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Design of single plate framing connections
Item Type text; Thesis-Reproduction (electronic)
Authors Hormby, David Edwin
Publisher The University of Arizona.
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Link to Item http://hdl.handle.net/10150/557687
DESIGN OF SINGLE PLATE FRAMING- CONNECTIONS
byDavid Edwin Hormby
A Thesis Submitted to the Faculty of the
DEPARTMENT OF CIVIL ENGINEERING AND ENGINEERING MECHANICS
In Partial Fulfillment of the Requirements For the Degree of
MASTER OF SCIENCE WITH A MAJOR IN CIVIL ENGINEERING
In the Graduate College
THE UNIVERSITY OF ARIZONA
1981
STATEMENT BY. AUTHOR
This thesis has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the-Library.
Brief quotations from this thesis are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended, quotation from, or reproduction of, this manuscript, in whole or in part, may be granted by the head of the major department or the Dean of the Graduate College when in his judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author.
SIGNEDt
APPROVAL BY THESIS DIRECTOR
This thesis has been approved on the date shown below:
/ Ralph M. Richard Professor of Civil Engineering
and Engineering Mechanics
ACKNOWLEDGMENTS
The author thanks Dr. Ralph M. Richard for his guidance and encouragement in this research. Thanks are also give to Professor James D. Kriegh for sharing his expertise and time in the physical testing.
This research was funded by a grant from The American Iron and Steel Institute, and the author expresses his gratitude for this financial support.
iii
TABLE OF CONTENTS
LIST OF ILLUSTRATIONS.............. .................. . . . viLIST OF T A B L E S ............................................ ixABSTRACT . ........ ...................................... x
1, INTRODUCTION . . . . ....................................... 1Objectives Procedures
2 o A307 GRADE B O L T S ................ .. . . ...........■ . . . . 4Single Bolt Single Shear T e s t s .............. .. . . . . 4Test Fixture . . . . .......................... 7Test Procedure . . ............ 7Failure Deformation and Modes . . . . . . . . . . . . . . 9Conclusions................................ 12
3. FULL SCALE BEAM TESTS ...................... 14Beam Eccentricity...................................... 14Test Procedure.................................... 14Connections with Slotted Holes .................. 18
A325 Bolts .................. 18A307 B o l t s ................ 23
Off-axis Connections................ 23Conclusions.......... 23
4. BEAMS OF GRADE 50 STEEL . ........................... 28Beam Line Solution.................................... 28
• Results . . . ................................ 28L/d L i m i t s .......... 30
5. COMPOSITE BEAMS WITH SHORED CONSTRUCTION . . . . . . . . . . 32Design Procedure ................ 32Summary of Design Curve . ................ . . . . . . . 38L/d L i m i t s .............. 38Support Conditions ................................ 39Results . . . . . o ............ 39Conclusions . . . . . . . . . . . . .............. 40
Page
iv
H CO
V
TABLE OF CONTENTS— Continued
Page
6. COMPOSITE BEAMS WITH UNSHORED CONSTRUCTION .................... 41
Beam Line for Unshored Beams .............................. 41R e S U l t S e e e e e e e e e - . o e e e e e e o e e e e . e e 43Conclusions . . . . e 0 0 . . . . . . . . 43
APPENDIX A: TEST RESULTS AND ANALYSIS..................... .. 47
APPENDIX B: DESIGN CURVES AND BEAM SCHEDULE . ............. 81
APPENDIX C: DESIGN EXAMPLES . . . . . . . . . . ............. 87
REFERENCES 91
LIST OF ILLUSTRATIONS
lo Single Plate Framing Connections ...................... „ 22. Test Plate Dimensions ................................... 63. Single Plate Test Apparatus ............ .............. 84. Failure Modes, Gaylord and Gaylord (1972). . . . . . . . . . 105. Minimum Bolt Diameters Required for 3/8-inch Plates . . . 136. Off-axis Bolt Groups................... 157. Full Scale Test Apparatus............ .................. 178. Three Bolt Symmetrical - Round vs. Slotted Holes........ 19
9. Four Bolt Off-axis - Round vs. Slotted Holes .......... 20
10. Three Bolt Six Inch Pitch - Round vs. Slotted Holes . . . 2111. Seven Bolt Symmetrical - Round vs. Slotted Holes . . . . . 2212. Center of Rotation Off-axis A325 Bolts Round Holes . . . . 2413. Center of Rotation Off-axis A325 Bolts Slotted Holes . . . 2514. Center of Rotation Off-axis A307 Bolts Slotted Holes . . . 2615. Beam Lines for A36 and A50 Steel Beams................... 29
16. Scatter Plot Symmetrical F^ = 50,.............. .. 3117. Composite Section . . . . . . . . . . . . .......... . . 3318. Beam Line for Unshored Construction.................... 4319. Equivalent Beam Line
Figure Page
vi
45
LIST OF TABLES
1. Test Schedule for A307 Bolts in A36 Steel Plates ........... 52. Failure Mode for A307 Bolts in Single Shear . . . , . . « . 11
3 o Recommended D/t Ratios for A307 B o l t s .................... 11
4. Full Scale Test Schedule and Eccentricities (In.). . . . . . 16/
5. Composite Beam and Bolt Schedule . . . . . . . . . . . . . . 356. Composite Beam and Bolt Schedule Light Cover Plates . . . . 367. Composite Beam and Bolt Schedule Heavy Cover Plates . . . . 378. Beam Schedule and Results - Unshored . . .................. 47
Table Page
vii
ABSTRACT
Results of single plate single shear, tests with A307 grade bolts
are presented. Full scale beam test results are reported for A325 and
A307 grade bolts used in symmetrical and off-axis single plate framing
connections. Connections with A307 grade bolts were tested with slotted
holes and A325 grade bolts were tested in round and slotted holes.
The design formula reported by Richard, Gillett, Kriegh and Lewis
(1980) is amended to accommodate Grade 50 steel beams and simply
supported composite beams with shored construction.
A beam line solution to the problem of simply supported composite
beams with unshored construction is proposed and recommendations for
further analysis and testing of composite beams are made.
It is concluded that A307 grade bolts require a D/t ratio of four
and they are not practical in single plate framing connections with round
holes. The design curve can be used to conservatively calculate the
eccentricity of connections with A325 bolts in slotted holes and, as
amended, it predicts the behavior of simply supported composite beams.
viii
/
CHAPTER 1
INTRODUCTION
Figure 1 shows four typical single plate framing connections.
They consist of a plate with prepunched bolt holes, shop welded to a
column or girder. Beams, also with prepunched bolt holes, are
field bolted to the plates. Because of their economy of material and
ease of erection, single plate framing connections are widely used.
Objectives
The design procedure for the single plate framing connection has
been to assume that it is a simply supported flexible connection with
each bolt carrying an equal portion of the shear. However, when single
plates are used in symmetrical connections (Figures 1c and Id),
their support may be considered fixed and Richard (1980) and Lipson
(1977) have shown that the connection resists a significant moment.
Richard (1980) introduced a simplified design curve to calculate this
moment (Appendix B).
Since it contains no flexural elements, the ductility of a single
plate framing connection comes only from bolt and bolt hole distortion
and out-of-plane bending of the plate. Along with the simplified design
curve, Richard (1980) proposed bolt diameter to plate thickness ratios
(D/t) and edge distance to bolt diameter ratios (e/D) (Figure 2) that
assure ductile behavior in single plate connections.
1
2
e- A
Figure 1. Single Plate Framing Connections.
3This study broadens the scope of the simplified design curve to
include beams of Grade 50 steel, simply supported composite beams, off-
axis bolt groups (Figure 6), and connections with slotted holes.
