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Design of single plate framing connections

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Authors Hormby, David Edwin

Publisher The University of Arizona.

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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-


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-


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


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 *


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 *


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


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


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 *


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-


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-


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-


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-


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


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-


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-


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,


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


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-


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$


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

83

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

87

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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