The following topics related to hydrostatic loading are available:
For pipe cross sections, external pressure tends to crush the pipe and internal pressure tends to stabilize it.
The inside static pressure is:
(12–16) |
where:
= internal pressure |
= input internal pressure (input as face 1 on the SFE command) |
= internal fluid density |
= acceleration due to gravity (input
as ACEL_Z on the ACEL command) |
= vertical coordinate of the point of interest |
= Z coordinate of free surface of internal fluid (input as face 3 on the SFE command) |
The external static pressure is:
(12–17) |
where:
= external (crushing) pressure due to hydrostatic effects |
= input external pressure (input as face 2 on SFE command) |
= external fluid (ocean) density |
= vertical offset from the global origin to the mean sea level (input on the OCDATA command) |
Buoyancy on the outside tends to raise the pipe to the water surface. The buoyant force for a completely submerged element acting in the positive Z direction is:
(12–18) |
where: |
= vertical load per-unit-length due to buoyancy |
= outside diameter including insulation |
= coefficient of buoyancy (input as Cb on the OCDATA command) |
Also, an adjustment for the added mass term is made.
Effective tension, subjected to internal and/or external pressures (effective force), is useful for determining, among other effects, whether a pipe model will buckle. Effective tension is calculated as:
(12–19) |
where:
= effective tension |
= force in pipe wall = |
= axial stress in pipe wall |
= internal pressure |
= inside area = |
= inside diameter = |
= outside diameter (input on the SECDATA command) |
= wall thickness (input on the SECDATA command) |
= external pressure |
= outside area = |
= effective diameter = |
= insulation thickness |
Exception: If KEYOPT(6) = 1 (PIPE288 and PIPE289), specifying that internal and external pressures do not cause loads on end caps.
To ensure that the problem is physically possible as input, a check is made at the element midpoint to see if the pipe cross-section collapses under the hydrostatic effects. The cross-section is assumed to be unstable if:
(12–20) |
where:
= Young's modulus (input as EY on MP command) |
= Poisson's ratio (input as PRXY or NUXY on MP command) |
Elements such as PIPE288 have three direct stress components: axial, hoop, and radial. Elements such as LINK180 and BEAM188, however, have only an axial stress component; therefore, an adjustment is necessary to include the effect of the three stress components of a hydrostatic load.
Consider the first line of Equation 2–2, assuming isotropic materials and no thermal effect:
(12–21) |
where:
= axial strain |
= Young’s modulus (input as EX on the MP command) |
= axial stress |
= Poisson’s ratio (input as PRXY or NUXY on the MP command) |
= = stresses normal to the axial direction |
For hydrostatic loads:
(12–22) |
where:
= hydrostatic pressure |
Combining Equation 12–22 and Equation 12–23:
(12–23) |
The factor () is used to give the correct strain. Thus, the following restrictions apply to this approach:
Material must be isotropic.
Material must be elastic.
Fluid pressure is assumed to be hydrostatic everywhere (that is, CTUBE and HREC beam subtypes presume that the flooding option is applied, and there is no option for removing it).
It is of course preferable to use the pipe element rather than the beam element, as doing so avoids the limitations that apply to the beam element with subtype CTUBE.
Because hydrostatic pressure (stress) is normally much lower than the working stress, the restrictions described above typically need to be considered only for extremely deep applications.