Evaluation of the Equivalent Tension Method for End Connections not Purely Axisymmetric
Authors: Owens J.H. 
Published: October 2008

Abstract
Results of nonlinear, 20, axisymmetric and nonlinear, 3D half model analyses are compared for two end connections, a 13-5/8 10000 API GBX flange and a segmented connector of the same nominal size. Strain gage results from a static bending test are included for the segmented connector. In both 20 models, nonaxisymmetric holes are approximated using plane stress with thickness input.
Results suggest that the ability of 20, axisymmetric analyses to predict maximum stress results may be determined by how close regions of maximum stress are to approximated nonaxisymmetric discontinuities and the selection of an equivalent radius.
Results also suggest that maximum Linearized stress values may occur on the compression side of bending and be overlooked in an axisymmetric analysis with equivalent tension.

Introduction
The object of what follows is to compare the results of 20, nonlinear, axisymmetric finite element analysis using equivalent tension with 3D, nonlinear, half model analyses using a pure applied moment. Makeup and 10000 psi working pressure cases are also compared.
Two end connections are considered: an API 13-5/8 10 000 GBX flange, and a 13-5/8 10000 psi segmented connector. The bases of comparison were magnitude and location of Primary Membrane plus Bending stress Intensity, [11 and hub face separation.
The flange Linearized stress Intensities are compared against stress Intensities calculated using the classical Taylor Forge method.
The mechanical connector Stress Intensity results from finite element analyses are compared against combined strain gage results from a full scale static bending test.

The Axisymmetric Assumption
End connections which are not altogether axisymmetric are frequently assumed to be so. The assumption removes the need to explicitly model a third dimension, thus simplifying the input and reducing model size and computer run time.
Axially and radially directed holes or slots are common and troublesome nonaxisymmetric discontinuities which must be approximated within the finite element program. Examples of usual methods for simulating these in an axisymmetric analysis are as follows:Reduce the Young's Modulus of the material in the region of the holes or slots by some proportion related to their number.Use the same Young's Modulus for the holes or slots as for the rest of the model but assume the material through them has a finite thickness related to their number.
Without considering the rigor of these assumptions, clearly the use of either might affect stress and displacement results in the region of use.
The axisymmetric assumption is on its surest footing when the external applied loads are themselves axisymmetric or nearly so. Bolt makeup loading only or internal pressure and bolt makeup, pure axial tension, or pure axial compression are examples.
When nonaxisymmetric loading is applied to an axisymmetric model, as in the case of an externally applied bending moment or shear load, one of two methods may likely be used:Harmonic loadingEquivalent tension.

Harmonic Loading
With this technique, a nonaxisymmetric load is simulated as a Fourier series [21. The method was used in [31 to calculate the capacities of API flanges.