bearing strength of cold formed steel bolted connections .../67531/metadc115135/m2/1/high_res... ·...
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APPROVED: Cheng Yu, Major Professor Diane Desimone, Committee Member Haifeng Zhange, Committee Member Leticia Anaya, Committee Member Enrique Barbieri, Chair of the
Department of Engineering Technology
Costas Tsatsoulis, Dean of the College of Engineering
James D. Meernik, Acting Dean of the Toulouse Graduate School
BEARING STRENGTH OF COLD FORMED STEEL BOLTED
CONNECTIONS IN TRUSSES
Mark Panyanouvong
Thesis Prepared for the Degree of
MASTER OF SCIENCE
UNIVERSITY OF NORTH TEXAS
May 2012
Panyanouvong, Mark. Bearing Strength of Cold Formed Steel Bolted
Connections in Trusses. Master of Science (Engineering Systems – Construction
Management), May 2012, 109 pp., 9 tables, 14 figures, 11 references.
The existing design provision in North American Specification for Cold-
Formed Steel Structural Member (AISI S100) for the bearing strength of bolted
connections were developed from tests on bolted connected sheets which were
restrained by bolt nut and head with or without washers. However, in the cold-formed
assemblies, particularly in trusses, the single bolt goes through both sides of the
connected sections, making the connected sheets on each side unrestrained. The
warping of the unrestrained sheet may reduce the bearing strength of the bolted
connection. This research investigates the behavior and strength of bearing failure in
bolted connections in cold-formed steel trusses. Tensile tests were conducted on
trusses connections with various material thicknesses. It was found that the AISI
S100 works well for thick connections but provides unconservative predictions for
thin materials. Based on the experimental results, a modified bearing strength
method is proposed for calculating the bearing strength of bolted truss connections.
The proposed method can be used for any cold-formed steel connections with
unrestrained sheet.
ii
Copyright 2012
by
Mark Panyanouvong
iii
ACKNOWLEDGEMENTS
I am heartily thankful to my supervisor, Cheng Yu, whose encouragement,
guidance and support from the initial to the final level enabled me to develop and
gain greater understanding of the subject. I would like to acknowledge my family and
Denial Pisuc who gave me the moral support and for being my back bone. I would
also like to give recognition to Stephen Triplett, who was able to help me through
composition of this thesis.
Many thanks go to Marcus Sanchez and Roger Rovira, whose efforts made
this thesis possible. Lastly, I offer my regards and blessings to all of those who
supported me in any aspect during the completion of the project.
iv
TABLE OF CONTENTS
Page ACKNOWLEDGMENTS ............................................................................................ iii LIST OF TABLES ...................................................................................................... vi LIST OF FIGURES ....................................................................................................vii CHAPTER 1 INTRODUCTION ................................................................................... 1 CHAPTER 2 BACKGROUND, RESEARCH OBJECTIVES ....................................... 3
2.1 Background ........................................................................................... 3 2.2 Research Objectives ............................................................................. 4
CHAPTER 3 LITERATURE REVIEW ......................................................................... 7
3.1 Research Work and Types of Failure Mode .......................................... 7 3.1.1 Longitudinal Shearing of Steel Sheets (Type I Failure) .............. 7 3.1.2 Bearing or Pilling Up of Steel Sheet (Type II Failure) ................. 8 3.1.3 Tearing of Sheet in Net Section (Type III Failure) ...................... 8 3.1.4 Shearing of Bolt (Type IV Failure) .............................................. 9
3.2 AISI Design Criteria for Bolted Connections ....................................... 10 3.2.1 Bearing Strength Proposed Methods ....................................... 10
CHAPTER 4 TESTING ............................................................................................. 13
4.1 Testing of Specimens ......................................................................... 13 4.2 Testing Equipment .............................................................................. 15 4.3 Specimens .......................................................................................... 16 4.4 Specimens Preparation....................................................................... 17
CHAPTER 5 TEST RESULTS ................................................................................. 19
5.1 Specimen Labeling ............................................................................. 19 5.2 Characterization of Typical Bearing Failure Mode .............................. 20
5.2.1 Material Properties ................................................................... 22 5.3 Discussion Proposed Design Method ................................................. 23
CHAPTER 6 CONCLUSIONS .................................................................................. 29
v
APPENDIX A: DIMENSIONS AND RESULTS OF BOLTED CONNECTIONS IN THE EVALUATION OF EXISTING DATA ........................................................................ 30 APPENDIX B: PHOTOGRAPHS AND SPECIMEN CONFIGURATION ................... 33 REFERENCES ....................................................................................................... 109
vi
LIST OF TABLES
Page 3.2.1 Bearing factor C, for bolted connections (AISI S100-2007) ........................... 11
3.2.2 Modification factor 𝑚𝑓, for type of bearing connection .................................. 11
4.1.1 Bolt diameter and sizes of bolt holes, inches ................................................. 14
4.1.2 Test matrix of the research project ................................................................ 14
5.2.1 Material properties of specimens ................................................................... 22
5.3 A. Proposed bearing factor, C, for bolted connection .................................... 24
B. Proposed modification factor 𝑚𝑓, for bolted connection ............................ 24
C. Test-to-predicted ratios for sheet bearing strength ................................... 25
D. Resistance factors and AISI factor of safety for proposed design methods for bearing in bolted connections ................................................................... 27
vii
LIST OF ILLUSTRATIONS
Page
2.1 Typical failures of bolted CFS connections ...................................................... 3
2.2 A. Typical sheet to sheet connections ............................................................. 5
B. Typical truss connections ............................................................................ 5
4.2 A. Instron 4482 Universal .............................................................................. 15
B. Hydraulic cylinder testing machine ............................................................ 15
4.3 A. Specimen set up for testing ....................................................................... 16
B. Specimen after testing .............................................................................. 16
4.4 Steps to setup the experiment ....................................................................... 17
5.1 Specimens labeling for sheet bearing and shear specimens ......................... 19
5.2 A. Typical curve bearing failure of a bolted connection ................................. 20
B. Typical bearing failure of a bolted connection without washers................. 20
C. Unchanged shape the bearing strength failure of a bolted connection without washers (118mil) ............................................................................... 21
5.3 A. Test results vs. design methods AISI S100 for bearing strength of bolted connections ................................................................................................... 23
B. The proposed design vs. design methods AISI S100 for bearing strength of bolted connections ......................................................................................... 25
1
CHAPTER 1
INTRODUCTION
Cold-formed steel (CFS) is a feasible material in buildings, home, office
furniture, automobiles, equipment, utility poles, highway products, drainage
facilities, and bridges. The popularity of CFS can be ascribed to ease of mass
production and prefabrication, uniform quality, lightweight designs, economy
in transportation and handling, fast and simple up righting or installation.
CFS structural members shapes are manufactured by pressed-
breaking or roll forming cold-or hot-rolled coils or sheets; both forming
operations being performed at ambient room temperature, that is, without
manifest addition of heat such as would be required for hot forming. Buckling
usually governs the strength of CFS members for construction.
The structural behavior of bolted connections in CFS construction is
somewhat different from that in hot-rolled heavy construction, mainly because
of the thinness of the connected parts. In the U.S., The design provisions for
CFS bolted connections are provided in the North American Specification for
Cold-Formed Steel Structural Member (AISI S100, 2007). Mexico and Canada
have also adopted this specification.
