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Modeling of symmetrically and asymmetrically loaded reinforced concrete slabs

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For the assessment of existing structures and the design of new structures, it is important to have a good understanding of the flow of forces, here applied to reinforced concrete solid slabs. Two analyti-cal methods are used: finite element models with 3D solid elements and a plasticity-based model that is suita-ble for hand calculations, the Modified Bond Model. The slabs that are modeled are half-scale models of rein-forced concrete solid slab bridges. As the Eurocode live load model prescribes more heavily loaded trucks in the first lane, the load model is asymmetric. For the finite element models, limited use is made of the redistri-bution capacity of the slab. For the Modified Bond Model, the influence of torsion and the edge effect need to be taken into account. The results of these studies improve the current state-of-the-art for analysis and design of reinforced concrete slabs.

Publié dans : Technologie
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Modeling of symmetrically and asymmetrically loaded reinforced concrete slabs

  1. 1. Challenge the future Delft University of Technology Modeling of symmetrically and asymmetrically loaded reinforced concrete slabs Eva Lantsoght, Ane de Boer, Cor van der Veen
  2. 2. 2 Overview • Introduction, plastic design models • Experiments • Finite element model: results • Extended strip model: results • Conclusions Slab shear experiments, TU Delft
  3. 3. 3 Introduction Problem Statement Bridges from 60s and 70s The Hague in 1959 Increased live loads heavy and long truck (600 kN > perm. max = 50ton) End of service life + larger loads
  4. 4. 4 Introduction Highway network in the Netherlands • NL: 60% of bridges built before 1976 • Assessment: shear critical in 600 slab bridges Highways in the Netherlands
  5. 5. 5 Introduction Modeling of concrete slabs • Linear elastic solutions • Classic plate theory • Equivalent frame method • Plastic methods • Strip method (Hillerborg) • Yield line method Slab shear experiments, TU Delft
  6. 6. 6 Experiments Size: 5m x 2.5m (variable) x 0.3m = scale 1:2 Continuous support, Line supports Concentrated load: vary a/d and position along width
  7. 7. 7 Experiments reinforcement 5000 200 200 Bottom side A-A B-B A-A B-B Top side Support1 Support2 Support3 2500 5000 300 250 265 300 50 100 A-A B-B10/240 10/240 20/120 20/120 20/120 10/240 20/12010/240 10/240 10/240 20/12020/120 50 265 300 IPE 700 L=2100 mm Specimen dimensions 5000x2500x300 mm 3 Dywidag 36 with load cells 2 IPE 700, L=3300mm Jack (Pmax=2000 kN) Load cell 2 HEM 300 Support 1 Support 2 Support 3Load plate 200x200 mm HEB240 Load cell 100 Ton, F205 Hinge (Pmax=3300 kN) 300 Hooked end reinforcement
  8. 8. 8 Experimental Results Bottom Flexural cracking Cracking around load towards support Shear failure Front face Flexural crack at 700 kN Crack width Failure at 954 kN, crack width 1.8 mm
  9. 9. 9 Numerical model (3 D solids) Concrete: 20 node solids 120x160x60 mm 5 elements over thickness slab Reinforcement: Embedded truss elements Perfect bond Dywidag bars: 2 node truss elements Support: Interface elements Material model: Concrete: crush and crack Reinforcement: yield 2969 2526 loading plate slab interface 20854 2969
  10. 10. 10 Numerical results 0 200 400 600 800 1000 0 2 4 6 8 10 Load(kN) Deflection (mm) NLFEA yielding of BOTF10T at step 14 (P=564.06 kN) crushing of concrete at step 20 (P=618.06 kN) yielding of TOPF10T at step 37 (P=776.06 kN) yielding of TOPF10L at step 40 (P=814.06 kN) peak load at step 45 (P=852.06 kN) experimental
  11. 11. 11 Numerical results Crack strain at peak load 0 0.5 1 1.5 2 2.5 3 0 0.001 0.002 0.003 s(N/mm2) e (-) Tensile stress strain
  12. 12. 12 Numerical results Crack strain at peak load Minimum principal strain at step 20 Start crushing of concrete -35 -30 -25 -20 -15 -10 -5 0 -0.02 -0.015 -0.01 -0.005 0 s(N/mm2) e (-) compressive stress strain -800 -600 -400 -200 0 200 400 600 800 -0.1 -0.05 0 0.05 0.1 s(N/mm2) e (-)Yielding bottom reinforcement Starts at 563 kN
  13. 13. 13 Numerical results 0 200 400 600 800 1000 0 2 4 6 8 10 Load(kN) Deflection (mm) Mean measured values of material strength Characteristic values of material strength Mean GRF values of material strength Design values of material strength experimental
  14. 14. 14 Numerical results unsymmetric load 20 200 200 x 8 mm plywood 2 sheets 100 x 5 mm 1 sheet 200 X 5 mm HEM 300 1 sheet 200 x 5 felt P50 Simplesupport 250100 1250 2500 5000 812438 300 300 600 2700 900 3200 100 750 200 400 Continuoussupport 20 200 200 x 8 mm plywood 2 sheets 100 x 5 mm 1 sheet 200 X 5 mm HEM 300 3 sheets 100 x 5 felt N100
  15. 15. 15 Experimental and numerical results Lateral front face At 400 kN crack width 0.15 mm At 800 kN first shear crack At 990 kN second shear crack Failure at 1154 kN 0 200 400 600 800 1000 1200 0 5 10 15 20 Load(kN) Deflection (mm) NLFEA crushing of concrete at step 17 (P=601.05 kN) peak load at steo 19 (P=622.05 kN) Experimental Results clearly affected by absence hooked end reinforcement Numerical failure load at 907 kN with hooked end
  16. 16. 16 Strip Model (1) • Alexander and Simmonds, 1990 • For slabs with concentrated load in middle
  17. 17. 17 Strip Model (2)
  18. 18. 18 Extended Strip Model (1) • Adapted for slabs with concentrated load close to support • Geometry is governing as in experiments • Maximum load: based on sum capacity of 4 strips • Effect of torsion: presentation of Daniel Valdivieso
  19. 19. 19 Unequal loading of strips • Static equilibrium • v2,x reaches max before v1,x ' 1, 0.166x c a v f d L a  
  20. 20. 20 Loads close to free edge Edge effect: when length of strip is too small to develop loaded length lw
  21. 21. 21 Extended Strip Model: results • S1T1: • PESM = 663 kN • Ptest/PESM = 1,44 • S4T1: • PESM = 775 kN • Ptest/PESM = 1,49 • Results similar for load in middle and at edge
  22. 22. 22 Summary & Conclusions • Live loads: asymmetric loading • Finite element models (3D solids): 2 direction asymmetric gives stress concentrations • Strip Model for concentric punching shear: plastic design method • Extended Strip Model performs well for asymmetric loading situations
  23. 23. 23 Contact: Eva Lantsoght E.O.L.Lantsoght@tudelft.nl // elantsoght@usfq.edu.ec +31(0)152787449

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