Help with Conversions. Derive height from area.

[agodina]

Our company needs to purchase a shelter for a customer. Our customer requires that the shelter can handle a snow load of 2 inches (in height). We have found a shelter but snow loading is stated to handle 40 lbs per square foot. Is it possible to find out whether the shelter we are looking at meets or exceeds the 2 inch snow load requirement?

So far I have figured the following:

There are 1728 cubic inches per square foot.

A square foot of ice weighs 57.41 lbs. That means a square inch would measure .033 lbs per square inch (57.41/1728).

Would that mean, at two inches, the snow/weight requirement would be .066 lbs (.033*2)?

I calculated 40 lbs per square foot to be .023 lbs per square inch (40/1728). At two inches (.023*2)that would be .46 lbs per square inch, meaning the shelter does fall within specified requirements.

Are my assumptions and calculations correct?

 

[mmm4444bot]

Are my assumptions and calculations correct?

I'm not sure because I did not carefully review them; I started thinking along different lines.

Let's assume that your weight for 1 cubic foot of ice is correct (57.41 lb).

That seems reasonable, since 1 cubic foot of liquid water (at 62 degrees Fahrenheit) weighs 62.4 lb (rounded). Frozen water weighs less by volume because it contains pockets of air.

Also, your conversion from feet^3 to inches^3 is correct.

1 cubic foot = 1728 cubic inches

Now, if we take that cubic foot of ice and cut off the top 10 inches, then we have a 12-inch by 12-inch by 2-inch block of ice.

Volume = 12 * 12 * 2 = 288

By cutting off the top 10 inches, we reduced the volume from 1728 cubic inches to 288 cubic inches.

How much does this smaller block weigh? In other words, how much does 2-inch thick ice weigh per square foot?

288/1728 = 0.1667

The smaller block's volume is 16.7% of one cubic foot, so its weight is 16.7% of 57.41 .

0.1667 * 57.41 = 9.57

We see that 2-inch thick ice weighs less than 10 lb per square foot.

The manufacturer claims that the roof supports 40 lb per square foot.

That particular roof can easily support 2 inches of ice. (Mathematically, it can support about 8¼ inches of ice.)

And, since ice is generally heavier than snow, that roof can probably support more than 8 inches of snow.

 

[agodina]

Thank you for reply.

I was confused on whether to use squared feet or cubic feet to figure this out. The spec is stated in squared feet (lbs per square foot) but it certainly seemed like a volume problem, not an area one.

Again, thank you for your help.