## Plotting of Concrete Reinforcement Ratio

About the development of the FEM module/workbench.

Moderator: bernd

HarryvL
Posts: 1042
Joined: Sat Jan 06, 2018 7:38 pm

### Plotting of Concrete Reinforcement Ratio

Further to the discussion here: https://forum.freecadweb.org/viewtopic. ... 20#p234491 I decided to start a new post dedicated to the plotting of concrete reinforcement ratio.
HarryvL
Posts: 1042
Joined: Sat Jan 06, 2018 7:38 pm

### Re: Plotting of Concrete Reinforcement Ratio

I coded the 13 closed form solutions for reinforcement ratio defined here: http://heronjournal.nl/53-4/3.pdf with Python and managed to reproduce the 11 test cases for single stress results (I changed the name for the reinforcement ratio from "Omega" to "Rho" in line with the paper):

Code: Select all

``````********************************
Case 1
Sigma:        2.000   -2.000    5.000    6.000   -4.000    2.000
Governing Eq.14    Rho: 0.02400 0.00400 0.01400
********************************
Case 2
Sigma:       -3.000   -7.000    0.000    6.000   -4.000    2.000
Governing Eq.10+   Rho: 0.00886 0.00000 0.00571
********************************
Case 3
Sigma:       -1.000   -7.000   10.000    0.000    0.000    5.000
Governing Eq.5     Rho: 0.00000 0.00000 0.02714
********************************
Case 4
Sigma:        3.000    0.000   10.000    0.000    5.000    0.000
Governing Eq.13    Rho: 0.01600 0.00000 0.03000
********************************
Case 5
Sigma:       10.000    7.000   -3.000    3.000    1.000   -2.000
Governing Eq.11-   Rho: 0.02533 0.02133 0.00000
********************************
Case 6
Sigma:        4.000   -7.000    3.000    7.000    0.000   -5.000
Governing Eq.14    Rho: 0.02200 0.01000 0.01600
********************************
Case 7
Sigma:        8.000  -14.000    6.000   14.000    0.000  -10.000
Governing Eq.14    Rho: 0.04400 0.02000 0.03200
********************************
Case 8
Sigma:        1.000    0.000    3.000   10.000   -8.000    7.000
Governing Eq.17    Rho: 0.02486 0.01750 0.01720
********************************
Case 9
Sigma:        0.000    0.000    0.000   10.000    8.000    7.000
Governing Eq.13    Rho: 0.03600 0.03400 0.03000
********************************
Case 10
Sigma:       15.000    0.000    0.000    0.000    0.000    0.000
Governing Eq.13    Rho: 0.03000 0.00000 0.00000
********************************
Case 11
Sigma:        0.000    0.000    0.000    5.000    0.000    0.000
Governing Eq.13    Rho: 0.01000 0.01000 0.00000
``````
Next step the integration in FreeCAD or Paraview
bernd
Posts: 8029
Joined: Sun Sep 08, 2013 8:07 pm
Location: Zürich, Switzerland

### Re: Plotting of Concrete Reinforcement Ratio

adding a new resumt in FreeCAD resultobject is not smart but easy.
HarryvL
Posts: 1042
Joined: Sat Jan 06, 2018 7:38 pm

### Re: Plotting of Concrete Reinforcement Ratio

What is a "resumt" Bernd?
HarryvL
Posts: 1042
Joined: Sat Jan 06, 2018 7:38 pm

### Re: Plotting of Concrete Reinforcement Ratio

Oops you mean result I guess

Why is that not smart?
HarryvL
Posts: 1042
Joined: Sat Jan 06, 2018 7:38 pm

### Re: Plotting of Concrete Reinforcement Ratio

Also: what would be the alternative if we want to show results derived from the base CCX outpost, like alternative stress plots (Mohr Coulomb instead of von Mises) or like I am trying here with reinforcement ratio?
bernd
Posts: 8029
Joined: Sun Sep 08, 2013 8:07 pm
Location: Zürich, Switzerland

### Re: Plotting of Concrete Reinforcement Ratio

HarryvL wrote:
Sat May 19, 2018 2:39 pm
Oops you mean result I guess

Why is that not smart?
because the result vectors are hard coded in the result object. https://github.com/FreeCAD/FreeCAD/blob ... py#L45-L82
bernd
Posts: 8029
Joined: Sun Sep 08, 2013 8:07 pm
Location: Zürich, Switzerland

### Re: Plotting of Concrete Reinforcement Ratio

HarryvL wrote:
Sat May 19, 2018 2:44 pm
Also: what would be the alternative if we want to show results derived from the base CCX outpost, like alternative stress plots (Mohr Coulomb instead of von Mises) or like I am trying here with reinforcement ratio?
HarryvL
Posts: 1042
Joined: Sat Jan 06, 2018 7:38 pm

### Re: Plotting of Concrete Reinforcement Ratio

HarryvL wrote:
Sat May 19, 2018 12:13 pm
Next step the integration in FreeCAD or Paraview
Well, I guess I can rule out Paraview, because FC does not write the shear stresses Sigxy, Sigxz and Sigyz to the VTK file and I can't find how to modify the VTK writer, if at all possible (?)

Remains the possibility to add a Result Object? To get a quick result, I guess I could just use and modify some of the existing results, e.g. Min/Max Principle Stress and Max Shear Stress ... to be replaced by Rhox, Rhoy and Rhoz.
HarryvL
Posts: 1042
Joined: Sat Jan 06, 2018 7:38 pm

### Re: Plotting of Concrete Reinforcement Ratio

I applied the dirtiest hack possible and used the existing Arrays for Maximum, Minimum Principal Stress and Maximum Shear Stress to produce this result (as proof of concept, so to say):

Concrete_Beam_Rho_x.png (45.79 KiB) Viewed 1425 times

This 4.0x0.1x0.3m concrete beam is loaded by a 100kN distributed load. The reinforcement ratio in x-direction is highest at the bottom center of the beam, as one would expect. The maximum value of 7% is realistic and high, as could be expected with a high load like this.

The reinforcement ratio in z-direction is highest near the support (where the shear force is high) and spread over the full height over the beam. Towards the center of the beam the shear stress reduced to zero and so does the corresponding reinforcement ratio (in practice you would apply a minimum ratio of course)

Concrete_Beam_Rho_z.png (46.06 KiB) Viewed 1425 times

Finally, the reinforcement ratio in y-direction is only high directly adjacent to the support, where the beam is constrained in the out-of-plane direction. Here the prevented lateral contraction causes high shear stresses.

Concrete_Beam_Rho_y.png (25.07 KiB) Viewed 1425 times

Still a lot of testing and tidying up to do, but certainly worth pursuing.