Plotting of Concrete Reinforcement Ratio
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Re: Plotting of Concrete Reinforcement Ratio
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.
Re: Plotting of Concrete Reinforcement Ratio
PS: in all analyses I use a yield strength of 500MPa for the re-bar.
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Re: Plotting of Concrete Reinforcement Ratio
Interesting.
Was not Concrete_Wall_Rho_y.png worth to upload here?
--
H.S.Rai
H.S.Rai
Re: Plotting of Concrete Reinforcement Ratio
Rho_y only had some coloring at the support.
Re: Plotting of Concrete Reinforcement Ratio
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.
Re: Plotting of Concrete Reinforcement Ratio
Fortunately this translator isn't that rowdly.
https://forum.freecadweb.org/viewtopic. ... 10#p184850
Re: Plotting of Concrete Reinforcement Ratio
Thanks @UR I will give it a try ...UR_ wrote: ↑Sun May 20, 2018 3:13 pm Fortunately this translator isn't that rowdly.
https://forum.freecadweb.org/viewtopic. ... 10#p184850
Re: Plotting of Concrete Reinforcement Ratio
I wrote a Mohr-Coulomb stress check in importToolsFem.py and it indeed shows that the top of the beam crushes (Sig_MC>0):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.
Let's next see how pre-stressing the beam changes reinforcement requirements and the crushing issue.
Re: Plotting of Concrete Reinforcement Ratio
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:
-
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:
to be continued in the next post...
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:
-
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:
to be continued in the next post...
Re: Plotting of Concrete Reinforcement Ratio
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:
-
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.
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...
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:
-
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.
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...