chapter 10 structural reliability: weakest link and fail-safe systems

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Chapter 10 Structural Reliability: Weakest Link and Fail- Safe Systems

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Page 1: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems

Chapter 10 Structural Reliability: Weakest

Link and Fail-Safe Systems

Page 2: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems

10.1 Introduction

dsdllsfSLPP LSf ),()( ,

Page 3: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 4: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems

10.2 Fundamental One Member-one Load Case

10.2.1 Probability of failure

Page 5: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 6: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems

10.2.2 Reliability index)0( MPPf

Page 7: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems

10.2.3 Bound on the probability of failure

Page 8: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 9: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 10: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 11: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems

10.3 Single Member Several Load Case

10.3.1 probability of failure

Page 12: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 13: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems

10.3.2 Bounds on the probability of Failure

Page 14: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems

The upper bound on R0

Page 15: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems

10.4 Several Members- One load case (series system

10.4.1 Probability of Failure

Page 16: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 17: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems

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ll

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i

10.4.2 simple bounds on the probability of failure

)(.....)()()()..........(121211 ....32121

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(10.30)

(10.33)

Page 18: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 19: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 20: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems

10.4.3 Ditlevsen bounds on the probability of failure

Page 21: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 22: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 23: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 24: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 25: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 26: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems

10.5 several members-several loads case (series system

10.5.1 Probability of failure

Page 27: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 28: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems

10.5.2 bounds on probility of failure

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Page 29: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 30: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 31: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems

10.5.3 Brittle material

10.6 Reliability Analysis of parallel system

10.6.1 Probability of Failure

Page 32: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 33: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 34: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems

10.6.2 Simple bounds on the probility of failure

Page 35: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 36: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems

10.6.3 Brittle material

Page 37: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 38: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 39: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 40: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 41: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 42: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 43: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems

10.7 Elastic-Plastic Analysis of Structure

10.7.1 Probability of failurew in I th collapse mode

Page 44: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 45: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 46: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems

dxxydPxYYydydPY iii )()()()( 22122112

10.7.2 over all probability of failure of the structure

Page 47: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 48: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 49: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 50: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 51: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 52: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 53: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 54: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 55: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 56: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems
Page 57: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems

10.8 Structure with correlation of element strength

10.8.1 series system

Page 58: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems

10.8.2 parallel systems

Page 59: Chapter 10 Structural Reliability: Weakest Link and Fail-Safe Systems