pre-stressed pre/post-tensioned concrete bridge

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HarryvL
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pre-stressed pre/post-tensioned concrete bridge

Postby HarryvL » Sun Aug 12, 2018 11:26 pm

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:


Bridge_without_prestress_deflection.jpg
Bridge_without_prestress_deflection.jpg (294.36 KiB) Viewed 757 times


Without pre-stressing, the maximum deflection of the bridge is 176mm (~ L/170), which exceeds typical design guidance (< L/300).


Bridge_without_prestress_reinforcement_ratio.jpg
Bridge_without_prestress_reinforcement_ratio.jpg (306.37 KiB) Viewed 757 times


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.
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kkremitzki
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Re: pre-stressed pre/post-tensioned concrete bridge

Postby kkremitzki » Sun Aug 12, 2018 11:48 pm

Excellent analysis!
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HarryvL
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Re: pre-stressed pre/post-tensioned concrete bridge

Postby HarryvL » Wed Aug 15, 2018 9:05 pm

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.
To simulate pre-tensioning, I add a 50x50mm rectangular steel strand to each beam.


CB_Cables.png
CB_Cables.png (26.57 KiB) Viewed 629 times


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.


CB_Pre_Tension_Weight.png
CB_Pre_Tension_Weight.png (195.15 KiB) Viewed 629 times


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.


CB_Pre_Tension_Weight_Load.png
CB_Pre_Tension_Weight_Load.png (179.82 KiB) Viewed 629 times


Next the more challenging case of post-tensioning ... watch this space ;)
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HarryvL
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Re: pre-stressed pre/post-tensioned concrete bridge

Postby HarryvL » Sun Aug 19, 2018 6:43 pm

>> INTERMEZZO <<

HarryvL wrote:
Wed Aug 15, 2018 9:05 pm
Next the more challenging case of post-tensioning ...
.. 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:


Contact_Fill.png
Contact_Fill.png (220.46 KiB) Viewed 554 times


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.


Contact_Cut.png
Contact_Cut.png (202.42 KiB) Viewed 554 times



Contact_Mesh.png
Contact_Mesh.png (31.65 KiB) Viewed 554 times


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.


Contact_Stick.png
Contact_Stick.png (87.9 KiB) Viewed 554 times


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)?
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bernd
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Re: pre-stressed pre/post-tensioned concrete bridge

Postby bernd » Sun Aug 19, 2018 7:23 pm

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 ...
separate-movement.fcstd
(845.74 KiB) Downloaded 11 times


Screenshot_20180819_211615.png
Screenshot_20180819_211615.png (249.06 KiB) Viewed 544 times


Screenshot_20180819_211843.png
Screenshot_20180819_211843.png (495.2 KiB) Viewed 544 times
UR_
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Re: pre-stressed pre/post-tensioned concrete bridge

Postby UR_ » Sun Aug 19, 2018 7:34 pm

HarryvL wrote:
Sun Aug 19, 2018 6:43 pm
how I can separate the two solids (
1. apply a tiny gap between the faces. (0,05 mm in example below)
not to much, because of introducing acceleration on first time step
2. turn off "Coherence Mesh"

FreeCAD 0.18-000037.png
FreeCAD 0.18-000037.png (13.93 KiB) Viewed 541 times
FreeCAD 0.18-000038.png
FreeCAD 0.18-000038.png (102.67 KiB) Viewed 541 times

example:
contact.FCStd
(696.13 KiB) Downloaded 12 times
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HarryvL
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Re: pre-stressed pre/post-tensioned concrete bridge

Postby HarryvL » Mon Aug 20, 2018 4:11 am

UR_ wrote:
Sun Aug 19, 2018 7:34 pm

2. turn off "Coherence Mesh"
Thanks Bernd and @UR_ for the fast response.

Just turning off Coherence does the trick. Are there any undesirable side-effects for BooleanFragments>CompSolids in the same mesh??


Contact_no_Coherence.png
Contact_no_Coherence.png (245.01 KiB) Viewed 521 times
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HarryvL
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Re: pre-stressed pre/post-tensioned concrete bridge

Postby HarryvL » Mon Aug 20, 2018 4:23 am

HarryvL wrote:
Mon Aug 20, 2018 4:11 am
Are there any undesirable side-effects for BooleanFragments>CompSolids in the same mesh??
Combining Compound and BooleanFragment>CompSolid seems to work fine


Contact_no_Coherence_CompSolid.png
Contact_no_Coherence_CompSolid.png (135.84 KiB) Viewed 519 times
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bernd
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Re: pre-stressed pre/post-tensioned concrete bridge

Postby bernd » Mon Aug 20, 2018 4:31 pm

UR_ wrote:
Sun Aug 19, 2018 7:34 pm
2. turn off "Coherence Mesh"
does the trick here too ...

separate-movement.fcstd
(865.04 KiB) Downloaded 13 times


Screenshot_20180820_183017.png
Screenshot_20180820_183017.png (351 KiB) Viewed 487 times
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bernd
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Re: pre-stressed pre/post-tensioned concrete bridge

Postby bernd » Mon Aug 20, 2018 4:32 pm

HarryvL wrote:
Mon Aug 20, 2018 4:23 am
HarryvL wrote:
Mon Aug 20, 2018 4:11 am
Are there any undesirable side-effects for BooleanFragments>CompSolids in the same mesh??
Combining Compound and BooleanFragment>CompSolid seems to work fine
keep a eye on this, especially if you gone work with mesh regions !