Plotting of Concrete Reinforcement Ratio

About the development of the FEM module/workbench.

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HarryvL
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Re: Plotting of Concrete Reinforcement Ratio

Postby HarryvL » Sat May 19, 2018 11:32 pm

And here a 6.0x2.5x0.1m wall, supported by .5 m wide columns and loaded by its own weight and 1MN distributed load on the top.

Concrete_Wall_Rho_x.png
Concrete_Wall_Rho_x.png (46.98 KiB) Viewed 444 times
Concrete_Wall_Rho_z.png
Concrete_Wall_Rho_z.png (39.48 KiB) Viewed 444 times
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HarryvL
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Re: Plotting of Concrete Reinforcement Ratio

Postby HarryvL » Sat May 19, 2018 11:37 pm

PS: in all analyses I use a yield strength of 500MPa for the re-bar.
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hardeeprai
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Re: Plotting of Concrete Reinforcement Ratio

Postby hardeeprai » Sun May 20, 2018 2:25 am

HarryvL wrote:
Sat May 19, 2018 11:32 pm
And here a 6.0x2.5x0.1m wall, supported by .5 m wide columns and loaded by its own weight and 1MN distributed load on the top.

Concrete_Wall_Rho_x.png

Concrete_Wall_Rho_z.png
Interesting.

Was not Concrete_Wall_Rho_y.png worth to upload here?
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HarryvL
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Re: Plotting of Concrete Reinforcement Ratio

Postby HarryvL » Sun May 20, 2018 3:31 am

Rho_y only had some coloring at the support.
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HarryvL
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Re: Plotting of Concrete Reinforcement Ratio

Postby HarryvL » Sun May 20, 2018 8:18 am

HarryvL wrote:
Sat May 19, 2018 10:51 pm
The maximum value of 7% is realistic and high, as could be expected with a high load like this.
By the way, such a high reinforcement ratio will probably lead to (brittle) crushing failure at the top of the beam. That's why you also need to check a compression/shear criterion, e.g. Mohr Coulomb. That could come instead of a von Mises check, which has no practical application for concrete. Next on my to do list.
UR_
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Re: Plotting of Concrete Reinforcement Ratio

Postby UR_ » Sun May 20, 2018 3:13 pm

HarryvL wrote:
Sat May 19, 2018 7:59 pm
... I guess I can rule out Paraview ...
:shock:

HarryvL wrote:
Sat May 19, 2018 7:59 pm
... because FC does not write the shear stresses ...

Fortunately this translator isn't that rowdly. :lol:
https://forum.freecadweb.org/viewtopic. ... 10#p184850
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HarryvL
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Re: Plotting of Concrete Reinforcement Ratio

Postby HarryvL » Sun May 20, 2018 9:29 pm

UR_ wrote:
Sun May 20, 2018 3:13 pm
Fortunately this translator isn't that rowdly. :lol:
https://forum.freecadweb.org/viewtopic. ... 10#p184850
Thanks @UR I will give it a try ...
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HarryvL
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Re: Plotting of Concrete Reinforcement Ratio

Postby HarryvL » Sun May 20, 2018 10:11 pm

HarryvL wrote:
Sun May 20, 2018 8:18 am
By the way, such a high reinforcement ratio will probably lead to (brittle) crushing failure at the top of the beam. That's why you also need to check a compression/shear criterion, e.g. Mohr Coulomb. That could come instead of a von Mises check, which has no practical application for concrete. Next on my to do list.
I wrote a Mohr-Coulomb stress check in importToolsFem.py and it indeed shows that the top of the beam crushes (Sig_MC>0):

Beam_Reinf_MC.jpg
Beam_Reinf_MC.jpg (33.97 KiB) Viewed 391 times

Let's next see how pre-stressing the beam changes reinforcement requirements and the crushing issue.
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HarryvL
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Re: Plotting of Concrete Reinforcement Ratio

