GRP top hat stiffener section modulus design

In "Principles of Yacht design " fourth edition by Larsson, Eliasson, Orych there is a diagram
for evaluating the SM of top hat stiffener (see attached copy). I would like to know the origin ( the reference of the book, article or code ) of this diagram because is not clear "including effective width of plating" but the plating thickness is not defined.
Thanks in advance.

 

In the days when computers did not exist, these graphics were very useful, they were "a treasure". Currently, with any CAD program, or even with Excel, the modules of top hat reinforcement can be calculated quite accurately and very quickly.
Not only is the thickness of the associated plate missing, but its width depends on several things, which are not taken into account in those texts, and the actual shape of the reinforcement is not taken into account either.

 

I am assuming that you are able to calculate the moment of inertia of various shapes
When you attach the upper channel to the skin/plating, (so long as the joint will be strong enough to accommodate the shear flow stresses, a reasonable assumption), to the skin, you should include some of the skin as it becomes part of the
stiffener. Ie it becomes part of the beam. ie top hat/channel with the additional lower PART of the skin which adds to the stiffener.

Just some numbers to help with the discussion

Assume that the top hat/channel is 5 cm by 5 cm and .5 cm (call it the top for now) and the skin is .5 cm thick
And say that the centerline distance between to channels is 30 cm.

So the skin creates a flange on the bottom which would increase the MOI, but (depending on whether the skin is in tension or compression) the flange, ie the part to the right or left of the channel MIGHT not be able to take the
stresses without some buckling or distortion which will reduce its strength that was the mathematically calculated. This distortion or buckling would occur near the center between two stiffeners.

In floor joist design, with a thick floor, an accepted practice is to use 1/2 the distance between joists, say up to 16 inch centers. But with the dimensions above, ie 30 cm, expecting that a 15 cm flange prox sticking out of each side of the
channel (1/2 of 30) I would not do calculations using the 1/2 the distance estimate.

Obviously as the skin thickness gets thinner, it ability to remain stable without the flange buckling is reduced and you need to reduce the width of the skin that you include in your calculations.

Perhaps Adhoc or Tansl can provide guidelines for Lloyds or others as the amount allowed should be covered in scantling requirements

I have seen where aluminum boat builders do not consider that the neutral axis needs to be established in order for wiring, fuel lines, pipeways etc can be cut near the NA instead of say 1/2 way down the channel if you want to optimize
the profile.

So to your comment "this diagram because is not clear "including effective width of plating"" The effective width of the plating that can be included in the moment of inertia/section modulus calculations can vary depending on the skin thickness as to how far that the skin outside the dimensions of the
channel/top hat sticks out.

 

The "effective width of the plating" is a structural concept about how much of the plating is effective to prevent buckling of the applied stiffener. It is generally expressed as some factor (F) * thickness so thickness really doesn't need to be defined; it is defined by other loads (i.e. primary bending, pressure loading, etc). What exactly factor (F) is is dependent on the material and the rules you are using. FWIW, Gibbs & Cox's Marine Design Manual for Fiberglass Reinforced Plastics took the effective width of the plating as twice the width of the top-hat flange which was also the span of the tabbing. This is conservative. Where that precise figure you referenced came from...<shrug> could be the authors own work derived from first principles laid out in any classic structural text.

 

You may find the following simple guide of interest for you. in calculating the modulus of top-hat stiffeners, in both single skin and sandwich construction, respectively:

Here:


And here:

 

USCG NVIC 8-87 as referenced above.
NAVIGATION AND VESSEL INSPECTION CIRCULAR NO. 8-87 With Change 1 Electronic Version for Distribution Via the World Wide Web Subj: Notes on Design, Construction, Inspection and Repair of Fiber Reinforced Plastic (FRP) Vessels
https://www.dco.uscg.mil/Portals/9/DCO Documents/5p/5ps/NVIC/1987/n8-87.pdf

 

This is what, being a little more detailed, you have to calculate in general (it's not taken from any book but it's normal practice)

The procedure does not change if the attached plate is of the sandwich type and its width depends on several factors, among which the spacing between reinforcements, the fixing of their ends and the mechanical properties of the laminate must be taken into account.