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Probability-Based Structural Fire Load

Book Description

In the structural design of airframes and buildings, probability-based procedures are used to mitigate the risk of failure as well as produce cost-effective designs. This book introduces the subject of probabilistic analysis to structural and fire protection engineers and can also be used as a reference to guide those applying this technology. In addition to providing an understanding of how fire affects structures and how to optimize the performance of structural framing systems, Probability-Based Structural Fire Load provides guidance for design professionals and is a resource for educators. The goal of this book is to bridge the gap between prescriptive and probability-based performance design methods and to simplify very complex and comprehensive computer analyses to the point that stochastic structural fire loads have a simple, approximate analytical expression that can be used in structural analysis and design on a day-to-day basis. Numerous practical examples are presented in step-by-step computational form.

Table of Contents

  1. Coverpage
  2. Half title page
  3. Dedication
  4. Title page
  5. Copyright page
  6. Contents
  7. Foreword by William F. Baker
  8. Preface
  9. Acknowledgments
  10. 1 Introduction
    1. 1.1 Deterministic Approach to Structural Fire Protection Engineering
    2. 1.2 Probability-Based Approach
      1. 1.2.1 Potential Failure Modes
      2. 1.2.2 Definition of Acceptable Probability of Failure (Target Probability)
      3. 1.2.3 Statistically Characterized Design Variables and Random Functions
      4. 1.2.4 Structural Reliability Assessment
      5. 1.2.5 Limit State Design
      6. Example 1.1
      7. 1.2.6 Partial Safety Factor ψ and Reliability Index β
      8. Example 1.2
    3. 1.3 Probability-Based Structural Fire Load as a Stochastic Process
    4. References
  11. 2 Introduction to Probability Theory
    1. 2.1 Random Variables: Definition of a Probability
      1. 2.1.1 The Classical Definition of Probability
      2. 2.1.2 Mutually Exclusive Events
      3. Exercises 2.1 through 2.9
      4. 2.1.3 Conditional Probability
      5. Exercise 2.10
      6. 2.1.4 Independent and Mutually Exclusive Events
      7. Exercises 2.11 through 2.13
    2. 2.2 Complete Probability Formula
    3. Exercise 2.14 Moving Fire
      1. 2.2.1 Bayes’ Theorem
    4. Exercises 2.15 through 2.22
    5. 2.3 Probability Distributions – Concept of Random Variable
      1. 2.3.1 The Binomial Probability Distribution
    6. Exercises 2.23 through 2.33
      1. 2.3.2 The Poisson Probability Distribution
    7. Exercises 2.34 through 2.38
      1. 2.3.3 Correlation and Dependence
    8. 2.4 Continuous Probability Distributions
      1. 2.4.1 Normal Probability Distributions
    9. Exercises 2.39 through 2.42
      1. 2.4.2 Weibull Distribution
      2. 2.4.3 Rayleigh Distribution
      3. 2.4.4 Chi-Squared Distribution
    10. 2.5 Joint Probability Distribution
    11. 2.6 Characteristic Functions
    12. 2.7 Functions of Random Variables and Their Distribution
    13. Exercises 2.43 through 2.45
      1. 2.7.1 One-to-One Functions of an Absolutely Continuous Random Variable
      2. 2.7.2 Probabilistic Transformation (Linearization) Method
    14. Exercise 2.46
    15. 2.8 Confidence Interval
    16. Exercise 2.47
      1. 2.8.1 Confidence Interval (Exponential Distribution)
      2. 2.8.2 Confidence Interval (Poisson Distribution)
      3. 2.8.3 Binomial Proportion Confidence Interval
    17. References
  12. 3 Random Processes
    1. 3.1 Definitions
      1. 3.1.1 Mean Value
    2. 3.2 Properties and Estimations
    3. 3.3 Stationary Random Processes
    4. Exercise 3.1
      1. 3.3.1 Stationary and Ergodic Random Processes
    5. Exercises 3.2 and 3.3
    6. 3.4 Power Spectrum
    7. Exercises 3.4 through 3.12
    8. 3.5 Exponential Distribution Flow
    9. Exercises 3.13 through 3.15
    10. 3.6 Poisson Distribution
