# Tension Leg Platform - Tendon Forces

1. Sep 20, 2011

### devrandom

1. The problem statement, all variables and given/known data

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

2. Relevant equations

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

3. 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.