# 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. Commented Apr 6, 2021 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. Commented Apr 6, 2021 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! Commented Apr 7, 2021 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.