GZ curve and critical axis

Hi all,

Thanks for your help in advance!

I want to get the GZ curve for my semisubmersible platform. Unlike the GZ curve for ships, first I need to get the critical axis for the platform. Does any one know how I can get the critical axis?

I don't have any commercial program available for my study. Thanks for this forum, I may use ArchimedesMB to get the GZ curze. But i am not sure if ArchimedesMB is capable of heeling around the "critical axis" rather than the longitudinal axis.

Any suggestions would be greatly appreciated!

Thanks!
Jason

 

Sorry, perhaps the answer is obvious, but I do not know it: what is that you call "critical axis"?

 

Hi TANSL,

Sorry for the unclear question.

Critical axis was introduced mainly in the offshore industry. For ships, the longitudinal axis is taken as the heeling axis, but for the offshore structure, the critical axis is not necessarily the longitudinal axis. It can be interpreted as the heel direction leading to the smallest area under the MR restoring moment, also it can be viewed as the axis direction for which a given heel angle is reached with the least effort.

Thanks!
Jason

 

I suppose, then, that will be the axis about which the flotation area has the lowest moment of inertia. With a CAD program (AutoCAD, for example) that axis can be obtained with a few attempts.

 

Then you first need to determine from the arrangement of the legs that gives the least second moment of inertia WPA.

 

This is a 1st year statics problem similar to finding the minimum sectional modulus of an angle, so you could look it up in Merriman or Marks. IIRC you need the centroid and products of inertia (Ixy) as well as the two principle moments (Ixx, Iyy)...been a while since I did one.

 

Went and found it (J L Merrriman, Engineering Mechanics, Vol 1,Statics) inclination of the principle axis about the centroid

.(edit maybe I shouldn't have done that...homework and all...will do him good to look it up.)

 

It was actually the late J.L. Meriam who was the original author of this book, now edited by L.G. Kraige.

 

And I shouldn't spell either.

 

But why does an engineering student need to remember statics and the content of similar basic courses when there will be software to do everything?

 

All of which is very well for a simple closed convex volume. But looking at a structure such as a platform that is being tilted and sunk, not so obvious.

I think what I would do is pick an arbitrary point on the surface and construct two parallel lines that are R away from the point. Calculate I of the waterplane about the two lines and sum. Rotate the lines by some increment and repeat. The lowest sum will occur parallel to the critical axis. This relies on the parallel axis theorem to eliminate the need to find the exact center. Once you have the angle, you can solve for the axis by interpolating the I values calculated for that angle. Ia - x^2*A = Ib - (2r - x)^2*A. Solve for x.

 

philSweet, it seems very laudable your intention to give a solution to the problem but I think without knowing the shape of the platform, or the shape of their flotation is useless venture a solution. The possibilities are so many that it is impossible to give a valid formula, imo.

 

There are standard equations for combining the second moments of inertia of the components of a system to obtain the second moments of inertia of the overall system, etc. Split the system into manageable chunks, calculate the moments for each chunk and then combine the results for the chunks.

 

Okay, that's step one. That's what I'm doing to get the inertia wrt one of those lines I described. Now how do you proceed to find the critical axis of an arbitrary structure from there? You can solve for the 2nd moment about the neutral axis for each angle and compare, but I was pointing out you don't need to do that. You can identify the orientation with out knowing the actual axis. This may be useful or may not be.

 

See jehardiman's posts above. If Ixx, Iyy, Ixy and the centroid locations are known then the location and orientation of the principal axis can be calculated directly.