SERVICEABILITY ANALYSIS FOR DEFLECTION OF REINFORCED CONCRETE FLOOR SLABS IN MULTI-STORY HIGH-RISE BUILDINGS

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SERVICEABILITY ANALYSIS FOR DEFLECTION OF REINFORCED CONCRETE FLOOR SLABS IN MULTI-STORY HIGH-RISE BUILDINGSA B S T R A C T   An analytical algorithm is developed to compute the mid-panel deflectiontime history for two-way reinforced concrete floor slabs in multi-story high- rise buildings.  Mid-panel deflection is determined using the crossing beam analogy, superimposing column strip and middle strip deflections.  The analysis procedure incorporates the effects of early-age construction loading. The algorithm determines the loading-time history of the slab based upon the details of construction schemes involving one level of shoring in conjunction with two, three, or four levels of reshoring.  Alternatively, the algorithm may operate based upon a prescribed loading-time history.  The analytical algorithm is implemented as an interactive C++ computer program using Microsoft Visual Basic C++ Standard Edition 2003.  A parametric study determines the sensitivity of the algorithm to variation in individual input parameters.  Comparison of program results with published experimental results justifies the program as a valid means of computing two-way slab deflection-time histories.          

TABLE OF CONTENTS

      List of Tables  ……………………………………………………………………………… vii List of Figures………………………………………………………………………………. ix List of Symbols…………………………………………………………………………….. xi       Chapter 1 – Introduction    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1       Introduction       . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2       Objective and Scope   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.3       Thesis Layout      . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2   Chapter 2 – Literature Review          . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1       Introduction       . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2       Construction Load Analysis:  The Simplified Method  . . . . . . . . . . 4 2.2.1 Assumptions       . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2.2 Construction Load Distribution     . . . . . . . . . . . . . . . . . . . . . . 5 2.2.3 Analytical Results      . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.4 Construction Schemes Involving Reshoring            . . . . . . . . . . . 9 2.3       Early Age Concrete Properties          . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3.1 Concrete Compressive Strength . . . . . . . . . . . . . . . . . . . . 10 2.3.2 Elastic Modulus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3.3 Creep            . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4       Two-Way Slab Serviceability Analysis            . . . . . . . . . . . . . . . . . . . . 15 2.4.1 Loads     . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.4.2 Crossing Beam Method        . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.4.3 Beam Deflection Equation       . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.4.4 Modified Moment of Inertia    . . . . . . . . . . . . . . . . . . . . . . . . 19 2.4.5 Correction Factors       . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.4.5.1            Boundary Condition Factor      . . . . . . . . . . . . . 21 2.4.5.2            Drop Panel Correction Factor     . . . . . . . . . . . 21 2.4.5.3            Strip Width Correction Factor   . . . . . . . . . . . 22 2.4.5.4            Slab Strip Moment Intensity Factor   . . . . . . . 22 2.4.6 Long-Time Multipliers        . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.4.7 Creep Recovery Factor        . . . . . . . . . . . . . . . . . . . . . . . . . . . 25   Chapter 3 – Method of Analysis       . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.1       Introduction       . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.2       Loading-Time History During Shoring/Reshoring        . . . . . . . . . . . 26 3.2.1 One Level of Shoring with Two Levels of Reshoring      . . . . 27 3.2.2 One Level of Shoring with Three Levels of Reshoring             . . 30 3.2.3 One Level of Shoring with Four Levels of Reshoring  . . . . 33 3.3       Long-Time Deflections          . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.4      Outline of the Computer Algorithm     . . . . . . . . . . . . . . . . . . . . . . . 37 3.5       Summary            . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56   Chapter 4 – Verification of the Method of Analysis        . . . . . . . . . . . . . . . . . . . . . 57 4.1       Introduction       . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.2       Input Data   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.3       Computer Algorithm Results           . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.4       Experimental Results (Guo & Gilbert)    . . . . . . . . . . . . . . . . . . . . . 63 4.5       Graphical Comparison of Algorithmic and Experimental Results      . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.6       Conclusion     . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68   Chapter 5 – Parametric Study   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.1       Introduction  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.2       Constants (Unless Otherwise Varied)        . . . . . . . . . . . . . . . . . . . . . 70 5.3       Outline of the Parametric Study       . . . . . . . . . . . . . . . . . . . . . . . . . . 70 5.4       Parameter:  Average Creep Multiplier, λc . . . . . . . . . . . . . . . . . . 75 5.5      Parameter:  28-Day Compressive Strength, f’c(28-day)           . . . . . . . . . 78 5.6       Parameters:  Casting Cycle, Stripping Time, Shoring/Reshoring Cycle           . . . . . . . . . . . . . . . . . . . . . . . . . 82 5.7       Parameter:  Short Direction Clear Span, l2      . . . . . . . . . . . . . . . . . 86 5.8       Parameter:  Slab Thickness, h       . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.9       Parameter:  Creep Recovery Factor      . . . . . . . . . . . . . . . . . . . . . . 92 5.10    Parameter:  Loading Age Creep Correction Equation   . . . . . . . . 95 5.11     Parameter:  Panel Location    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 5.12     Significance of Construction Load Analysis       . . . . . . . . . . . . . . . 101 5.13    Conclusion     . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104   Chapter 6 – Conclusions & Recommendations      . . . . . . . . . . . . . . . . . . . . . . . . 106 6.1       Summary            . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 6.2      Construction Load Analysis & Two-Way Slab Analysis      . . . . . . 106 6.3       Method of Analysis     . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 6.4      Validity of the Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 6.5      Parametric Study      . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 6.6      Recommendations   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108   References      . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110   Appendix:  C++ Computer Program Text File       . . . . . . . . . . . . . . . . . . . . . . . . 113 CHAPTER 1 INTRODUCTION      