Guidelines for the use of A307 grade bolts are presented, as well as a
beam line solution to the problem of simply supported composite beams with unshored construction,,
Procedures
A307 bolts and A36 plates were tested in single shear to
determine load deformation relationships and the limiting bolt diameter
to plate thickness ratios that assure ductile behavior.
Program BEAMLINE, Lewis (1980), was used to compare the
inflection points for Grade 50 steel beams and composite beams calculated
by beam line theory and a modified design curve. This computer analysis
covered an extensive schedule of beam sections, beam lengths, and single
plate connections.
Inflection points measured in full scale beam tests were compared
to analytical results. The test schedule included symmetrical and off-
axis A325 bolt groups in round or slotted holes with three- and six-inch
spacing. A307 bolts were tested in symmetrical and off-axis bolt groups
in slotted holes.
Simply supported unshored composite beams were analyzed by a
modified beam line method and the results compared to shored composite
beams and the design curve solution.
CHAPTER 2
A307 GRADE BOLTS
Gillett (1978) and Lewis (1980) presented the results of a series
of single shear bolt tests for a range of bolt diameters and plate
thicknesses typical of single plate framing connections. One objective
of the tests was to develop a nonlinear finite element shear connector
model. The model lumped together all the linear and nonlinear response
of the plates, bolt, and bolt hole, including out-of-plane plate bending.
Moment rotation curves were then developed using this model and program
INELAS, Richard(1968), a nonlinear finite element program. The testsi ■
were also used to establish guidelines that assure ductility in single
plate framing connections consisting of ASTM A325 and ASTM A4 90 bolts
with ASTM A36 and ASTM A575 Grade 50 steel plates. This study expands
these results to include ASTM A307 grade bolts with ASTM A36 plates.
Single Bolt Single Shear Tests
The test schedule in Table 1 was used with the following
limitations:
1. All plates were of ASTM A36 steel with sheared edges.
The resulting microcracks and fissures constitute the
most critical case.
2. Plate dimensions were as shown in Figure 2. These
dimensions simulate those commonly used in single
plate connections.
4
Table 1 Test Schedule for A307 Bolts in A36 Steel Plates
PLATES A307 BOLTS
Material Thickness 3/4 7/8 1 1-1/8 1-1/4 1-1/2
A-36/
1/4 X X X
5/16 X X X
3/8 X
X - Tests (3 each)
6
PUNCHED
2 - V DIA.DRILLED
Bolt Dia. in. t-in. e-in. L-in.
3/4 1/4 1-1/2 87/8 1/4 1-3/4 101 1/4 2 101 5/16 2 10
1-1/8 5/16 2-1/4 101-1/4 5/16 2-1/2 101-1/2 3/8 3 10
Figure 2 Test Plate Dimensions
73 o Bolt holes were punched (1/16 inch oversize)»
The plates were made by a local fabricator from his own stock.
Tensile coupons tested from the same stock met ASTM A36 standards (see
Appendix A), All plates were without loose rust and the mill scale was
left undisturbed. The bolts were also from the fabricator’s stock and,
of the nine bolts that failed in shear, seven had factors of safety
within +5% of three (the 7/8 inch diameter bolts had safety factors of
3,68 and 4,0 5),
Test Fixture
A 200,000 pound screw type Tinius-Olsen testing machine was used
to apply tension at points A and B of the test jig shown in Figure 3,
One-inch diameter hardened steel pins attached the jig at these points to
heavy brackets which were, in turn, attached to the heads of the testing
machine. Shims were used to avoid loading the plates eccentrically.
Dial gauges were mounted on both sides to compensate for out-of-plane
bending of the plates.
Test Procedure
After the test jig was assembled and mounted in the testing
machine, a preload of 500 pounds was applied and the bolts were tightened
but not torqued. The load was removed and the probes and dial gauges
were mounted. The bolt and plate were loaded slowly and both dial gauges
were read at appropriate intervals until the bolt sheared or a 0,3 inch
deformation was obtained. The resulting load deformation data are
presented in Appendix A,
8
Shims Top and Bottom
Dial gauges both sides
Plates
Probesbothsides
Figure 3, Single Plate Test Apparatus.
9
Failure Deformations and Modes
Gaylord and Gaylord (1972) list three failure modes for bolts in
single shear as shown in Figure 4. Bolt shear is the most critical and
undesirable failure mode since the connection has no load capacity after
this type of failure. Connections that fail by transverse tension
tearing continue to carry some load, but at a much reduced level. The
bearing mode of failure, where the plate yields around the bolt hole with
no loss of capacity, results in a desirably ductile connection.
Table 2 shows the failure mode for each bolt tested in this
study. Bolt and plate combinations that accommodated 0.3 inch
deformation without tension tearing or bolt shear were considered bearing
failures. This limiting deformation is 1.25 times the outermost bolt
deformation in an eleven bolt connection on a 60-foot long W36 beam
subject to a uniform load equal to 1.5 times its working load; that is.
F La S - = 2(36) (60 x 12)simple 3 E d 3(30 x 103)36
hsimple 2
= 0.016 RAD
1.25(0.016)4? 0.3 in.1,25 Atop bolt ~ 1 *25 ^
where h is the depth of the bolt pattern.
To avoid transverse tension tearing in connections with A325 and
A490 bolts, Richard (1980) recommends an e/D ratio of 2.0 (see Figure 2).
This is also adequate for A307 bolts.
The nonductile bolt shear failure with A307 bolts is circumvented
by limiting the D/1 ratio to 4.0 as shown in Table 3. This limit is
somewhat conservative for the 1-1/8 diameter bolts where the D/t ratio
can be dropped to 3.6.
10
Bolt Shear
Plate Bearing
Tension Tearing
Figure 4, Failure Modes, Gaylord and Gaylord (1972).
Table 2. Failure Mode for A307 Bolts in Single Shear
BoltDiameter
PlateThickness D/
Failure Mode Test Number*
Inches Inchest
i 2 3
3/4 1/4 3.0 S S S7/8 1/4 3.5 B S B1 1/4 4.0 B B ' B-S1 5/16 3.2 S S S
1-1/8 5/16 3.6 B B B1-1/4 5/16 4.0 B B B1-1/2 3/8 4.0 B B B
* B = Bearing Failure S = Shear Failure
Table 3o Recommended D/t Ratios for A307 Bolts
Bolt Size Web or Plate Thickness
Inches 1/4 5/16 3/8 7/16
i 4.0 3.2 2.7 2.31-1/8 4.5 3.6 3.0 2.61-1/4 5.0 4.0 3.3 2.91-1/2 6.0 4.8 4.0 3,4
>|<3------------------ Limits - A307vs ------o
D/t Ratios
12
Conclusions
Figure 5 compares the A307 and A325 bolts required for 3/8 inch
plates. It is apparent that the large D/t ratio required for A307 bolts
makes them impractical in single plate connections with round holes.
However, since they are not torqued, A307 bolts will slip in slotted
holes and the D/t ratio can be relaxed for single plate framing
connections with slotted holes.
13
1 - 1/2 A307
Figure 4. Minimum Bolt Diameters Required for 3/8-Inch Plates.
CHAPTER 3
FULL SCALE BEAM TESTS
Richard (1980) reported the results of five full scale tests of
beams with single plate framing connections. The moment resisted by
these connections was compared to the moment predicted by the simplified
design curve, beam line analysis, and program INELAS, a nonlinear finite
element analysis program, Richard (1968). This study continues those
tests by investigating the following three common design practices:
1) use of slotted holes that, aid in erection, 2) off-axis bolt groups
(Figure 6), and 3) the use of A307 bolts.
Beam Eccentricity
The parameter used to compute the connection moment is the beam
eccentricity, defined as the horizontal distance from the centerline of
the bolt group to the inflection point of the beam (see Figure B.l, Appendix B). Using this measure allows the distance from the bolt line
to the weldment, a, to vary. Having measured or calculated e, the moment
at the weldment is then,
M = (e + a)R,beam
Test Procedure
Test numbers three through fourteen in Table 4 were run using the
apparatus shown in Figure 7. Tests one and two were reported by Richard
(1980) and are included here for comparison. The test beam was a 32-foot- 1 4
15
•'!
