pre-stressed pre/post-tensioned concrete bridge
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pre-stressed pre/post-tensioned concrete bridge
Hi, starting a new little project to try and model the 2 ways of pre-stressing concrete, i.e. pre and post tensioning.
Pre-tensioning I tried before here: https://forum.freecadweb.org/viewtopic. ... 10#p234999. It is mostly used in pre-fabrication of concrete elements that are later transported to and erected on site. Strands are pre-tensioned in a reaction rig, concrete poured and external reaction forces released after the concrete has sufficiently cured. In FreeCAD/Calculix this process can be mimicked by reducing the temperature of the strands, as explained here: https://forum.freecadweb.org/viewtopic. ... 0#p234065 .
In the Post-tensioning process cables are left free to move in sheaths, so they can be tensioned after the concrete is cured. The advantage is that in this case the cables can follow curved paths and thus (like in suspension bridges) directly counter-act external loads. I will try to model this behaviour via contact constraints.
The example I will use is one of a simple bridge deck (30x7.5m), supported by two 1.2x0.2m beams. The loads on the bridge are self-weight (24kN/m^3) and live load (10kPa). The pre-stressing cables/tendons are taken to be curved in both the pre and post tensioned cases, even though it will be clear from the above that this is only realistic for the post-tensioned case.
First the results for the bridge without pre-tensioning:
Without pre-stressing, the maximum deflection of the bridge is 176mm (~ L/170), which exceeds typical design guidance (< L/300).
The maximum reinforcement required in the beams (see: https://forum.freecadweb.org/viewtopic. ... 21#p234582 ) for this case is also quite high, i.e. 12.5%.
Both the deflection and the required reinforcement indicate that we should be considering a different design concept.
Pre-tensioning I tried before here: https://forum.freecadweb.org/viewtopic. ... 10#p234999. It is mostly used in pre-fabrication of concrete elements that are later transported to and erected on site. Strands are pre-tensioned in a reaction rig, concrete poured and external reaction forces released after the concrete has sufficiently cured. In FreeCAD/Calculix this process can be mimicked by reducing the temperature of the strands, as explained here: https://forum.freecadweb.org/viewtopic. ... 0#p234065 .
In the Post-tensioning process cables are left free to move in sheaths, so they can be tensioned after the concrete is cured. The advantage is that in this case the cables can follow curved paths and thus (like in suspension bridges) directly counter-act external loads. I will try to model this behaviour via contact constraints.
The example I will use is one of a simple bridge deck (30x7.5m), supported by two 1.2x0.2m beams. The loads on the bridge are self-weight (24kN/m^3) and live load (10kPa). The pre-stressing cables/tendons are taken to be curved in both the pre and post tensioned cases, even though it will be clear from the above that this is only realistic for the post-tensioned case.
First the results for the bridge without pre-tensioning:
Without pre-stressing, the maximum deflection of the bridge is 176mm (~ L/170), which exceeds typical design guidance (< L/300).
The maximum reinforcement required in the beams (see: https://forum.freecadweb.org/viewtopic. ... 21#p234582 ) for this case is also quite high, i.e. 12.5%.
Both the deflection and the required reinforcement indicate that we should be considering a different design concept.
- kkremitzki
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Re: pre-stressed pre/post-tensioned concrete bridge
Excellent analysis!
Re: pre-stressed pre/post-tensioned concrete bridge
To simulate pre-tensioning, I add a 50x50mm rectangular steel strand to each beam.HarryvL wrote: ↑Sun Aug 12, 2018 11:26 pm
Without pre-stressing, the maximum deflection of the bridge is 176mm (~ L/170), which exceeds typical design guidance (< L/300).
The maximum reinforcement required in the beams (see: https://forum.freecadweb.org/viewtopic. ... 21#p234582 ) for this case is also quite high, i.e. 12.5%.
Both the deflection and the required reinforcement indicate that we should be considering a different design concept.