1.1      INTRODUCTION

  Accurate analysis of construction loads in floor slabs of multi-story highrise concrete buildings is essential to understanding the structural effects created via the construction process.  Construction loads, if not designed for properly, can lead to detrimental effects, such as slab cracking and excessive deflection.  Because construction loads act upon a structure long before it has entered into the “service” phase of its life cycle, construction loads have the potential to significantly impact the service life of the structure.    Because the long-term effects of construction loads are significant, construction loading distribution and corresponding slab deflection computations are present topics of debate within the structural engineering community.  

1.2      OBJECTIVE AND SCOPE

  The objective of this study was to develop a simplified analysis procedure to evaluate the effects of construction loading on long-time deflections of two-way reinforced concrete floor slabs.  The analysis procedure accounts for various shoring and reshoring scenarios.  The objective was achieved within the following scope:  

  1. A literature review was conducted to determine the primary factors affecting long-time slab deflections including methods to account for construction loading.
  2. A method of analysis suitable for incorporation in a spreadsheet or computer program was developed.
  3. The analysis procedure was evaluated by comparing computed results with those obtained from slab tests available in the literature.
  4. The effects of various parameters on the computed results were evaluated by conducting a parametric study.
  5. Based on the results of the study recommendations were made for design and construction of two way slabs to ensure adequate control of long-time deflections. It is anticipated that the analysis procedure will be helpful to engineers and contractors evaluating proposed shoring and reshoring schemes.

   

1.3      THESIS LAYOUT

  The thesis is divided into six chapters.  Chapter 1 is the introduction, detailing the scope and objective of the thesis.  Chapter 2 provides a review of literature on the topics of construction load analysis and two-way slab analysis. Chapter 3 uses the methodology outlined in Chapter 2 to perform load ratio analyses for construction scenarios involving one level of shoring with two levels of reshoring, one level of shoring with three levels of reshoring, and one level of shoring with four levels of reshoring.  Chapter 3 also contains a step-by-step outline of the computer algorithm written to compute the deflection-time history for two-way concrete floor slabs. Chapter 4 provides verification of the computer algorithm by comparing algorithmic results to experimental results, while Chapter 5 provides a parametric study in which input parameters are varied one-by-one to determine parameter sensitivity.  Chapter 6 provides overall conclusions and recommendations. The main body of the report is followed by a list of references for all works referenced within the thesis.  An appendix also accompanies the report.  The appendix contains the text file for the C++ computer program used to perform the analysis procedures detailed within the main body of the report.  The C++ computer program was written and implemented using Microsoft Visual Basic C++ Standard Edition 2003. SERVICEABILITY ANALYSIS FOR DEFLECTION OF REINFORCED CONCRETE FLOOR SLABS IN MULTI-STORY HIGH-RISE BUILDINGS

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