Cantilever rod spring

[TeejT]

I need to design a cantilever rod spring contraption to reduce the bend radius of some heavy tension cable. I don't need advice on the idea, but I want to verify that the procedure/number crunching is correct.

I am treating this as a point load P of 1000 lbf (4450 N) at the end of the cantilever circular rod.
I want the rod to return to its initial position after P is removed (no plastic deformation).
I am using 304 stainless steel, 7" long rod, 3/8" diameter.
Yield stess ~ 276 MPa

I think the only loading issue here is shear stress, and V(max) = P. Please correct me if this is not the case.

I (moment of inertia) = 1/4*(pi)*r^4

Then Shear Stress = (VQ)/(It) -> this works out to Shear Stress = 83.4 MPa for me, which is less than 276 MPa so I think the rod will NOT DEFORM PERMANENTLY (PURE ELASTIC DEFORMATION). AM I MISSING ANYTHING HERE?

Now to calculate the displacement of the end of the rod:

E (modulus of elasticity) ~ 193 GPa

Displacement (end of rod) = -(P*L^3) / (3*E*I)

For the 3/8" rod I get end displacement ~ -4.3 in.

Does this look correct? Thank you!

 

[Ltwine]

Make sure bending stress is below yield, f=Mc/I.

 

[TeejT]

Forgot about that! That's over 9 GPa!

 

[Ltwine]

Yeah, figured it would by looking at the deflection.

 

[TeejT]

Thanks!

 

[msquared48]

You might want to reduce the stree seen by the rod considering that fatigue will be an issue with time as you repeatedly stress up to or near the elastic limit.

Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask

 

[Ltwine]

You welcome.

 

[TeejT]

Yeah fatigue would be an issue but as it turns out I'm WAY over the yield strength anyway.