3
CHAPTER 2
BACKGROUND, RESEARCH OBJECTIVES
2.1 Background
CFS bolted connections may fail in four typical modes as illustrated in
Figure 2.1: shear failure of sheet (Type I), bearing failure of sheet (Type II),
rupture in the net section (Type III), and shear failure of bolt (Type IV). This
research is focused on the Type II bearing failure of the sheet.
Type I Shear Failure of Sheet
Type II Bearing Failure of Sheet
Type III Rupture in the Net Section
Type IV Shear Failure of Bolt
Figure 2.1 Typical Failures of Bolted CFS Connections
4
The AISI S100 (2007) provides design provisions for these four types
of failure respectively. AISI S100 provisions for the bearing strength of bolted
connections were developed from tests on sheet connections, in which the
connected sheets were restrained by bolt nut and head with or without
washers on both sides of the group of sheets. However in the cold-formed
assemblies, for example trusses, framing, racking, etc., the single bolt goes
through both sides of the connected sections, making the connected elements
on each side unrestrained. The unrestrained elements may yield significant
out of plan deformation under loading; the deformation may greatly affect the
bearing strength of the bolt connection. A comprehensive research project is
needed to investigate the behavior and strength of CFS bolted connections
with unrestrained elements.
2.2 Research Objectives
This research is aimed at investigating the behavior and strength of
CFS bolted truss connections with unrestrained elements. The investigated
truss connections contain three elements. The first element used was the
web. The tests used using webs of seven different thicknesses such as:
27mil, 33mil, 43mil, 54ml, 68mil, 97mil and 118mil. The second element, the
chord had the same seven thicknesses like the web; 27mil, 33mil, 43mil,
54mil, 68mil, 97mil and 118mil. With those 23 same thickness combinations of
web and chords we used for testing our third element, four bolts with different
diameters; 3/8, 1/2, 5/8 and 3/4 inch. To verify that the results are precise and
accurate; the tests used repeated once for each thickness, for a total of 46
tests.
5
The main objective for this research is to investigate the behavior and
the strength of bearing failure of bolted connections in cold-formed steel in
trusses where the connections in cold-formed steel (CFS) sheets are not
restrained by bolt nut or head on both sides. The bolted connection of the
bearing strength of cold-formed steel bolted without nut is presented with the
testing inside of the web having no nut. To determine through mechanical
method whether or not having a nut on the inside of the web influences the
peak load.
This study focused on the different combination of web and chord
thickness with varying size bolts. This research also determined the how the
failure points vary based on bolt diameter, web and chord with no support or
nut along the inside wall of the web. The experiments conducted were:
• Examine the difference of the two elements between the web and
chord for each configuration.
• Show the result of the reaction of the web and the chord when the bolt
size are different.
Figure 2.2A Typical sheet to sheet connections
Figure 2.2B Typical truss connections
6
• Use different type the bolt size of 3/8, 1/2, 5/8, and 3/4 inch for
connections.
• Show how the chord and web thicknesses are affected by the lack of
support or use of additional washers or nuts inside the web.
We compared our experiment testing data to the regular 2-sheet connected
with a nut.
7
CHAPTER 3
LITERATURE REVIEW
3.1 Research Work and Types of Failure Mode
Prior to 1980, the American Iron and Steel Institute (AISI) determined
the design specification of bolted connections. These were developed on the
basis of the Cornell tests supervised under the direction of George Winter and
other institutes. One of the most recognizable works in this area is the
research done by Yu (1982).
3.1.1. Longitudinal Shearing of Steel Sheets (Type I Failure)
Longitudinal shearing of the steel sheet along two almost parallel
planes, where the distance of separation is close to the bolt diameter is a
Type I Failure. It was discovered by several researchers and they found that
the shear strength of the sheet type I failure is the relationship between the
ratio of edge distance 𝑒 and the bolt diameter 𝐶 which indicate the bearing
stress at failure can be predicted by
de
Fub =
σ (Eq.3.1A)
where bσ Ultimate bearing stress between bolt and connected part, ksi
Fu Tensile strength of connected part, ksi
e Edge distance, in.
d Bolt diameter, in.
8
3.1.2 Bearing or Piling Up of Steel Sheet (Type II Failure)
When the edge distance is sufficiently large or when we have large 𝑒 𝐶
ratios, the failure of connections may occur in front of the bolt. The University
of Missouri-Rolla conducted the research on the failure and recognized that
the hole extension prior to reaching the bearing strength, limited a bolted
connection. The limitation of the connection movement was 0.25 in. or (6.4
mm). The deformation around the bolt holes ( ) is a design consideration,
according to the Supplement to the 1996 edition of the Specification [1.333]: is
given by:
Pn = (4.6t + 1.53)dt Fu (with t in inches) (Eq.3.1B.1)
For SI units:
Pn = (0.831t + 1.53)dt Fu (with t in mm) (Eq.3.1B.2)
where: t Thickness of connected part
d Diameter of bolt (in.)
Fu Tensile strength of steel (ksi) or (MPa)
Bearing strength
3.1.3 Tearing of Sheet in Net Section (Type III failure)
Cornell University conducted the tests by using connections under bolt
head and nut to eliminate the stress concentration for the low ductility steel. In
1992, Zadoanfarrokh and Bryan investigated the shear failure and bearing
failure in connections sheets. In order to prevent the rupture failure the width
𝑤 of the specimens’ connection has to be sufficiently large and thus set up
(w=6.25d) for bearing tests with the nominal bolt diameter d ≥ 0.4 in. Besides
Pn
Pn
9
finding the type III failure of tearing of sheet in the net section, the effects of
the 𝐶 𝑠 ratio on the tensile strength of bolted connections with washers were
observed.
The following formulas have been developed to predict the failure stress in the
net section:
a) When 𝐶 𝑠 ≤ 0.3, 𝜎𝑛𝑒𝑡 = [ 1- 0.9r + 3r(d/s)]𝐶𝑢 ≤ 𝐶𝑢 (3.1C.A) b) When 𝐶 𝑠 > 0.3, 𝜎𝑛𝑒𝑡 = 𝐶𝑢 (3.1C.B)
Where 𝜎𝑛𝑒𝑡 Failure stress in net section, ksi
r Force transmitted by bolt or bolts at the section considered, divided by the force in the member at that section
d Bolt diameter, in.
s Spacing of bolts perpendicular to line of stress, in.
𝐶𝑢 Ultimate tensile strength of steel sheets, ksi
3.1.4 Shearing of Bolt (Type IV Failure)
The shearing of bolt failure is the type of failure by shearing of the bolt
that occurs at the strength equal to 0.6 times the tensile strength of the bolt
[Yu, 2000]. For the type IV failure, this research was not focus on this mode of
failure.
10
3.2 AISI Design Criteria for Bolted Connections
The design bearing strength of bolted connections shall be determined
by the design bearing strength of bolted connections by tests,𝑃𝑛, bearing
factor, C, to account for the influence by the bolt diameter to sheet thickness
ratio, 𝐶 𝑡 . A modification factor is used to reflect the washer option as well as
connection type for single shear connections without a washer with standard
holes, ( 𝑚𝑓 = 0.75 ).
