# Stresses in materials due to curvature and bending

Discussion in 'Boat Design' started by mc_rash, Feb 12, 2022.

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### mc_rashSenior Member

Regarding to PsiPhi's post "Design for review" you can read about curvature of chines and stresses in the curved material. I guess this is only applicable to materials below the yield point (for example steel) or materials without plastic behavior (for example wood).
Is there a simple way to calculate these stresses from a mathematical/engineering point of view?
Is the most simple way to calculate these stresses with S = M*c/I
where
S = sigma/bending stress
M = Moment about neutral axis
y = distance to neutral axis
I = Second moment of area
If, as in PsiPhi's post, the chine is not of rectangular shape but has edges of different length, maybe curved edges, etc. i.e. a complex shape, is the formula above still enough to calculate the stress?
A chine could be seen as a beam with two forces applied at both ends of the beam, and on force (roughly) in the middle in opposite direction to the other two forces. How would you calculate the forces? Would you use the deflection of the beam (or, distance from the outer edge of the chine to the stem) to calculate how big the force needs to be to bend the beam to this point, and then calculate the applied bending moment?
I hope my question is understandable and maybe the question is just a simple one. But for marine engineers/naval architects/ boat designers curvature and stresses are quiet important and, my guess, a daily task. Although today one can calculate with software nearly everything, what is the way to go if stresses in chines are calculated manually?

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### mc_rashSenior Member

Conversion from chine to beam:

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### mc_rashSenior Member

Distance from straight chine to stem (a) and stern (b).

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### Ad HocNaval Architect

You're approaching this in the wrong way.
You need to look at the minimum bend radius of a material of a given thickness; before the material becomes stressed owing to the work applied to the metal, in creating 'shape'.

It is give by this simple relationship:

You can read up more on this in Proboat Magazine's "Altered Properties", Feb/March 2014 issue No.147.

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### AlanXSenior Member

I have a paper for bucking stress for various curved shapes.
For a cylinder:
Scr ~ 0.16*E*t/R, where Sc is the critical stress, E is Young's modulus, t is the plate thickness and R is the surface radius.

I use R ~ (4*d^2+s^2)/d/8, where d = depth and s = span.

When I used these equations I converted stress to pressure by assuming the hoop stress equation applies:
S=P*R/t, where P is the pressure.

Therefore the critical pressure is:
Pcr ~ 0.16*E*(t/R)^2

This is probably the equation you are looking for?
It is what I wanted when looking at monocoque hulls.

Hope that helps, AlanX

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Last edited: Mar 12, 2022
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