Missouri University of Science and Technology Scholars' Mine Wei-Wen Yu Center for Cold-Formed Steel Center for Cold-Formed Steel Structures Library Structures 01 Feb 1980 Ultimate strength of cold-formed steel z-purlins M. A. A. Razak Teoman Peköz Follow this and additional works at: https://scholarsmine.mst.edu/ccfss-library Part of the Structural Engineering Commons Recommended Citation Razak, M. A. A. and Peköz, Teoman, "Ultimate strength of cold-formed steel z-purlins" (1980). Center for Cold-Formed Steel Structures Library. 143. https://scholarsmine.mst.edu/ccfss-library/143 This Technical Report is brought to you for free and open access by Scholars' Mine. It has been accepted for inclusion in Center for Cold-Formed Steel Structures Library by an authorized administrator of Scholars' Mine. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact Department of Structural Engineering School of Civil and Environmental Engineering Cornell University Report No. 80 - 3 - PROGRESS REPORT - ULTIMATE STRENGTH OF COLD-FORMED STEEL Z-PURLINS by M.A.A. Razak Teoman Pekoz, Project Director A Research Project Sponsored by the American Iron and Steel Institute and the Metal Building Manufacturers Association Ithaca, New York February 1980 PREFACE This progress report is based on a thesis presented to the faculty of the Graduate School of Cornell University for the degree of Master of Science. The sponsorship of the American Iron and Steel Institute and of the Metal Building Manufacturers Association as well as the cooperation of the committees of the sponsors are gratefully acknowledged. TABLE OF CONTENTS CHAPTER Page 1. INTRODUCTION 1 1.1 General 1 1.2 Previous Studies . 1 1.3 Objectives of this Study . 3 2. STABILITY ANALYSIS 5 2.1 Introduction . 5 2.2 Stabil i ty Analys is . 6 2.2.1 Portion of Compression Flange Acting as a Column . 6 2.2.2 The Effect of Torsional Instability . 7 2.2.2.1 Stability Condition . 7 2.2.2.2 Simplification of Stability Condition . 11 2.2.2.3 Design Approximation for Torsional Reduction Factor 14 3. EXPERIMENTAL INVESTIGATION 19 3.1 General .......................................... 19 3.2 General Procedure . 19 3.3 Vacuum Tests . 20 3.4 Beam Test s . 21 3.5 Rotational Restraint Tests . 22 3.6 Shear Rigidity Tests . 23 3.7 Ma t eria1 Propertie 5 ......•.••••••.•.••..•..••..•• 24 3.8 Section Dimensions . 24 3.9 Discussion of Test Results . 24 3.9.1 Tests Results . 24 3.9.2 Discussion of Vacuum Test Results . 28 3.9.3 Discussion of Beam Test Results . 29 4. ANALYSIS OF RESULTS 30 4.1 General . 30 4.2 Background for Evaluation of Results . 30 4.2.1 AISI Design Specification . 30 4.2.2 Discussion of Design Specification . 34 4.2.3 Adequacy of Compression Flanges . 36 4.3 Evaluation of Resul ts . 37 4.3.1 Test Ultimate Loads . 37 4.3.2 Test Ultimate Stresses . 38 4.3.3 Test Ultimate Rotations . 39 4.3.4 Rotational Restraint Factor, F . 40 v CHAPTER Page 4.3.5 Shear Rigidity of Panels 41 4.3.6 Initial Sweeps of Compression Flanges 42 4.4 Ultimate Loads.................................. 43 4.4.1 General 43 4.4.2 Computations Based on Full Widths of Flanges 43 4.4.3 Computations Based on Effective Widths CArSI) 45 4.4.4 Computations Based on Desmond's Flange and Stiffener Adequacy Requirements 46 4.5 Discussion of Analysis 48 4 . 6 Summary 50 5. CONCLUSION........................................... 52 5.1 Summary of Resul ts 52 5.2 Recommendations 53 5.3 Suggestions for Future Work 54 APPENDICES 55 A. Location of Shear Center for Equivalent Column 55 B. Design Method for Edge Stiffened Element 57 REFERENCES 63 TABLES .....................................•............. 64 FIGURES 78 vi LIST OF TABLES TABLE Page 3.1 Material Properties (Tensile) 65 3.2 Average Pur1in Dimensions 66 3.3 Summary of Test Results 67 4.1 Test Ultimate Stresses 69 4.2 Test Ultimate Rotations and F Values 70 4.3 Rotational Deformation of Pur1in Web 71 4.4 Yield and Ultimate Stresses...................... 