The structural behavior of cold-formed steel members with perforated elements

139 Pages·2016·5.93 MB·English

by  Charles S. Davis

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Doctoral Dissertations Student Theses and Dissertations
1972
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Charles S. Davis
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Davis, Charles S., "The structural behavior of cold-formed steel members with perforated elements"
(1972). Doctoral Dissertations. 2091.
https://scholarsmine.mst.edu/doctoral_dissertations/2091
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Department of Civil Engineering
School of Engineering
UNIVERSITY OF MISSOURI-ROLLA
Final Report
THE STRUCTURAL BEHAVIOR
OF COLD-FORMED STEEL MEMBERS
WITH PERFORATED ELEMENTS
by
Charles S. Davis
Research Assistant
Wei-Wen Yu
Project Director
A Research Project Sponsored by
American Iron and Steel Institute
ROLLA, r-USSOURI May, 1972
ii-iv
P~F~E
This report was originally a dissertation presented to the Faculty
of the Graduate School of the University of Missouri-Rolla in partial
fulfillment of the requirements for the Degree of Doctor of Philosophy
in Civil Engineering, for conferment in May 1972.
The research project described within was sponsored by American
Iron and Steel Institute through a Special Engineering Fellowship in
the fiscal year 1970-71.
The author wishes to thank Dr. Wei-Wen Yu, Associate Professor
of Civil Engineering, University of Missouri-Rolla for his invaluable
guidance in his joint capacity as the project director and as major
advisor of my advisory committee. Thanks are due to Mr. L.A. Barron,
Vice President - Engineering and Dr. A.L. Johnson, Senior Research
Engineer of American Iron and Steel Institute for their advice and
cooperation. Appreciation should also be expressed to the AISI committee,
for which Dr. J.B. Scalzi was the chairman.
v
TABLE OF CONTENTS
Page
PREFACE......•.•..•.••...•.....•••.••••.....••....•.•..•.•••..•••.•.• ii-iv
LIST OF FIGURES...................................................... viii
LIST OF TABLES... . . . . • . . . . . . . . . . . . . •. . . . . . . . . . . . . . . . . •. . . . . • . • . . . •. . . x
............................................................
NOTATION xii
I. INTRODUCTION.•...•...•.....•...•.•...•.•••••.•...•.•.••.•... 1
A. General . 1
B. Purpose of Investigation. 2
C. Scope of Investigation. 3
II. REVIEW OF LITERA.TURE.•••••..•..•.•••......•••.•..•••..•..••• 5
A. Intraduction . 5
B. Strength of Thin Plates in Compression••...•.••• 5
C. Compressive Strength of Perforated Cover Plates••.....•• 12
D. Stability of Perforated Plates•.•....•••••••••.• 19
E. Shear Buckling of Perforated Plates and Members.•••••..• 23
F. Web Crippling . 24
G. Current Design Provisions for Steel Sections with
Perforations•.. 25
III. LOCAL BUCKLING AND POST-BUCKLING STRENGTH OF PERFORATED
STIFFENED COMPRESSION ELEMENTS.............................. 29
. .
A. Analytical Investigation. 29
1. Local Buckling . 29
a. Simply Supported Square Plate Having a
Central Circular Hole........................... 30
b. Simply Supported Square Plate Having a
Central Square Hole............................. 31
vi
Page
.
