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**Bending Stress, release 3, issued 23 Jan 2009. AUDIT version.**

This worksheet calculates combined stress in a tube resulting from bending stress and axial stress. For example, a conductor pipe cemented in place has a TOC some distance below the BOP. The top of the conductor can move laterally because of the low top of cement. How much stress does this put on the pipe at the TOC? Could fatigue be a problem? With a subsea BOP, the riser tensioners normally keep the axial force neutral point at the connector between BOP and LMRP – so the weight of the BOP will reduce the axial force and therefore stress in the pipe (make it less tensile / more compressive).

*User input*

-60000 |

kgflbfNkN |

Net axial forces at the point of interest, eg arising from BOP weight (compressive is -ve). F_{a} =

80 |

feetmetres |

Distance from TOC to the point where lateral movement is constrained. Lcs =

30 |

inchesmm |

Casing OD. L_Dcs =

28 |

inchesmm |

Casing ID. L_dcs =

2 |

inchesmm |

Casing deflection at point of lateral constraint. Ldf =

**Click here when any values are modified to update the result.**

*Calculations*

Calculate 2nd moment of area

Calculate the force required to give the stated deflection of , or .

Calculate the bending moment at the top of cement, = force x length.

Calculate the stress at the pipe OD resulting from the bending moment.

Calculate the stress resulting from the axial forces acting above the TOC (weight of pipe, weight of BOP etc).

Calculate the maximum stress on the outside of the bend.

Calculate the minimum stress on the inside of the bend.

Calculate the reduction factor arising due to cycling between tensile and compressive stress. (Note; this is used for the pipe body when not significantly affected by residual welding stresses).

Calculate the stress range between max and min stress.

*Results*

Lateral force required to give the stated deflection

Stress arising from bending only at pipe OD

Maximum combined stress in the pipe

Minimum combined stress in the pipe

Stress range (max stress – min stress)

Stress reduction factor for non-welded pipe body

*Worksheet references*

Version 1 of this worksheet released on 21 January 2009 by Steve Devereux.

Version 2 added in reduction factor and stress range.

Version 3 removed the calculated axial stress arising from pipe above the point of interest, leaving the user to enter the total axial force Fa acting above the point of interest.

SG of steel from http://www.simetric.co.uk/si_metals.htm taken as 7.85.

Benham & Warnock, 1973. “*Mechanics of Solids and Structures*“. Published by Pitman ISBN 0 273 36191.

Det Norsk Veritas, April 2008. Recommended Practice DNV-RP-C203 “*Fatigue design of offshore steel structures*“.