=P5
K>e
W 24X55
W24X55
Figure 6. Off-axis Bolt Groups.
Table 4. Full Scale Test Schedule and Eccentricities (In,)
BoltsTestNo,
No. of Bolts
Hole & Pattern
Beam Line Theory Design Curve Experimental Results
1 7Round
Concentric 48.0 49.5 42.22 3
RoundConcentric (.6" sp) 17.3 14.2 19.3
3 3Round
Off-Axis 00 O 7.1_______ 8.6
7/8 in. 4 4Round
Off-Axis 17.1 14.1 H O
5 7Slotted
Concentric 48.0 49.5 33.1. A325
6 5Slotted
Concentric 39.8 23.6 26.8
7 3Slotted
Concentric 8.0 7.1 9.88 3
SlottedConcentric (6" sp 0) 17.3 14.2 12.0
9 4Slotted
Off-Axis 17.1 14.1 15.0L 10 3Slotted
Off-Axis oCO 7.1 9.0
.7/8 in,1 ii , ..7Slotted
1 Concentric 12.5
A3 07 12 5Slotted
Concentric _ _ 5.013 3
SlottedConcentric to o
14 4Slotted
Off-Axis 2.5 HON
17
PSingle Framing Plate
14 Strain Gauges at 6" -30 t Jack
W 24X 55
14 Strain Gauges at 6 "
Rigid Support -
2 Outside Dial Gauges
Gauge Mounts on Beam flange
Inside Dial Gauges Rotation Bar Mounted on Plate
on Beam Web
Figure 7. Full Scale Test Apparatus.
18
long W24 x 55 section connected at one end by a 3/8 inch A36 single
framing plate to a rigid backup structure and simply supported at the
other endo A325 grade bolts were tightened by the turn-of-the-nut
method, whereas the A307 grade bolts were made snug with a socket wrench,,
A thirty ton jack was used to load the beam in increments up to 105 times
the working load„ The eccentricity was measured with strain gauges on
the top and bottom beam flanges and rotations were measured with four
dial gauges as shown in Figure 7„ The results are in Appendix A and
eccentricities at 1o5 times working load are summarized in Table 4„
Connections with Slotted Holes
A325 Bolts
The behavior of connections with slotted holes and A325 bolts
torqued by the turn-of-1he-nut method differ little from the behavior of\
the same connections with round holes,, Figures 8, 9, 10 and 11 show the
eccentricities for round holes versus slotted holes for off-axis and
symmetrical connections at 1„5 times working load,, In all the tests with
A325 bolts in slotted holes (Tests 5 through 10) the calculated design
curve eccentricities compared favorably with the measured eccentricities.
When the connections were dismantled there was no apparent damage to the
bolts or bolt holes. Although the three- and four-bolt connections made
some creaking and popping noises as they were loaded, there was no
perceptible bolt slip. The three-bolt connection with six-inch pitch made the same noises and the dial gauges did indicate some slip.
Top
& Bo
ttom
Str
ain
in B
eam
in M
icro
inch
es
19
200-
Distance in Feet From Bolt Center Line
Figure 8. Three Bolt Symmetrical - Round vs. Slotted Holes.
Bolt C
ente
r Li
ne
Stra
in i
n Be
am i
n Mi
croi
nche
s
20
500-1
400—
200-
Distance in Feet From Bolt Center Line
Figure 9. Four Bolt Off-axis - Round vs. Slotted Holes.
Cent
er
Bott
om S
trai
n in B
eam
in M
icro
inch
es
21
500-1
S'H
200-
Distance in Feet From Bolt Center Line
4U
CQ
Figure 10. Three Bolt Six Inch Pitch - Round vs. Slotted Holes.
Cent
er L
ine
Bott
om S
trai
n in B
eam
in M
icro
inch
es
22
Distance in Feet From Bolt Center Line
Figure 11. Seven Bolt Symmetrical - Round vs. Slotted Holes.
Cent
er L
ine
23
A307 Bolts
Because of the large D/t ratios required for connection
ductility, A307 grade bolts were tested in slotted holes only. Since
these bolts were snug but not torqued, there was significant slip in the
connections. The measured eccentricities were far below the
eccentricities predicted by the design curve and the eccentricities
measured for A325 grade bolts. After disassembling the connections, some
of the nuts could not be run up to the top of the threads but there was
no other apparent bolt or bolt hole damage in these tests.\
Off-axis Connections
Four A325 bolt connections and one A307 bolt connection were
tested with off-axis bolt groups. As shown in Table 4, the
eccentricities for off-axis bolt groups varied from those for symmetrical
connections by, at most, +9%. More importantly, the center of rotation
for the off-axis connections was at the center of the bolt group as shown
in Figures 12, 13 and 14. This was true for all off-axis connections
tested.
Conclusions
Test results support the following conclusions:
1. A325 bolts tightened by the turn-of-the-nut, or equivalent
method, behave essentially the same in round or slotted
holes.
2. The moment-rotation response of a single plate framing con
nection is unaffected by the location of the neutral axis
of the beam it supports.
ROTA
TION
IN
IN
. CE
NTER
OF
RO
TATIO
N
24
LOAD IN KIPSA 3 2 5 B o l t s R ound h o les
(a)
0---
LOAD IN KIPSA 325 Bolts Round holes
(b)
Figure 12. Center of Rotation Off-axis A325 Bolts Round Holes.
CENT
ER
OF
ROTA
TION
IN
IN
. CE
NTER
OF
RO
TATIO
N
25
LOAD IN KIPSA 3 2 5 Bolts S lotted holes
(a)
0---
LOAD IN KIPS A 3 2 5 B o lts S lo t te d holes
(b)
Figure 13. Center of Rotation Off-axis A325 Bolts Slotted Holes
26
LOAD IN KIPSA 3 0 7 Bolts S lotted holes
Figure 14. Center of Rotation Off-axis A307 Bolts Slotted Holes.
27
3« The design curve presented in Appendix B satisfactorily
predicts the eccentricity of single plate connections with
off-axis A325 bolts„ The same curve can be used to conser
vatively calculate eccentricity for connections with A325
bolts in slotted holes.
4. A307 bolts slip in slotted holes and the design curve in
Appendix B is not applicable to this case. The slip that
can occur with slotted holes justifies relaxing the D/t
ratios recommended for A325 and A490 bolts.
CHAPTER 4
BEAMS OF GRADE 50 STEEL
The design curve reported by Richard (1980) is to be used for
beams of A36 Grade steel (see Appendix B). This study seeks to find a
suitable correction factor for beams of Grade 50 steel.
Beam Line Solution
The only effect of a higher beam yield stress on the beam line
solution is to move the beam line out on both axes of the moment rotation
curve, Figure 15. Since the connection moment-rotation curve is nearly
flat where it intersects the beam lines, the moments for the two beams
will be nearly equal. Equating these two moments and noting that the end
shear for the Grade 50 steel beam is 50/36 times the end shear for the
Grade A36 beam, it follows that
= e V —50 36 36
Results
A correction factor of 36/F^ was added to the design curve making it read,
(e/h) - <e/h)re£ (B, £y
e36 V36 = e50 V50and
'36 50
28
Mome
nt
Figure 15. Beam Lines for A36 and A50 Steel Beams.
30
Program BEAMLINE (Lewis 1980)' was used with the schedule in
Appendix B to compare the beam line solution to the solution of this
modified design curve for about 1,000 beams. The middle line in Figure
16 is the recommended (e/h)ref and the symbols are the values of (e/h)ref necessary to make the design curve solution match the beam line solution.