2. Post-Buckling Strength. .. 32
B. Experimental Investigation.••...•.•.•••••.••.•.••.•.•••. 39
1. Column Tests 39
a. Fabrication of Test Specimens•••••.•.•..•.•.•..• 39
b. Location of Strain Gages....•••••.•••...••.••••. 40
c. Mechanical Properties. 41
d.. Test Procedures.................................................................. 41
e. Discussion of Results........................... 41
2.. Beam Tests 43
a. Fabrication of Test Specimens. 43
b. Location of Strain Gages...•..••••..••..••..•.•• 43
c. Mechanical Properties. .. .. 43
d.. Test Procedures 44
e. Discussion of Results•....•...•...••..••.••...•• 44
C. Summ.ary .. 47
IV. BEHAVIOR OF UNSTIFFENED COMPRESSION ELEMENTS WITH CIRCULAR
PERFORA.TIONS.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .... 48
A. Analytical Investigation.•• 48
B. Experimental Investigation..•...•••.•.••...••..••.•...•. 49
1. Fabrication of Test Specimens•••..•..•..••.•.....•.• 50
2. Location of Strain Gages..•••.••..•..••••.•••••.•.•• 50
3. Mechanical Properties. .. 50
'
4. Test Procedures 51
5. Discussion of Results.••..•••.•.•..••.•...•••....••. 51
C.. SutDDlary.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .... 54
vii
Page
V. BUCKLING BEHAVIOR OF WEBS HAVING A CIRCULAR HOLE•••••••.•••• 55
A. General. . . . . . . . . . . •. •. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 55
B. Experimental Investigation•••••••.•.•.•••••••••..••••••• 55
1. Fabrication of Test Specimens••..•.••••••••••••••••• 55
2. Test Procedures••••...•••.............•...........•. 56
3. Discussion of Results.•.......................•..... 56
c..
SUlIllD.ary.. • •.. .. .. •.. .. .. •.. •.. .. .. •.. .. .. ••.. •.. .. ••••••.. .. .. ••• •.. •.. •.. .. •.. •• 58
VI. CRIPPLING STRENGTH OF PERFORATED WEBS••••••••••.•••••.•••••• 59
A.. General. .. .. .. .. .. .. .. .. . . .. .. . .. . .. .. .. . .. . .. . .. . . .. . .. . . .. .. . . . . . . .. . . .. .. .. . .... 59
B. Experimental Investigation•••••••.•.•.••••.••••••.•••••• 59
1. Fabrication and Testing of Specimens•••••••••••••••• 60
2. Discussion of Results 60
C. SUUIDlary.. .. .. •.. .. .. ••.. •••.. .. .. •••.. .. .. ••.. •••••.. .. ••.. • •••••.. •••••.... 64
D. Stability of Perforated Plates Subjected to Equal and
Opposite Point Loads..•••......•........................ 64
VII. SUMMARY AND CONCLUSIONS..................................... 66
A. Local Buckling and Post-Buckling Strength of
Perforated Stiffened Compression Elements•••••••.••.•••• 66
B. Behavior of Unstiffened Compression Elements with
Circular Perforations 67
C. Buckling Behavior of Webs Having a Circular Hole•••••••• 67
D. Crippling Strength of Perforated Webs•••••.••.•••..•.••• 68
BIBLIO~RAPHY••••••••••••••••••••••••••••••••••••••••••••••••••••••• ••122
viii
LIST OF FIGURES
Figure Page
1. Effective Width of Stiffened Compression Elements.•••.•••.....•• 69
2. Dimensions Used in the Specifications•.......••.•...•..•.•..••.. 70
3. Buckling Coefficient VS. d/w Ratio.•..••.•.....•..••.•.•••..•... 71
4. Perforated Plate Stress Distributions••••.•.••..••.•........•.•• 72
5. Finite Element Idealization for a Simply Supported Square
Plate ". " " " ".. " ". " " 73
6. Buckling Coefficient VS. h /w Ratio..••.•...••.•...•.•.•..•••••• 74
s
7. Effect of Shapes of Holes on Buckling Coefficient.••.•..•.•.•.•• 75
8. Influence of Holes on Effective Width of Stiffened Elements.•... 76
9. Dimensions of Test Specimens.•..••••..••.•....•.••.•••.•.•..••.• 77
10. Test Set-Up ".. "".""."." " " ".. " "." .. ".". 78
11. Typical Load-Strain Diagram....•.•..••••.....••••••••••••••••••• 79
12. Comparison of Test Data with Theoretical Buckling Coefficients.. 80
13. Comparison of Test Data with Theoretical Buckling Coefficients•• 81
14. Comparison of Effective Width•.•••...•.•.•.••..••.•..•.•••.•..•. 82
