Design of a Deep Concrete Beam with Opening

About the development of the FEM module/workbench.

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HarryvL
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Design of a Deep Concrete Beam with Opening

Postby HarryvL » Fri Dec 28, 2018 3:08 pm

The FIB Practitioners' Guide to Finite Element Modelling of Reinforced Concrete Structures contains a design example of a deep concrete beam with opening. The example is used in that report to demonstrate the "Strut-and-Tie" method that Thomas and Bernd discussed in an earlier post (https://forum.freecadweb.org/viewtopic. ... 35#p232799). I will use it here to compare/validate the method I coded in FreeCAD (https://forum.freecadweb.org/viewtopic.php?f=18&t=28821).

For reasons of copyright I cannot cut and past information from the aforementioned report, but will discuss the problem using the FreeCAD model:


FIB_Deep_Concrete_Beam_Model.png
FIB_Deep_Concrete_Beam_Model.png (336.13 KiB) Viewed 1092 times


The beam dimensions are 11x4x0.6m and it is loaded at the top by a distributed load of 120kN/m and a load of 5000kN introduced by a 1m wide column.

The factored compressive strength of the concrete is 0.75 x 0.6 x fc = 0.45 * 35 = 15.8MPa and the factored yield strength of the reinforcement steel is 315MPa.

The reinforcement ratios and principal concrete stresses (compression only) derived with FreeCAD are shown below:


FIB_Deep_Concrete_Beam.png
FIB_Deep_Concrete_Beam.png (158.38 KiB) Viewed 1092 times


The required horizontal reinforcement (below in red) is determined by integration of the horizontal reinforcement ratio over the vertical cuts of interest (below in black). This is done using a Paraview integration filter.


FIB_Reinforcement(2).jpg
FIB_Reinforcement(2).jpg (125.07 KiB) Viewed 1092 times


The insert to the above figure shows a comparison of reinforcement requirements (in mm^2 of steel) determined with FreeCAD to those in the FIB report.

In general the two sets of result are in good agreement, except at the corners of the opening, where FreeCAD requires double the amount of reinforcement. As theoretical stresses at sharp corners are infinite, the result will be sensitive to modelling assumptions. Interestingly, this is not discussed or considered in the FIB report. Rounding of the corners in the model would stabilise the result.

Anyway, the FreeCAD approach holds promise and I will work on making it available in my Github repository

I will compare the vertical reinforcement ratio in a future post
Last edited by HarryvL on Sat Jun 22, 2019 1:40 am, edited 1 time in total.
thschrader
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Re: Design of a Deep Concrete Beam with Opening

Postby thschrader » Fri Dec 28, 2018 10:46 pm

Hi Harry,
Z88 Arion now has the option to smooth the optimized shape and export it as stl.
But the stl looks creepy. No chance to convert it to a solid and do a new FEM run with FC.
FC_stl.JPG
FC_stl.JPG (61.62 KiB) Viewed 1052 times
arion.JPG
arion.JPG (77.98 KiB) Viewed 1052 times
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HarryvL
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Re: Design of a Deep Concrete Beam with Opening

Postby HarryvL » Sat Dec 29, 2018 7:43 am

Scary stuff Thomas :o However, this holds promise for the Tie-and-Strut method. One of the problems with a very coarse approximation like this would be control of crack width? It would stand up, but not be durable, especially in a humid or marine environment.
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HarryvL
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Re: Design of a Deep Concrete Beam with Opening

Postby HarryvL » Sat Dec 29, 2018 11:28 pm

I analysed the same problem with a refined mesh,


FIB_Reinforcement_Refined.jpg
FIB_Reinforcement_Refined.jpg (210.47 KiB) Viewed 984 times


...but did not find any significant changes to the required reinforcement.

This is what I find for the vertical reinforcement requirements:


FIB_Reinforcement_Vertical.jpg
FIB_Reinforcement_Vertical.jpg (123.36 KiB) Viewed 984 times


And finally a picture of how the integration over lines of interest works in Paraview


FIB_Reinforcement_ry.jpg
FIB_Reinforcement_ry.jpg (250.65 KiB) Viewed 984 times
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bernd
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Re: Design of a Deep Concrete Beam with Opening

Postby bernd » Sun Dec 30, 2018 8:16 am

last pic seams not to be the wireframe from refined mesh?

Harry your concrete stuff is cool! I really need to leave the development TODO for some days and play with this. Is it done with your principal stress branch?
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HarryvL
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Re: Design of a Deep Concrete Beam with Opening

Postby HarryvL » Sun Dec 30, 2018 8:22 am

Hi Bernd. Yes when I saw small difference I returned to coarse mesh.