3.2.1 Bearing Strength Proposed Methods
The bearing strength of bolted connections with standard holes is
shown in equation 3.2-1 (𝐸𝑞. E3.3.1-1 of AISI S100 2007). When deformation
around the bolt holes is not a design consideration, the nominal bearing
strength [resistance], 𝑃𝑛, of the connected sheet for reach loaded bolt
determined as follows:
𝑃𝑛 = 𝑚𝑓Cdt𝐶𝑢 (Eq. 3.2.1) where
C Bearing factor, which shall be determined according to Table 3.3.1.
d Nominal bolt diameter
t Uncoated sheet thickness
Fu Tensile strength of sheet as defined
𝑚𝑓 Modification factor for type of bearing connection, which shall be determined according to Table 3.2.2.
USA and Mexico Canada Ω (ASD) ɸ (LRFD) ɸ (LSD)
2.50 0.60 0.50
11
Table 3.2.1 Bearing Factor, C, for Bolted Connections (AISI S100 2007)
Thickness of Connected Part, t,
(inch) (mm)
Ratio of Fastener Diameter to Member
Thickness
d/t
C
0.024 ≤ t < 0.1875
(0.61 ≤ t < 4.76)
d/t < 10 3.0
10 ≤ d/t ≤ 22 4 – 0.1(d/t)
d/t > 22 1.8
Table 3.2.2 Modification Factor, 𝑚𝑓, for Type of Bearing Connection
Type of Bearing Connection 𝑚𝑓
Single Shear and Outside Sheets of Double Shear Connection with Washers under Both Bolt Head and Nut
1.00
Single Shear and Outside Sheets of Double Shear Connection without Washers under Both Bolt Head and Nut, or with only one washer
0.75
Inside Sheet of Double Shear Connection with or without Washers
1.33
13
CHAPTER 4
TESTING
4.1 Testing of Specimens
We will compare our experiment testing data to the regular 2-sheet
connected with a nut.
• CFS steel sheet nominal thickness range from 27mil to 118mil with
minimum yield strength from 33 ksi to 50 ksi.
• Bolted Connections is referring to the design criteria and the
requirements for the bolted connections used for cold-formed steel
structural members in which the thickness of the thinnest connected
part is less than 3/16 in. (4.76 mm). [1] American Society for Testing
Material (ASTM), A307 (Type A) bolts, carbon steel bolts and studs,
have less than 60,000 PSI Tensile Strength for bolts with nominal
diameters of 3/8, 1/2, 5/8 and 3/4 in.
• Minimum Edge and End Distances according to AISI S100 (2007). The
minimum distance between centers of bolt holes shall provide sufficient
clearance for bolt holes and shall provide sufficient clearance for bolt
heads, nuts, washers. Also the wrench shall not be less than 3 times
the nominal bolt diameter, d. (e=3d).
14
Table 4.1.1 Bolt diameter and Sizes of Bolt Holes (inches)
Nominal bolt diameter, d (in.)
AISI Standard Hole Diameter d (in.)
3/8 13/32
1/2 9/16
5/8 11/16
3/4 13/16 Note: 1 in. = 25.4 mm.
Table 4.1.2 Test matrix of the research project
Nominal
bold diameter
(in.)
Web with Chord (mil.)
27 x 27 33 x 33 43 x 43 54 x 54 68 x 68 97 x 97 118 x 118
3/8 inch Yes Yes Yes Yes Yes NO NO
1/2 inch Yes Yes Yes Yes Yes Yes Yes
5/8 inch Yes Yes Yes Yes Yes Yes Yes
3/4 inch Yes Yes Yes Yes NO NO NO
We repeat each configuration once, resulting in a total of 46 tests.
15
4.2 Testing Equipment
The testing was separated by two machines to properly test the varying
web and chord thicknesses. For thickness of 27mil to 97mil, a 20 kip capacity
Instron 4482 universal testing machine was used. For the thickness of 118mil,
the test was performed at the high-bay area by the hydraulic cylinder that is
able to handle over 20 kip as shown in Fig.4.2B. Most tests conducted were
stopped shortly after the deformation point and once maximum load had been
achieved as shown in Fig.4.2A.
Figure 4.2A Instron 4482 Universal Figure 4.2B Hydraulic Cylinder
Testing Machine
16
4.3 Specimens
The same sheet steel thicknesses were used for the web and the chord
for each of the 46 tests to create the specimens with 4 different kinds of bolt.
A coupon test was performed for every thickness in order to get the yield
stress 𝐶𝑦, ultimate stress 𝐶𝑢, and the thickness of the sheet steel and
percentage of elongation. Each thickness was tested 3 times in order to
achieve the same results and determine that the tests were precise.
Figure 4.3A Figure 4.3B Specimen setup for testing Specimen after testing
e=3d
d
t1
t2
17
4.4 Specimens Preparation
Two sheets steel with the same thickness were cut into 2 pieces,
measurement based upon the testing specifications for each and every test.
The hole punch distance varies with the bolt diameter used as according the
AISI standard hole diameter specification as shown in the Figure 4.4.
Figure 4.4 Steps to setup the experiment
18
The sheets were then folded using a brake press machine with the web
fold points slight closer so that the web will accurately fit into the chord.
The web and chord were connected by the bolt specimen based on the
test specifications and secured with a nut to insure the body of the bolt
specimen was within the testing area of the web and chord and that the
threads of the bolt would not create a point of failure during the tests. The
testing specimens were connected to the testing machine using mounting
brackets to insure the load of the machine is being evenly distributed across
specimen.
19
CHAPTER 5
TEST RESULTS
The testing results and the geometric properties can be found in the
Appendices (Table A1, A2, A3 and A4). Here, it is also included the
comparison between the bearing strength of the actual test capacity and the
new bearing capacity calculated with adjustment with preferable the ratio
closest to one (𝑃𝑡𝑒𝑠𝑡 𝑃𝑛𝑒𝑤 =1). The comparisons are shown in the Table A1
(Appendix A).
5.1 Specimen Labeling
The labeling specimens were assigned by the same format to identify the test
specimens:
33-1/2-T1
Figure 5.1 Specimens Labeling for Sheet Bearing and Shear Specimens
Web/Chord Thickness in mil
Nominal diameter of bolt in inches
Test Number
20
5.2 Characterization of Typical Bearing Failure Mode
The graph below illustrates the typical curve of the bearing failure for
the specimens. With the initial load applied, the sheet steels experienced
slippage against the bolt. With the load still being applied, sheets steel started
yielding at to the maximum load. At which point the specimen continued to
deform and stopped the testing at around 1 or 1.2 inch.
Figure 5.2A Typical curve bearing failure of a bolted connection
Figure 5.2B Typical bearing failure of a bolted connection without washers
0 0.2 0.4 0.6 0.8 1 1.2 1.40
2000
4000
6000
8000
10000
12000
14000
16000
18000
Appl
ied
load
per
bol
t (lb
s.)
