Still Water Bending Moment

I'm trying to make a workable spreadsheet for a boat we are trying to check the longitudinal hull girder strength of. I have on hand the weight distribution of the boat per section and the buoyancy per section. I tabulated these datas, Weight-Buoyancy = net load. And with these net loads the values for shear forces. What I'm stuck on is how to tabulate these shear forces to have the bending moments per section on the boat. I've tried reading up on the matter but it seems I'm missing something. Could someone kindly point me in the right direction. Or if I've done anything wrong from what I've described let me know.

 

Welcome to the forum.

You need to calculate the LCB and LCG. Because the shear curve does not look like the LCG is over the LCB, which means that the ship is not in trim. Once the ship is in trim, then recalculate.

EDIT: Yeah, I checked it real quick and you are over 1/2 a frame spacing off. And also I really don't believe that your frame spacing is constant over the length of the vessel.

 

Hi, Thank you for your reply.

The ship is already in the water, and we are trying to see if our ship can withstand additional ballast. We have a huge amount of ballast at the aft part of the vessel which was added before (I heard) since the boat is top-heavy.

Will the hull girder analysis not work when the LCG and LCB are not on the same line?

What do you mean that I'm 1/2 spacing off? It is true that the frame sections of this ship are not equal but the distribution I was given is equally spaced.

Apologies if these are stupid questions, been a while since I did these kinds of calculations and I am still trying to relearn. Thank you for your patience.

EDIT: Also is the tabulation of the loads correct, resulting in the moment? I'm not confident I'm understanding mathematics completely. Thank you again.

 

I agree with @jehardiman , LCG should be equal to LCB.
Once that is achieved, you must check that the trim you have calculated matches the one the boat presents in the water.
Then check that the sum of the weights exactly matches the total buoyancy.
With all that, all you have to do is calculate the results in the "support" points of the hull.
Finally, to calculate the bending moment at a point located at a distance "x" from the APP, take moments of the forces that are to the right of that point with respect to it.
It is an approximate method since the integration should be continuous and we are making it discrete, but it should suffice.

 

If the LCB and LCG don't vertically align that means that you are missing a moment somewhere. Therefore the hull girder analysis will not be correct.

By your tabulation, the LCG is at FR 52.29 but the LCB is at FR 52.83; so something is forcing the stern (?, anyway FR 0) up by 696 FR-tonnes (whatever frame spacing is).

 

I see what you mean now by the LCB not matching the LCG now. I'll recalculate these then.

When you say "Take moments of the forces that are to the right of that point with respect to it". This is where I have a difficult time wrapping my head around. So I just take moments from one side of one point (ignoring the left)? So I could assume that my moment at x is the sum of all the moments to the right of it, then I could use that sum of moments to at least have a rough estimate of the nominal stress of that vessel at point x.

So if Im understanding correctly, I also made a mistake by not positioning the distribution equidistantly from each other (upon checking the distances are based on actual framing so they vary a bit by frame). This is why the integration is not working correctly.

 

Thanks for your reply. You're right. i will recalculate these then. The framing is off.

 

You are correct.

No that is not necessary.

On the other hand, both the curve that defines the buoyancy in each section and the one that marks the distribution of weights should be continuous. The first is relatively easy to define if the submerged areas of each frame are known. But the second one is more difficult because, apart from the local weights, the distribution of the weight of the structure along the total length is not easy to do correctly. So, in a very preliminary approximation, you could define this curve (or graph) discretely. But, as I warned you before, before doing any other calculations, check that the total weight/buoyancy defined by both graphs are the same.

 

Thank you. These are all very helpful to me.