PSI - Issue 5

Martin Krejsa et al. / Procedia Structural Integrity 5 (2017) 1283–1290

1284

Martin Krejsa et al. / Structural Integrity Procedia 00 (2017) 000 – 000

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load stress over a long time. The bearing structure is crucial for safety and reliability. A substantial increase in the overall weight load from vehicle axles and crossing frequencies leads to higher fatigue damage than was considered during the design of bridges. Due to these and a number of other reasons, it is highly relevant to develop methods for the calculation and assessment of the residual fatigue life and time-dependent analysis of the reliability of existing steel bridges and structures under cyclic loadings, e.g. Xiang and Liu (2011), Ye et al. (2014) or Halama et al. (2016). One category of relevant approaches for the quantification of the reliability of structures are represented by stochastic methods, which determine the failure probability, see e.g. Melchers (1999), Kralik (2013) and Lu et al. (2017). A substantial part of these methods are based on the crude Monte Carlo simulation method (MC), e.g. Kala (2007) and Sanches et al. (2015), whose disadvantage is poor efficiency due to the need of a high number of simulation steps. Advanced and stratified simulation methods, for e.g. Markov chain Monte Carlo simulations (MCMC), also applied in fatigue damage prognosis – see e.g. Guan et al. (2011), Tong et al. (2016) and Schneider et al. (2017), strive to increase the efficiency of these computational methods. The paper focuses the approach based on optimized numerical integration - the Direct Optimized Probabilistic Calculation method (DOProC), which is being developed now and was comprehensively published e.g. in Krejsa et al. (2016). The DOProC method is distinguished by higher accuracy than the simulation methods. Another advantage is the easy implementation on platforms with multiple processing units or cores, enabling the parallel computing of this probabilistic procedure, for e.g., on supercomputers. This probabilistic computational method was applied in the solution of some engineering problems, among others, the assessment of reliability of steel bridge structures loaded by fatigue – Krejsa et al. (2017). Probabilistic modelling of fatigue crack progression leads to designing a system of regular inspections of structures and is based on linear fracture mechanics and Paris-Erdogan law, e.g. as in Krejsa and Tomica (2011).

Nomenclature a

fatigue crack length

a 0 a d

initial fatigue crack length

detectable length of the fatigue crack acceptable length of the fatigue crack

a ac

N number of fatigue cycles d a /d N rate of crack growth per cycle C , m material constants  K

range of the stress intensity factor

constant stress range

  f ( a )

calibration function g ( R , E ) safety margin function R

random fatigue resistance of the element random variable effects of the extreme load

E P

probability

P f P d t , T

probability of failure

designed failure probability time of structural operation

U , D , F random phenomena h

height of the rectangular cross-section width of the rectangular cross-section

b s

span of the element

F 3 PB

force in three-point bending test yield stress of the specimen

f y