My repo on principal stresses only has the plotting of principal stresses. I will start a new one soon that also includes reinforcement ratios. It is all ready and working but needs tiedying up.
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HarryvL
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Re: Design of a Deep Concrete Beam with Opening

Postby HarryvL » Wed Jan 02, 2019 3:23 pm

Some further "infotainment":

Bridging the gap between finite element output and strut-and-tie (STM) input?


FIB_Reinforcement_STM_1.jpg
FIB_Reinforcement_STM_1.jpg (247.85 KiB) Viewed 866 times


Perhaps consider pre-stressing instead (or in addition)?


FIB_Reinforcement_STM_2.jpg
FIB_Reinforcement_STM_2.jpg (238.78 KiB) Viewed 866 times
thschrader
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Re: Design of a Deep Concrete Beam with Opening

Postby thschrader » Wed Jan 02, 2019 7:16 pm

bernd wrote:
Sun Dec 30, 2018 8:16 am
Harry your concrete stuff is cool!
Yeah, it is!
I like the STM pics from above. The "density" of the red lines correspond
to the Z88 Arion result. You can imagine the optimized shape.
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HarryvL
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Re: Design of a Deep Concrete Beam with Opening

Postby HarryvL » Thu Jan 03, 2019 6:50 am

Thanks guys.

Here are the tensile forces (obtained with a Paraview integration filter) that would need to be compensated by pre-tensioning:


FIB_Reinforcement_STM_3.jpg
FIB_Reinforcement_STM_3.jpg (249.5 KiB) Viewed 802 times


As a starting point, I would propose 1.2MN pre-tension in the upper tendon and 1.7MN in the lower. Assuming use of 270 ksi (1860 MPa) strands, the applied tension should not exceed 0.8*1860 ~ 1500 MPa. So we would need at least 800mm2 pre-tensioning steel in the upper region and 1100mm2 in the lower region.

As the pre-tensioning does not fully compensate for the concrete tension under load, it would be interesting to try and re-analyse the problem with pre-tensioning to see what remaining reinforcement requirements are found:


FIB_Reinforcement_PT.jpg
FIB_Reinforcement_PT.jpg (147.8 KiB) Viewed 802 times


The simplest way to do so would be by following the approach here: https://forum.freecadweb.org/viewtopic. ... 86#p250492
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HarryvL
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Re: Design of a Deep Concrete Beam with Opening

Postby HarryvL » Fri Jan 04, 2019 5:48 pm

I managed to get the pre-tensioning to work and learnt a lot along the away. I swept the strands along B-spline sketches, found a combination of Young’s modulus, x-section and temperature loading for the strands that ensures mesh quality while reducing spurious lateral contraction and used a programmable filter in ParaView to remove principal tensile stresses in the tendons. It may not sound much to some, but I am pretty pleased :D

So here some plots of the results:

The deformed mesh with von Mises stress in the strands:


5D03676B-49E9-44A8-B520-9A4EB1D0FBEB.jpeg
5D03676B-49E9-44A8-B520-9A4EB1D0FBEB.jpeg (179.01 KiB) Viewed 721 times


The average stresses in both tendons can be obtained from integrating the major principal stress over the artificial cross section of the strand. This gives 1.4MN for both strands:


5A74E3DF-E86A-477A-BAD6-F0E59597784E.jpeg
5A74E3DF-E86A-477A-BAD6-F0E59597784E.jpeg (438.51 KiB) Viewed 721 times


Tension is highest in the strands and near the top right-hand corner of the beam. The top strand reaction forces need to be transferred to the support on the right and this will require significant reinforcement:


868A9476-E7AB-4E30-8100-FFAA03680A88.png
868A9476-E7AB-4E30-8100-FFAA03680A88.png (374.16 KiB) Viewed 721 times



The major principal stress vectors superimposed on the tensile stress field, after surgically removing the stresses from the tendons (they are so big that they would dwarf the stresses in the concrete):


2F76C76F-6AE9-4181-8A8A-784303201D97.png
2F76C76F-6AE9-4181-8A8A-784303201D97.png (225.06 KiB) Viewed 721 times


This reconfirms the requirement of a “tie” back to the support on the right.

Finally a somewhat cluttered picture of horizontal reinforcement requirements and compressive stress vectors. This shows that introduction of pre-tension reduces the requirement for passive reinforcement. It also shows a less concentrated compressive stress flow, indicating better utilization of both steel and concrete:


CFF47DBE-8086-4755-953C-06D5619AA638.png
CFF47DBE-8086-4755-953C-06D5619AA638.png (381.06 KiB) Viewed 721 times