Collapse Due to Bending and External Pressure Per API RP 1111, 4th Edition
Authors: Nogueira Andre C. , Harrison Gary E. 
Published: October 2011

Abstract
The API Recommend Practice 1111, " Design, Construction, Operation, and Maintenance of Offshore Hydrocarbon Pipelines (Limit State Design)?? [Ref. 1], one of the leading offshore deepwater pipeline codes, has been revised and updated in the Fourth Edition, December 2009, hereafter RP1111. The authors, both members of the RP1111 committee, review the methodology for designing deepwater pipelines subjected to external pressure with or without bending. The precise methodology, yet underlying simplicity, which is present in the RP1111 code when dealing with external pressure design, is the result of equations based on first principles of mechanics. Such philosophy, in turn, leads to straightforward definitions of pipeline capacity as a function of the external pressure and bending strain.
With a single fundamental equation to describe the collapse limit state, and bending strain as the only independent variable to characterize the effects of bending, RP1111 provides a clear characterization of the limit state, and thus avoiding any confusion on the loading path. This powerful methodology is an advantage to engineers that use RP1111 as the deepwater pipeline code of choice. RP1111 has been used successfully in numerous projects and avoids potential confusion by users as well as reviewers. This clarity promotes safe, cost effective, schedule-driven, and readily auditable projects.
This paper first reviews the basic principles of pipeline collapse due to external pressure, and second describes the RP1111 simple and precise methodology for designing pipelines to withstand collapse due to external pressure. Design examples are provided which may serve as a guide for users of the code. Deepwater world record projects which have successfully used the RP1111 for design are also presented and discussed.

Introduction
The API Recommend Practice 1111, " Design, Construction, Operation, and Maintenance of Offshore Hydrocarbon Pipelines (Limit State Design)??, one of the leading offshore deepwater pipeline codes, has been revised and updated in December 2009. The authors, both members of the RP1111 committee, review the fundamentals of the methodology for designing deepwater pipelines subjected to external pressure with or without bending. The underlying simplicity, which is present in the RP1111 code when dealing with external pressure design, is the result of equations based on first principles of mechanics. Such simple yet precise philosophy, in turn, leads to straightforward definitions of pipeline capacity as a function of the external pressure and bending strain.
With basically one fundamental equation capable of describing the collapse limit state—and bending strain as the only independent variable to characterize the effects of bending—RP1111 avoids difficult discussions on characterization of the limit state, and avoids confusion regarding the loading path. This powerful methodology is an advantage to engineers that use RP1111. RP1111 has been used successfully in several leading projects and avoids potential confusion by users as well as reviewers, promoting safe, cost effective, schedule driven, and straightforward auditable projects.

External Pressure Collapse
Timoshenko and Gere [2] derived the fundamental equation for elastic buckling collapse due to external pressure on a ring of a long pipeline in two different ways. In section 7.3 they derived the critical buckling pressure by describing the section stability with a trigonometric expansion, and in section 7.4 by a traditional non-trivial solution of the governing differential equation.
Of course, both methods lead to the same value for the elastic critical buckling pressure, Pe of a pipeline, shown below in Eq. 1. Timoshenko and Gere [2] noted that this result was earlier obtained by Bresse [3].