Plotting of Concrete Reinforcement Ratio

[HarryvL]

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 (46.98 KiB) Viewed 445 times

Concrete_Wall_Rho_z.png (39.48 KiB) Viewed 445 times

[HarryvL]

PS: in all analyses I use a yield strength of 500MPa for the re-bar.

[hardeeprai]

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?

[HarryvL]

Rho_y only had some coloring at the support.

[HarryvL]

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_]

... I guess I can rule out Paraview ...

... because FC does not write the shear stresses ...

Fortunately this translator isn't that rowdly.
https://forum.freecadweb.org/viewtopic. ... 10#p184850

[HarryvL]

Fortunately this translator isn't that rowdly.
https://forum.freecadweb.org/viewtopic. ... 10#p184850

Thanks @UR I will give it a try ...

[HarryvL]

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 (33.97 KiB) Viewed 392 times

Let's next see how pre-stressing the beam changes reinforcement requirements and the crushing issue.

[HarryvL]

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 (56.31 KiB) Viewed 366 times

-

Pre_Stressed_Beam_2_Weight_RR_z<0.0015.jpg (92.38 KiB) Viewed 366 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 (39.98 KiB) Viewed 366 times

to be continued in the next post...

[HarryvL]

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 (56.87 KiB) Viewed 362 times

-

Pre_Stressed_Beam_2_Weight_Load_RR_z<0.006.jpg (82.15 KiB) Viewed 362 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 (41.4 KiB) Viewed 362 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...