Page 79 - Pipelines and Risers

52 Chapter 3

(3.30)

(3.31)
Solving for w:

(3.32)

Inserting the values for utem and ucow gives:

(3.33)

(3.34)
(3.35)

3.4.3 The Bending Moment
The bending moment capacity of the pipe can now be calculated as, see Figure 3.6:
M&.p. =-(A-IymrPl +L,,,2Ymp2bmp +A,.Y-u,, (3.36)

Where Acornpi, &Omp~ and A,, are as defined above. y is the distance along the bending plan
from origin to the mass center of each area.
(3.37)

(3.38)

(3.39)
A-ly-l = 2rr:[sin(w)-sin(fl)] (3.40)

(3.41)

(3.42)

Inserted this gives the following expression for the bending moment capacity:

M&~ -2r: [sin(y)-k, sin@)]u,,, +2rr: sin(v)u, (3.43)
=
(3.44)