# Modeling of symmetrically and asymmetrically loaded reinforced concrete slabs

Assistant Professor at Universidad San Francisco de Quito en Universidad San Francisco de Quito
21 de Sep de 2016
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### Modeling of symmetrically and asymmetrically loaded reinforced concrete slabs

• 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 Overview • Introduction, plastic design models • Experiments • Finite element model: results • Extended strip model: results • Conclusions Slab shear experiments, TU Delft
• 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 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 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 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 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 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 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 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 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 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 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 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 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 Strip Model (1) • Alexander and Simmonds, 1990 • For slabs with concentrated load in middle
• 17. 17 Strip Model (2)
• 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 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 Loads close to free edge Edge effect: when length of strip is too small to develop loaded length lw
• 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 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 Contact: Eva Lantsoght E.O.L.Lantsoght@tudelft.nl // elantsoght@usfq.edu.ec +31(0)152787449