Pavel%20Marek%201,%20David%20Pustka%202

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Posudek trvanlivosti ocelových konstrukcí metodu
SBRA Durability Assessment of Steel Structures
Using SBRA Method

• Pavel Marek 1, David Pustka 2
• and Petr Konecný 3

1 Institute of Theoretical and Applied Mechanics,
Academy of Sciences of the Czech Republic, Prague
and Technical University of Ostrava 2 Institute
of Theoretical and Applied Mechanics, Academy of
Sciences of the Czech Republic, Prague 3
Technical University of Ostrava
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Durability assessment using SBRA method

• Corrosion, fatigue, carbonation of concrete and
  other time-dependent effects.
• Inspection intervals and maintenance of steel and
  composite structures.
• Two applications of SBRA method follow.

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Example A - assignment

• Goal Calculation of safe service time of simply
  supported steel beam exposed to time-dependent
  random variable loads and corrosion.

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Input data geometry, materials

• The beam is made of rolled section IPE 360, steel
  V 10425

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Input data - loadings

• Random variable forces F1 and F2

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Loadings calculation

• Time-dependent load components

Dead load
Long-lasting load
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Resistance calculation considering corrosion

• Time-dependent cross-section modulus

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Reliability assessment

• Time - dependent bending resistance

• Time - dependent bending load effect

• Time dependent safety function

• Reliability criterion

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Resistance and Load Effects

• A- priori estimate in the range 0 up to 50 years

Resistance
Bending moment
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Probability of Failure Calculation

• Calculation of probability of failure
  corresponding to time T 25 years (AntHill
  for Windows output)

RFMR-ME
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A-priori estimate of probability of failure

• A-priori estimate of probability of failure in
  the range 0 up to 50 years and proposed
  inspection planning

1st inspection at time T25 years ? corrosion
model and load model correction
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Second probability of failure estimate

• Second estimate of probability of failure and
  following inspection planning

2nd inspection at time T40 years ? corrosion
model and load model correction
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Resistance and Load Effects

• Second estimate after corrections based on
  inspection

A-priory model
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Example B

• Please, see following movie.

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Long video
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Assignment

• Goal Remaining fatigue life of tubular steel
  post exposed to axial force and to vortex
  vibration due to wind load.
• Consideration of the relationship between wind
  velocity, amplitude, frequency and time
• Application of the SBRA method for calculation
  the relation between the probability of failure
  and the remaining fatique life.

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Assessment procedure

• The wind velocities spectrum corresponding to one
  week determination,
• The critical location stress range spectrum
  determination corresponding to one week,
• The Wohlers curve definition,
• Random variables variation estimation and
  introduction,
• Reliability function analysis using M-Star and
  Anthill programs.

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Reliability assessment

• Numbers of cycles to failure corresponding to Dsc

• Damage corresponding to one block of stress
  ranges cycles ni/week

• Safety function (Palmgren-Miner criterion)

• Reliability criterions

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M-Star and AntHill programs output

• Probability of failure estimation using M-Star
  program

• Probability of failure due to service time using
  Anthill program

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Remaining fatigue life

• The resulting probabilities of failure Pf ,
  correspond to the fatigue life (defined by
  number of weeks).
• The mass of the post were adjusted 153 120
  33 weeks before the post would fail with Pf
  0,05.

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Summary and Conclusions

• The solution of examples, based on SBRA,
  contributes to better understanding of the
  significance of individual variables and their
  interaction related to the assessment of
  durability.
• The examples indicate the transition from
  deterministic to probabilistic approach to the
  durability assessment.

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Thank You

• Pavel Marek 1, David Pustka 2
• and Petr Konecný 3

1 Institute of Theoretical and Applied Mechanics,
Academy of Sciences of the Czech Republic, Prague
and Technical University of Ostrava 2 Institute
of Theoretical and Applied Mechanics, Academy of
Sciences of the Czech Republic, Prague 3
Technical University of Ostrava
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8th International Conference on Inspection,
Appraisal,Repairs and Maintenance of
Structures 18- 20 December 2003, Singapore
Thank you for your attention

• Pavel Marek 1, David Pustka 2
• and Petr Konecný 3

1 Institute of Theoretical and Applied Mechanics,
Academy of Sciences of the Czech Republic, Prague
and Technical University of Ostrava 2 Institute
of Theoretical and Applied Mechanics, Academy of
Sciences of the Czech Republic, Prague 3
Technical University of Ostrava