ON DESIGN OF COMPOSITE BEAMS WITH CONCRETE CRACKING

Transcription

1 ON DESIGN OF COMPOSITE BEAMS WITH CONCRETE CRACKING prof. Ing. Ján BUJŇÁK CSc. Ing. Jaroslav ODROBIŇÁK Department of Building Structures and Bridges Faculty of Civil Engineering University of Žilina Komenského Žilina The Slovak Republic Tel.: , Fax: bujnak@fstav.utc.sk, odrobinak@fstav.utc.sk

2 Concrete craking consideration Non-prestressed continuous steel-concrete composite bridges concrete in tension - cracking areas serviceability flexural stiffness changing along the length carrying capacity FEM analysis non-linear models with concrete cracking and tension stiffening consideration at lest two step analysis of the linear models simplified methods for analysis of the linear models

3 ω method for influence of concrete cracking on flexural stiffness Using common CAD-FEM programs 1. Internal forces and stresses 2. Flexural stiffness changes additional deformations of structure elements Ea I 2,ts(x) = Ea I 1(x) ξ(x) + Ea I 2(x) 1 ξ(x) M(x) 1 ξ(x) I 2(x) I 1(x) ϖ(x) = 3 3 Ea I 1(x) ξ(x) I 2(x) I 1(x) I 2(x) ξ(x) 3. Structure reloading with deformations 4. Additional internal forces, stresses and deflections

4 Experimental measurements - 2 models (bottom concrete slab) 1st SET IPE 3-26 REINFORCED CONCRETE 4x4-7 MATERIALS Steel: Reinforcement: Concrete: f ya = MPa f ua = MPa f ys = MPa f us = 65.8 MPa f ck, cube = 41.5 MPa

5 Experimental measurements - 4 models (beam with cantilevers) 2nd SET 5 P 1x P 12x3 33 P 2x2 2 beams studs φ 1 mm 2 beams - studs φ 16 mm MATERIALS Steel: Reinforcement: Concrete: f ya = MPa f ua = 39. MPa f ys = MPa f us = MPa f ck, cube = 57.4 MPa

6 σ [MPa] Steel of the beam 5 15 x ε Numerical non-linear FEM analysis of 1st SET σ [MPa] Reinforcement 5 15 x ε σ [MPa] Concrete - compression x ε Concrete element failure: - failure of a brittle material - 3D failure surface - cracking and (or) crushing σ [MPa] Concrete - tension f ct ,6 f ct x ε

7 RESULTS - beams with the bottom concrete slab under tension (1st SET) M [knm] 25 2 EI [MNm 2 ] δ [mm] N1 N2 EC4 ω - metóda method ANSYS 5 M [knm] N1 N2 EC4 ω -- metóda method Deflection at the mid-span Flexural stiffness of the composite beam derived from the deflection at mid-span crosssection (without influence of shear)

8 3 25 M [knm] M [knm] Eps_total - N1 Eps_total - N1 Eps_total - N2 Eps_total - N2 Ansys ω - method 5 5 Ansys ω -- method ε [1 6 ] ε [1 6 ] Strains at the top flange of the rolled IPE beam (compression) Strains at the bottom flange of the rolled IPE beam (tension)

9 RESULTS - beams with the overhanging cantilevers (2nd SET) N 9 - studs 16 N 11 - studs 1 EC4 N 1 - studs 16 N 12 - studs 1 ω - metóda method M [knm] M [knm] δ [mm] δ [mm] Deflection at the mid-span Deflection of the cantilever under loading point

10 N 9 - studs 16 N 11 - studs 1 EC4 N 1 - studs 16 N 12 - studs 1 ω - metóda method M [knm] M [knm] ε [1 6 ] ε [1 6 ] Strains at the bottom flange of steel girder at the mid-span (compression) Strains at the top flange of steel girder at the mid-span (tension)

11 Conclusions S S Good approximation of the time-dependent FEM modelling to the experiment observation can be concluded. Accordance of non-linear modelling of concrete cracking in ANSYS with reality is sufficient enough. Simplifiedω-method for stiffness changing due to concrete cracking are handy for practical use. The method can be easy combined with the most of common commercial CAD-FEM programs. The results obtained from the method are in a quite good coincidence with the real behaviour of composite girders. Moreover, application of this method can approximate complicated processes in the concrete deck with sufficient accuracy without need for a complicated and time consuming non-linear analysis of common steel-concrete composite bridges.

12 Thank You for Your attention

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16 - non-linear calculation Newton Raphson - time-dependent transient II. order analysis - influence of large deflection Number of finite elements: 7682 Number of nodes: 828 Number of load steps: 23 Number of load substeps: 1468 Number of iterations: 8368 Computing time: 198:42:4