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 52 1 26 Žilina The Slovak Republic Tel.: +421 41 513 5651, Fax: +421 41 513 569 E-mail: bujnak@fstav.utc.sk, odrobinak@fstav.utc.sk
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
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) 3 3 3 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
Experimental measurements - 2 models (bottom concrete slab) 1st SET 7 3 4 24 26 325 15 325 3 7 8 IPE 3-26 REINFORCED CONCRETE 4x4-7 MATERIALS Steel: Reinforcement: Concrete: f ya = 371.6 MPa f ua = 493.1 MPa f ys = 442.2 MPa f us = 65.8 MPa f ck, cube = 41.5 MPa
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 25 85 13 35 85 25 33 MATERIALS Steel: Reinforcement: Concrete: f ya = 243.1 MPa f ua = 39. MPa f ys = 477.5 MPa f us = 733.1 MPa f ck, cube = 57.4 MPa
σ [MPa] 6 5 4 3 2 Steel of the beam 5 15 x ε Numerical non-linear FEM analysis of 1st SET σ [MPa] 7 6 5 4 3 2 Reinforcement 5 15 x ε σ [MPa] -45-4 -35-3 -25-2 -15-1 -5 Concrete - compression -.5-1.5-2.5-3.5 x ε Concrete element failure: - failure of a brittle material - 3D failure surface - cracking and (or) crushing σ [MPa] Concrete - tension 4. 3.5 f ct 3. 2.5 2.,6 f ct 1.5 1..5...1.2.3.4.5.6 x ε
RESULTS - beams with the bottom concrete slab under tension (1st SET) M [knm] 25 2 EI [MNm 2 ] 5 45 4 35 15 3 25 2 15 5 1 -.5.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 δ [mm] N1 N2 EC4 ω - metóda method ANSYS 5 M [knm] 5 15 2 25 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)
3 25 M [knm] M [knm] 3 25 2 2 15 15 Eps_total - N1 Eps_total - N1 Eps_total - N2 Eps_total - N2 Ansys ω - method 5 5 Ansys ω -- method -25-2 -15 - -5 2 3 4 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)
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 4 35 3 M [knm] M [knm] 4 35 3 25 25 2 2 15 15 5 5-3. -2.5-2. -1.5-1. -.5..5 δ [mm]. 2.5 5. 7.5 1. 12.5 15. 17.5 2. δ [mm] Deflection at the mid-span Deflection of the cantilever under loading point
N 9 - studs 16 N 11 - studs 1 EC4 N 1 - studs 16 N 12 - studs 1 ω - metóda method 4 35 3 25 2 15 5 M [knm] M [knm] 4 35 3 25 2 15 5-2 -15 - -5 ε [1 6 ] 2 3 4 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)
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.
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- 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