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.
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%).
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.
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.
… to be continued in the next post.