# Minimum inertia for GRP stiffener

Discussion in 'Class Societies' started by DUCRUY Jacques, May 24, 2012.

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### DUCRUY JacquesJunior Member

Hello,

I don't understand the formula used by ISO 12215-5 for calculate the minimum moment of inertia for a GRP stiffener.

In DIS 2004, the formula was the same than ABS ORY 1986 :
I = (26040 P s l^3) / E
with P in KN/m², s and l in meter et E in N/mm², for a deflection of 1/100 of unsupported length.

The actual formula is :
I = (26 * P s l^3) / (K1s E) * 10^-11
with P en kN/m², s and l in mm, E in N/mm² and K1s = 0.05.

The result is very different (I don't take in account the curvature factor for simplicity).

Best Regards

Jacques

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### TANSLSenior Member

Although it is impossible to know what the creators of ISO have done, I dare to venture a few possibilities :
• The width of associated plate with the stringer, according to ISO, is considerably less than that allowed by the Classification Societies. Therefore, the moment of inertia of the profile + attached plate has to be lower in the ISO.
• Depending on the type of fastening of profile ends, the maximum supported bending moment varies considerably : BMb (built-in) = pl ^ 2/12. BMs (supported) = pl ^ 2/8 = 1.5 *BMb.
We need to know what is considered in each case (C.S. or ISO)
• The stiffness (δ/L) value admissible for the beam can also vary greatly from C.S. to ISO.
I think in one of these points, or all three, may be the explanation for your questions

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### DUCRUY JacquesJunior Member

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### fcfcSenior Member

I do not see much difference.

The maximum deflection of a fully supported beam both ends, with a uniform load is f=qL^4 / 384 * EI (flèche d'une poutre encastrée aux 2 extrémités avec charge uniformement répartie).

Can be rewritten as :

I = (1/384) * qL^4 /Ef

f = deflection is a percentage of beam lengh : kL k = 1% in 2004, and 5% in 2008 rule.

q is the load per lengh unit = P * s.

1/384 = 0.0026040

and now you have I = 26 10^?? * P*s*L^3 / k * E * 10^???

The computation of exponent of 10 is left to the reader

The two formulaes are the same. Apart for units (mm vs m), and in 2004, the allowed deflection of the stringer was 1% of the stringer length and in 2008, it has been allowed to go up to 5%.

BTW, deflection for FRP plating was checked in 2004 (equation 37 with the cubic root). It is no longer checked in 2008 version of the ISO.

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### Silver RavenSenior Member

Gooday 'Jacques' - - with all due respect - What are you on about ??? - What does this have to do with anything about building a boat ??? I've never heard anything like this subject (then why would I) & I've only been building boats for a few (50) years ??? What's your question - - really - - all about - - that is i- - n plain English ??? Ciao, james

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### J FeenstraJunior Member

I = Inertia,
en.wikipedia.org/wiki/Inertia

thats what it has to do with boating, namely that it has the strenght to withstand waves and things....

I never did a project with GRP materials, but it looks like a lot of fun!

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### DCockeySenior Member

It appears that Jacques is comparing rules for sizing fiberglass stiffeners for a hull or deck from ABS and ISO. Definately relevant to boatbuilding if you are following one of those sets of rules.

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### daiquiriEngineering and Design

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### DUCRUY JacquesJunior Member

Hello,

In fact, I am surprised by the difference of allowable deflection for a stringer (or a transverse frame) : 1 % of unsupported length in 2004, and 5 % in 2008.

In ABS ORY rule, you have 2 % of allowable deflection for the plating, and 1 % of allowable deflection for stiffener.

I know that ISO dont take in account this criteria for plating (except for sandwich plating : 1.7 %).

But for the stiffener, the allowable deflection of 5 % may give a hull too flexible, no ?

Best Regards

Jacques

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### fcfcSenior Member

Flexible : yes. Break probably not.

Beware that if you are using this formulae for stiffeners, it means that you are on the very low end of manufacturing. This apply for stiffeners made with similar materials (title of chapter 11.4). ie Your hull is made mat roving, and your stiffener is also made with mat roving.

Low end manufacturing allowed to flex does not surprise me.

With dissimilar material (ie more normal manufacturing : biax for web, and UD for crown), you have to revert to annex H.

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### TANSLSenior Member

I agree. You may have a stiffener that meets the thickness and inertia but when you make a layer by layer analysis, Annex H, may be that some of the layers is overloaded.

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### DUCRUY JacquesJunior Member

Thank you again.

If my unterstanding is correct, the "standard" formula of inertia for stiffener concern especially the "low end manufacturing" (mat + roving).

Regards

Jacques

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### TANSLSenior Member

What I understand of Chapter 11.5 is that when we use mateirals whose physical properties differed in more than 25% (eg, MAT 600, with E = 6400 and WR500, with E = 13240), one can not consider the shear stress, or bending moment, of the furthest from the neutral axis fiber, but of the first fiber than reaches the design stress. That's why you need to calculate layers according to ANNEX H.
What do you think FCFC?

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