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Design of a Deep Concrete Beam with Opening
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thschrader
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Re: Design of a Deep Concrete Beam with Opening
I found a way to simplify the application of pre-tension in a 2D analysis. Instead of modeling the tendon in the plane of the analysis, I now put it perpendicular to this plane. The main advantage is that the tendon now plays no role in the modeling and meshing of the analysis plane. This avoids the need for extreme mesh refinement and prevents spurious deformations due to 1) lateral contraction introduced by the pre-tension strain and 2) discontinuities in young's modulus between concrete and tendon. I can now also use realistic x-sectional areas for the tendons, without worrying about deformations in the plane. Here is what it looks like for the deep beam:
It also implies a significant simplification of FreeCAD workflow. I can now simply extrude the B-spline sketches of the tendons and include those extrusions in a Boolean Fragment object with the plane of interest.
To model the >1100 mm2 steel required for each tendon, I use a strip of 50mm wide and 25mm high, centered on the plane of analysis.
To compensate for the high reinforcement requirements in the top right-hand corner that I found in the earlier analysis, I add an additional tendon that ties the reaction force of the upper tendon back to the support.
The reduction in horizontal reinforcement requirement this achieves is clear:
Like before, the pre-tension achieved in the analysis can be calculated with an integration filter:
The integration panel shows an integrated major principal stress value of 54524 MPa*mm, implying an average tension of 54524/50 = 1090 MPa. This multiplied by the cross sectional areas of the tendon yields a force of 1090*50*25 = 1.36 MN, which is indeed in the range I tried to achieve.
Finally, the plot of major prinicpal stress shows greatly reduced tension in the beam, supporting the conclusion from the reinforcement plot on the benefit of additional pre-stressing.
- FIB_Concrete_Deep_Beam_BHB_PT_Simple_rev0_Tendons.png (296.96 KiB) Viewed 349 times
It also implies a significant simplification of FreeCAD workflow. I can now simply extrude the B-spline sketches of the tendons and include those extrusions in a Boolean Fragment object with the plane of interest.
To model the >1100 mm2 steel required for each tendon, I use a strip of 50mm wide and 25mm high, centered on the plane of analysis.
To compensate for the high reinforcement requirements in the top right-hand corner that I found in the earlier analysis, I add an additional tendon that ties the reaction force of the upper tendon back to the support.
- FIB_Concrete_Deep_Beam_BHB_PT_Simple_rev0_Tie.png (97 KiB) Viewed 349 times
The reduction in horizontal reinforcement requirement this achieves is clear:
- FIB_Concrete_Deep_Beam_BHB_PT_Simple_rev0_RRx.png (75.35 KiB) Viewed 349 times
Like before, the pre-tension achieved in the analysis can be calculated with an integration filter:
- FIB_Concrete_Deep_Beam_BHB_PT_Simple_rev0_Force.png (241.57 KiB) Viewed 349 times
The integration panel shows an integrated major principal stress value of 54524 MPa*mm, implying an average tension of 54524/50 = 1090 MPa. This multiplied by the cross sectional areas of the tendon yields a force of 1090*50*25 = 1.36 MN, which is indeed in the range I tried to achieve.
Finally, the plot of major prinicpal stress shows greatly reduced tension in the beam, supporting the conclusion from the reinforcement plot on the benefit of additional pre-stressing.
- FIB_Concrete_Deep_Beam_BHB_PT_Simple_rev0_PV1.png (108.84 KiB) Viewed 349 times