A Load-Indentation Relationship for Tubular Members
Authors: Padula J.A. , Ostapenko A. 
Published: October 2008

Abstract
A simplified analytical method for estimating the load vs. dent depth response of tubular members subjected to "knife-edge" loading was developed. The load-deformation behavior is given by a three-term series whose coefficients are readily determined from the geometric and material characteristics of the member. The method is based on a parametric study and multi-variable regression analysis of experimental data taken from available literature. The estimated load vs. dent depth response compared favorably with the results of a finite element analysis.

1. Introduction
In the design of offshore platforms, it is necessary to consider the possibility of structural damage resulting from accidental impact during construction or operation, a ship/platform collision, ice hazards, or severe cases of overloading. Of these, ship/platform collisions occur fairly frequently and are probably the single most common type of offshore accident resulting in structural damage. [1] The design process must include consideration of probable collisions with supply vessels or other light ship traffic with the objective of limiting the consequences of damage so that the integrity of the structure is not significantly compromised or that it can be maintained until repairs can be effected. This requires that the designer be able to estimate the extent of damage that may be expected as well as the residual strength of the structure after damage.
Although elastic vibrations may dissipate much of the energy from minor ship/platform collisions or accidental impacts, plastic deformations will develop at least at the point of contact. [1] In structures framed with steel tubular members, the result of a collision usually takes the form of localized dents and/or overall deflection of a member(s). With the knowledge of the member/structure response, in an impact or collision, the energy absorption characteristics can be determined and thereby provide a means for estimating the extent of damage for a given "design collision" with a known mass and velocity.

1.1. Previous Work
A number of researchers have investigated the indentation of tubular members as it relates to accidental damage in offshore structures. [2,3,4,5,6] The approaches to the problem ranged from the development of simplified analytical models and the use of numerical techniques such as the finite element method to experimental work. For example, Taby's work on the residual strength of damaged tubular members has involved extensive experimental work including the indentation of tubular members. [7] On the other hand, Wierzbicki and Suh have presented a purely theoretical analysis of the denting of tubular members under combined bending and axial loading. [6] Soares and Soreide have presented a simplified analysis of tubular members whose primary mode of deformation was overall beam deflection and a correlation of the results with finite element analysis. [3]
Probably the most significant shortcoming of the experimental research reported so far is the lack of work on tubular members fabricated by cold-rolling and welding, which is the usual method of fabrication for offshore structures, and of the consideration of members with large D/t ratios. The work described here addresses these needs, at least in part.