The outer lines are ±20% bounds. The number of points outside these
bounds is slightly less for Grade 50 steel beams than for the Grade 36
steel beams as reported by Richard (1980). This correction factor is
considered adequate.
L/d Limits
To assure connection ductility by avoiding bolt shear and tension
tearing, end rotations are limited to two-thirds of the rotation that
causes 0.3 inch deformation in the outermost bolts. As shown in Chapter
2 this limiting rotation is calculated by,
A . 2 ___Oil.11m 3 (n-l)3.0
where n is the number of bolts and the bolt pitch is equal to three
inches.
To satisfy this requirement for symmetrical (noncomposite) beams,
it is necessary to impose the following restrictions on the L/d ratios:
Symmetrical Beams Fy = 36 ksi L/d < 36
Symmetrical Beams Fy “ 50 ksi L/d < 24
Beams longer than these limits should be checked for excessive endrotation.
E/H
(REF
)
31
5.000 10.000o.ooo 15.000 25.00020.000 30.000
S Y M M E T R I C A L BEAMS F Y = 5 0 K S I
Scatter Plot Symmetrical =Figure 16. 50.
CHAPTER 5
COMPOSITE BEAMS WITH SHORED CONSTRUCTION
An extensive analytical study was made with program BEAMLINE to
develop design aids for single plate framing connections used with simply
supported composite bearns0 Since full scale beam tests of off-axis bolt
groups resulted in essentially the same moment-rotation and center of
rotation response as symmetrical connections, it is concluded that the
behavior of the single plate is not affected by the location of the
beam's neutral axis* For shored construction then, the beam line
solution does not differ from the beam line solution for symmetrical
beams, except that the beam line itself must be located using the
appropriate transformed section modulus.
Design Procedures
Using the beam and bolt schedules in Tables 5, 6 and 7, more than
5,000 designs were analyzed resulting in the following recommended
changes to the design procedure for noncomposite beams presented in
Chapter 3:
Case 1 - Composite with No Cover Plates
Ao Steel Stress Governs
Same as noncomposite beam except:
I, Use the beam depth, d, as defined in Figure 17,
to compute L/d,
32
Concrete ShearConnector
(Noncomposite) N a te )( W i t h Plate)
Figure 17. Composite Section.
34
Table 5. Composite Beam and Bolt Schedule.
BeamSlab
ThicknessIn.
SectionModulus
In.3
BoltDiameter
In.
W14X22 4 46.4 3/4W16X26 4 59J ' 3/4W16X40 4 92.8 " 3/4W18X35 4 86.2 3/4W18X55 4 137 3/4
W21X44 4 120 . 1 3/4
W18X55 41 142 7/8W21X44 41 124 7/8W21X68 41 196 7/8W24X76 41 241 7/8W24X84 41 266 7/8W24X94 41 298 7/8W27X94 41 ; . 325 7/8W24X94 5 307 1W27X94 5 334 1W30X116 5 443 1W33X118 5 485 1W33X141 5 587 1W36X135 51 | 600 1W 36X1601 ____—----- 51 . iI • 719 1
Table 6. Composite Beam and Bolt Schedule Light. Cover Plates,
BeamSlab
ThicknessIn.
PlateSizeIn.
SectionModulus
In.3
BoltDiameter
In.
W14X22 . 4 iX4 . 75.6 3/4W16X26 4 iX4 96.3 3/4W16X40 4 |X6 142 3/4W18X35 4 iX5 131 3/4W18X50 4 178 3/4W21X44 4 |X 5 | 176 3/4W18X50 # |X6 184 7/8W21X44 iX 5 | 182 7/8W21X62 # iX7 . 252 7/8W24X68 |X8 308 7/8W27X84 H 1X9 405 7/8W27X94 H 1X9 441 7/8W27X94 5 1X9 452 7/8W27X84 5 1X9 415 1W27X102 5 1X9 480 1W30X99 5 1X9 503 1W33X118 5 1X10 642 1W33X130 5 1X10 695■ 1W36X135 5* 1X10 770 1W36X170 |1_____£ L ____ 1X10 933
Table 7. Composite Beam and Bolt Schedule Heavy Cover Plates,
Slab Plate Section BoltBeam Thickness Size Modulus Diameter
In. In. In.3 In.
W14X22 4 1X4 105 • 3/4W16X26 4 1X41 133 3/4W16X40 4 11X6 238 3/4W18X35 4 11X5 220 3/4W18X50 4 11X6 283 3/4W21X44 4 11X51 287 3/4W18X50 ** 11X6 292 7/8W21X44 41 11X51 295 7/8W21X62 41 11X7 395 7/8W24X68 41 11X8 492 7/8W27X84 41 11X9 634 7/8W27X94 41 11X9 669 7/8W27X94 5 11X9 685 7/8W27X84 5 11X9 649 .1W27X102 5 11X9 713 1W30X99 5 11X9 758 iW33X118 5 11X10 951 1W33X130 5 11X10 1000 1W36X135 51 11X10 1110 1W36X170 51 11X10 1270 1
37
Case 2
2= Use the transformed steel section modulus. Str»of the composite section in place of the beam
section modus in the design equation for (e/h).
Bo Concrete Stress Governs
Same as above except:
lo Use the concrete (top) transformed section modulus,
S£, instead of Str °2 o Since the concrete governs, do not use the 36/Fy
correction factor for higher grade steel.
- Composite with Cover Plates
A. Steel Stress Governs
Use the same procedure as for no cover plates, except
multiply (e/h) by the additional term (Strnp/^tr^ where
Strap = Transformed steel section modulus
with no cover plate
Sj-r = Transformed steel section modulus Bo Concrete Stress Governs
Use the procedure of Case 2-A, except:
I. Use the concrete (top) section moduli in the
correction factor
where
Stnp
St
Transformed concrete (top) section modulus without cover plates
Transformed concrete (top) section
modulus
2 o
38:
Since the concrete governs, do not use the 36/F^
correction factor for the higher grade steels.
Summary of Design Curve
For noncomposite beams, or composite beams with or without cover
plates, compute (e/h) from the following equation:
(e/h)
where
(e/h),
L
d
n
N
gnp
yg
(e/h)rcf(B)( ref) ( gnp) 36 N . S S Fg g yg
0.06 L/d - 0.15 Beam length
Beam depth as defined in Figure 17
Number of bolts5 for 3/4-inch and 7/8-inch bolts, and 7 for 1-inch bolts
100 for 3/4-inch bolts, 175 for 7/8-inch bolts, and 450 for 1-inch bolts
Governing section modulus
Governing section modulus with no cover plates
Governing minimum steel yield stress except for sections where concrete stress governs (F = 36).
L/d Limits
As with noncomposite beams, it is necessary to limit end
rotations to two-thirds of the rotation that causes 0.3 inch of
deflection in the outermost bolt. Since the off-axis full scale beam
39
tests show that the center of rotation coincides with the center of the
bolt group, the limiting rotation can still be calculated from2 0.3 \
‘aim 3 (n-l)3.0
The seventh edition of the Steel Construction Manual recommends
the following limits on L/d for composite beams:
L/d < 22 for F ' = 36 ksi
L/d < 16 for Fy = 50 ksi
Although these limits are set to control deflections, they can be
conservatively used to limit rotations also.
Support Conditions
It is assumed throughout this analysis that the composite beams
are simply supported. Slabs with negative reinforcing steel continuous
over the supports constitute additional end restraint. Although the
moment-rotation behavior of a single plate connection is independent of
the beam section properties, it will be affected by these additional
restraints.
The simply supported composite beam is a limiting case and single
plate framing connections used with continuous slabs are expected to be
less critical.
