column of solid collapsing under its own weight

[thebillsfan]

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this problem has always stumped me...what information do you NEED to have in order to be able to answer this type of question?

"A column of concrete can be made how tall before it collapses under its own weight?"

density, bulk modulus, area of the base, and yield point?

and if you have all of that information, how would you go about solving the problem?

 

[RogueUnicorn]

you would use young's modulus here not bulk, as the compression occurs in one direction.

that being said, this question rather confusing... what does "collapse" imply? because theoretically speaking, as you build the column up, it just gets more and more compressed.

 

[thebillsfan]

you would use young's modulus here not bulk, as the compression occurs in one direction.

that being said, this question rather confusing... what does "collapse" imply? because theoretically speaking, as you build the column up, it just gets more and more compressed.

yeah, sorry, i meant young's. collapse meaning eventually the weight of the column will be so great that it exerts a pressure above the yield point.

 

[RogueUnicorn]

yeah, sorry, i meant young's. collapse meaning eventually the weight of the column will be so great that it exerts a pressure above the yield point.

is this yield point provided to you? because if so, you don't even need modulus.

 

[thebillsfan]

oh, i see. so if you have the yield point, which i believe is given in terms of pressure, would you just set that equal to density*g*h, and solve for h? what if you dont have the yield point (i'm assuming you can't do this problem w/o the yield point)?

 

[RogueUnicorn]

oh, i see. so if you have the yield point, which i believe is given in terms of pressure, would you just set that equal to density*g*h, and solve for h? what if you dont have the yield point (i'm assuming you can't do this problem w/o the yield point)?

remember, P=F/A, so you need the cross sectional area as well. i suppose the yield point can be calculated, but i wouldn't really know where to start until i can see what hints the question tosses my way

 

[thebillsfan]

that's what i was thinking too, but if the yield point is in terms of pressure, and the expression density*g*h always is in terms of pressure, why should the cross sectional area matter as well?

 

[RogueUnicorn]

oh sorry, i didn't pay attention to your formula. yes you are correct, area unneeded

 

[wanderer]

oh sorry, i didn't pay attention to your formula. yes you are correct, area unneeded

I can see why from the equation you wouldn't need area, but intuitively the taller something is, the wider it must be so that it doesn't collapse. What is the source of my confusion?

 

[thebillsfan]

I can see why from the equation you wouldn't need area, but intuitively the taller something is, the wider it must be so that it doesn't collapse. What is the source of my confusion?

the wider it must be so that it doesnt tip over. would it necessarily collapse?

 

[wanderer]

the wider it must be so that it doesnt tip over. would it necessarily collapse?

I don't believe it's an issue of torque.

 

[RogueUnicorn]

I don't believe it's an issue of torque.

you absolutely sure about that? tall buildings have to withstand a lot of windshear

 

[wanderer]

you absolutely sure about that? tall buildings have to withstand a lot of windshear

That's true. Still, I don't think it's solely about torque.

 

[loveoforganic]

Wanderer - increasing area, increasing weight that can be carried, but also increasing pressure. In the case of real buildings, you're not dealing with just straight columns generally. They're filled with rebar. I'm not sure in what way that changes the situation, but it definitely changes it somehow!

 

[Hemichordate]

So is bulk modulus only dependent on compressibility, or on other factors as well?

 

[thebillsfan]

So is bulk modulus only dependent on compressibility, or on other factors as well?

i think bulk mod. IS defined as compressibility. its a constant that we will be given.

 

[RogueUnicorn]

i think bulk mod. IS defined as compressibility. its a constant that we will be given.

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