Assuming use of 270 ksi (1860 MPa) strands, the applied tension should not exceed 0.8*1860 = 1490 MPa. Following the method proposed here: https://forum.freecadweb.org/viewtopic. ... 10#p234999, applying an artificial temperature drop of 500 degrees will achieve a nominal pre-tension of 12E-6 * 500 * 210000 = 1260 MPa, leaving some room for stress increase due to live load.
In the absence of live load, the pre-stress will cause the bridge to deflect 27mm upward. The maximum tension achieved in the strands is only 1190 MPa due to elastic shortening of the beam. The Mohr Coulomb stress plot shows that the compression in the concrete (with an assumed uni-axial compressive strength of 30MPa) becomes too high. This could be remedied by a combination of 1) reducing pre-stress, 2) increasing concrete compressive strength, 3) applying compression reinforcement, 4) increasing the width of the beam. I will not do that for the moment, but focus on the modeling and the general effect of pre-stress instead.
After applying live load, the beam deflects 88mm down, which is exactly half of the deformation obtained without pre-tension. The tension in the strands increases to 1298 MPa, which is still below the limit of 1490 MPa. Again, the Mohr Coulomb stresses indicate compressive failure of the concrete and would require further attention. Unfortunately no reliable information for reinforcement ratio could be obtained due to the high local shear stresses induced at the interface of strands and concrete. However, at midspan, the required reinforcement ratio outside the direct influence zone of the strand appears to reduce to 5-6%, compared to the 12.5% obtained without pre-stressing.
Next the more challenging case of post-tensioning ... watch this space
Re: pre-stressed pre/post-tensioned concrete bridge
>> INTERMEZZO <<
The primary difficulty is to make sure that nodes at the interface between strand and concrete get duplicated. So a BooleanFragment>CompSolid is definitely not the answer ... but then, what is?
To investigate this, I modeled a small block partly embedded in a bigger block:
To try and force the duplication of nodes I 1) used two separate small blocks (one to cut a hole in the larger block and one to insert in the cut), 2) combined the assembly in a Compound, rather than a BooleanFragment object and 3) defined a mesh region for the smaller block that is finer than the block in which it is embedded.
As can be seen from the result mesh, this strategy was partly successful. Separate meshes were generated and where nodes in the same plane do not coincide, the solids move independently. HOWEVER, where node coordinates happen to coincide, only one node gets generated and the two solids stick together.
Obvious question: does anybody know how I can separate the two solids (without generating 2 meshes, because FC cannot export that to a CCX INP file)?
.. well that was an understatement. I found myself going on a tangent to figure out how to define the contact between an embedded solid (the steel strand) and its surroundings (concrete).
The primary difficulty is to make sure that nodes at the interface between strand and concrete get duplicated. So a BooleanFragment>CompSolid is definitely not the answer ... but then, what is?
To investigate this, I modeled a small block partly embedded in a bigger block:
To try and force the duplication of nodes I 1) used two separate small blocks (one to cut a hole in the larger block and one to insert in the cut), 2) combined the assembly in a Compound, rather than a BooleanFragment object and 3) defined a mesh region for the smaller block that is finer than the block in which it is embedded.
As can be seen from the result mesh, this strategy was partly successful. Separate meshes were generated and where nodes in the same plane do not coincide, the solids move independently. HOWEVER, where node coordinates happen to coincide, only one node gets generated and the two solids stick together.
Obvious question: does anybody know how I can separate the two solids (without generating 2 meshes, because FC cannot export that to a CCX INP file)?
Re: pre-stressed pre/post-tensioned concrete bridge
Mhh, AFAIK they used to be not connected for a Compound. May be this only is for a Netgen mesh. Problem ATM Netgen mesh crashes for me at a Compound ... File attached ...
Re: pre-stressed pre/post-tensioned concrete bridge
keep a eye on this, especially if you gone work with mesh regions !