How to determine the diameter of a cable

[packersfan851]

A Cable that has a yield strength of 620 MPa and a safety factor of 3. This cable must be able to support 5 buckets which must be able to carry up 5,429.554 kg each.
Bucket mass is negligible.

Stress = Mass/Area
Area = force/stress

My attempt at a solution:
Total weight 5 buckets must carry = 5,429.554 kg * 5 = 27147.77 kg

Area = 27147.77kg * 9.8ms^2 / 206.667MPa x 10^6
Area = .00128

.00128 = ∏d^2 / 4
.00164 = d^2
.040496m = d
or 40.497mm

I know this is probably all wrong.

 

[rock.freak667]

That looks correct to me, your method at least, I don't have a calculator right now to check your numbers.

 

[CWatters]

Calculation looks ok as well.

 

[cmmcnamara]

Wouldn't this methodology be a bit wasteful design wise? In addition to utilizing a specified factor of safety the loading is then taken to be occurring in one specific point as a combined whole when in reality the buckets are five distinct and spaced point loads?

 

[CWatters]

I guess you are right. You could use a different diameter for each section of rope. eg getting thicker as you go up and the load increases. Not clear if that would reduce cost though. In practice the joints and method of attaching the buckets would complicate the issue.