Plotting of Concrete Reinforcement Ratio

About the development of the FEM module/workbench.

Moderator: bernd

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

Re: Plotting of Concrete Reinforcement Ratio

Postby HarryvL » Mon May 21, 2018 10:26 pm

Load Case 3 - Self weight + Pre-tension

In this and the next case the effect of pre-tensioning of the beam will be analysed - in particular the impact on the reinforcement ratios and shear/crushing failure of the beam.

In this Load Case 3 the situation before applying live load will be considered. The applied pre-tension counter-acts the effect of self-weight. In fact the applied tension is so high that the self weight is over-compensated and causes an upward deflection of 2.7mm. The effective maximum stress in the pre-tension cable is 234MPa. This is lower than the “applied” stress of 252 MPa due to shortening of the beam after release of the external pre-tension.

The plot for the reinforcement ratio in x-direction indeed shows that tension develops at the top of the beam, thus requiring light reinforcement of 0.54%. In addition high stresses develop near the release points of the pre-tension cables, which would require dedicated reinforcement in that area.

Pre_Stressed_Beam_2_Weight_PreTension_RR_x<0.0054.jpg
Pre_Stressed_Beam_2_Weight_PreTension_RR_x<0.0054.jpg (65.53 KiB) Viewed 239 times
-
Pre_Stressed_Beam_2_Weight_PreTension_RR_z<0.01.jpg
Pre_Stressed_Beam_2_Weight_PreTension_RR_z<0.01.jpg (71.42 KiB) Viewed 239 times

The reinforcement ratio in z-direction is somewhat surprising. A band of high demand (~1%) exists just above the tension cables and this may have to do with the high shear stresses that are introduced due to shortening of the cables after release.

Pre_Stressed_Beam_2_Weight_Pretension_MC.jpg
Pre_Stressed_Beam_2_Weight_Pretension_MC.jpg (44.87 KiB) Viewed 239 times

The Mohr Coulomb plot shows that applying weight and pre-tension does not lead to crushing or shearing of the concrete. However, it is again evident that release of external tension on the pre-tension cables introduces high shear at the interface of steel and concrete. In addition, the numerical trick of applying pre-tension by cooling down the steel creates an effect that is not present in reality, i.e. lateral shrinkage of the cables. This will introduce tension at the interface of concrete and cable and make the shearing effect worse. Although the current model is suitable for designing overal reinforcement and judging beam crushing and shear, it is not so for designing the details near the supports and pre-tension cables.

to be continued in the next post...
User avatar
HarryvL
Posts: 1042
Joined: Sat Jan 06, 2018 7:38 pm

Re: Plotting of Concrete Reinforcement Ratio

Postby HarryvL » Mon May 21, 2018 10:35 pm

Load Case 4 - Self weight + Pre-tension + Live load

In a final step the effect of applying live load is considered. The maximum deflection under this load is 7.7mm, which should be compared to the 10.6mm without pre-tension. The stress in the cable increase further to 388MPa..

The required reinforcement ratio in x-direction is 3.4%, which is still higher than a typical maximum ratio, but much improved over the 5.4% for the beam without pre-tension. A Mohr Coulomb check further-on will give some indication of the acceptability of such a high ratio.

Pre_Stressed_Beam_2_Weight_PreTension_Load_RR_x<0.0339.jpg
Pre_Stressed_Beam_2_Weight_PreTension_Load_RR_x<0.0339.jpg (53.85 KiB) Viewed 238 times
-
Pre_Stressed_Beam_2_Weight_PreTension_Load_RR_z<0.0047.jpg
Pre_Stressed_Beam_2_Weight_PreTension_Load_RR_z<0.0047.jpg (79.72 KiB) Viewed 238 times

The plot for the vertical reinforcement ratio shows a combination of effects described in Case 2 (beam shear) and Case 3 (cable effect). The required reinforcement of ~0.5% is in the normal range.

Finally, the Mohr Coulomb plot for this load case shows that no crushing or shear failure occurs in the beam. The only problem area is near the support, where the effects described before require careful attention in detailing the local reinforcement.

Pre_Stressed_Beam_2_Weight_PreTension_Load_MC.jpg
Pre_Stressed_Beam_2_Weight_PreTension_Load_MC.jpg (45.5 KiB) Viewed 238 times

Although no crushing or shearing is evident, the high reinforcement percentage may lead to insufficient ductility (rotation capacity) of the beam. This is an effect that cannot be analysed with a linear finite element analysis.

This concludes the case study of a concrete beam with reinforcement and pre-tension.