Results
In Appendix A, results from the modified design curve are
compared to the beam line solutions. As in Figure 16, the middle line is
the recommended (e/h)re^ as a linear function of L/d and the outer lines
are the +20% bounds. The symbols are the values for (e/h)re^ necessary
to make the design curve solution match the beam line solution. The L/d
40
ratios are limited on the high end to conform with the recommendations in
this chapter and on the low end so that the beam lengths do not govern
the maximum allowable effective flange widths* Girder spacing is also
assumed not to govern the effective flange width.
Envelope errors and mean errors for the composite beams are
comparable to those for noncomposite beams. The results are best for
moderately proportioned designs. Very short beams and beams with deep
bolt patterns tend to have larger errors.
Conclusion
The design procedure recommended by Richard (1980) with the
modifications recommended in this chapter can be used for composite
beams. Appendix C contains examples of this procedure.
CHAPTER 6
COMPOSITE BEAMS WITH UNSHORED CONSTRUCION
In the derivations in Chapter 5 9 it was assumed that temporary
shoring supported the composite beam until the concrete hardened,, Under
these circumstances the entire load is supported by the beam acting
compositely0 It is also common design practice to omit temporary shores,,
In this case, the initial dead load is supported by the rolled shape
alone* Subsequent loads are resisted by the beam acting compos itely with
the slab* A beam line solution for unshored simply supported composite
beams is derived here and the eccentricities calculated from it are
compared to the design curve solutions*
Beam Line for Unshored Beams
Analysis of unshored composite beams requires segregating the
load into the initial dead load of the rolled shape and concrete slab,
W i dI, and the superimposed load, , required to take the composite
beam to first yield* Under the initial dead load the bare beam and
single framing plate rotate to point A, Figure 18(a)* The beam line is
defined by the fixed end moment, M ^ p and the free end rotation,
due to the initial dead load*
Since the connection moment-rotation curve is not a function of
the section modulus, the connection continues to move along the same> M-^
curve when the additional load, W p is applied, Figure 18(b)* The
41
42
l k
(a)
Auxilary Beam Line
Additional rotation
Rotation
(b)
Figure 18. Beam Line for Unshored Construction.
43
additional rotation, § of the now composite beam can be no more than
the free end rotation, caused by the additonal loado Likewise, the
additional moment, cannot exceed the fixed end moment, Sincethe composite beam is in the linear range up to first yield, the
additional moment and rotation due to W must vary linearly and be on
auxiliary beam line 2, Figure 18(b)o Intersection point B is the
solution,,
An equivalent beam line can be constructed by extending the
auxiliary beam line of Figure 18(b) to the plate M-<J> axes as shown in
Figure 19„ Point B can then be located by the usual beam line method
using the fixed end moment, M* , and free end rotation, 6* „ M andeq T eq idl^idl are calculated from the initial dead load beam lineo By similar
triangles,
a ■ Midi1 - *idi (“ 'I/*',)
Thus,
M'=q = Midl + *'l * ♦idi (M'1/<|>1)(j)' = <f> + cf>' + M ($' /M* )eq idl 1 idl 1 1This derivation is for simply supported composite beams. As with
the shored beams, continuity of negative moment reinforcing steel in the
slab over the supports constitutes additional constraint and this
solution is not valid for that case. It is also assumed that the plate
response follows one M-41 curve. Since the M-<f> curve is a function of
(e/h), this is not strictly true, but examination of the eccentricity
load curves in Appendix A shows that e drops as the load is increased and
44
M
Figure 19. Equivalent Beam Line.
45
(e/h) is usually greater than one. The error in using one M-<f> curve is
slight and conservative.
Results
Table 8 is a schedule of beams analyzed by the modified beam line
and modified design curve method. Designs were limited to girder
spacings greater than the maximum allowable effective flange width and
less than half the span length. For comparison, all designs were
analyzed for shored and unshored construction.
Conclusions
Unshored construction has two offsetting effects on connection
moment. Part of the load is supported by the bare steel alone resulting
in a more flexible beam. This moves the beam line out on the § axis and
increases the moment. On the other hand, the first yield load drops,
which lowers the beam line on the ordinate and decreases the moment. As
seen in Table 8, either of these phenomena can dominate. It is not
possible to conclude that unshored construction will always result in
more or less connection moment. It does appear, however, from this very
limited beam schedule that the two construction techniques result in
modest changes in connection moment and the design curve still gives
satisfactory results.
It is recommended that program BEAMLINE be modified for unshored
construction and a schedule of 5,000 or 6,000 beams analyzed. This
comparison will indicate with more certainty whether the design curve is
adequate, as it is, for unshored composite beams.
Table 8 Beam Schedule and Results - Unshored.UNSHORED VS. SHORED
BEAM t(In.)
L(Ft.)
MOMENT - (KIP. IN.) DESIGN CURVE ERROR %UNSHORED . SHORED DESIGN
CURVEW14 x 22 4 30 83.9 78.2 95.4 13.7W14 x 22 4 35 86.4 81.7 97.3 12.6W16 x 40 4 30 109 89.6 128 17.4W16 x 40 4 40 116 109 133 14.6W24 x 94 4-1/2 40 589 529 746 26.7W24 x 94 4-1/2 50 390 362 463 18.7W24 x 94 5 40 443 544 465 5.0W24 x 94 5 50 214 177 241 12.6W24 x 94 5 60 222 204 246 10.8W36 x 160 5-1/2 80 960 1098 949 -1.1W36 x 160 5-1/2 90 632 603 577 -8.7W36 x 160 5-1/2 100 640 617 583 — 8 e 9
APPENDIX A
TEST RESULTS AND ANALYSES
47
Table A. 1 Tensile Coupon Tests.
SpecimenNumber
PercentElongation
YieldStressksi
UltimateStressksi
la 26.4 36.0 60.3
lb 27.2 36.0 59.8
• 1 avg. 26.8 36.0 60.0
2a 28.0 36.9 54.0
2b 24.4 37.6 58.0
2 avg. 26.2 37.2 56.0
3a 38.0 49.5 63.5
3b 40.4 49.3 63.1
3 avg. 39.2 49.4 63.3
LOAD
(K
IPS)
49
§
-0.000 0.040 0.080 0.160
DEFORMATION (INCHES)0.120 0.200 0.240
3/4 A307 BOLTS - 1/4 IN. A36 PLATES
Figure A.l Load Deformation Plot - 3/4 In. A307 Boltand 1/4 In. A36 Plate.
Table A«2 Load Deformation 3/4 Inch Diameter A307Bolt and 1/4 Inch A36 Plate.
----- ^ ...............
* 3/4 A307 Bolts -■ 1/4 In. A36 Plates *
FIRST TEST SECOND TEST THIRD TEST6 POINTS 10 POINTS 8 POINTS
LOAD DEF o -3 LOAD DEFo “ 3 LOAD DEF, =3KIPS INo X10 KIPS INoXlO KIPS INoX10
g S S O S3 S3 S S s -4 - s s = S3 c a s s s s s s B s o a s s n o o « f r - o s s 3 0 o a o s a s o s i o o o a a o o a o - ^ a D s s o a s o o o o o
OoO OoO 0,0 0 ,0 0 ,0 0 ,02 o 0 2o0 2 o 0 2 oO 2,0 1 ,04 o 0 5,5 4 o 0 5 oO 4,0 10,0tioO 42,5 b oO 25 o 0 6 ,0 12 ,0
12 o 0 100,0 8 o 0 44 o 5 8,0 41 ,513o0 ISiOoO 10 ,0 65 oO 10,0 60 ,5
12 ,0 100,0 12,0 110,512 o 5 121,5 12,5 143,513 o 0 149,513 o 0 168,5
LOAD
(KI
PS)
51
§
-0.000 0.060 0.120 0.240
DEFORMATION (INCHES)0.180 0.300 0.360
7/8 A307 BOLTS - 1/4 IN. A36 PLATES
Figure A.2 Load Deformation Plot - 7/8 In. A307 Boltand 1/4 In. A36 Plate.