Sheets and Bolt Slippage
Elastic Deformation
Plastic Deformation
Bearing Failure Maximum load
Displacement (inch)
21
In this research 46 experiments with 4 different sizes of bolts were
conducted. The chord and the web connections when the load was applied
were observed. Since, there was no support along the inside wall of the web,
the testing results showed the reaction of the web conformed to the perimeter
contour after the load applied as shown in Figure 5.2B., resulting in type II
failures or piling during tests. The same reaction also occurred with same
thickness of testing from 27mil until 97mil. In contrast, for the sheets steel
connections of 118mil, the results of the shape remaining unchanged after the
maximum load was reached and the test was stopped here. Great elongation
was observed in this case as shown in Figure 5.2C. Due to the thickness of
the 118mil steel, most failures were type I, (failure of the steel sheet).
Figure 5.2C Unchanged shape the bearing strength failure of a bolted connection without washers (118mil)
22
5.2.1 Material Properties
Coupon tests were conducted according to ASTM 307 (2007)
“Standard Test Method and Definitions for Mechanical Testing of Steel
Products” to obtain the actual properties of the test materials in this research.
The coupon test results are summarized in Table 5.2. The coating on the steel
was removed by hydrochloric acid prior to the coupon tests. The coupons
tests were conducted on the INSTRON 4482 universal testing machine. An
INSTRON was employed to measure the tensile strain. The tests were
conducted in displacement control at a constant rate of 0.05 in./min. A total of
four coupons were tested for each member, and the average results are
provided in Table 5.2.1
Table 5.2.1 Material Properties of specimens
Nominal
sheet thickness
uncoated thickness
(in.)
Actual 𝐶𝑦
(ksi)
Actual 𝐶𝑢
(ksi)
𝐶𝑢𝐶𝑦
Elongation on 2-in.
gage length
Ductility
27 mil 0.0227 50.30 57.80 1.15 18.65% high 33 mil 0.0361 44.60 54.10 1.21 18.95% high 43 mil 0.0437 66.00 79.60 1.21 16.75% high 54 mil 0.0566 60.32 78.25 1.30 10.00% high 68 mil 0.0698 46.10 54.50 1.18 15.50% high 97 mil 0.1017 69.92 75.22 1.08 10.00% high
118 mil 0.1305 45.30 52.20 1.15 16.90% high
23
5.3 Discussion Proposed Design Method
According to previous research (LaBoube and Yu 1995, Wallace,
Schuster, and LaBoube 2001a), the experience adopted the same equations
(Eq. E3.3.1-1) for the bearing failure of bolted connections based on the AISI
S100 (2007) specifications as bearing factor C and the modification factor 𝑚𝑓
listed on Table 3.2.2 and 3.2.3 respectively for bearing single shear and
outside sheets of double connection without washers uses 𝑚𝑓 = 0.75.
After the test results achieved and compared to the current AISI S100
predictions are lower than predictions when the ratio of d/t had a big number.
In order to accurately predict the bearing strength, the research revised the
formula of the bearing factor, C, and the modification factor, 𝑚𝑓.
Figure 5.3A Test Results vs. Design Methods AISI S100 for Bearing Strength of Bolted Connections
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00
P/(F
u dt
)
d/t
Data Testing
Current AISIS100 Design
24
A new bearing factor and modification factor (Table 5.3A) were
proposed in order for the test results to be more in line with the original AISI
S100 standard. The Y-axis represents the normalized peak loads, 𝑃𝑡𝑒𝑠𝑡/(𝐶𝑢𝐶𝑡),
which is equivalent to the value of the bearing factor and modification factor
(C 𝑚𝑓). The new proposed method adopted a non-linear curve for the C factor
in order to get the factor of safety and resistance factor approach to AISI S100
values.
Table 5.3A Proposed Bearing Factor, C, for Bolted connection
Ratio of fastener diameter to member thickness, d/t New Method for Bearing Factor C
d/t < 5 3
5 ≤ d/t ≤ 28 0.33 + 13.33/(d/t)
d/t > 28 0.81
Table 5.3B Proposed Modification Factor,𝑚𝑓, for Bolted Connection
Type of Bearing Connection 𝑚𝑓
Single Shear and Outside Sheets of Double Shear Connection without
Washers under Both Bolt Head and Nut
0.675
25
Figure 5.3B The Proposed Design vs. Design Methods AISI S100 for Bearing Strength of Bolted Connections
The ratio for the new design method is 𝑃𝑡𝑒𝑠𝑡/𝑃𝑛𝑒𝑤. The new method
gives an average test ratio of 1.05, with a standard deviation of 0.28 and
coefficient of 0.24.
Table 5.3C Test-to-Predicted Ratios for Sheet Bearing Strength
Hole config.
No. of tests
𝑃𝑇𝑒𝑠𝑡/𝑃𝐴𝐼𝑆𝐼 𝑃𝑇𝑒𝑠𝑡/𝑃𝑁𝑒𝑤 Avg. Std.
dev. COV Avg. Std.
dev. COV
Trusses connections
46 0.66 0.25 0.38 1.16 0.28 0.24
Current AISI Proposed Design Data from Testing
d/t
𝑃 𝑛/(𝐶𝐶𝐶 𝑢
)
26
Proposing bearing strength method, the resistance factor ɸ for (LRFD)
and factor of safety Ω (ASD) were determined according Chapter F of AISI
S100 (2007), with a target reliability index 3.5 for connections for the LRFD.
Considering the equation Eq.5.3A and from AISI S100 (2007) Eq. F1.1-2 the
resistance factor ɸ can be determined as follows:
ɸ = 𝐶ɸ(𝑀𝑚𝐶𝑚𝑃𝑚) 𝑒−𝛽0𝑉𝑀2 + 𝑉𝐹2 + 𝐶𝑃𝑉𝑃2 + 𝑉𝑄2 Eq.5.3A
where:
𝐶ɸ Calibration coefficient 1.52 for the United States
𝑀𝑚 Mean value of material factor, M, listed in Table F1 for type of component involved (AISI S100-2007)
𝐶𝑚 Mean value of fabrication factor, F, listed in Table F1 for type of component involved (AISI S100-2007)
𝑃𝑚 Mean value of professional factor, P, for tested component
𝛽0 Target reliability index 3.5 for the United States
𝑉𝑀 Coefficient of variation of material factor listed in Table F1 for type of component involved
𝑉𝐹 Coefficient of variation of fabrication factor listed in Table F1 for type of component involved
𝐶𝑃 Correction factor (1+1/n)m/(m-2) for n≥4
𝑉𝑃 Coefficient of variation of test results, but not less than 6.5%
m Degree of freedom (n-1)
n Number of tests
𝑉𝑄 Coefficient of variation of load effect 0.21
𝑒 Natural logarithmic based 2.718
27
According to the AISI, by knowing the resistance factor, ɸ, the
corresponding safety of factor can be computed as follows:
Ω = 1.533ɸ
Eq.5.3B
The resistance factor ɸ and the factor of safety Ω can be determined
based upon the test results and the calibrations AISI S100 (2007), Table F1 of
the bolted connections with and without washers
Table 5.3D: Resistance Factors and AISI factor of Safety for Proposed Design Methods for Bearing in Bolted Connections
Number of Specimens 46 Mean 1.16 Std. Dev. 0.28 COV (𝑉𝑃) 0.24 𝑀𝑚 1.10 𝑉𝑀 0.08 𝐶𝑚 1.00 𝑃𝑚 1.16 𝑉𝐹 0.05 m 45 𝐶𝑃 1.07 β(LRFD) 3.5 𝑉𝑄 0.21 AISI S100 ɸ (LRFD) 0.6 0.6 Ω (ASD) 2.56 2.50
The new method yielded an equivalent resistance factor of 0.6
compared to AISI S100 standard, while the safety factor was slightly higher
than the AISI S100 standard value. Based on the testing value and similar
equation values, the AISI S100 would be acceptable to adapt to the same
type of connection.
