I recently discovered a strange phenomenon. Using a card made of hard paper, I can fold it at a certain angle and place it standing up. What is more interesting is that and it is able to support the weight of my 520 gram empty ceramic cup at certain angle values, which will be mentioned later. This card was $10.6cm$ long and $8.5cm$ wide, and it folded at the half-point of the length. I calculated that the angle should be between $30^o$ and $108^o$ in order to support the weight of the cup. I would like to know why this happens; how can something so thin support something more than 50 times it's weight(Paper was about 10 grams)? I would also like to know why the card could not support the mass if the angle was smaller than $30^o$, or larger than $108^o$. Any help or explanation would be greatly appreciated!
$\begingroup$
$\endgroup$
2
-
$\begingroup$ Does the structure lean over, or actually bend and fail, when the angle is outside of the good range? $\endgroup$– JMacCommented Jan 4, 2018 at 12:02
-
$\begingroup$ Yea, it just leans over. $\endgroup$– QuIcKmAtHsCommented Jan 4, 2018 at 12:03
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
2
by folding that card, you have greatly increased something called the section modulus for bending, and in its folded state that card can then support much greater weight. this technique is used throughout the mechanical engineering world to enhance the stiffness of thin structural plates. for a shallow bend angle (two edges of the card nearly touching), the folded card loses most of its its section modulus and stops behaving as what is called a "short column" (which would fail in compressive shear) and begins behaving as a "slender" column (which fails by elastic buckling), and the card collapses under the weight of the cup. for a wide fold angle, the section modulus is again small and the card collapses as well.
answered Jan 4, 2018 at 18:22
-
$\begingroup$ This was my original take on what was happening; but based on comments from the OP it may be even more simple. He said it leans over, not bends and fails. For that reason; I think it could also just be a simple issue of stability. The side with low dimensions has very little tolerance for unbalanced weight before toppling. $\endgroup$– JMacCommented Jan 4, 2018 at 18:37
-
$\begingroup$ sounds like an excuse for some fun experiments! $\endgroup$ Commented Jan 4, 2018 at 20:28