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Prestress and buckling

Prestress and buckling

Prestress and buckling

(OP)
For my master thesis I am working on a bridge with an initial prestressing force. So these prestress cables are connected with the concrete.

I have learned that this kind of prestress system cannot buckle. So I researched why. Probably a very basic thing. 
But I couldn't find in any study book. The cable gives an effect that is exactly the opposite of the 2nd order effect by bending it. 

In differential equation terms:
DV:= EI* d^4 w(x) / dx^4 + P * d^2 w(x) / dx^2 - P * d^2 w(x) /dx^2 .................... equation (1)

The "+ P * d^2 w(x) / dx^2"-term gives the cable a second order effect.
The "- P * d^2 w(x) / dx^2"-term gives the cable an effect that will undo the second order effect.

So that leaves equation (1) to:
DV:= EI* d^4 w(x) / dx^4 


This also gives the conclusion that without second order effect the system would be unstable. So 2nd order is necessary.

Is it really as simple as 1 + 1 - 1 = 1? Or have I done something terribly wrong?

Could someone please review this? I would be very thankful.

RE: Prestress and buckling

I think you've nailed it. Check out this thread: Link.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

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