TeejT
Mechanical
- Jan 19, 2010
- 80
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!
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!
