Load-Shortening Behavior of Damaged Tubular Columns
Authors: Padula J.A. , Ostapenko A.A. 
Published: October 2008

Abstract
A simple "engineering" method was formulated for computing the axial load vs. axial shortening relationship of pin-ended tubular members damaged by a dent and/or out-of-straightness. The method predicts the pre- and post-ultimate load-shortening response, and can be used in analyzing the strength and behavior of offshore platform frames containing damaged members. It is valid for member geometries and material properties typically found in faxed offshore platforms. The method was developed from a parametric study and regression analysis of a database containing load-shortening relationships from published test results on small-scale damaged specimens and data generated by elite element analysis. The elite element analysis considered the effects of geometric and material nonlinearity and was verified by comparison with test results.
The regression model is based on a parametric study of the influence of geometric and material variables on the axial behavior of damaged columns. The variables considered were: column slenderness, D/t ratio, dent depth to diameter ratio, out-of-straightness, yield stress, and axial shortening. The regression analysis of the load shortening relationships in the database resulted in a set of 96 coefficients. In application of the method to a member with known damage, geometry and material properties, these 96 coefficients are reduced to a 4-term approximating function for the load-shortening response. The procedure is illustrated with comparisons with test results and a sample application.

1. Introduction
Design of offshore structures for strength, stability, and serviceability under applied loads requires consideration of the structure in a deteriorated condition. Although some degree of damage tolerance is implicit in any redundant structure, quantification of the residual strength of a damaged member(s) and of the whole structure is needed for a rational approach to efficient, cost-effective design and maintenance. Typically the effect of dents and/or out-of straightness of a tubular member results in a reduction of the stiffness and/or capacity of the member, and this may significantly affect the strength and/or serviceability of the structure. Residual strength of the structure depends on the pre- and post-ultimate behavior of the damaged member since it is likely that service loads may cause nobleman response of the damaged member leading to redistribution of forces in the structure. Analysis of the pre- and post-ultimate load shortening behavior of damaged tubular columns with state-of-threat finite element programs is impractical even if possible since it requires consideration of large deformations and material non~ linearity, and there is a need for a simplified yet reasonably accurate "engineering method".
In previous work, a parametric study was conducted by using finite element, beam-column analysis of initially crooked tubular columns and experiments on small-scale specimens. [1] The effect of dents was also analyzed by modifying the stress-strain relationship for fibers in the dent affected area. [2] An analytical method based on a impelled physical model for which the governing relations were fitted to empirical data from 109 small-scale tests was proposed for estimating the load-deformation response of dented and/or initially crooked simply supported columns. [3, 4, 5, 6]