Investigation of Rigid Frame by Integrated Force Method

ABSTRACT: When an indeterminate frame is acted on by external loads and couples internal stresses in the members and displacements at the joints will be produced. Calculation of the stresses in the members and joint displacements are needed in structural design. The two main methods for the analysis of frames are the classical force method and the displacement method. A third method called the Integrated Force Method (IFM) has been developed for analysis of structural mechanics problems. This method treats all independent internal forces as unknown variables that can be calculated by simultaneously coupling both equilibrium equations and compatibility conditions. The advantage of the Integrated Force Method is that compatibility conditions are generated by algebraic operations on the nodal equilibrium equations. These algebraic operations are Null Space of the equilibrium matrix and the Singular Value Decomposition of the equilibrium matrix. These algebraic operations are easily carried out by computer algebra systems like Mathematica7. An extension of the Integrated Force Method is the Dual Integrated Force Method (IFMD). The primary unknowns in the Dual Integrated Force Method are the joint displacements. To obtain the joint displacements the structure global stiffness matrix is generated by using the equilibrium matrix and the unconnected stiffness matrix of the structure. The advantage of the Dual Integrated Force Method is that the global stiffness matrix is generated easily by computer algebra systems like Mathematica7 by simple matrix multiplication commands. In this thesis two analysis packages for analysis of indeterminate rigid frames by Integrated Force Method (IFM) have been developed. These packages are: Integrated Force Method via Null Space, Integrated Force Method via Singular Value Decomposition. One additional analysis package using Dual Integrated Force Method have been developed. All three analysis packages have been coded using Mathematica7. In all three analysis packages all the calculation steps are presented, explained and they can be edited according to the needs of the user. The user can see the program code and its corresponding output at each calculation step. All of these specific characteristics make the analysis packages useful and practical. Many problems have been analyzed by these packages and all the results have been compared with the results obtained from Mastan2 v3.2. All the results fully agree. Keywords: Frame Analysis, Integrated Force Method (IFM), Dual Integrated Force Method (IFMD), Compatibility conditions. ……………………………………………………………………………………………………………………………………………………………………………………………………………………