Large Deflections and Stability of Elastic Frame

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Abstract
The analysis of large deflections of rectilinear frames subjected to arbitrary discrete loads and boundary conditions is presented. The problem is formulated as a system of simultaneous nonlinear equations obtained by combining the general solution of the exact nonlinear differential equation of bending and the equilibrium equations obtained for each of the segments between load points and/or points of discontinuity in curvature, along with the prescribed boundary conditions. The system of equations is solved by a modified Newton-Raphson procedure. A stability criterion dependent upon the properties of the load-deflection curve and the relationships between the displacements is used to study the stability of the frame. These curves are readily constructed for the entire loading history of the frame by the incremental load method, thus making it possible to study the pre-buckling as well as the post-buckling behavior of the frame. Examples are given to illustrate the method of analysis for a frame which remains stable throughout its entire loading history and for frames which exhibit either a bifurcation or a snap-through type of instability.

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