    11. 3.7 Erlang Distribution
    12. 3.8 Markov Process: A Class of Random Processes
    13. 3.8.1 Definitions
    14. 3.8.2 Queuing Theory (Markov Chain)
    15. Exercises 3.16 through 3.25
      1. 3.8.3 Engset Formula
      2. Exercises 3.26 through 3.31
    16. References
  13. 4 Very Fast Fire Severity: Probabilistic Structural Fire Resistance Design
    1. 4.1 Introduction
      1. 4.1.1 Very Fast Fire: Statistical Data (0 < γ < 0.05)
    2. 4.2 The First-Order Reliability Method (FORM)
      1. 4.2.1 Most Probable Point Methods
    3. 4.3 Limit State Approximation
    4. 4.4 Partial Safety Factor ψ and Reliability Index β
    5. 4.5 Confidence Interval – Maximum Dimensionless Temperature
    6. Example 4.1
    7. Example 4.2
    8. 4.6 Confidence Interval – Dimensionless Parameter “γ”
    9. 4.7 Confidence Interval – Dimensionless Time “τmax”
    10. 4.8 Flashover Point (T2 Method – Probabilistic Approach)
    11. 4.9 Structural Failures in Time
    12. 4.9.1 Structural Fire Load as a Stochastic Process
    13. 4.10 Ergodicity
    14. 4.11 The First-Occurrence Time Problem and the Probability Density P (a, t)
    15. Example 4.3
    16. Example 4.4
    17. References
  14. 5 Fast Fire and Life-Cycle Cost Analysis
    1. 5.1 Fire Load and Severity of a Real Fire
    2. 5.2 Fast Fire: Statistical Data (0.05 < γ < 0.175)
    3. 5.3 Reliability Index
    4. 5.4 Confidence Interval – Maximum Dimensionless Temperature
    5. Example 5.1
    6. Example 5.2
    7. Example 5.3
    8. Example 5.4
    9. 5.5 Confidence Interval – Dimensionless Parameter “γ”
    10. 5.6 Confidence Interval – Dimensionless Time “τmax”
    11. 5.7 Flashover Point (T2 Method – Probabilistic Approach)
    12. 5.8 Structural Failures in Time
    13. 5.8.1 Structural Fire Load as a Stochastic Process
    14. 5.9 The First-Occurrence Time Problem and the Probability Density P (a, t)
    15. 5.10 Life-Cycle Cost Analysis (Probability-Based Structural Damage Due to Fire)
      1. 5.10.1 Introduction
      2. 5.10.2 Developing CERs
    16. Example 5.5
    17. References
  15. 6 Medium Fire Severity and Thermal Diffusivity Analysis
    1. 6.1 Introduction
    2. 6.2 Medium Fire: Maximum Temperature Statistical Data (0.175 < γ < 0.275)
    3. 6.3 Reliability Index β
    4. Example 6.1
    5. 6.4 Confidence Interval – Dimensionless Parameter “γ”
    6. 6.5 Random Variable “τmax”: Confidence Interval (Dimensionless Time “τmax”)
    7. 6.6 Structural Failures in Time
    8. 6.7 Spectral Function
    9. 6.8 The First-Occurrence Time Problem and the Probability Density P (a, t)
    10. 6.9 Probability-Based Thermal Analyses
      1. 6.9.1 Introduction
      2. 6.9.2 Autocorrelation Function – Output (Method #1)
      3. 6.9.3 Autocorrelation Function – Output (Method #2)
      4. 6.9.4 Autocorrelation Function – Output (Method #3)
    11. 6.10 Definitions of Random Fire Rating and Practical Applications
      1. 6.10.1 Case 1: Probability P(θ11< 4) – Stochastic Process
      2. 6.10.2 Case 2: Reliability Method
      3. 6.10.3 Case 3: Structural Design (Reliability Method)
      4. Example 6.2
      5. 6.10.4 Case 4: Statistical Linearization Method
    12. References
  16. 7 Slow Fire Severity and Structural Analysis/Design
    1. 7.1 Introduction
    2. 7.2 Structural Systems under Stochastic Temperature-Time Fire Load
    3. 7.3 Autocorrelation Function: Dynamic Analysis
    4. 7.4 Slow Fire: Maximum Temperature Statistical Data (0.275 < γ < 1.0)
    5. 7.5 Reliability Index β
    6. 7.6 Random Variable “γmax”: Confidence Interval (Dimensionless Time “τmax”)
    7. 7.7 Random Variable “τmax”: Dimensionless Time
    8. 7.8 Autocorrelation and Spectral Functions
    9. 7.9 The First-Occurrence Time Problem and the Probability Density P (a, t)
    10. 7.10 Applications: ODOF Structural Systems
    11. Example 7.1
    12. Example 7.2
    13. Example 7.3: 15 Story Building
    14. References
  17. Annex 1
  18. Annex 2
  19. Annex 3
  20. Annex 4
  21. Index