# Impact load from falling ice?

1. Apr 25, 2012

### Microcephalus

Hello

I'm tasked to evaluate the roof of a small power station situated beneath a rather high tower in an alpine landscape, by means of FEA.

One requirement is that the roof shall endure chunks of ice falling on it. Problem is, I am stumped as how to find the loads. The Eurocode norms I am expected to use just shrugs at impact loads and suggests that it be left to "experts". Well, I am the ordained resident "expert" here...

Had it been a ball of steel or some such and strictly elastic behaviours, it would not have been that hard - preservation of energy, the kinetic energy should equal the stored energy of the elastically deflected roof. Then I get the theoretical deflection and if I put it into the FE analysis I get the stresses on the roof components.

Unfortunately, it's not that simple. Primarily because the ice will fracture, secondarily because the forces involved do seem at a first glance to be unreasonable in all aspects.

I mean, a 3 kg ball of ice that falls 60 m has a kinetic energy of about 1800 joule. Slightly less because of drag, but let's ignore that for now.
The roof bends about 45 mm for a 1 kN load, so its "spring factor" is about k = 22 kN/m.
The required spring force for absorbing a certain energy is F = √2kE → F = 8.9 kN.
That is a 900 kg force right there. And the elastic deflection required is ca 400 mm.

So far I am inclined to believe the numbers - problem is that I think the ice will shatter. The chunk will be smashed into snow. That will probably dissipate a bit of the energy.

Or will it?

See - according to a laboratory study I found on the web, they found that a puck of ice hammered with a pressure sensor at 100 ft/s (incidentally more or less identically to the impact speed I expect) will shatter into snow. At some 10-14 MPa pressure, or about 15 kN. And that was a small ø38 mm specimen.

Other sources also list the crush strength of ice at some 5-10 MPa or so depending on temperature and deformation rate.

Am I to suppose that "my" 3 kg ice chunk, estimated to ø100 mm diameter, will need a whopping 100 kN or so to get pulverized? That is ten tons! And if the roof only deflects 400 mm @ 8.9 kN, the ice chunk will not shatter but just bounce off ?

I have a hard time interpreting these numbers. Anyone has any idea what to make of them?

2. Apr 25, 2012

### 256bits

So you have you 3 kg chunk of ice traveling at 35 m/s.

Here is a site regarding hail
http://www-das.uwyo.edu/~geerts/cwx/notes/chap09/more_hail.html
When a hailstone strikes the roof of a car it makes a dent in the metal, and the bigger the size of the hailstone the bigger the dent. Most times the hailstone will strike and bounce and not shatter into snow. You might want to take that into consideration as a comparison to what will happen to your ice chunk ( depending upon the integrity of the ice chunk - will it shatter into many small pieces or remain intact )

The springiness of the car metal roof has little to do with the impact damage as the metal roof as a whole does not react quickly enough to the impact to absorb the shock and only the local stressed area is affected.

You might want to reconsider your analysis and attempt to find out which is worse for the roof - an elastic or inelastic collision, and how big of a chunk of falling ice can the roof withstand before maybe ripping through the sheathing or causing a failure in one of the support structures.

Is that what is being asked from by the evaluation?

3. Apr 25, 2012

### AlephZero

I'm not a civil engineer, but I would have thought the quasi-static loading effects would be negligible, compared with the weight of conventional snow loadng etc, or the weight of somebody working on the roof moving around.

Your proposal about looking at the strain energy from a statics analysis ignores the dynamic response of the roof. The impact would excite the vibration modes of the roof, in different proportions depending where on the roof the impact occurred, and the vibrations would then be damped out. The stress distribution could be very different from a static load applied at the impact point. But again, I would think the loads would be small compared with other design load cases.

That leaves the question is what impact damage might occur, which as 256bits said would probably be about cracking or penetrating the panels, not damaging the structural framework of the building.

The easiest way to answer the question of impact damage is probably by testing some roof panels. If they were intended for use in thse conditions, the manufacturers may already have done that. You could contemplate modeling this with a specialist FE program like DYNA3D or Abaqus Explicit, but there would be a big learning curve and you would still need some test data to validate the models.

Another unknown is how much ice is going to fall. If there was a mini-avalanche of snow-melt from the roof of the tower structure, you could get hit with a lot more than 3 kg.

4. Apr 25, 2012

### Microcephalus

Well, the roof surface should withstand 3 kg without penetration. The hut should withstand 20 kg without the equipment inside taking damage, though it is allowed for the roof to get smashed up, I suppose. And then there is the deposits of snow and ice and wind loads as well - so there are several loadcases to think of.

The snow/ice & wind are easy, there is an abundance of info and methods to use.

I'm more concerned about the penetration resistance of the roof by the 3 kg chunks, and how it (probably) collapses from a 20 kg chunk.

"An 8 cm stone weighs about 0.7 kg and falls at 48 m/s (171 km/h)! It is not surprising then that this hailstorm caused insured damage of over \$300 million (1). The largest hailstone ever measured fell in Kansas in September of 1970: it weighed 755 grams, had a diameter of 14 cm, and fell at about 57 m/s (i.e. 207 km/h). "

If a 0.7 kg lump of snowy ice can make such damage at 48 m/s, I suppose it is not at all strange if a 3 kg chunk at 34 m/s indeed gives the numbers I get.

"The springiness of the car metal roof has little to do with the impact damage as the metal roof as a whole does not react quickly enough to the impact to absorb the shock and only the local stressed area is affected."

I suppose that the momentum indicates this - a 0.7 kg item hitting a 50 kg (?) item at 48 m/s, then the resultant velocity after impact should be only 0.66 m/s. Thus, the car roof does not much absorb the energy by its elastic deflection.

"You might want to reconsider your analysis and attempt to find out which is worse for the roof - an elastic or inelastic collision, and how big of a chunk of falling ice can the roof withstand before maybe ripping through the sheathing or causing a failure in one of the support structures.

Is that what is being asked from by the evaluation? "

They want help designing a proper roof, so I have some freedom changing things to meet the requirements.

I've seen references on the web to gratings being used above equipment in such cases, to split up falling chunks before they hit the equipment. I'm contemplating a web of chains, to also absorb some kinetic energy.