WWeesstteerrnn UUnniivveerrssiittyy SScchhoollaarrsshhiipp@@WWeesstteerrnn Electronic Thesis and Dissertation Repository 1-28-2013 12:00 AM SSiimmpplliififieedd TToooollss ffoorr PPeerrffoorrmmaannccee--BBaasseedd DDeessiiggnn ooff RReeiinnffoorrcceedd CCoonnccrreettee FFrraammeess EExxppoosseedd ttoo FFiirree Salah El-Din F. El-Fitiany, The University of Western Ontario Supervisor: Dr. Maged A. Youssef, The University of Western Ontario A thesis submitted in partial fulfillment of the requirements for the Doctor of Philosophy degree in Civil and Environmental Engineering © Salah El-Din F. El-Fitiany 2013 Follow this and additional works at: https://ir.lib.uwo.ca/etd Part of the Structural Engineering Commons RReeccoommmmeennddeedd CCiittaattiioonn El-Fitiany, Salah El-Din F., "Simplified Tools for Performance-Based Design of Reinforced Concrete Frames Exposed to Fire" (2013). Electronic Thesis and Dissertation Repository. 1151. https://ir.lib.uwo.ca/etd/1151 This Dissertation/Thesis is brought to you for free and open access by Scholarship@Western. It has been accepted for inclusion in Electronic Thesis and Dissertation Repository by an authorized administrator of Scholarship@Western. For more information, please contact [email protected]. SIMPLIFIED TOOLS FOR PERFORMANCE-BASED DESIGN OF REINFORCED CONCRETE FRAMES EXPOSED TO FIRE (Integrated Article) by Salah El-Din Farouk El-Fitiany Graduate Program in Civil and Environmental Engineering A thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy The School of Graduate and Postdoctoral Studies The University of Western Ontario London, Ontario, Canada © Salah El-Fitiany 2013 Abstract Fire safety of Reinforced Concrete (RC) buildings is an important design aspect that ensures structural integrity during fire events. As new codes are moving from prescriptive methods towards performance based design and full scale experiments and numerical simulations are expensive and time consuming. Practitioners are in need of rational design tools to assess the strength and serviceability of individual RC elements and the structure as a whole during a fire event. This thesis provides such tools for RC frames. A previously developed sectional analysis method is extended to cover RC beams subjected to fire from three sides. An extensive parametric study is conducted to propose simple equations expressing the equivalent stress-block parameters at elevated temperatures. These equations can be utilized by designers to estimate the flexure capacity of RC beams exposed to fire. A novel method to track the behavior of continuous RC beams during standard fire exposure is proposed and validated. The proposed method is based on separating the effects of thermal deformations and vertical loads. The effective flexural stiffness and the thermal deformations of fire-exposed RC beams are estimated using simple expressions that are developed based on a comprehensive parametric study. Designers can apply the proposed method to assess the structural fire safety of RC continuous beams. A simple method to construct the full interaction diagram of RC columns exposed to fire is developed and validated. An existing simplified heat transfer method is extended to predict the average temperature distribution. A number of reasonable approximations are assumed to allow reaching a closed form solution for the concrete compressive forces that correspond to a specific strain distribution. The closed form solution provides formulas that engineers can use to sketch the interaction diagrams. A practical approach to track the fire performance of RC frames during fire exposure is proposed and validated. The effective flexural and axial stiffnesses as well as unrestrained thermal deformations of heated RC sections are evaluated. Their values are used to conduct a quick assessment of the integrity of a fire exposed structure and ensure the safety of emergency response teams during fire evacuation and extinguishing. ii Keywords Concrete; Elevated temperatures; Heat transfer; Sectional analysis; Fire resistance, Stress- block parameters; Flexural stiffness; Design; Interaction diagrams; Fire performance; Frames; Thermal Restraint. iii They will ask thee concerning the Spirit. Say: "The Spirit is by command of my Lord, and of knowledge ye have been vouchsafed but little." Holy Quran, Chapter 17, Verse 85 To my wonderful parents, Enas, Farouk, Wafaa, and Ahmed To my beloved wife Marwa To my beautiful daughter Laila To my siblings Eman, Omar, and Mohamed And, To the martyrs of the January 25th revolution in Egypt iv Co-Authorship Statement All analytical work presented in this thesis was performed by Salah El-Fitiany. Chapters 2 and 3 of this thesis were accepted for publication in the ACI journal. Chapters 4 – 6 of this thesis will be submitted to scholarly journals as manuscripts co-authored by Salah El-Fitiany and Maged Youssef . v Acknowledgments I am deeply thankful to Dr. Maged Ali Youssef for his supervision, guidance, and care during my research program. Dr. Youssef has devoted a lot of his time as a research advisor and mentor to me during my doctoral studies. During the past five years, we’ve had a meeting nearly every week even when he was travelling or on vacation. Dr. Youssef’s enthusiasm and encouragement not only contributed to my technical development but also helped me in terms of personal growth. The Natural Science and Engineering Research Council, the Government of Ontario, and the University of Western Ontario all provided me with financial support. I’d like also to thank my late colleague, Mr. Mohamed Moftah, for sharing his knowledge and valuable references in structural fire safety with me which was really helpful to me. I gratefully acknowledge the assistance provided by Ghaly, Dessouki, Hadir, and Eltalmas for proofreading parts of this thesis prior to submission. This dissertation would not have been possible without the support and enthusiasm of several unseen individuals who in one way or another contributed in the completion of this work. These individuals are my parents, brothers and sisters, father and mother in-law, and friends. My first daughter, Laila, was born during this work, and having her sitting on my lap and innocently looking at this thesis encouraged me a lot. My wife, Marwa, is the reason I was able to finish. We’ve got married during the third year of my PhD. Marwa’s patience and lovely spirit were tremendous and allowed me to work on my PhD especially in the past year, thank you dear Marwa. vi Table of Contents Abstract .............................................................................................................................. ii  Co-Authorship Statement ................................................................................................ v  Acknowledgments.............................................................................................................. vi  Table of Contents ........................................................................................................... vii  List of Tables ................................................................................................................... xiv  List of Figures ................................................................................................................... xv  List of Abbreviations, Symbols, and Notation.................................................................. xx  Chapter 1 ............................................................................................................................. 