Table A.3 Load Deformation 7/8 Inch Diameter A307 Boltand 1/4 Inch A36 Plate.
» 7/8 A307 BOLTS - 1/4 IN, A36 PLATES *
FIRST TEST SECOND TEST THIRD TEST16 POINTS 15 POINTS 17 POINTS
LOAD DEF , - 3 LOAD DEF, =3 LOAD DEF, - 3KIPS IN,X10 KIPS I N ,X 10 KIPS INoXlO
s S' :s n s s e e S S S 5 S 3 E 5 S S O Q S S O G S O ^ O O O O O S O O O S O O c c s o o s £ 3 O G « 0 » c a i 3 o a s n o G a n a
OoO 0,0 0 ,0 0 = 0 15,0 85 ,02 o 0 2,5 1 ,0 ,5 16,0 64 ,04„0 4,5 2 ,0 1,5 0 ,0 0 ,05 o 0 7d5 3 ,0 3,0 2 ,0 7 ,08 o 0 15,0 4 ,0 4,5 4 ,0 4,5
10 ,0 25,0 5 ,0 7 ,0 6 ,0 14,012 ,0 37,5 6 ,0 11 ,0 8 ,0 26 ,014,0 50,5 7 ,0 16,0 10,0 34,516 ,0 66,0 8 = 0 20,5 12,0 45 ,018 ,0 86,5 9 ,0 25,0 14,0 5 7 ,019,0 102,0 10 ,0 30,5 16,0 72 ,020,0 123,5 11,0 36,0 18 oO 91,021 ,0 158,0 12,0 41 ,5 19,0 107,022,0 205,5 13,0 48,0 20,0 129,023,0 26 3,5 14,0 55,5 21,0 158,524 ,0 33 9,5 22,0 204,5
22,1 235,5
LOAD
(K
IPS)
§
-O.000 0.070 0.140 0.280 0.350 0.420
DEFORMATION ( INCHES)
1 A307 BOLTS - 1/4 IN. A36 PLATES
Figure A.3 Load Deformation Plot - 1 In. A307 Bolt and1/4 In. A36 Plate.
Table A.4 Load Deformation 1 Inch Diameter A307 Boltand 1/4 Inch A36 Plate»
* 1 A 307 BOLTS - 1 /4 IN, A36 PLATES *
FIRST TEST SECOND TEST THIRD TEST13 POINTS 14 POINTS 12 POINTS
Load DEF, -3 LOAD DEF. -3 LOAD DEF,KIRS 1 N , XI0 KIPS IN.X10 KIPS IN.X10
S 23 S S3 £3 S 55 £2 S S S S 5 5 S S 5 5 3 5 S S s g a n s s s D S s a - > a 8 S 5 3 C 3 $ 3 o z 3 s a a o a o s a s a o a ^ o a o o s s a D
. OoO 0,0 0 .0 0 .0 0 ,0 0,04o0 2,0 4 .0 2.0 4 = 0 1.58 o 0 12.0 8 ,0 15.5 8 ,0 12.0
12,0 30=0 12 .0 36,5 12.0 29.514,0 3 9 = 5 14,0 47 .5 14.0 41 ,016,0 54,5 16.0 63 ,5 16.0 54 ,018 .0 69,0 18 = 0 71 .0 18,0 69 .520 ,0 89.5 20 .0 8 9 .0 20 ,0 87.522 ,0 125.5 22,0 112.0 22.0 115.023,0 165.5 23,0 131.0 23.0 142.524 ,0 235.0 24,0 165.5 24 ,0 204.524,5 296,5 25 ,0 239,0 24,2 215.024 ,6 373.5 25.5 304,0
25 ,7 342.5
LOAD
(K
IPS)
i
DEFORMATION (INCHES)
1 0307 BOLTS - 5/16 IN. 036 PLOTES
Figure A.4 Load Deformation Plot - 1 In. A307 Bolt and5/16 In. A36 Plate.
Table A.5 Load Deformation 1 Inch Diameter A307 Boltand 5/16 Inch A36 Plate*
* 1 A 307 tiOLTS = 5 /16 IN . ' A36 PLATES »
FIRST re ST SECOND TEST THIRD TEST13 POINTS 13 POINTS 12 POINTS
LOAD OFF. -3 LOAD DEF. =3 LOAD DEF. -3KIPS IN.X10 KIPS IN.X10 KIPS IN.X10
E E S O 53 S3 S S S 4- S S S3 23 2 3 2 3 S S S S S 3 S SStZSOOSOSS *331305353 13 53 O S3 2 $3 S O O O D D 0 3 S 3 0 « 5 > O a O O O S 2 23 2 3 C a a a
OoO OoO 0.0 0 .0 4 .0 3.54 .0 4 o 0 4 .0 6.5 8.0 9 .0B. 0 1 3.0 8.0 2 7 = 5 12.0 23.0
12 .0 31.3 12.0 45.5 14.0 32.014 .0 42.0 14 .0 56 .5 16.0 43=516=0 52.5 16 .0 70 .0 18.0 57=010.0 67.0 18 .0 85.0 20.0 73.520.0 86.5 20 .0 104.5 21.0 84. 521 .0 95.5 21 .0 118.0 22.0 104.022 = 0 113 = 5 22.0 140.5 23.0 134.023 = 0 15 1.0 23.0 185.5 24 .0 187.024 .0 191.0 • 23 .8 242.5 24.2 232.02 4 .1 272.0 0 .0 0.0
LOAD (
KIPS)
57
§
0.3600.240 0.3000.120 0.180
DEFORMATION (INCHES)- 0.000 0.060
1 1/8 A307 BOLTS - 5/16 IN.' A36 PLATES
Figure A.5 Load Deformation Plot - 1 In. A307 Bolt and5/16 In. A36 Plate.
Table A.6 Load Deformation 1-1/8 Inch Diameter A307 Boltand 5/16 Inch A36 Plate,
» 1 1/8 A307 BOLTS - 5/16 IN. A36 PLATES *
FIRST TEST SECOND TEST THIRD TEST15 POINTS 15 POINTS 14 POINTS
LOAD DBF . =3 LOAD DEF. -3 LOAD DEF. =3KIRS IN.X10 KIPS IN.X10 KIPS IN.X10530 e O 53 O c 53S^SOOO 2500520000 30S0Z30S0S3<$-SSOOQOSOS352a a S3 O C S a S3 53 O a 0 S 53 a C 23 Q n 53 a 53 S3 53OoG Oo 0 0 = 0 0.0 0.0 0.04.0 6.0 4.0 4.0 4.0 25.58o0 23 = 0 8.0 16.0 8.0 49.0
12.0 41.0 12.0 33.0 12.0 70.0lb.0 64.0 16.0 55.0 16.0 93.518.0 82.0 18.0 69.0 18.0 110.520.0 108.0 20.0 90.0 20.0 131.5
. 22.0 140 = 0 22.0 119.5 22.0 164.023.0 158.5 23.0 142.0 23.0 182.024.0 180.5 24.0 167.5 24.0 203.525.0 207 = 5 25.0 194.0 25.0 235.026.0 234.0 26.0 219.0 26.0 255.027.0 257.5 27.0 246 = 5 27.0 281.028.0 29 = 0
289.0325=0
28.029.0
280.5319.0
2 8=0 312.5
LOAD (
KIPS)
59
o8
0.120
DEFORMATION (INCHES)1 1/4 A307 BOLTS - 5/16 IN. A36 PLATES
Figure A.6 Load Deformation Plot - 1-1/4 In. A307 Boltand 5/16 In. A36 Plate.
Table A.7 Load Deformation ] and 5/16 Inch A36
-1/4 Inch Diameter A307 Bolt Plate.
