Pseudo-Static Hydrodynamic Loading - CAESAR II - Help

CAESAR II Users Guide (2019 Service Pack 1)

Language
English
Product
CAESAR II
Search by Category
Help
CAESAR II Version
11.0 (2019)

You can model individual pipe elements that experience loading due to hydrodynamic effects.

SHARED Tip Fluid effects can impose a substantial load on the piping elements in a manner similar to, but more complex than wind loading.

Use wave theories and profiles to compute the water particle velocities and accelerations at the node points. Then use, Morrison’s equation, F = ½ * r * Cd * D * U * |U| + p/4 * r* Cm * D2* A to compute the force on the element.

Where:

r - is the fluid density

Cd- is the drag coefficient

D - is the pipe diameter

U - is the particle velocity

Cm - is the inertial coefficient

A - is the particle acceleration

The particle velocities and accelerations are vector quantities that include the effects of any applied waves or currents. In addition to the force imposed by Morrison’s equation, piping elements are also subjected to a lift force and a buoyancy force. The lift force is defined as the force acting normal to the plane formed by the velocity vector and the axis of the element. The lift force is defined as:

Fl = ½ *r * Cl * D * U2

Where:

r - is the fluid density

Cl - is the lift coefficient

D - is the pipe diameter

U - is the particle velocity

The buoyancy force acts upward and is equal to the weight of the fluid volume displaced by the element.

A piping system can be described by using the standard finite element equation:

[K] {x} = {f}

Where:

[K] - is the global stiffness matrix for the entire system

{x} - is the displacement / rotation vector to solve for

{f} - is global load vector

Calculate pseudo-static hydrodynamic loading

  1. Place the element loads generated by the hydrodynamic effects in their proper locations in {f}, similar to weight, pressure, and temperature.

  2. Perform a standard finite element solution on the system of equations to finalize [K] and {f}.

  3. Use the resulting displacement vector {x} to compute element forces.

  4. Use the computed element forces to compute the element stresses.

Except for the buoyancy force, all other hydrodynamic forces acting on the element are a function of the particle velocities and accelerations.