1  1  Introduction .................................................................................................................... 1  1.1  Development of Compartment Fires ....................................................................... 1  1.1.1  Stage 1: Growth (Pre-Flashover) ................................................................ 1  1.1.2  Stage 2: Flashover Phenomenon ................................................................. 2  1.1.3  Stage 3: Post-Flashover............................................................................... 2  1.1.4  Stage 4: Decay ............................................................................................ 3  1.2  Standard Time-Temperature Curve ........................................................................ 3  1.3  Fire Severity ............................................................................................................ 3  1.3.1  Time Equivalence ....................................................................................... 4  1.3.2  Minimum Load Capacity Concept .............................................................. 4  1.4  Prescriptive Methods .............................................................................................. 4  1.5  Performance-Based Fire Design ............................................................................. 5  1.6  Spalling ................................................................................................................... 6  1.7  Research Objectives ................................................................................................ 6  1.8  Outline of Thesis ..................................................................................................... 7  1.9  References ............................................................................................................... 9  vii Chapter 2 ........................................................................................................................... 11  2  Stress-Block Parameters for Reinforced Concrete Beams during Fire Events ............ 11  2.1  Research Significance ........................................................................................... 12  2.2  Sectional Analysis at Ambient Temperature ........................................................ 12  2.3  Sectional Analysis at Elevated Temperatures ....................................................... 13  2.3.1  Concrete and steel constitutive models ..................................................... 15  2.3.2  Heat transfer model ................................................................................... 19  2.4  Analysis Steps of RC Beams under Fire Loading ................................................ 26  2.4.1  Validation of the sectional analysis methodology .................................... 26  2.5  Stress-Block Parameters at Ambient Temperature ............................................... 29  2.6  Stress-Block Parameters at Elevated Temperatures ............................................. 30  2.6.1  Behavior of beams subjected to sagging moments during fire ................. 32  2.6.2  Stress-block parameters for beams subjected to sagging moments .......... 35  2.6.3  Flexural capacity for beams subjected to sagging moments ..................... 38  2.6.4  Calculation of stress-block parameters for beams subjected to Hogging moments .................................................................................................... 41  2.6.5  Stress-block parameters for beams subjected to hogging moments ......... 43  2.6.6  Flexural capacity for beams subjected to hogging moments .................... 46  2.7  Summary and Conclusions ................................................................................... 46  2.8  Acknowledgments................................................................................................. 47  2.9  References ............................................................................................................. 47  2.10 Appendix I ............................................................................................................ 49  2.11 Appendix II ........................................................................................................... 52  Chapter 3 ........................................................................................................................... 54  3  Simplified Method to Analyze Continuous RC beams during Fire Exposure ............. 54  3.1  Research Significance ........................................................................................... 55  viii 3.2  Sectional Analysis at Elevated Temperatures ....................................................... 55  3.3  Statically Determinate RC Beams during Fire ...................................................... 58  3.3.1  Simply supported beam (sagging moments) ............................................. 58  3.3.2  Cantilever beam (hogging moments) ........................................................ 60  3.4  Moment–Curvature Relationships of Fire-Heated RC Sections ........................... 61  3.5  Statically Indeterminate RC Beams during Fire ................................................... 63  3.5.1  Proposed method for continuous RC beams ............................................. 63  3.5.2  Validation of the proposed methodology .................................................. 66  3.5.3  Modeling and analysis of B-124 ............................................................... 67  3.6  Evaluation of Thermal and Effective Stiffness Parameters .................................. 74  3.6.1  Unrestrained thermal curvature ................................................................. 76  3.6.2  Proposed expressions for the unrestrained thermal curvature (cid:2032) ............. 78  (cid:3036) 3.6.3  Effective flexural stiffness ........................................................................ 80  3.6.4  Proposed expressions for the effective flexural stiffness (cid:1831)(cid:1835) ................ 81  (cid:3032)(cid:3033)(cid:3033) 3.6.5  Practical application of the proposed method ........................................... 83  3.7  Summary and Conclusions ................................................................................... 84  3.8  Acknowledgments................................................................................................. 85  3.9  References ............................................................................................................. 85  Chapter 4 ........................................................................................................................... 87  4  Practical Method to Predict the Axial Capacity of RC Columns Exposed to Fire ...... 87  4.1  Axial Behavior of RC Columns Exposed to Fire .................................................. 88  4.1.1  Section Analysis Method .......................................................................... 88  4.1.2  Error Analysis ........................................................................................... 92  4.2  Proposed Method .................................................................................................. 93  4.3  Average Temperature Distribution ....................................................................... 94  4.3.1  Wickstrom Simplified Formulas ............................................................... 94  ix