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Analysis of composite bridge sections using SBRA method and Monte Carlo simulation. Ensuring reliability for ultimate and serviceability limit states. Consideration of material variability and load effects.
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Euro-SiBRAM‘2002 Prague, June 24 to 26, 2002, Czech Republic Reliability assessment of composite steel concrete cross section of roadway bridge Ing. Miloš Rieger VŠB – Technical University of Ostrava, Faculty of Civil Engineering, L. Podéště 1875, 708 00 Ostrava-Poruba
Summary of reliability conditions Euro-SiBRAM‘2002 Prague, June 24 to 26, 2002, Czech Republic STEEL: fyd = fy / a , where a 1 for ULS a = 1 for SLS CONCRETE: fcd = 0,85 fck / c , where c 1 for ULS c = 1 for SLS REINFORCING STEEL: fsd = fsk / s , where s 1 for ULS s = 1 for SLS Ultimate limit states
Summary of reliability conditions Euro-SiBRAM‘2002 Prague, June 24 to 26, 2002, Czech Republic STEEL: fyd = fy / a , where a 1 for ULS a = 1 for SLS CONCRETE: fcd = 0,85 fck / c , where c 1 for ULS c = 1 for SLS REINFORCING STEEL: fsd = fsk / s , where s 1 for ULS s = 1 for SLS Serviceability limit states
Euro-SiBRAM‘2002 Prague, June 24 to 26, 2002, Czech Republic Example – simple beam of the span 34,7m Exploitation of cross section Analyzed cross section 2000 x 250 220 x 18 Concrete C25/30 1318 x 12 Steel S355 343 x 32
Euro-SiBRAM‘2002 Prague, June 24 to 26, 2002, Czech Republic Bending resistance of the cross section - SBRA method - Simulation Based Reliability Assessment Reliability function : FS = ( R - S ) Analysis of reliability function and final value of probability of failure is performed using Monte Carlo simulation technique and corresponding computer programs M-Star™ and AntHill™ R ... resistance of structure S ... load effect Reliability criterion : Pf < Pd Pf ... probability of failure Pd ... target probability of design Common level of probability: Pd = 0,000070 for ULS Pd = 0,070 for SLS (see ČSN 73 1401-1998)
Euro-SiBRAM‘2002 Prague, June 24 to 26, 2002, Czech Republic Definition of input variables Variable of yield stress and chracterristic compressive strength of concrete are expressed by bounded histograms : Yield stressS355 FFy Compressive strength of concreteC25/30 FFck Variability of loads and cross-section area are expressed by bounded histograms : Dead load FDLvar Long lasting load FLLvar Short lasting load FSLvar Temperanture F TLvar Cross-section area FWvar
Euro-SiBRAM‘2002 Prague, June 24 to 26, 2002, Czech Republic Reliability assessment of composite steel concrete cross section of roadway bridge Final reliability in connection with ČSN 73 1401 :
Euro-SiBRAM‘2002 Prague, June 24 to 26, 2002, Czech Republic Summary and Conclusions The article demonstrates analysis of composite steel concrete bridge cross section with use of fully probabilistic SBRA method based on the application of Monte Carlo simulation technique. Service life was considered according to ČSN 73 1401 Td = 80 years. Use of bounded histograms, which represent duration of individual load category, enables better multicomponent load simulation, in a real way the alternate character of temperature changes can be modeled.
Euro-SiBRAM‘2002 Prague, June 24 to 26, 2002, Czech Republic Discussion of Results Reference level in probabilistic design: achievement of yield stress Pd = 0,000070 for ULS – (plastic behaviour) Pd = 0,070 for SLS – (elastic behaviour) elasto-plastic ? Material histograms: in case of material testing (tensile test, …) ?
Euro-SiBRAM‘2002 Prague, June 24 to 26, 2002, Czech Republic Thanks for your attention
