Tension Leg Platform - Tendon Forces

[devrandom]

Homework Statement

I am trying to work out the forces acting on the tendons of a tension leg platform.

I am given:

a) Young's Modulus, length of the tendons and cross-sectional area (and thus can work out k)
b) The displacement against time of the platform in three degrees of freedom (surge, heave and pich).
c) Pretension on the cables (in N)
d) Weight of the platform (can work out buoyancy forces etc)
e) Depth of the water

What I need:
a) Tendon forces acting in each degree of freedom
b) Tendon moments in each degree of freedom

Homework Equations

k = EA/L
F = kx (where x is the the deformation of the spring)

The Attempt at a Solution

I worked out the buoyancy force using Archimedes' principle.

For the surge condition (if d represents the amount the platform has moved):
The stretched tendon length is:
$\sqrt{d^2 + depth^2} = L_s$

As such, the deformation of the tendon is:

$L - L_s = x$

From this, we can use F = kx to get the force applied to the tendon.

I'm not sure if this is right because I'm not very experienced with forces (I'm an electrician). The rest of the degrees of freedom have me totally stumped - I'm fairly sure I'm looking at it incorrectly - I know that there will be a resultant force, caused by all three degrees of freedom.

 

[mark726]

Hi there,

It seems like you are on the right track with your solution for the surge condition. However, keep in mind that the tendon is not a spring and will not behave exactly like a spring. The relationship between force and displacement may not be linear, especially if the tendon is being stretched beyond its elastic limit.

To calculate the tendon forces for the other degrees of freedom, you will need to consider the direction and magnitude of the displacement, the angle at which the tendon is being pulled, and the pretension force. You may also need to use vector analysis to determine the resultant force on the tendon.

For the moments, you will need to consider the distance from the pivot point and the direction of the force acting on the tendon. You can use the equation M = Fd to calculate the moment for each degree of freedom.

It may also be helpful to create a free body diagram for each degree of freedom to visualize the forces and moments acting on the tendon.

I hope this helps and good luck with your calculations!