Page 70 - Pipelines and Risers

BucklingKollapse of Deepwater Metallic Pipes 43

(3.8)

The initial yielding condition is expressed below for a rectangular cross-section with height of
wall-thickness and width of unit (1):

(T, +(Tb =cry (3.9)

where ‘oa’ is the (membrane) stress induced by the external pressure and ’ob’ is the stress
induced by the bending moment. The pressure-induced stress is defined as:
(3.10)

The relationship between bending stress and moment in the elastic region is as below:
(3.11)

where ‘q’ is the distance from the center for moment of inertia to the outer fiber, ‘ray’ the
initial curvature and ‘I’ the moment of inertia. From Equation (3.8) it is seen that for small
the
values of the ratio ‘~JP~,~’, change in the elliptical of the pipe due to pressure can be
neglected and the maximum bending moment is obtained by multiplying the compressive
not
force ‘pexrav’ by the initial deflection ‘~1’. When the ratio ‘p/~~,~’ small, the change in
is
the initial elliptical of the pipe should be considered and Equation (3.8) must be used in
calculating ‘M-’. Thus it is found that
(3.12)

Assuming that this equation can be used with sufficient accuracy up to the yield point stress
of the material, the following equation can be obtained:
(3.13)

from which the value of the uniform pressure, ‘py’, at which yielding in the extreme fibers
begins, can be calculated as:

(3.14)

It should be noted that the pressure ‘py’ determined in this manner is smaller than the pressure
at which the collapsing of the pipe occurs and it becomes equal to the latter only in the case of
a perfectly round pipe. Hence, by using the value of ‘py’ calculated from Equation (3.14) as
the ultimate value of pressure, the results are always on the safe side.