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STRUCTURAL RELIABILITY AND RISK ANALYSIS – 4 Year FILS

Table of Contents

1. INTRODUCTION TO RANDOM VARIABLES THEORY................................................ 6
1.1 Data samples .................................................................................................................... 7
1.2 Indicators of the sample ................................................................................................... 7
1.3 Probability........................................................................................................................ 9
1.4 Random variables........................................................................................................... 10
1.5 Indicators of the probability distributions ...................................................................... 12
2. DISTRIBUTIONS OF PROBABILITY.............................................................................. 15
2.1. Normal distribution ....................................................................................................... 15
2.2. Log-normal distribution ................................................................................................ 19
2.3. Extreme value distributions........................................................................................... 21
2.3.1. Gumbel distribution for maxima in 1 year............................................................. 22
2.3.2. Gumbel distribution for maxima in N years........................................................... 25
2.4. Mean recurrence interval............................................................................................... 27
3. FUNCTION OF RANDOM VARIABLES ......................................................................... 29
3.1 Second order moment models........................................................................................ 29
4. STRUCTURAL RELIABILITY ANALYSIS..................................................................... 33
4.1. The basic reliability problem......................................................................................... 33
4.2. Special case: normal random variables ......................................................................... 35
4.3. Special case: log-normal random variables................................................................... 36
4.4. Calibration of partial safety coefficients ....................................................................... 37
5. SEISMIC HAZARD ANALYSIS........................................................................................ 41
5.1. Deterministic seismic hazard analysis (DSHA)............................................................ 41
5.2. Probabilistic seismic hazard analysis (PSHA) .............................................................. 42
5.3. Earthquake source characterization............................................................................... 43
5.4. Predictive relationships (attenuation relations)............................................................. 46
5.5. Temporal uncertainty .................................................................................................... 46
5.6. Probability computations............................................................................................... 47
5.7. Probabilistic seismic hazard assessment for Bucharest from Vrancea seismic source . 47
6. ACTIONS ON STRUCTURES. SNOW LOADS............................................................... 53
6.1 Introduction .................................................................................................................... 53
6.2 Snow load on the ground................................................................................................ 53
6.3 Snow load on the roof .................................................................................................... 56
6.4 Roof shape coefficients .................................................................................................. 58
6.5 Local effects ................................................................................................................... 60
6.5.1 Local verification .................................................................................................... 60
6.5.2 Exceptional snow drift on the roof.......................................................................... 61
7. ACTIONS ON STRUCTURES. WIND ACTION .............................................................. 62
7.1. General .......................................................................................................................... 62
7.2 Reference wind velocity and reference velocity pressure.............................................. 63
7.3 Wind turbulence ............................................................................................................. 67
7.4 Peak values..................................................................................................................... 67
7.5 Wind actions................................................................................................................... 68
7.5.1 Wind pressure on surfaces....................................................................................... 69
7.5.2 Wind forces ............................................................................................................ 70
8. ACTIONS ON STRUCTURES. SEISMIC ACTION ......................................................... 71
8.1 Introduction .................................................................................................................... 71
8.2 Representation of the seismic action.............................................................................. 71
8.3 Design spectrum for elastic analysis .............................................................................. 74

UTCB, Technical University of Civil Engineering, Bucharest 3