* 1 1/4 A307 Bolts - 5/16 IN. A36 Plates *
FIRST TEST SECOND TEST THIRD TEST14 POINTS 21 POINTS 14 POINTSLOAD DEF. -3 LOAD DEF. -3 LOAD DEF. -3-KIPS IN. XI0 KIPS IN.X10 KIPS IN.X1023 23 a s s e s s s - 6 - s s s s s s s s s s s s s s a o Q s s s o ^ s s s c s s n o s s s s $ 2 0 0 0 0 0 o s a ^ a o n o o o s a a a o o
OoO 0.0 0.0 0.0 0=0 0.0OoO 14.0 4.0 2.5 8=0 11.516. 0 47.3 8.0 23.0 16.0 41.020.0 67.0 12.0 35.5 20.0 58.022.0 81.0 16.0 50.5 22.0 70.524.0 99.0 18.0 58.5 24=0 89.526.0 123.5 20.0 68.5 26.0 112.5• 28.0 147.5 21.0 73.5 28=0 138=530.0 183.0 22 = 0 81.0 30.0 170.531.0 210.5 23.0 86.0 31.0 193.532.0 238.5 24.0 101.0 32=0 215.533.0 268.6 25.0 112.0 33.0 243.034.0 304 = 0 26.0 124.5 34.0 271.036.0 343.0 27.0 136.5 35.0 306.028.0 149.529.0 168.530.0 193 = 031.0 215.032.0 240.533.0 272.034.0 305.5
LOAD (
KIPS)
61
© A
0 / A
0.240
DEFORMATION (INCHES)0.300 0.3600.060 0.120
1 1/2 A307 BOLTS - 3/8 IN. A36 PLATESFigure A. 7 Load Deformation Plot - 1/1/2 In. A307 Bolt
and 3/8 In. A36 Plate.
Table A.8 Load Deformation 1-1/3 Inch Diameter A307 Bolt and3/8 Inch A36 Plate.
* 1 1/2 A307 BOLTS ~ 3/8 IN, A36 PLATES *
FIRST TEST SECOND TEST THIRD TESTlb POINTS 16 POINTS 16 POINTSLOAD DEF , -3 LOAD DEF, —3 LOAD DEF, —3KIPS IN,X10 KIPS IN,no KIPS IN,X10as soeaoo E$« -naoa ssosaass asssasaoa s sssaaassasa asQQDasaa«0*aaaaassaaassOoO 0,0 0,0 0,0 0,0 0,04 „0 6,5 4,0 5,0 4,0 6,58 o 0 20,0 8,0 13,5 8,0 20, 512 o 0 32,0 12,0 22,0 12,0 38,516 o 0 47,0 16,0 34,0 16,0 52,520,0 66,5 20,0 55,5 20,0 72,024,0 93,5 22,0 68,5 24,0 99,026,0 110,5 24,0 80,0 26,0 115,528,0 127,5 26,0 95,5 28,0 133,030 = 0 148,0 28,0 115,5 30,0 152,532 = 0 170,5 30,0 135,0 32,0 171,534,0 198,5 32,0 156,0 34,0 192,036,0 236,0 34,0 181,0 36,0 220,038 = 0 283,5 36,0 218,0 38,0 257,539,0 307,5 38,0 268,0 39,0 284,040=0 331,5 40,0 316,0 40,0 306,5
cnK>
Bott
om S
trai
n in B
eam
in M
icro
inch
es63
500-i
400-
Distance in Feet From Bolt Center Line
Figure A.8 Eccentricity 3-7/8-in. A325 Bolts Round Off-axis Holes.
Bolt C
ente
r Li
ne
Bott
om S
trai
n in B
eam
in M
icro
inch
es64
500-1
400-
300-
Distance in Feet From Bolt Center Line
Figure A.9 Eccentricity 4-7/8-in. A325 Bolts Round Off-axis Holes.
Bolt C
ente
r Li
ne
Bott
om S
trai
n in B
eam
in M
icro
inch
es65
500-1
400
300-
Distance in Feet From Bolt Center Line
Figure A.10 Eccentricity 9-7/8-in. A325 Bolts Slotted Holes.
Bolt
Cen
ter
Line
Bott
om S
trai
n in B
eam
in M
icroincl
66
'400-
Distance in Feet From Bolt Center Line
Figure A.11 Eccentricity 5-7/8-in. A325 Bolts Slotted Holes.
Bolt C
ente
r
Bott
om S
trai
n in B
eam
in M
icro
inches67
500-i
CL
2
400“
300-
200-
100-
I
I
0
Distance in Feet From Bolt Center Line
Figure A. 12 Eccentricity 3-7/8-in. A325 Bolts Slotted Holes.
Bolt C
ente
r Li
ne
Bott
om S
trai
n in B
eam
in M
icro
inch
es68
400“
200-
Distance in Feet From Bolt Center Line
Figure A. 13 Eccentricity 3-7/8-in. A325 BoltsSlotted Holes at 6-in. Pitch.
Bolt C
ente
r Li
ne
Bott
om S
trai
n in B
eam
in M
icro
inch
es
500-1
Figure A. 14 Eccentricity 4-7/8-in. A325 BoltsSlotted Off-axis Holes.
Bolt C
ente
r Li
ne
Bott
om S
trai
n in B
eam
in M
icro
inch
es
70
400“
300-
Distance in Feet From Bolt Center Line
Figure A.15 Eccentricity 3-7/8-in. A325 BoltsSlotted Off-axis Holes.
Cent
er L
ine
Bott
om S
trai
n in B
eam
in M
icro
inch
es
71
500-1
400-
300-
200-
100-
<0 Kip,
Distance in Feet From Bolt Center Line
Figure A. 16 Eccentricity 7-7/8-in. A 307 BoltsSlotted Holes.
Cent
er
Bott
om S
trai
n in B
eam
in M
icro
inches
72
Distance in Feet From Bolt Center Line
Figure A,17 Eccentricity 5-7/8-in. A307 Bolts Slotted Holes.
Bo]t C
ente
r Line
Bott
om S
trai
n in B
eam
in M
icro
inch
es73
500-1
200-
Distance in Feet From Bolt Center Line
Figure A. 18 Eccentricity 3-7/8-in. A307 BoltsSlotted Holes.
Bolt C
ente
r Li
ne
Bott
om S
trai
n in B
eam
in M
icro
inch
es74
400H
300-4
4 0 Kip$
Distance in Feet From Bolt Center Line
Figure A. 19 Eccentricity 4-7/8-in. A307 BoltsSlotted Off-axis Holes.
Bol t
Cen
ter
Line
E/H(REF)
75
24.00016.000 20.00012.000
L/D8.0000.000 4.000
COMP. - NO PLATE FY=36 KSI
Figure A.20 Design Curve with ±20% Bounds Composite No PlateF =36 Ksi.y
E/H(REF)
76
8.0000.000 4.000 12.000 16.000 20.000 24.000
COMP. - LT. PLATE FY-36 KSI
Figure A.21 Design Curve with ±20% Bounds Composite Light PlateF = 36 Ksi.y
E/HIREF)
77
24.00016.000 20.00012.0000.000 4.000 8.000
COMP. - HVY. PLATE FY=36 KSI
Figure A.22 Design Curve with ±20% Bounds Composite Heavy PlateF = 36 Ksi.y
E/H(REF)
78
Figure A.23 Design Curve with ±20% Bounds Composite NoF = 50 Ksi.y
I18.000
Plate
E/HIREF)
79
9.000 15.000 18.00012.0006.0003.0000.000
COMP. - LT. PLATE FY=50 KSI
Figure A.24 Design Curve with ±20% Bounds Composite Light PlateF = 50 Ksi.y
E/H(
REF)
80
0.000 3.000 6.000 9.000 12.000 15.000 18.000
COMP. - HVY. PLATE FY-50 KSIFigure A.25 Design Curve with ±20% Bounds Composite Heavy Plate
F = 50 Ksi.Y
DESIGN CURVES AND BEAM SCHEDULE
APPENDIX B
81
APPENDIX B
Richard (1980) introduced a simplified design curve to calculate the nondimensional parameter (e/h), for single plate framing connections with A325 and A490 bolts. The beam eccentricity9 e9 is defined to be the horizontal distance from the bolt line to the point of inflection on the beam, Figure 45. The parameter h is the depth of the bolt pattern. The equation is
S 0.4(e/h) = (e/h)ref (§) M r )
where
(e/h)n
ref 0.06 L/d - 0.15 number of bolts
N 5 for 3/4-in. and 7/8-in. bolts, and 7 for 1-in. bolts
Sref 100 for 3/4-in. bolts, 175 for 7/8-in. bolts, and 450 for 1-in. bolts
S section modulus of beam
This curve is used with the following procedure to design single plate framing connections:
8 2
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Beam Moment Diagram
Figure B.l Definition of Eccentricity.
