h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Intuition tells us that if we want to make something stronger, we increase its size. So in designing a building, for example, the columns and beams will resist earhquakes better/allow us to build higher/etc if we increase their cross-section.

Is it as simple as that, though? Isn't there a counter-argument whereby thicker sections are stiffer, causing more stress concentration when cycled, and hence thicker sections may fail quicker in fatigue? Reeds bend in the wind when thick trunks may snap, that sort of idea?

What's the governing science of all this?

My gut instinct to this question was to drag out all my Euler beam theory, but it doesn't quite add up.

I would suggest that the weight of the beam itself contributes sufficiently to the bending moment to overcome any factor contributed by the second moment of area, which is (broadly speaking) the factor that decides the stress on a beam.

Plus, of course, wood is very weak under compression, so if the compressed face of the tree suffers fatigue stresses, it will lead to critical failure sooner rather than later. A similar thing, in reverse, would happen with concrete beams, but it'd be hard to justify the same thing in steel.

B

Also, it's a scale problem. Especially with horizontal members, you soon get the problem that the increase in own weight is out of proportion to the strength gained, especially if you increase the width rather than the height (x vs z).

Thanks guys.

But I don't just mean a self-weight contribution to bending. This is true for columns too, and for any cyclical loading in torsion, shear, whatever, and it happens with steel.

It's something like the increased section confers stiffness, which reduces deflection and so increases stress locally. Fatigue then starts a crack. Although the increased section means the crack has to propagate further to cause failure, the earlier initiation means that the larger section fails quicker through fatigue than a smaller one would.

What I really need is a text book that sets it all out. Can anyone suggest one?

Hmmm, mine wouldn't help, they're all in German

German's pretty good for Mech Eng. Russian's even better!

Well, as long as there are pretty pictures...

I'd just recommend my statics professor's chat forum, but you need a Uni password.