# Minimum drum wall thickness when rope wrapped around it

I need to design a hollow drum that holds steel wire rope under tension. The wire rope gets pulled from both ends with a force of 200kN, it is wrapped around the drum 5 times. The outer diameter needs to be 1m and I was thinking of using S355 for this application.

My question is: How would I go about calculating the minimum wall thickness of the drum, as to withstand the ''crushing'' pressure of the wire wrapped around it?

if you cut the drum longitudinally into two half-cylinders you will have 10 cut ropes with a tension of 200kN.

Let's say the center to center distance of each rope is L inches (moderately small WRT. to the radius) then you have to calculate the area of the section of the barrel between the ropes and a thickness,t, and a safety factor of 1.6

$$1.6*200kN/(L*t)< \sigma y_{steel}$$

$$t> 1.6 \frac{200kN}{L \sigma y_{steel}}$$

• You also need to consider bucking of the drum, which is complicated (and knowing only the diameter is not enough data). See abbottaerospace.com/aa-sb-001/… for example. – alephzero Apr 6 at 15:21
• @alephzero, i treated this loosely as a barrel under external uniform pressure. It is handled in the industry the same. of course, the assumption is spotty. But is a good approximation. – kamran Apr 6 at 16:39
• I agree there is nothing wrong with the approximation as a static analysis. On the other hand buckling failures are like walking around near the edge of a cliff wearing a blindfold. Either you fall over the edge or you don't. You don't get any warning signs (like excessive bending or permanent plastic deformation) before it happens! – alephzero Apr 7 at 12:23

I suggest checking hoop stress due to torsion against the allowable shear stress of the drum as graphically shown below. It should be a multi steps process - 1) Assume line element with thickness t and diameter d ≈ D, then solving for t. 2) From the obtained t, solve d, then check the stress again. 3) Adjust t and repeat step 2 if necessary.