Page 73 - Pipelines and Risers

46 Chapter 3

3.2.4 Pure Bending

A pipe subjected to increasing pure bending will fail as a result of increased ovalisation of the
cross section and reduced slope in the stress-strain curve. Up to a certain level of ovalisation,
the decrease in moment of inertia will be counterbalanced by increased pipe wall stress due to
strain hardening. When the loss in moment of inertia can no more be compensated for by the
strain hardening, the moment capacity has been reached and catastrophic cross sectional
collapse will occur if additional bending is applied. For low D/t, the failure will be initiated on
the tensile side of the pipe due to stresses at the outer fibers exceeding the limiting
longitudinal stress. For D/t higher than approximately 30-35, the hoop strength of the pipe
will be so low compared to the tensile strength that the failure mode will be an inward
buckling on the compressive side of the pipe. The geometrical imperfections (excluding
corrosion) that are normally allowed in pipeline design will not significantly influence the
moment capacity for pure bending, and the capacity can be calculated as, SUPERB (1996):
[ "1 (3.17)
Mc(Fd,pd) = 1.05-0.0015,- t .SMYS.D' .t

where D is the average pipe diameter, t the wall thickness and SMYS the Specified Minimum
Yield Strength. (1.05 -0.0015.Dlf).sMYs represents the average longitudinal cross sectional
stress at failure as a function of the diameter to wall thickness ratio.

3.25 Pure Internal Pressure
For pure internal pressure, the failure mode will be bursting of the cross-section, the pipe
cross section expands, the pipe wall thickness decreases. The decrease in pipe wall thickness
is compensated for by an increase in the hoop stress due to strain-hardening effect. At a
critical pressure, the material strain hardening can no longer compensate the pipe wall
thinning and the maximum internal pressure has been reached. The bursting pressure can in
accordance with API (1998) be given as:
2.t
pkr, = O.S(SMTS f SMYS).- (3.18)
D
where O.S(SMTS+SMYS) is the hoop stress at failure.

3.2.6 Pure Tension
For pure tension, the failure of the pipe will be, as for bursting, the result of pipe wall
thinning. When the longitudinal tensile force is increased, the pipe cross section will narrow
down and the pipe wall thickness will decrease. At a critical tensile force, the cross sectional
area of the pipe will be reduced until the maximum tensile stress for the pipe material is
reached. The maximum tensile force can be calculated as:
F, =SMTS.A (3.19)
where A is the cross sectional area and SMTS the Specified Minimum Tensile Stress.