29
CHAPTER 6
CONCLUSION
A total of 46 CFS bolted truss connections were tested in this research.
The specimen parameters include the thickness of the material and the bolt
diameter. The experimental results show that the truss connections with thick
materials (118mil and 97mil) do not demonstrate significant out of plan
deformation in the unrestrained elements. The existing AISI provisions give
good prediction for the beating strength of those connections. However for
thin materials (68 mil or thinner), significant out of plane deformation was
observed, the test results of those connections are lower than the AISI
predictions. On average, the ratio of test to AISI predicted is 0.66 for all 46
specimens.
Based on the test results, new equations for the bearing factor, C, and
new value for modification factor, 𝑚𝑓, are proposed to add to the existing AISI
bearing equation. The new factors can be used to predict the bearing strength
of bolted connections with unrestrained elements including truss connections,
framing connections, racking system connections, etc. the proposed new
factors were adjusted so that the existing resistance factor and safety factor in
AISI S100 for bearing strength shall also be permit for the connections with
unrestrained elements.
30
APPENDIX A
DIMENSIONS AND RESULTS OF BOLTED CONNECTIONS
IN THE EVALUATION OF EXISTING DATA
31
27Mil,33Mil,43Mil, 54Mil, and 68Mil with 3/8" Bolt
No. Speciment Uncoated Uncoated Bolt Bolt d/t e Yield Tensile Fu/Fy Pn(AISI) P (Test) Elongation Δ Δ Shape P(test)/P(AISI) P (0.25") Pn(AISI) P(new) P(test)/Label Thickness Thickness Type Dia. Stress Strength without defo. for one side 2 in. gage at peak After Test without for two with mf = 0.675 P(New)
Sheet#1 (in.) Sheet#2 (in.) d (in.) (in.) Fy (ksi) Fu (ksi) Ratio (lbf) (lbf) length (%) (in.) deformation sides deformation1 27-3/8-T1 0.0227 0.0227 A307 0.375 16.520 1.125 50.30 57.80 1.15 866.46 619.60 18.65 0.9515 Changed 0.715 687.78 804.62 377.58 1.6412 27-3/8-T2 0.0227 0.0227 A307 0.375 16.520 1.125 50.30 57.80 1.15 866.46 572.00 18.65 0.6610 Changed 0.660 653.42 804.62 377.58 1.5153 33-3/8-T1 0.0361 0.0361 A307 0.375 10.388 1.125 44.60 54.10 1.21 1626.55 1173.00 18.95 1.0610 Changed 0.721 1449.67 1243.22 797.51 1.4714 33-3/8-T2 0.0361 0.0361 A307 0.375 10.388 1.125 44.60 54.10 1.21 1626.55 1280.00 18.95 0.8690 Changed 0.787 1397.05 1243.22 797.51 1.6055 43-3/8-T1 0.0437 0.0437 A307 0.375 8.581 1.125 66.00 79.60 1.21 2935.00 1454.25 16.75 0.6485 Changed 0.495 2865.50 2260.30 1658.33 0.8776 43-3/8-T1 0.0437 0.0437 A307 0.375 8.581 1.125 66.00 79.60 1.21 2935.00 1376.10 16.75 1.1060 Changed 0.469 2115.43 2260.30 1658.33 0.8307 54-3/8-T1 0.0566 0.0566 A307 0.375 6.625 1.125 60.32 78.25 1.30 3736.93 2430.35 10.00 0.9390 Changed 0.650 4509.00 2977.29 2625.50 0.9268 54-3/8-T2 0.0566 0.0566 A307 0.375 6.625 1.125 60.32 78.25 1.30 3736.93 2572.10 10.00 0.3435 Changed 0.688 5093.15 2977.29 2625.50 0.9809 68-3/8-T1 0.0698 0.0698 A307 0.375 5.372 1.125 46.10 54.50 1.18 3209.71 3719.75 15.50 0.5440 Changed 1.159 4687.79 2644.62 2706.90 1.374
10 68-3/8-T2 0.0698 0.0698 A307 0.375 5.372 1.125 46.10 54.50 1.18 3209.71 3510.05 15.50 0.3925 Changed 1.094 4942.28 2644.62 2706.90 1.297
27Mil,33Mil,43Mil, 54Mil, 68Mil, 97Mil and 118Mil with 1/2" Bolt
No. peciment Labe Uncoated Uncoated Bolt Bolt d/t e Yield Tensile Fu/Fy Pn(AISI) P (Test) Elongation Δ Δ Shape P(test)/P(AISI) P (0.25") Pn(AISI) P(new) P(test)/Thickness Thickness Type Dia. Stress Strength without defo. for one side 2 in. gage at peak After Test without for two with mf = 0.675 P(New)Sheet#1 (in.) Sheet#2 (in.) d (in.) (in.) Fy (ksi) Fu (ksi) Ratio (lbf) (lbf) length (%) (in.) deformation sides deformation
1 27-1/2-T1 0.0227 0.0227 A307 0.5 22.026 1.5 50.30 57.80 1.15 885.64 647.00 18.65 0.9515 Changed 0.731 722.69 1072.82 414.12 1.5622 27-1/2-T2 0.0227 0.0227 A307 0.5 22.026 1.5 50.30 57.80 1.15 885.64 631.50 18.65 0.6610 Changed 0.713 760.81 1072.82 414.12 1.5253 33-1/2-T1 0.0361 0.0361 A307 0.5 13.850 1.5 44.60 54.10 1.21 1915.14 1435.00 18.95 1.0610 Changed 0.749 1182.28 1657.62 851.89 1.6844 33-1/2-T2 0.0361 0.0361 A307 0.5 13.850 1.5 44.60 54.10 1.21 1915.14 1425.50 18.95 0.8690 Changed 0.744 1412.08 1657.62 851.89 1.6735 43-1/2-T1 0.0437 0.0437 A307 0.5 11.442 1.5 66.00 79.60 1.21 3725.28 1634.00 16.75 0.6485 Changed 0.439 2467.65 3013.73 1755.18 0.9316 43-1/2-T1 0.0437 0.0437 A307 0.5 11.442 1.5 66.00 79.60 1.21 3725.28 1607.50 16.75 1.1060 Changed 0.432 1886.71 3013.73 1755.18 0.9167 54-1/2-T1 0.0566 0.0566 A307 0.5 8.834 1.5 60.32 78.25 1.30 4982.57 2808.00 10.00 0.9390 Changed 0.564 3682.15 3969.72 2748.82 1.0228 54-1/2-T2 0.0566 0.0566 A307 0.5 8.834 1.5 60.32 78.25 1.30 4982.57 2696.50 10.00 0.3435 Changed 0.541 3509.80 3969.72 2748.82 0.9819 68-1/2-T1 0.0698 0.0698 A307 0.5 7.163 1.5 46.10 54.50 1.18 4279.61 3537.00 15.50 0.5440 Changed 0.826 3807.78 3526.16 2812.82 1.257
10 68-1/2-T2 0.0698 0.0698 A307 0.5 7.163 1.5 46.10 54.50 1.18 4279.61 3321.00 15.50 0.3925 Changed 0.776 4807.52 3526.16 2812.82 1.18111 97-1/2-T1 0.1017 0.1017 A307 0.5 4.916 1.5 69.92 75.22 1.08 8606.11 8370.00 10.00 1.0860 Unchange 0.973 3844.30 7657.10 7745.50 1.08112 97-1/2-T2 0.1017 0.1017 A307 0.5 4.916 1.5 69.92 75.22 1.08 8606.11 8830.00 10.00 0.9605 Unchange 1.026 6405.90 7657.10 7745.50 1.14013 118-1/2-T1 0.1305 0.1305 A307 0.5 3.831 1.5 45.30 52.20 1.15 7663.61 9570.96 16.90 1.0745 Unchange 1.249 5424.18 7273.69 6897.25 1.38814 118-1/2-T2 0.1305 0.1305 A307 0.5 3.831 1.5 45.30 52.20 1.15 7663.61 9724.69 16.90 1.0226 Unchange 1.269 9560.67 7273.69 6897.25 1.410
Table A1: Test Results of Bolted Connections
32
27Mil,33Mil,43Mil, 54Mil, 68Mil, 97Mil and 118Mil with 5/8" Bolt
No. peciment Labe Uncoated Uncoated Bolt Bolt d/t e Yield Tensile Fu/Fy Pn(AISI) P (Test) Elongation Δ Δ Shape P(test)/P(AISI) P (0.25") Pn(AISI) P(new) P(test)/Thickness Thickness Type Dia. Stress Strength without defo. for one side 2 in. gage at peak After Test without for two with mf = 0.675 P(New)Sheet#1 (in.) Sheet#2 (in.) d (in.) (in.) Fy (ksi) Fu (ksi) Ratio (lbf) (lbf) length (%) (in.) deformation sides deformation
