Buckling of a Bucket

A lazy Sunday afternoon on my apartment balcony, a friend sitting beside me on a bucket. Conversing rubbish most probably. As he got up to leave, the bucket he was sitting on crumbled. A normal occurrence with thin buckets.

See, in my practice, that crumbling of bucket is called buckling. And rightly so, buckling came to my mind. So, what of it? Not that I have to design the bucket to resist my friend's weight. But you might agree with me on my intuition. 

The formula for critical buckling load is quite eye catching. It's one of the easiest to remember, if you get what I mean.




So, as you might have guessed it by now. My quest began to find the elastic modulus of the plastic. 

First, I got a measuring tape to measure the dimensions. A bucket with a smaller diameter of 23 cm, large diameter of 32 cm and a Height of 32 cm.

The bucket in question. 
Those are actually the diameters and not radius as I wrote on my stickons.

Taking pinned connection at the bottom, as it is not fixed to the bottom. The KL in the formula above becomes the Height of the bucket. 
My friend has a weight of 60 kg. As he was sitting on it, let's assume 50 kg was upon the bucket. Or rather let's take a load of 500 N was over the bucket.
I used the formula for hollow cylinder while calculating the Moment of Inertia, as it is mostly hollow. Taking an average diameter of 28 cm with a thickness of 0.1 cm.

On calculating, I got an Elastic modulus of 0.000608 GPa. On checking the internet, the material which comes close is PVC (polyvinyl chloride) which has a min value of 0.001 Gpa to max of 1 GPa. 

I would say it's made of PVC, although my calculations should be more accurate.

The units are in GPa (min and max)

Conclusion: The Euler buckling formula has various assumptions. One is that the length of the column must be significantly larger than the cross sectional dimensions. There might be other assumptions I made that were wrong.

Always open for discussion.

It's just a minor side project of mine. It does not have any relation with my Job.







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