Fishing rod mechanics and curvature calculations

[cardboard]

i am trying to make a piece of stainless steel of varying thickness bend in such a way that it creates a cam profile in much the same way a fishing rod works.

for example if the thick end has a 5mm by 10mm cross section and the thin end is 1mm by 10mm crosssection and the change in thickness is uniform down the length then a certain profile will be induced when the beam is bent if the thick end is fixed.

if the transition from 5mm to 1 mm is not uniform i.e. the first 100mm of the beam is 5mm and the last 100mm is 1mm then a different profile would be induced when bent about the thick end.

i need a method of calculating what rate of change in thickness i need to give a certain profile?

can anyone help?

thanks

 

[ank_gl]

Finite Element Analysis!

Hmm deriving the variation of cross section from the deformed geometry is sort of reverse of what the usual trend is. But it can surely be done with a sound understanding of the subject.

 

[cardboard]

are you asking for more detail or saying you don't have the knowledge in this area?!

 

[minger]

From what I understand, the deflection in a beam is a 4th order ordinary differential equation. I would assume that if you assume a function for the displacement, then you can integrate (or maybe derivate) to obtain a function for the moment of inertia.

 

[ank_gl]

are you asking for more detail or saying you don't have the knowledge in this area?!

I am telling you the easiest way out. Just crunch in numbers in a software & wollaa.(hit & trial method)

From what I understand, the deflection in a beam is a 4th order ordinary differential equation. I would assume that if you assume a function for the displacement, then you can integrate (or maybe derivate) to obtain a function for the moment of inertia.

Exactly. I just thought that would be a bit too much maths.

there you go...
http://www.efunda.com/formulae/solid_mechanics/beams/theory.cfm