1 27-5/8-T1 0.0227 0.0227 A307 0.625 27.533 1.875 50.30 57.80 1.15 1107.05 514.90 18.65 0.9515 Changed 0.465 683.49 1341.03 450.65 1.1432 27-5/8-T2 0.0227 0.0227 A307 0.625 27.533 1.875 50.30 57.80 1.15 1107.05 521.90 18.65 0.6610 Changed 0.471 616.92 1341.03 450.65 1.1583 33-5/8-T1 0.0361 0.0361 A307 0.625 17.313 1.875 44.60 54.10 1.21 2076.93 1225.50 18.95 1.0610 Changed 0.590 1314.90 2072.03 906.27 1.3524 33-5/8-T2 0.0361 0.0361 A307 0.625 17.313 1.875 44.60 54.10 1.21 2076.93 1133.40 18.95 0.8690 Changed 0.546 1098.53 2072.03 906.27 1.2515 43-5/8-T1 0.0437 0.0437 A307 0.625 14.302 1.875 66.00 79.60 1.21 4190.19 1348.40 16.75 0.6485 Changed 0.322 2284.56 3767.17 1852 0.7286 43-5/8-T1 0.0437 0.0437 A307 0.625 14.302 1.875 66.00 79.60 1.21 4190.19 1357.05 16.75 1.1060 Changed 0.324 2531.54 3767.17 1852 0.7337 54-5/8-T1 0.0566 0.0566 A307 0.625 11.042 1.875 60.32 78.25 1.30 6011.80 1734.50 10.00 0.9390 Changed 0.289 2821.48 4962.15 2872.1 0.6048 54-5/8-T2 0.0566 0.0566 A307 0.625 11.042 1.875 60.32 78.25 1.30 6011.80 1786.85 10.00 0.3435 Changed 0.297 3559.73 4962.15 2872.1 0.6229 68-5/8-T1 0.0698 0.0698 A307 0.625 8.9542 1.875 46.10 54.50 1.18 5349.52 3472.20 15.50 0.5440 Changed 0.649 4463.90 4407.70 2918.7 1.190
10 68-5/8-T2 0.0698 0.0698 A307 0.625 8.9542 1.875 46.10 54.50 1.18 5349.52 3329.95 15.50 0.3925 Changed 0.622 3926.98 4407.70 2918.7 1.14111 97-5/8-T1 0.1017 0.1017 A307 0.625 6.1455 1.875 69.92 75.22 1.08 10757.64 8384.50 10.00 1.0860 Changed 0.779 2901.48 9571.37 8065.2 1.04012 97-5/8-T2 0.1017 0.1017 A307 0.625 6.1455 1.875 69.92 75.22 1.08 10757.64 7677.05 10.00 0.9605 Changed 0.714 8811.81 9571.37 8065.2 0.95213 118-5/8-T1 0.1305 0.1305 A307 0.625 4.7893 1.875 45.30 52.20 1.15 9579.52 9309.00 16.90 1.0745 Unchanged 0.972 8948.44 9092.11 8621.6 1.08014 118-5/8-T2 0.1305 0.1305 A307 0.625 4.7893 1.875 45.30 52.20 1.15 9579.52 9579.00 16.90 1.0226 Unchanged 1.000 7550.03 9092.11 8621.6 1.111
27Mil,33Mil,43Mil, and 54Mil with 3/4" Bolt
No. peciment Labe Uncoated Uncoated Bolt Bolt d/t e Yield Tensile Fu/Fy Pn(AISI) P (Test) Elongation Δ Δ Shape P(test)/P(AISI) P (0.25") Pn(AISI) P(new) P(test)/Thickness Thickness Type Dia. Stress Strength without defo. for one side 2 in. gage at peak After Test without for two with mf = 0.675 P(New)Sheet#1 (in.) Sheet#2 (in.) d (in.) (in.) Fy (ksi) Fu (ksi) Ratio (lbf) (lbf) length (%) (in.) deformation sides deformation
1 27-3/4-T1 0.0227 0.0227 A307 0.75 33.04 2.25 50.30 57.80 1.15 1328.46 590.35 18.65 0.9515 Changed 0.444 673.82 1609.24 487.18 1.2122 27-3/4-T2 0.0227 0.0227 A307 0.75 33.04 2.25 50.30 57.80 1.15 1328.46 599.45 18.65 0.6610 Changed 0.451 578.26 1609.24 487.18 1.2303 33-3/4-T1 0.0361 0.0361 A307 0.75 20.776 2.25 44.60 54.10 1.21 1977.42 1290.75 18.95 1.0610 Changed 0.653 1234.36 2486.43 960.65 1.3444 33-3/4-T2 0.0361 0.0361 A307 0.75 20.776 2.25 44.60 54.10 1.21 1977.42 1410.20 18.95 0.8690 Changed 0.713 1583.35 2486.43 960.65 1.4685 43-3/4-T1 0.0437 0.0437 A307 0.75 17.162 2.25 66.00 79.60 1.21 4468.55 2041.10 16.75 0.6485 Changed 0.457 2394.63 4520.60 1948.9 1.0476 43-3/4-T1 0.0437 0.0437 A307 0.75 17.162 2.25 66.00 79.60 1.21 4468.55 2180.65 16.75 1.1060 Changed 0.488 2457.45 4520.60 1948.9 1.1197 54-3/4-T1 0.0566 0.0566 A307 0.75 13.251 2.25 60.32 78.25 1.30 6663.97 2631.70 10.00 0.9390 Changed 0.395 2152.48 5954.58 2995.5 0.8798 54-3/4-T2 0.0566 0.0566 A307 0.75 13.251 2.25 60.32 78.25 1.30 6663.97 2455.30 10.00 0.3435 Changed 0.368 2453.43 5954.58 2995.5 0.820
Table A1: Test Results of Bolted Connections (Continued)
33
APPENDIX B
PHOTOGRAPHS AND SPECIMEN CONFIGURATION
34
TESTING # 1
27Mil, 33Mil, 43Mil, 54Mil and 68Mil
WITH 3/8” BOLT
35
Test Label: 27-3/8-T1
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results: 27mil/24gage Test#1
Maximum load = 1.2392e+003 Displacement = 0.9585
0 0.2 0.4 0.6 0.8 1 1.2 1.40
200
400
600
800
1000
1200
1400
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
36
(Continued: Test Label: 27-3/8-T1)
37
Test Label: 27-3/8-T2
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results: 27mil/24gage Test#2
Maximum load = 1.1420e+003 Displacement = 0.7945
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-200
0
200
400
600
800
1000
1200
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
38
(Continued: Test Label: 27-3/8-T2)
39
Test Label: 33-3/8-T1
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results: 33mil/20gage Test#1
Maximum load = 2.3479e+003 Displacement = 0.8300
0 0.2 0.4 0.6 0.8 1 1.2 1.40
500
1000
1500
2000
2500
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
40
(Continued: Test Label: 33-3/8-T1)
41
Test Label: 33-3/8-T2
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results: 33mil/20gage Test#2
Maximum load = 2.5600e+003 Displacement = 0.8390
0 0.2 0.4 0.6 0.8 1 1.2 1.40
500
1000
1500
2000
2500
3000
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
42
(Continued: Test Label: 33-3/8-T2)
43
Test Label: 43-3/8-T1
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results: 43mil/18gage Test#1
Maximum load = 2.9085e+003 Displacement = 0.2725
0 0.1 0.2 0.3 0.4 0.5 0.6 0.70
500
1000
1500
2000
2500
3000
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
44
(Continued: Test Label: 43-3/8-T1)
45
Test Label: 43-3/8-T2
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results: 43mil/18gage Test#2
Maximum load = 2.7522e+003 Displacement = 0.3680
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
500
1000
1500
2000
2500
3000
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
46
(Continued: Test Label: 43-3/8-T2)
47
Test Label: 54-3/8-T1
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results: 54mil/16gage Test#1
Maximum load = 4.8607e+003 Displacement = 0.2960
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
