output can be obtained in tabular form but this often requires further time consuming efforts to answer the engineer’s needs. Since this system operates with an analytic description of the geometric properties of the structure, graphic outputs such as sketches of the structure, parts of the structure, moment diagrams, etc., can be obtained by proper treatment of the stored data and results of computation. In other words, once the data are entered into the system, the preparatory documents and drawings could be discarded and the entire description of the structure and its solution could be recon structed from the contents of the computer.

PURDUE UNIVERSITY • Agricultural Experiment Station • Lafayette, Indiana