Ing. Milo

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Euro-SiBRAM2002 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. Podéšte 1875, 708 00
Ostrava-Poruba
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Summary of reliability conditions
Euro-SiBRAM2002 Prague, June 24 to 26, 2002,
Czech Republic
Ultimate limit states
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
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Summary of reliability conditions
Euro-SiBRAM2002 Prague, June 24 to 26, 2002,
Czech Republic
Serviceability limit states
Classification of cross section Assessment 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
All classes deformation, vibration, formation of crack elastic characteristic (service) values creep, shrinkage of concrete, effects of temperature and assembling shall be taken into account
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Euro-SiBRAM2002 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
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Euro-SiBRAM2002 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 lt 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 CSN 73 1401-1998)
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Euro-SiBRAM2002 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 stress S355 F Fy
Compressive strength of concrete C25/30 F Fck
Variability of loads and cross-section area are
expressed by bounded histograms
Dead load F DLvar
Long lasting load F LLvar
Short lasting load F SLvar
Cross-section area F Wvar
Temperanture F TLvar
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Euro-SiBRAM2002 Prague, June 24 to 26, 2002,
Czech Republic
Reliability assessment of composite steel
concrete cross section of roadway bridge
Final reliability in connection with CSN 73 1401
fibre elastic behaviour for ULS plastic behaviour for ULS
upper fibres of steel Pf 0,003564 ? Pd 0,000070 (dangerous) Pf lt 0,000001 (excessive safety), simultaneously elastic behaviour of cross section is conserved for SLS Pf,el. 0,003564 lt Pd 0,07
lower fibres of steel Pf 0,000368 ? Pd 0,000070 (dangerous) Pf lt 0,000001 (excessive safety), simultaneously elastic behaviour of cross section is conserved for SLS Pf,el. 0,003564 lt Pd 0,07
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Euro-SiBRAM2002 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 CSN 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.

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Euro-SiBRAM2002 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, )

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