Structural Integrity

[Soter Salem]

I've got a general question about how something's shape affects it's, uh, strength?

 

Perhaps an example would be more helpful; when eating pizza, the front of the slice will fold down unless the eater bends the slice vertically, what's up with that?

A similar scenario occurs with a flat piece of paper, it'll droop unless folded to make a parabolic shape, why does this occur?

[J.C.MacSwell]

I've got a general question about how something's shape affects it's, uh, strength?

 

Perhaps an example would be more helpful; when eating pizza, the front of the slice will fold down unless the eater bends the slice vertically, what's up with that?

A similar scenario occurs with a flat piece of paper, it'll droop unless folded to make a parabolic shape, why does this occur?

 

http://en.wikipedia.org/wiki/Second_moment_of_area

[Soter Salem]

http://en.wikipedia...._moment_of_area

 

This just discusses the general aspects of shearing and bending, the operative line that I couldn't find more on was "The deflection of a beam under load depends not only on the load, but also on the geometry of the beam's cross-section." Maybe I just missed it, but the page really didn't get into that, which is what I was attempting to ask about with my question.

[J.C.MacSwell]

This just discusses the general aspects of shearing and bending, the operative line that I couldn't find more on was "The deflection of a beam under load depends not only on the load, but also on the geometry of the beam's cross-section." Maybe I just missed it, but the page really didn't get into that, which is what I was attempting to ask about with my question.

 

Choose an axis of bending and look at the cross section of the flat paper or pizza. When you fold it as described (which would be perpendicular to aforementioned axis) you greatly increase the area moment of inertia of that cross section, and therefore the stiffness.

 

The paper or pizza is displaced from the neutral axis of bending and therefore gains "leverage" to support the load.

[baxtrom]

I've got a general question about how something's shape affects it's, uh, strength?

 

Perhaps an example would be more helpful; when eating pizza, the front of the slice will fold down unless the eater bends the slice vertically, what's up with that?

A similar scenario occurs with a flat piece of paper, it'll droop unless folded to make a parabolic shape, why does this occur?

 

 

Resistance to bending greatly depends on the cross-sectional geometry of the pizza. Compare bending of a plastic ruler - if oriented in its weak direction, it is very flexible. On the other hand it is very stiff if rotated 90 degrees. This is because bending is produced by a moment carried as tension in the upper part of the pizza cross-section and compression in the lower part. If the cross-section is made bigger in the vertical direction, the distance between these opposing forces becomes larger (forces get better leverage) and thus the pizza can carry a greater bending moment.