Modelling of Post-tensioned Concrete

About the development of the FEM module/workbench.

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HarryvL
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Modelling of Post-tensioned Concrete

Postby HarryvL » Mon Sep 03, 2018 8:12 pm

In another post (https://forum.freecadweb.org/viewtopic.php?f=18&t=30286) I discussed how to model pre-stressed concrete with FreeCAD. There I explained the two ways to pre-stress concrete, i.e. by pre or post tensioning. The first is relatively easy to model, but the second requires a contact analysis to model the interaction between the pre-stressing tendons and the concrete. Here I share some of the modelling aspects and the results.

I consider a simply supported concrete beam of 4x0.4x0.15m loaded by a uniformly distributed load of 75kN/m and self weight (24kN/m3). In addition, two 50mm steel anchor plates are modeled to allow introduction of tendon anchor loads.


PT_None_Model_001.png
PT_None_Model_001.png (14.52 KiB) Viewed 778 times


The below plots show that without pre-tensioning the beam would crush at the top (Mohr Coulomb Stress > 0) and require significant reinforcement at the bottom (7.7%).


PT_None_Results_001.png
PT_None_Results_001.png (63.97 KiB) Viewed 778 times


Next I will show the simplest form of post-tensiong by adding a tendon at the center of the beam. To ensure a sensible mesh, I model the tendon as a relatively large 50X50mm square section put under 250MPa pre-tension. This is (from a pre-tension point of view) equivalent to a more realistic 14mm radius circular tendon under 1000Mpa pre-tension, but is easier to mesh and will have better contact convergence properties.

As the tendon needs to move freely under tensioning, the sheath is chosen to be 51x51mm, i.e. slightly bigger than the tendon. The full assembly therefore consists of 5 solids: the beam, the sheath, the tendon and two anchor blocks. The sheath block is subtracted from the beam in a Boolean cut object and this, the tendon and the anchor blocks are subsequently combined in a Boolean fragments object (type Compsolid). The resulting model is shown below.


PT_Center_Model_001.png
PT_Center_Model_001.png (20.13 KiB) Viewed 778 times


To model the contact between the tendon and the surrounding concrete two FemConstraintDisplacement objects are introduced, one for the top contact and one for the bottom. In both cases, the concrete faces are chosen as master and the steel faces as slave. For the selection of the embedded faces I use the macro by Markus Hovorka (https://github.com/drhooves/SelectionTools). Please note that all objects need to be combined into a single Boolean fragments object before all faces are available to the selection tool.

The results for this analysis show that (as can be expected), the central pre-tension increases the crushing problem at the top of the beam, but helps reduce the requirement for reinforcement slightly at the bottom (from 7.7% to 6.1%). All-in-all not a sensible engineering solution.


PT_Center_Results_001.png
PT_Center_Results_001.png (101.01 KiB) Viewed 778 times


… to be continued in the next post.
Last edited by HarryvL on Mon Sep 03, 2018 8:33 pm, edited 1 time in total.
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HarryvL
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Re: Modelling of Post-tensioned Concrete

Postby HarryvL » Mon Sep 03, 2018 8:17 pm

If the tendon is shifted to below the beam center line an upward moment is created that reduces compression at the top and tension at the bottom.


PT_Excentric_Model_001.png
PT_Excentric_Model_001.png (19.51 KiB) Viewed 775 times


The results show that moving the tendon down indeed solves the crushing issue and further reduces the need for conventional reinforcement (from 6.1% to 2.6%). However, it also shows that now reinforcement is required at the top of the beam, near the support. This is because here the upward moment introduced by the tendon does not get counteracted by a downward moment from weight and live load.


PT_Excentric_Results_001.png
PT_Excentric_Results_001.png (75.14 KiB) Viewed 775 times


The ultimate refinement is to apply a curved tendon. Under tension the curved tendon wants to straighten out but gets resisted by the concrete. It therefore exerts an upward uniform load on the beam. This results in a maximum upward moment at mid-span and a zero upward moment at the supports.


PT_Curved_Model_001.png
PT_Curved_Model_001.png (24.27 KiB) Viewed 775 times


As can be seen from the results, applying a curved tendon reduces the need for structural reinforcement near the supports, while leaving the mid-span largely unaffected.


PT_Curved_Results_001.png
PT_Curved_Results_001.png (80.15 KiB) Viewed 775 times


In the above cases it is assumed that the live load is present all the time. This is not realistic and a check should be performed for zero live load. This is especially important for the case of eccentric tendons, where the upward action may actually damage the “unloaded” beam.

… to be continued in the next post.
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HarryvL
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Re: Modelling of Post-tensioned Concrete

Postby HarryvL » Mon Sep 03, 2018 8:27 pm

As a last step I analysed the beam with curved tendon in the absence of live load. This indeed shows that a moderate amount of conventional reinforcement is required near the top of the beam to prevent damage under all loading conditions


PT_Curved_No_Live_load_Results_001.png
PT_Curved_No_Live_load_Results_001.png (69.22 KiB) Viewed 773 times


The design could be further optimised by varying the value of post tension, tendon eccentricity and/or concrete compressive strength. Also effects of tension losses due to friction between tendon and sheath could be modelled. However, I will not do this here as the focus was on proving that post-tensioned concrete could be modelled with FreeCAD.
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bernd
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Re: Modelling of Post-tensioned Concrete

Postby bernd » Mon Sep 03, 2018 8:56 pm

I just had the time fly over your posts, since I'm in vacations ...

But for selecting inner faces you could also use the FreeCAD FEM clipping plane tool, which cuts everything at a selected plane. Selecting is than easy.

bernd
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HarryvL
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Re: Modelling of Post-tensioned Concrete

Postby HarryvL » Tue Sep 04, 2018 11:03 am

Thanks Bernd. Is this different from the clipping plane in the VTK pipeline?
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Re: Modelling of Post-tensioned Concrete

Postby bernd » Tue Sep 04, 2018 6:35 pm

HarryvL wrote:
Tue Sep 04, 2018 11:03 am
Thanks Bernd. Is this different from the clipping plane in the VTK pipeline?
yes, the two blue icons in FEM. Select a face click on add clipping plane icon. You can move, turn and zoom the clipping plane. You can add multiple clipping planes too. The other icon removes all clipping planes.