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# Bending stiffness of Tube rod assembly

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## Bending stiffness of Tube rod assembly

(OP)

A polymer tube 2.5mm diameter with a Youngs Modulus = 2 GPa that contains a metal rod diameter
0.75mm with a Young's modulus of 107 GPa. I need to know the overall bending stiffness of the
assembly.

If both materials were touching it would be simple i.e.

k = EI , where I = 2nd moment of area. and just add the two stifness values.

However, i need to know how to calculate the stiffness for the above conditions i.e. material not
touching.

### RE: Bending stiffness of Tube rod assembly

Ignore the polymer tube in your calculations and you would have a safe, conservative design. The polymer tube would have to have spacers between the inside face and the outside face of the metal rod to allow the total assembly bend as one. The connections would have to be good enough to allow no internal movement between the rod and the tube. Good luck!

### RE: Bending stiffness of Tube rod assembly

Your on the right track. Let's keep in mind that the deflection under load is equal for both beams. If we set the applied load Ft = F1 + F2, and considering for example a simply supported beam where y = Pl^3/48EI, we can write
y = F1 * l^3 / 48*E1*I1 = F2 * l^3 / 48*E2*I2.
F1/F2 = E1I1/E2I2, F1 = F2(E1I1/E2I2),
Ft = F2(E1I1/E2I2) + F2 = F2(E1I1/E2I2 + 1)
Now, given the Ft, E1, I1, E2, and I2, we can find the deflection y.
You can then use the calculated value for y to back calculate the effective stiffness of the assembly.
Look this over and post.
Thanks

GEFought
jfought@invacare.com

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