15. Comparison of Failure Modes... ••. . . . . •. •. . •••. . . ••••. . . •. ••. •••. 83
16. Dimensions of Beam Speci.mens.................................... 84
17. Set-Up for Beam Tests 85
18. Load VS. Midspan Deflection••••••...•••.•........••..•.•.....•.. 86
19. Finite Element Idealization for Unstiffened Plate•.••.••.•...•.. 87
20. Cross-Section of Test Specimens•••.•.•.••.......••.••..•..••...• 88
21. Perforated Unstiffened Element Test at Three Stages of Loading.. 89
22. Reduction Factor, qub' for Perforated Unstiffened Compression
Element • ""...•.•••.. "". ".. ". ".. ". " " "". ". ". . . . . . . . .. 90
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Page
23. Comparison of Test Data with Analytical Shear Buckling
Reduction Factor q ........•.......•............................ 91
s
24. Shear Buckling Test Set-Up 92
25. Load VS. Lateral Deflection Diagram 93
26. Crippling Test Specimens..•..........................•.......... 94
27. Crippling Test Loading Condition. . . . . . . . . •. . . . . . . . . . . . . . . •. . . . .. 95
28. Load Reduction Factor q VS. d/h Ratio for Circular
wcc
Perforations 96
29. Load Reduction Factor q VS. h /h Ratio for Square
wcs s
Perforations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 97
30. Finite Element Idealization for a Simply Supported Square Plate
Subjected to Equal and Opposite Point Loads at the Center 98
31. Effect of Locally Distributed Loads on Simply Supported Plates.. 99
x
LIST OF TABLES
Table Page
I. Stiffened Compression Plate Boundary Conditions••.•...•...•.• 100
II. Buckling Coefficient Ratio for a Simply Supported Square
Plate Having a Central Circular Hole••••....••...•.•.•.••.••. 101
III. Dimensions and Sectional Properties of Column Specimens with
Circular Perforations 102
IV. Dimensions and Sectional Properties of Column Specimens with
Square Perforations 103
V. Mechanical Properties of Steel Test Specimens••••..••••••••.• 104
VI. Experimental Buckling Coefficient Ratio for Column Specimens
with Circular Perforations••••...•••....••.•.•••..•..••..•••• 105
VII. Experimental Buckling Coefficient Ratio for Column Specimens
with Square Perforations .•••••.••.•....••...•.••.••••.•.•.••• 105
VIII. Tested Ultimate Loads and Computed Effective Widths Based on
Short ColutDn Tests 106
IX. Dimensions and Properties of Beam Specimens with Circular
Perforations 107
Co
X. Experimental Buckling Coefficient Ratio for Beam Specimens
with Circular Perforations•..••.•••..•..••.•..•...•.•••••..•• 107
XI. Comparison of the Computed and Tested Yield Moments.•..•..••. 108
XII. Comparison of Centerline Deflections for Beam Tests ••..•••••• 108
XIII. Comparison of Effective Widths•.••••....••.•.•••.•••.•.•.•••. 109
XIV. Unstiffened Compression Plate Boundary Conditions•..••••••••• 110
XV• Dimensions of Test Specimens having Unstiffened Elements •..•• III
XVI. Experimental Critical Buckling Loads and Stress Reduction
Factor, qub.................................................................................................... 112
xi
Page
XVII. Dimensions of Specimens Used for Shear Buckling Test•......•. 113
XVIII. Experimental Shear Buckling Loads and Shear Buckling
Reduction Factor, q .. 114
s
XIX. Dimensions of Web Crippling Test Specimens with Circular
Perforations 115
XX. Dimensions of Web Crippling Test Specimens with Square
Perforations 116
XXI. Experimental Ultimate Loads and Ultimate Load Reduction
Factor, q ,for Web Crippling Specimens with Circular
wcc
exp
Perforations 117
XXII. Experimental Ultimate Loads and Ultimate Load Reduction
Factor, q ,for Web Crippling Specimens with Square
wcs
exp
Perforations 118
XXIII. Comparison of Test Results with Results of Winter and Pian..• 119
XXIV. Boundary Conditions for Perforated Plate..••..•...••••......• 120
XXV. Critical Buckling Loads and Load Reduction Factor, q b 121
w s