Young's modulus-TPR workbook

[bluequestions]

In the passage, it's talking about the stress put on a homogenous pole, three equations are given:
1) Youngs modulus (E) = stress applied to pole/fractional change in pole length
2) fractional change in pole length (ε) = delta length/length of pole
3) the pressure on the pole due to the pole's own weight: stress = rho(g)(h), where rho=density of pole, and h=height of pole above a given point

Question: How tall could the pole become before buckling under its own weight if it collapses when compressed by more than a factor of ε_c (the critical fractional change)?

I was able to get the answer height of pole = (ε_c)(E)/(rho)(g) through just doing algebra with the given equation, however I'm confused about the concept. When we compress the pole, that puts more stress on the pole, and by the given equation stress = rho(g)(h), doesn't this mean that the pole's height is getting larger? But when we compress things, shouldn't the length become smaller, not larger?

Thanks!

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[aldol16]

Well, the "stress" you mention here is the pressure on the pole due only to the pole's own weight. When you're compressing it, you're adding on another force that is external to the pressure that the pole is already under from its weight. Also remember that the "h" you're mentioning here is the height of the pole, not a fractional change in height upon compression/elongation.