civilengineerNL
Civil/Environmental
- Mar 15, 2015
- 6
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.
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.