48
(Continued: Test Label: 54-3/8-T1)
49
Test Label: 54-3/8-T2
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results : 54mil/16gage Test#2
Maximum load = 5.1442e+003 Displacement = 0.2631
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80
1000
2000
3000
4000
5000
6000
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
50
(Continued: Test Label: 54-3/8-T2)
51
Test Label: 68-3/8-T1
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results: 68mil/14gage Test#1
Maximum load = 7.4395e+003 Displacement = 0.6245
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
1000
2000
3000
4000
5000
6000
7000
8000
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
52
(Continued: Test Label: 68-3/8-T1)
53
Test Label: 68-3/8-T2
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results: 68mil/14gage Test#2
Maximum load = 7.0201e+003 Displacement = 0.8655
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
1000
2000
3000
4000
5000
6000
7000
8000
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
54
(Continued: Test Label: 68-3/8-T2)
55
TESTING # 2
27MIL, 33MIL, 43MIL, 54MIL, 68MI, 97MIL and 118MIL
WITH 1/2” BOLT
56
Test Label: 27-1/2-T1
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results: 27mil/24gage Test#1
Maximum load = 1.2424e+003 Displacement = 0.9515
57
(Continued: Test Label: 27-1/2-T1)
58
Test Label: 27-1/2-T2
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results: 27mil/24gage Test#2
Maximum load = 1.2059e+003 Displacement = 0.6610
0 0.2 0.4 0.6 0.8 1 1.2 1.40
200
400
600
800
1000
1200
1400
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
59
(Continued: Test Label: 27-1/2-T2)
60
Test Label: 33-1/2-T1
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results : 33mil/20gage Test#1
Maximum load = 2.8188e+003 Displacement = 1.0610
0 0.2 0.4 0.6 0.8 1 1.2 1.40
500
1000
1500
2000
2500
3000
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
61
(Continued: Test Label: 33-1/2-T1)
62
Test Label: 33-1/2-T2
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results : 33mil/20gage Test#2
Maximum load = 2.7941e+003 Displacement = 869.0100e-003
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
500
1000
1500
2000
2500
3000
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
63
Test Label: 43-1/2-T1
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results : 43mil/18gage Test#1
Maximum load = 3.2150e+003
Displacement = 648.5000e-003
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
500
1000
1500
2000
2500
3000
3500
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
64
65
Test Label: 43-1/2-T2
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results : 43mil/18gage Test#2
Maximum load = 3.1613e+003 Displacement = 1.1060e+000
0 0.2 0.4 0.6 0.8 1 1.2 1.40
500
1000
1500
2000
2500
3000
3500
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
66
Test Label: 54-1/2-T1
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results : 54mil/16gage Test#1
Maximum load = 5.5619e+003
Displacement = 0.9390
0 0.2 0.4 0.6 0.8 1 1.2 1.40
1000
2000
3000
4000
5000
6000
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
67
(Continued: Test Label: 54-1/2-T1)
68
Test Label: 54-1/2-T2
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results : 54mil/16gage Test#2
Maximum load = 5.4115e+003 Displacement = 0.3435
0 0.1 0.2 0.3 0.4 0.5 0.6 0.70
1000
2000
3000
4000
5000
6000
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
69
(Continued: Test Label: 54-1/2-T2)
70
Test Label: 68-1/2-T1
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results : 68mil/14gage Test#1
Maximum load = 6.9997e+003 Displacement = 0.5440
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
71
(Continued: Test Label: 68-1/2-T1)
72
Test Label: 68-1/2-T2
Specimen Configuration
Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results : 68mil/14gage Test#2
Maximum load = 6.5874e+003 Displacement = 392.5000e-003
0 0.1 0.2 0.3 0.4 0.5 0.6 0.70
1000
2000
3000
4000
5000
6000
7000
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
73
Test Label: 97-1/2-T1
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results : 97mil/12gage Test#1
Maximum load = 16.6738e+003 Displacement = 1.0860e+000
0 0.2 0.4 0.6 0.8 1 1.2 1.40
2000
4000
6000
8000
10000
12000
14000
16000
18000
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
74
Test Label: 97-1/2-T2
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results : 97mil/12gage Test#2
Maximum load = 17.6005e+003 Displacement = 960.5100e-003
0 0.2 0.4 0.6 0.8 1 1.2 1.40
2000
4000
6000
8000
10000
12000
14000
16000
18000
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
75
76
Test Label: 118-1/2-T1
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results : 118mil/10gage Test#1
Maximum load = 18.9113e+003 Displacement = 1.0745e+000
-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4-5000
0
5000
10000
15000
20000
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
77
Test Label: 118-1/2-T2
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results : 118mil/10gage Test#2
Maximum load = 19.2208e+003 Displacement = 1.0226e+000
-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4-5000
0
5000
10000
15000
20000
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
78
TESTING # 3
68Mil, 97Mil and 118Mil
WITH 5/8” BOLT
79
Test Label: 68-5/8-T1
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results: 68mil/14gage Test#1
Maximum load = 6.9444e+003 Displacement = 0.3845
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80
1000
2000
3000
4000
5000
6000
7000
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
80
(Continued: Test Label: 68-5/8-T1)
81
Test Label: 68-5/8-T2
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results: 68mil/14gage Test#2
Maximum load = 6.6599e+003 Displacement = 0.8035
0 0.2 0.4 0.6 0.8 1 1.2 1.40
1000
2000
3000
4000
5000
6000
7000
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
82
(Continued: Test Label: 68-5/8-T2)
83
