1. Ing. Miloš Rieger Reliability assessment of composite steel concrete cross section of roadway bridge VŠB – Technical University of Ostrava, Faculty of Civil Engineering, L. Podéště 1875, 708 00 Ostrava-Poruba Euro-SiBRAM2002 Prague, June 24 to 26, 2002, Czech Republic

2. Summary of reliability conditions Classification of cross section Assessment Behaviour of cross section Loading Class 1 or 2 resistance to bending plastic design (extreme) values – creep, shrinkage of concrete, effects of temperature and assembling may be neglected Class 3 (Class 4 not recommended) resistance to bending elastic design (extreme) values – creep, shrinkage of concrete, effects of temperature and assembling shall be taken into account All classes fatigue resistance elastic characteristic (service) values – only repeated fatigue loading, assembling shall be taken into account STEEL: f yd = f y / a, where a 1 for ULS a = 1 for SLS CONCRETE: f cd = 0,85 f ck / c, where c 1 for ULS c = 1 for SLS REINFORCING STEEL: f sd = f sk / s, where s 1 for ULS s = 1 for SLS Euro-SiBRAM2002 Prague, June 24 to 26, 2002, Czech Republic Ultimate limit states

3. Summary of reliability conditions Euro-SiBRAM2002 Prague, June 24 to 26, 2002, Czech Republic Classification of cross sectionAssessment Behaviour of cross section Loading All classes limitation of stresses elastic characteristic (service) values – creep, shrinkage of concrete, effects of temperature and assembling shall be taken into account deformation, vibration, formation of crack elastic characteristic (service) values – creep, shrinkage of concrete, effects of temperature and assembling shall be taken into account Serviceability limit states STEEL: f yd = f y / a, where a 1 for ULS a = 1 for SLS CONCRETE: f cd = 0,85 f ck / c, where c 1 for ULS c = 1 for SLS REINFORCING STEEL: f sd = f sk / s, where s 1 for ULS s = 1 for SLS

4. Exploitation of cross section Example – simple beam of the span 34,7m Analyzed cross section 1318 x 12 343 x 32 2000 x 250 220 x 18 Steel S355 Concrete C25/30 Euro-SiBRAM2002 Prague, June 24 to 26, 2002, Czech Republic

5. Reliability criterion : P f < P d Common level of probability: P d = 0,000070 for ULS Reliability function : FS = ( R - S ) P f... probability of failure S... load effect R... resistance of structure P d... target probability of design 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 Euro-SiBRAM2002 Prague, June 24 to 26, 2002, Czech Republic method - Simulation Based Reliability Assessment Bending resistance of the cross section - SBRA (see ČSN 73 1401-1998) P d = 0,070 for SLS

6. Variability of loads and cross-section area are expressed by bounded histograms : Dead load DLvarLong lasting load LLvarShort lasting load SLvar Cross-section area WvarTemperanture TLvar Definition of input variables Variable of yield stress and chracterristic compressive strength of concrete are expressed by bounded histograms : Yield stress S355 FyCompressive strength of concrete C25/30 Fck Euro-SiBRAM2002 Prague, June 24 to 26, 2002, Czech Republic

7. fibre elastic behaviour for ULS plastic behaviour for ULS upper fibres of steel P f = 0,003564 P d = 0,000070 (dangerous) P f < 0,000001 (excessive safety), simultaneously elastic behaviour of cross section is conserved for SLS : P f,el. = 0,003564 < P d = 0,07 lower fibres of steel P f = 0,000368 P d = 0,000070 (dangerous) Final reliability in connection with ČSN 73 1401 : Reliability assessment of composite steel concrete cross section of roadway bridge Euro-SiBRAM2002 Prague, June 24 to 26, 2002, Czech Republic

8. 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 T d = 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-SiBRAM2002 Prague, June 24 to 26, 2002, Czech Republic

9. Discussion of Results Reference level in probabilistic design: achievement of yield stress P d = 0,000070 for ULS – (plastic behaviour) P d = 0,070 for SLS – (elastic behaviour) Euro-SiBRAM2002 Prague, June 24 to 26, 2002, Czech Republic elasto-plastic ? ? Material histograms: in case of material testing (tensile test, …)

10. Thanks for your attention Euro-SiBRAM2002 Prague, June 24 to 26, 2002, Czech Republic