84I* Select plate thickness + 1/16-in. thickness of
supported beam web.2 o Compute the number of bolts required based upon
allowable beam shear and allowable bolt loads.
Insure connection ductility by limiting the D/t and e/D ratio (see Chapter 2).
3. Calculate (e/h)ref and (e/h).Compute h:
h = (n-1) x pwhere
n = number of boltsp = pitch
Compute e from e/h and h.
4. Compute the moment at the weldment:M = Vx(e+a)
where
5.
V = beam shear forcee = eccentricity from Step 3a = distance from the bolt line to the
weldment (Figure 45)
Check the plate normal and shear stresses:M
1/4 tb2
fVVbt
85where
t = plate thickness b = plate depth
60 Design the weldment for the resultant of the stresses from Step 5:
n
fr + f )0.5
Table B.l Beam and Bolt Schedule for Design Curves
BeamSection Modulus
T 3 In,Bolt
Diameter
W 14 X 22 29.0 3/4"W 16 X 26 38.3 3/4"W 16 X 40 64.6 3/4"W 18 X 35 57.9 3/4"W 18 X 55 98.4 3/4"
' W 21 X 44 81.6 3/4"W 18 X 55 98.4 7/8"W 21 X 44 81.6 7/8"W 21 X 68 140.0 7/8"W 24 X 76 176.0 7/8"W 24 X 84 197.0 7/8"W 24 X 94 221.0 7/8"W 27 X 94 243.0 7/8"W 24 X 94 221.0 1"W 27 X 94 243.0 1"W 30 X 116 329.0 1"W 33 X 118 359.0 1"W 33 X 141 448.0 1"W 36 X 135 440.0 1"W 36 X 182 662.0 1"
APPENDIX C
DESIGN EXAMPLES
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DESIGN EXAMPLE
Beam:
Span:
Loading:
Step
1
2
3
4
5
6
W 24 x 61, A572 Grade 50 Steel, S = 130 in3 247j Laterally Supported Uniform with W = 119^
Design Action
Select A 36 plate with t = 7/1611 (t = 0.419")plate webTry 7/8" A325 bolts, R = 119/2 = 59.5k D/t =7/8 1 7/16 = 2.
Nreq’d = 59.5^/12.63^ = 5 bolts(e/h)^^^ = 0.06 1/d - 0.15 = 0.57 (From A 36 Design Curve)(e/h) = 0.57 x (ir) x ° ' = 0.642With p = 3", h = (5-1) x 3 =12", and F = 50 ksi36 _X_____ ____e = 0.642 x 12 x = 5.55"For a=3", V = R =59.5^M = 59.5 x (5.55 + 3.) = 509.in-k
fb - 'O f r j -fis* ■ 20-7 ksl < 24 ksl= 59.5
v 0.4375 x 15 = 9.07 ksifr = (20.72 + 9.072)1/2 = 22.6 ksi
70 xx Weld req'd = 2 2 4 3 7 5 = 10.6/16ths ,Use 3/8" fillets each side
DESIGN EXAMPLE
Beam; W 21 x 44 with 1/2" x 5 1/2" plate, A572 Grade 50 Steel4" slab, St = 481 in3. S' = 406 in3
Span: 301
Loading; Uniform with W. = 130.k
Design ActionStep12
Select A36 plate with t . = 5/16" (t . = 0.348")plate webTry 3/4" A325 bolts, R = 130-./2 = 65.0kD/t = 3/4 t 5/16 =2.4
N ,. = 65k/9.28k = 7 boltsreq d.(e/h) _ = 0.06 1/d - 0.15 = 0.697ret
(e/h) = 0.697 x Cj) x x = 0.478With p = 3", h = (7-1) x 3 = 18"e = 0.478 x 18 = 8.61"For a = 3", V = R = 65.0kM = 65.0 x (8.61 + 3) = 755 in-k
4 x 755b 0.3125 x 21
_ 65.0v 0.3125 x 21
t = 21.9 ksi < 24 ksi
9.90 ksi
fr = (21.92 + 9.92)1/2 = 24.0 ksi
70 xx Weld req’d. = 24^ ^ gg3125 = 8.08/16thsUse 1/4” fillets each side
90
DESIGN EXAMPLE
Beam: W 16 x 40, A36 Steel with 4" Slah,. S- = 92.8 in^Span: 24*
kLoading: Uniform with W = 61.9
Step
12
3
4
5
6
DESIGN ACTION
Select A 36 plate with tp^ate " 5/16" (twe^ ~ 0.307")Try 3/4" A325 bolts, R = 61.9/2 = 30.9kD/t = 3/4 f 5/16-2.4N = 30.9k/9.28k = 4 boltsreq d(e/h)ref = 0,06 1/d “ 0.15 = 0.714
(e/h) = 0.714 x (-g) x = 0.589With p = 3", h = (4-1) x 3 = 9"9 and F =36 ksiy .e = 0.589 x 9 = 5.39"
For a=3"s V = R = 30.9 , M = 30,9 x (5.30 + 3.) = 256.1n-k 4 x 256
b 0.3125 x 12
= , ,30.9 . ;v 0.3125 x 12
= 22.8 ksi < 24 ksi
8.24 ksi
f = (22.82 + 8.242)1/2 = 24.2 ksi
70 xx Weld req'd = 24* g ^ 3125 = 8.13/16ths
Use 5/16" fillets each side
REFERENCES
Gaylord, Edwin H., Jr., and Charles N. Gaylord, Design of Steel Structures, Second Edition, McGraw-Hill, Inc., New York, 1972.
Gillett, Paul E., and Ralph M. Richard, "Strength and Ductility of Single Plate Framing Connections," final report for Project No. 302 submitted to the American Iron and Steel Institute, 1978.
Lipson, Samuel L., "Single-Angle Welded Bolted Connections," Journal of the Structural Division, American Society of Civil Engineers, Vol. 103, No. ST3, Proc. paper 12813, March 1977.
Lewis, Brett Allan, "Design of the Single Plate Framing Connection," Master’s report presented to The University of Arizona, at Tucson, Arizona, in partial fulfillment of the requirements for the degree of Master of Science, 1980.
Manual of Steel Construction, 8th Edition, AISC, New York, 1980.Manual of Steel Construction, 7th Edition, AISC, New York, 1970.Richard, Ralph M., Paul E. Gillett, James D. Kriegh, and Brett A.
Lewis, "The Analysis and Design of Single Plate Framing Connections," Engineering Journal, American Institute of Steel Construction, Vol. 17, No. 2, 1980.
Richard, Ralph M., "User’s Manual for Nonlinear Finite ElementAnalysis Program INELAS," Department of Civil Engineering, The University of Arizona, Tucson, Arizona, 1968.
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