Test Label: 97-5/8-T1
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results : 97mil/12gage Test#1
Maximum load = 1.6769e+004 Displacement = 0.8735
0 0.2 0.4 0.6 0.8 1 1.2 1.40
2000
4000
6000
8000
10000
12000
14000
16000
18000
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
84
(Continued: Test Label: 97-5/8-T1)
85
Test Label: 97-5/8-T2
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results : 97mil/12gage Test#2
Maximum load = 1.5354e+004 Displacement = 0.8920
0 0.2 0.4 0.6 0.8 1 1.2 1.40
2000
4000
6000
8000
10000
12000
14000
16000
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
86
(Continued: Test Label: 97-5/8-T2)
87
Test Label: 118-5/8-T1
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results : 118mil/10gage Test#1
Maximum load = 1.8618e+004 Displacement = 0.8721
-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4-5000
0
5000
10000
15000
20000
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
88
(Continued: Test Label: 118-5/8-T1)
89
Test Label: 118-5/8-T2
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results : 118mil/10gage Test#2
Maximum load = 1.9158e+004 Displacement = 1.1257
-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6-5000
0
5000
10000
15000
20000
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
90
TESING # 4
27Mil, 33Mil, 43Mil and 54Mil
WITH 3/4” BOLT
91
Test Label: 27-3/4-T1
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results: 27mil/24gage Test#1
Maximum load = 1.1807e+003 Displacement = 0.1805
0 0.05 0.1 0.15 0.2 0.25 0.3 0.350
200
400
600
800
1000
1200
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
92
(Continued: Test Label: 27-3/4-T1)
93
Test Label: 27-3/4-T2
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results : 27mil/24gage Test#2
Maximum load = 1.1989e+003 Displacement = 0.5355
0 0.1 0.2 0.3 0.4 0.5 0.6 0.70
200
400
600
800
1000
1200
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
94
95
(Continued: Test Label: 27-3/4-T2)
96
Test Label: 33-3/4-T1
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results : 33mil/20gage Test#1
Maximum load = 2.5815e+003 Displacement = 0.7480
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90
500
1000
1500
2000
2500
3000
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
97
98
(Continued: Test Label: 33-3/4-T1)
99
Test Label: 33-3/4-T2
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results : 33mil/20gage Test#2
Maximum load = 2.8204e+003 Displacement = 0.7720
0 0.2 0.4 0.6 0.8 1 1.2 1.40
500
1000
1500
2000
2500
3000
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
100
(Continued: Test Label: 33-3/4-T2)
101
Test Label: 43-3/4-T1
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results : 43mil/18gage Test#1
Maximum load = 4.0822e+003 Displacement = 0.7785
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90
500
1000
1500
2000
2500
3000
3500
4000
4500
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
102
(Continued: Test Label: 43-3/4-T1)
103
Test Label: 43-3/4-T2
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results : 43mil/18gage Test#2
Maximum load = 4.3613e+003 Displacement = 0.9760
0 0.2 0.4 0.6 0.8 1 1.2 1.4-500
0
500
1000
1500
2000
2500
3000
3500
4000
4500
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
104
(Continued: Test Label: 43-3/4-T2)
105
Test Label: 54-3/4-T1
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results : 54mil/16gage Test#1
Maximum load = 5.2634e+003
Displacement = 0.5190
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80
1000
2000
3000
4000
5000
6000
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
106
(Continued: Test Label: 54-3/4-T1)
107
Test Label: 54-3/4-T2
Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results : 54mil/16gage Test#2
Maximum load = 4.9106e+003 Displacement = 0.3380
0 0.1 0.2 0.3 0.4 0.5 0.6 0.70
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
Appl
ied
load
per
bol
t (lb
s.)
Displacement (inch)
108
(Continued: Test Label: 54-3/4-T2)
109
REFERENCES
ASTM A370 (2007). “A370-07b Standard Test Methods and Definitions for Mechanical Testing of Steel Products,” American Society for Testing and Materials, West Conshohocken, PA.
Chong, K.P., Matlock, R. B. (1975). “Light-Gage Steel Bolted Connections without Washers,” Journal of the Structural Division, ASCE, vol 101.
Gilchrist, R.T., Chong, K. P. (1979). “Thin Light-Gage Bolted Connection without Washers,” Journal of the Structural Division, ASCE, vol 105.
Winter, G. (1956a), “Light Gage Steel Connections with High-Strength, high-Torqued Bolts,” Publications, IABSE, Vol. 16, 1956.
Winter, G (1956b), “Tests on Bolted Connections in Light Gage Steel,” Journal of the Structural Division, ASCE, Wol.82, No. ST2, February 1956.
LaBoube, R. A., Yu, W. W. (1995). “Tensile and Bearing Capacities of Bolted Connections,” Final Summary Report, Civil Engineering Study 95-6, Cold-Formed steel Series, Department of Civil Engineering, University of Missouri-Rolla.
NAS (2007). “North American Specification for the Design of Cold-Formed Steel Structural Members, 2007 Edition,” American Iron and Steel Institute, Washington, DC.
Wallace, J., Schuster, R., and LaBoube, R. (2001a). “Testing of Bolted Cold-Formed Steel Connections in Bearing (With and Without Washers),” Research Report PR01-4, American Iron and Steel Institute, Washington, DC.
Wallace, J., Schuster, R., and LaBoube, R. (2001b). “Calibrations of Bolted Cold-Formed Steel Connections in Bearing (With and Without Washers),” Research Report PR01-5, American Iron and Steel Institute, Washington, DC.
Yu, W. W. (1982). “AISI Design Criteria for Bolted Connections,” Proceeding of the 6th International Specialty Conference on Cold-Formed Steel Structures, University of Missouri-Rolla.
Zadanfarrokh, F., Bryan, E. R. (1992) “Testing and Design of Bolted Connections in Cold Formed Steel Sections,” Proceedings of Eleventh International Specialty Conference on Cold-Formed Steel Structures, St. Louis, Missouri.