Scaling Up for Giants

[Teguci]

Thought some engineering analysis would be appropriate for this article. Basically, if you scale a structure up (and its associated loads), by what factor would you need to increase all dimensions? In this article the author has checked compression on the leg of a chair. What do you guys think? What about bending? If not a linear scale, then what?

http://www.wired.com/wiredscience/2012/05/big-person-on-a-big-chair/

 

[a7x1984]

I think you have to know which limit state controlled for the initial design, right? Take the initial member who's limit state controlled the design, and determine their geometric proportionality to the person (say d^3 for computing Ix for bending if bending controlled). The relative member stiffness will be the same, therefore the load distribution will be the same. Therefore, scale the chair based on the dimension that was controlling in the 'weakest' limit-state.

"Structural engineering is the art of modelling materials we do not wholly understand into shapes we cannot..."...ah...screw it, we don't know what the heck we are doing.

 

[MiketheEngineer]

What are you scaling?

Like an elephant - if you double its size in 2-D you most certainly more than double its weight in 3-D

 

[paddingtongreen]

If you double my linear dimensions, I become eight times the weight. If you double the height of the chair, the legs are twice as long but carry eight times the load. Their diameter must be increased by 2.83 to keep the stress the same. The radius of gyration must at least double to maintain KL/R

Now, consider my legs, they would also be increased by a greater margin if they were to carry my body.....and the lower part of my body...

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[Teguci]

Thank you Paddingtongreen. So if x is the scaling factor then the planar dimensions need to be scaled up by x^1.5. Is that good for bending too?

 

[paddingtongreen]

No, that was just one consideration, there is still flexure. I was pointing in the direction that you cannot just scale up. I tried to show that my legs would have to increase beyond the scale up and that that would mean more load still. By the same proportion, my lower body would need to be bigger to support the upper body, thus increasing the load some more.

Michael.
Timing has a lot to do with the outcome of a rain dance.