My experience with concrete design is very limited, so I welcome any practical input or suggestions you may have.
thschrader
Posts: 1407
Joined: Sat May 20, 2017 12:06 pm
Location: Germany

Re: Plotting of Concrete Reinforcement Ratio

Postby thschrader » Tue May 22, 2018 9:43 am

HarryvL wrote:
Mon May 21, 2018 10:35 pm
My experience with concrete design is very limited, so I welcome any practical input or suggestions you may have.
Here is a testcase you can run.
8-m 2-field beam, loading self-weight and constant 20 kN/m. The static calculation
was done with my commercial software.
2_field_beam_static_calculation.pdf
(260.8 KiB) Downloaded 20 times
2_Field_Beam.FCStd
(20.72 KiB) Downloaded 14 times
testcase.JPG
testcase.JPG (67.54 KiB) Viewed 226 times
thschrader
Posts: 1407
Joined: Sat May 20, 2017 12:06 pm
Location: Germany

Re: Plotting of Concrete Reinforcement Ratio

Postby thschrader » Tue May 22, 2018 10:16 am

@Harry:
About prestressing.
When you use straight prestressed rebars, you get a negative constant moment in the beam.
You can compensate the max M (from selfweight/loading) in the middle of
the beam, but at the end of the beams you have unnecessary negative moments.
The rebars for prestressing should have the layout according to the momentum line
you want to compensate.
prestressing.JPG
prestressing.JPG (21.91 KiB) Viewed 222 times
User avatar
HarryvL
Posts: 1042
Joined: Sat Jan 06, 2018 7:38 pm

Re: Plotting of Concrete Reinforcement Ratio

Postby HarryvL » Tue May 22, 2018 10:26 am

thschrader wrote:
Tue May 22, 2018 9:43 am
Here is a testcase you can run.
8-m 2-field beam, loading self-weight and constant 20 kN/m. The static calculation
was done with my commercial software.
2_field_beam_static_calculation.pdf
2_Field_Beam.FCStd
testcase.JPG
Thanks Thomas, that's an interesting one to test. Let me see what my FC routine comes up with for this case.
User avatar
HarryvL
Posts: 1042
Joined: Sat Jan 06, 2018 7:38 pm

Re: Plotting of Concrete Reinforcement Ratio

Postby HarryvL » Tue May 22, 2018 10:29 am

thschrader wrote:
Tue May 22, 2018 10:16 am
@Harry:
About prestressing.
When you use straight prestressed rebars, you get a negative constant moment in the beam.
You can compensate the max M (from selfweight/loading) in the middle of
the beam, but at the end of the beams you have unnecessary negative moments.
The rebars for prestressing should have the layout according to the momentum line
you want to compensate.
prestressing.JPG
That would be perfect. Do you know how to model a curved cylinder in FC? I made a CompSolid of a cube with 2 cylinders, but curved cables requires something more fancy. I would be keen to try...
thschrader
Posts: 1407
Joined: Sat May 20, 2017 12:06 pm
Location: Germany

Re: Plotting of Concrete Reinforcement Ratio

Postby thschrader » Tue May 22, 2018 11:31 am

OK,
here is your beam from above with 2 parabolic shaped rebars.
parabolic_rebar.FCStd
(14.04 KiB) Downloaded 14 times
parabolic.JPG
parabolic.JPG (41.15 KiB) Viewed 208 times
User avatar
HarryvL
Posts: 1042
Joined: Sat Jan 06, 2018 7:38 pm

Re: Plotting of Concrete Reinforcement Ratio

Postby HarryvL » Tue May 22, 2018 11:44 am

Thanks Thomas. I will give it a try. Did you try to mesh this model?
thschrader
Posts: 1407
Joined: Sat May 20, 2017 12:06 pm
Location: Germany

Re: Plotting of Concrete Reinforcement Ratio

Postby thschrader » Tue May 22, 2018 5:31 pm

HarryvL wrote:
Tue May 22, 2018 11:44 am
Thanks Thomas. I will give it a try. Did you try to mesh this model?
Yes, but the meshing on the parabolic rebars gives a mesh only for the beam itself.
Seems, that gmsh ignores the rebars (the sweeps). When using straight rebars (cube/cylinder)
the meshing works.
parabolic.JPG
parabolic.JPG (161.37 KiB) Viewed 187 times
cylinder_in_cube.JPG
cylinder_in_cube.JPG (125.3 KiB) Viewed 187 times
cube_in_cube.JPG
cube_in_cube.JPG (91.72 KiB) Viewed 187 times
User avatar
HarryvL
Posts: 1042
Joined: Sat Jan 06, 2018 7:38 pm

Re: Plotting of Concrete Reinforcement Ratio

Postby HarryvL » Tue May 22, 2018 5:43 pm

Did you combine beam and bars into BooleanFragments object with type turned to CompSolid?