Postby HarryvL » Mon May 21, 2018 10:07 pm

I spent some time exploring the application of the Reinforcement Ratio and Mohr Coulomb routines for concrete design. For this I analysed the beam of previous posts, with and without pre-tension. The dimensions and properties of the beam are as follows:

Beam Dimensions:
4.0x0.3x0.1m

Elastic parameters concrete:
as per FreeCAD defaults for concrete

Strength parameters concrete (defining Mohr Coulomb failure criterion):
uniaxial cylinder compression strength fck=30MPa (C30/37)
friction angle 30 degrees

Elastic parameters steel:
as per FreeCAD defaults for Calculix steel

Strength parameters steel:
Yield strength fy=500MPa

Loads:
Specific gravity of the concrete: 24kN/m^3
Live load: 25kN/m
pre-tension: 12E-6 * 100 * 210000 = 252 MPa (see here: https://forum.freecadweb.org/viewtopic. ... 10#p234065 for explanation)

Load cases:
1) Self weight only
2) Self weight + Live load (no pre-tension)
3) Self weight + pre-tension
4) Self weight + pre-tension + Live load

Load Case 1 - Self weight only

The maximum deflection of the beam under self weight is only 0.3mm and the induced stress in the passive cables is 4.6 MPa.

The required reinforcement ratios for this load case, as per the method described in previous posts, is very low:

Pre_Stressed_Beam_2_Weight_RR_x<0.0016.jpg
Pre_Stressed_Beam_2_Weight_RR_x<0.0016.jpg (56.31 KiB) Viewed 365 times
-
Pre_Stressed_Beam_2_Weight_RR_z<0.0015.jpg
Pre_Stressed_Beam_2_Weight_RR_z<0.0015.jpg (92.38 KiB) Viewed 365 times

In fact those ratios are likely to be around (Rho_x=0.16%) or less (Rho_z=0.015%) than the minimum allowable ratios as per code (of the order 0.15-0.20%).

The Mohr-Coulomb shows that no crushing/shear failure occurs anywhere in the beam:

Pre_Stressed_Beam_2_Weight_MC.jpg
Pre_Stressed_Beam_2_Weight_MC.jpg (39.98 KiB) Viewed 365 times

to be continued in the next post...
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HarryvL
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Re: Plotting of Concrete Reinforcement Ratio

Postby HarryvL » Mon May 21, 2018 10:20 pm

Load Case 2 - Self weight + Live load (no pre-tension)

This second case represents a simply reinforced beam without pre-tension.

The maximum deflection of the beam for this case is 10.6mm and the induced stress in the passive cables is 162 MPa … they act as reinforcement bars.

The required reinforcement ratios for this load case are:

Pre_Stressed_Beam_2_Weight_Load_RR_x<0.054.jpg
Pre_Stressed_Beam_2_Weight_Load_RR_x<0.054.jpg (56.87 KiB) Viewed 361 times
-
Pre_Stressed_Beam_2_Weight_Load_RR_z<0.006.jpg
Pre_Stressed_Beam_2_Weight_Load_RR_z<0.006.jpg (82.15 KiB) Viewed 361 times

This time the required reinforcement in x-direction is very high (5.4%) and exceeds typical maximum percentages allowed by code (1.5-2.5%) to prevent brittle failure. The required reinforcement in z-direction is 0.5-0.6% near the supports, which induce high shear stresses.

The Mohr Coulomb plot shows indeed that beam is prone to crushing on the compression side, as would be expected with a very high reinforcement percentage.

Pre_Stressed_Beam_2_Weight_Load_MC.jpg
Pre_Stressed_Beam_2_Weight_Load_MC.jpg (41.4 KiB) Viewed 361 times

This plot also shows that supporting a single line of nodes introduces artificially high local shear stresses. In reality the beam will be supported over a wider area, thus reducing this effect. Still, the support of a beam deserves detailed attention to prevent local damage.

to be continued in the next post...