72 4.5 Summary of Analysis Types 73 4.6 Comparison of Observed and Computed Ultimate Loads in Vacuum Tests 74 4.7 Comparison of Observed and Computed Ultimate Loads in Beam Tests 75 4.8 Minimum Stiffener Requirement According to AISI 76 4.9 Effective Widths of Compression Flanges and Lip-Stiffeners (Desmond Method) 77 vii LIST OF FIGURES FIGURE Page 2.1 Mode of Buckling 79 2.2 Force Normal to Buckled Flange 79 2.3 Force Normal to Buckled Web 79 2.4 Three Possible Types of Supporting Elastic Frame for Equivalent Column 80 2.5 The Effect of the Ratio blh on Rand S for Cas e I 81 2.6 T vs. Length Curves.............................. 81 3.1 Vacuum Test Setup 82 3.2 Section of Vacuum Test Setup . 83 3.3 Views Showing Beam Test Setup 84 3.4 Details of Beam Test Setup . 85 3.5 Z-Section Dimensions 86 3.6 Initial Sweeps of Compression Flanges in Vacuum Test s ........•............... : . 87 3.7 Panel Cross-Section . 88 3.8 Initial Sweeps of Compression Flanges in Beam Tests . 89 3.9 Location of Strain Gages 90 3.10 F Test: Diaphragm-Braced Pur 1 in . 91 3.11 F Test: Channel-Braced Purlin 92 3.12 Shear Rigidity Test Setup 93 3.13 Local Buckles in Test VI and VS . 94 3.14 Local Buckles in Test Bl, B2 and B3 . 95 3.15 Local Buckle in Test V2 . 96 3.16 Local Buckles in Test V4 and B6 . 97 viii FIGURE Page 3.17 Local Buckles in Test V3 and B4 98 3.18 Local Buckles in Test V6 and B7 99 4.1 Compression Area of Z-Section 100 4.2 Displacement Sign Convention 100 4.3 Load vs. Strain (Test VS) 101 4.4 Load vs. Strain (Test V2) 102 4.5 Load vs. Strain (Test V4) 103 4.6 Load vs. Strain (Test V3) 104 4.7 Load vs. Strain (Test V6) 105 4.8 Load vs. Strain (Test B3) 106 4.9 Load vs. Strain (Test Bs) 107 4.10 Load vs. Strain (Test B6) 108 4.11 Load vs. Strain (Test B4) 109 4.12 Load vs. Strain (Test B7) 110 4.13 Comparison of Stresses (Pur1in Type A) 111 4.14 Comparison of Stresses (Pur1in Type B) 112 4.15 Comparison of Stresses (Pur1in Type C) 113 4.16 Comparison of Stresses (Pur1in Type D) 114 4.17 Comparison of Stresses (Pur1in Type E) 115 4.18 Vacuum Tests: Load-Rotation Curves 116 4.19 Beam Tests: Load-Rotation Curves 116 4.20 Rotational Restraint Tests (Diaphragm-Braced Pur1ins): Moment-Rotation Curves 117 4.21 Rotational Restraint Tests: Pur1in Type E (Diaphragm-Braced Pur1ins): Moment-Rotation Curves 117 4.22 F Tests (Channel-Braced Pur1ins): Moment-Rotation Curves 118 ix FIGURE Page 4.23 Hit vs. F 119 4.24 Shear Rigidity Test: Load-Deflection Curve 120 A.l Location of Shear Center for Equivalent Column . 121 B.l Typical Edge Stiffened Elements 121 x CHAPTER 1 INTRODUCTION 1.1 General Cold-formed steel structures are being widely used in various forms of construction such as industrial plants, gym- nasiums, hangars and metal buildings. One important feature of metal building construction is the use of light gage roof panels connected to purlins, particularly of the Z-section. This section is, besides the channel-section, the simplest two- flange section which can be produced by cold-forming. The pur- lins have span lengths of 20 to 25 feet, generally made contin- uous over the building rigid frames by nesting. Construction details vary from manufacturer to manufacturer. The purlins available would typically have prepunched holes for connection of various types of bracings, overlapping connections, etc. 1.2 Previous Studies Studies involving such purlin-panel assemblies have been carried out by a limited number of investigators. Cornell University carried out a series of studies on channel and Z- section behavior as regards lateral, flexural, torsional and flexural-torsional buckling. It is not the intention of this particular study to investigate any of such buckling modes as these have been well reported in the various Cornell University reports referenced and others. 1