## Stress on strap wrapped around a drum

## Stress on strap wrapped around a drum

(OP)

Sometimes it's the easiest problems that give you the most trouble...

I'm estimating the fatigue life of a thin load carrying strap that's .008" thick and .75" wide, wrapped around a Ø0.1 m drum.

Fatigue from axial loading is as expected (10^9, not a high axial load).

For stress due to winding around the drum, I'm using the simple flexural stress equation: σ = E*c/ρ

You can't screw that calc up.

Stainless steel material. E = 193 GPa

c = 1/2t = 0.5*.008"*25.4/1000 = .0001016m

ρ = .05m

σ = E*c/ρ = (193e9 Pa)*(.0001016m)/.05m = 392 MPa

Sy is 207 GPa

Sut is 517 GPa

According to this calc, I'm nearly double Sy, well into the plastic range, and I should be seeing ~5500 cycles to failure.

Testing, however, has demonstrated around 100k cycles.

I'm at a loss as to where I've steered wrong. I even dug out an old strengths textbook and there's nearly an identical example with the same results.

Thoughts? Thanks in advance.

I'm estimating the fatigue life of a thin load carrying strap that's .008" thick and .75" wide, wrapped around a Ø0.1 m drum.

Fatigue from axial loading is as expected (10^9, not a high axial load).

For stress due to winding around the drum, I'm using the simple flexural stress equation: σ = E*c/ρ

You can't screw that calc up.

Stainless steel material. E = 193 GPa

c = 1/2t = 0.5*.008"*25.4/1000 = .0001016m

ρ = .05m

σ = E*c/ρ = (193e9 Pa)*(.0001016m)/.05m = 392 MPa

Sy is 207 GPa

Sut is 517 GPa

According to this calc, I'm nearly double Sy, well into the plastic range, and I should be seeing ~5500 cycles to failure.

Testing, however, has demonstrated around 100k cycles.

I'm at a loss as to where I've steered wrong. I even dug out an old strengths textbook and there's nearly an identical example with the same results.

Thoughts? Thanks in advance.

Wise men learn more from fools, than fools do from the wise.

## RE: Stress on strap wrapped around a drum

=(weight/2)/Area Strap

## RE: Stress on strap wrapped around a drum

But to your point, I agree that it seems this model is not the correct fit. However, numerous textbook examples demonstrate similar scenarios, including a steel cable around a drum (think overhead crane).

Ignoring the fatigue side of this, the resultant stress just seems much higher than it should be.

Wise men learn more from fools, than fools do from the wise.

## RE: Stress on strap wrapped around a drum

## RE: Stress on strap wrapped around a drum

But there is a separate stress related to the bending of the material as it passes over the drum. That's where my discrepancy is.

Wise men learn more from fools, than fools do from the wise.

## RE: Stress on strap wrapped around a drum

## RE: Stress on strap wrapped around a drum

## RE: Stress on strap wrapped around a drum

## RE: Stress on strap wrapped around a drum

## RE: Stress on strap wrapped around a drum

## RE: Stress on strap wrapped around a drum

Cheers

Greg Locock

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## RE: Stress on strap wrapped around a drum

## RE: Stress on strap wrapped around a drum

The small drum and bend radius likely invalidates the beam curvature assumption that this formula is built on.

## RE: Stress on strap wrapped around a drum

https://www.engineersedge.com/spring_material/cons...

Or, go all in and read this.

https://journals.sagepub.com/doi/10.1177/168781402...

## RE: Stress on strap wrapped around a drum

## RE: Stress on strap wrapped around a drum

## RE: Stress on strap wrapped around a drum

Edit: your quoted material strengths are in GPa, I assume you meant MPa. 200 MPa is about 30 ksi.

## RE: Stress on strap wrapped around a drum

MintJulep - it's not a constant spring, but good idea. However, the equation referenced there is the same equation I was using.

dvd - These are excellent resources, thank you!

Interestingly, their equations use Poisson's ratio. When I crunch the numbers, I get a higher value of stress than using my first equation. They also list a helpful belt life expectancy based on pulley diameter to belt thickness, which for my scenario puts me around 800,000 cycles. They don't explain how they arrive at these numbers however.

I also notice that all of the materials they use in that guide have high tempers (full hard), giving large values for yield strength, which likely explains the high numbers for life expectancy.

So, I think I can conclude that my calculations are correct and the stresses from simply wrapping the strap around the drum are fairly high. However, this does not solve the question as to why I am greatly exceeding my estimated life. I think I need to take a harder look at my fatigue calcs.

Again - thank you all for your input!

Wise men learn more from fools, than fools do from the wise.

## RE: Stress on strap wrapped around a drum

I was not assuming the strap material, it is annealed 302/304, and those values are accurate.

Wise men learn more from fools, than fools do from the wise.

## RE: Stress on strap wrapped around a drum

minimumyield and tensile strength.I am now thinking that the actual values are much higher than that.

Wise men learn more from fools, than fools do from the wise.

## RE: Stress on strap wrapped around a drum

## RE: Stress on strap wrapped around a drum

Wise men learn more from fools, than fools do from the wise.

## RE: Stress on strap wrapped around a drum

I think the material properties are greatly understated.

What a rabbit hole this has become....

Wise men learn more from fools, than fools do from the wise.

## RE: Stress on strap wrapped around a drum

Big thanks to everyone for your input!

Wise men learn more from fools, than fools do from the wise.

## RE: Stress on strap wrapped around a drum

During the wrap around the drum, the strap will be split into three different zones. The outside (top) of the strap will be in tension at 2X the normal tension.

The center will be a neutral plane

The bottom will be in compression. All the tension that used to be in this section are transferred to the top of the strap.

The strap section that is not around the drum will have equal tension throughout the strap.

## RE: Stress on strap wrapped around a drum

Also, could find good info on stresses related to bandsaw blades and wheels.

## RE: Stress on strap wrapped around a drum

## RE: Stress on strap wrapped around a drum

Who knows.... I got my answer regarding higher tensile and yield strength, and that satisfied me. :)

Wise men learn more from fools, than fools do from the wise.

## RE: Stress on strap wrapped around a drum