BEHAVIOR STEEL BEAM·TO·COLUMN CONNECTIONS · 2010-05-07 · design is the moment-resisting...
Transcript of BEHAVIOR STEEL BEAM·TO·COLUMN CONNECTIONS · 2010-05-07 · design is the moment-resisting...
by
Joseph S. Huang
Wai F. Chen
Lynn s. Beedl~
Beam-fa-Column ·,Connections
BEHAVIOR AND DESIGN OF
STEEL BEAM·TO·COLUMN
MOMENT CONNECTIONS
. -
Fritz Engineering Laboratory R'eportNo. 3'33.20
;.,
Beam-to-Column Connections
BEHAVIOR AND DESIGN OF
STEEL·BEAM-TO-COLlillN MOMENT CONNECTIONS
by
Joseph S. Huang
Wai F. Chen
Lynn S. Beedle
This work. has been carried out as part of an investigation sponsored jointly by the American Iron and SteelInstitute and the Welding Research Council.
Department of Civil Engineering
Fritz Engineering LaboratoryLehigh University .
Bethlehem) Pennsylvania
May 1973
Fritz Engineering Laboratory Report No. 333.20
333.20
TABLE OF CONTENTS-----'----~~_~--...--.
ABSTRACT
1. INTRODUCTION
1.1 Purpose
1.2 Previous Research
1.3 Scope of ·the Investigation
2. DESIGN CONDITIONS
2 t 1 Design Concepts and Criteria
2.2 Design Variables
2.3 Design Provisions
2.3.1 J!lember Size and ~oading Conditions
2.3.2 Fasteners
2.3.3 Bearing Stress
3 . THEORETICAL ANALYSIS
3.1 Deformation of Beam Due to Bending
3.2 Deformation of Beam Due to Shear
3$3 Deformation of Panel Zone
3.3.1 Elastic Behavior
3.3.2 Inelastic Behavior
4 . EXPERIMENTAL PROGRAM:
4.1 Description and Fabrication of Specimens
4.2 Calibration and Installation of Bolts
4.3 Test Setup
4.4 Instrumentation
L,·.5 Mechanical Proper'ties
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5 ~ COlvIPARISON OF TEST IillSULTS WITH TIIEORY
5.1 Load~Deflection Curves
5.2 Panel Zone Deformati.on.
S i") Maximum Load0':>
5~4 Failure Mode
6. SUl1.MARY AND CONCLUSIONS
7 • ACKNO\VLEDGr.lENTS
8. NOMENCLATURE
9. TABLES M~D FIGURES
10. REFERENCE'S
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Table
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LIST OF TABLES...--.-.---.• ~~~*,........",.--..~~~--
Test Specimens
Mechanical Properties ~f Sections
Test Results
Descr~ption of Failure
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LIST OF FIGIJRES
iv
1 Interior Bealu-to-Column Connection under Symmetrical Loads 56
2 Design RecoDunendation for Bearing Stress for AllowableStress Design (17) 57
3 Load-Midspan Deflection Curve of a W14x38 Beam (AlSteel) (12) 58
4 Load-Deflection Curve of Specimen ell 59
5 Specimen ell after Testing 60
6 Load-Deflection Curves of Specimens Cl and ClO 61
7 Load-Deflection Curve of Specimen C12 62
8 Specimen C12 After Testing 63
9 Normal Stress Distribution Along Beam-to~Column Juncturein Fig. 28 Section A-A 64
10 Normal Stress Distribution Along Beam-to-Column Juncture.in Fig. 28 Section A-A 65
11 Connection Deflection Comp~nents 66
12 Idealized Stress-Strain Curve of A572 Gr. 55 Steel 67
13 Nondimensional.Moment-Curvature Relationship 68
14 Predicted Deflection Components 69
15 Shear Stress-Strain Curve of A572 Gr. 55 Steel 70
16 Comparison of Test Values with TI1eoretical Predictions ofInelastic Shear Buckling of Beam Web- 71
17 Prediction of Panel Zone Deformation 72
18 Connection Panel Zone Modelled by an Elastic Foundation 73
19 Comparison of Test Value with Theoretical Prediction ofBuckling of Column Web 74
20 Column Flanges Modelled by a Continuous Beam 75
21 Continuous Beam Models ·and Mechanism for Ultimate Load 76
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Joint Details of Specimen C12
Joint Details of Specimen C2
Joint Details of Specirnen C3
Gaged Bolts (1 tr AL~90)
Calibration of Gaged Bolts
Test Setup
Instrumentation of Test Specimen C12
Comparison of Predicted Deflection Components withLoad-Deflection Curve of Specimen C12
Comparison of Proposed Theory with Other Methods ofAnalysis
Load-Deflection Curves of Specimens C2, C3 and C12
Deformation at Failure of a Joint Having Slotted Holesin Web Shear Plate (C3)'
Panel Zone Deformation in the Compression Region ofSpecimen C12
Panel Zone Deformation in the Tension Region of SpecimenC2
Fracture of Weld at Tension Flange of Specimen C12
Fracture along Beam Web Groove Weld of Specimen C12
Panel Zoue of Specimen Cl2 After Testing
Tearing of Column Web Along Web-to-Flange Juncture ofSpecimen C2
Fracture at the Heat-Affected Zone of the Groove Weld atthe Tension Flange of Specimen C3
Panel Zone and Joints of Specimen C3 After Testing
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ABSTRACT--~---,~~~""~--
This investigation is concerned. with bea~~t6-column mome~t
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connections that are proportioned to resist a combination of high shear
force and plastic moment of the beam section. A theory based upon
mathematical models and physical models is developed to predict the
over-all load-deflection behavior of connections 0 In the analysis,
it is assumed that the bending moment exceeding the yield moment of
the beam section is carried by flanges due to strain-hardening, and
~he shear force is resisted by the web. The deformation of the connec~
tion panel zone is considered. Predictions by current plastic analysis
and a finite element analysis are also included for comparison.
Experiments were carried out on specimens made of ASTM A572
Gr 5 55 steel, with fully-welded or with bolted web attachments having
round ·holes and slotted holes. These specimens ,vere designed incor-
porating all possible limiting cases in practical connection design,
and were subjected to monotonic loading. Web attachments were fastened
by A490 bolts utilizing a higher· allowable shear stress of 40 ksi for
bolts in bearing-type connections.
A good correlation between the theDretical predictions and
test results was obtained. It is concluded that flange-\velded web-
bolted connections may be used under the assumption that full plastic
moment of the beam section is developed as well as the full shear
s trel1.gt11.
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1. I N T ~ Q Due T ION
One of the determining factors of economy in structural steel
design is the moment-resisting beam-to-coluffi11 connections. The selec
tion of connections is often based upon simplicity, duplication and
ease of erection. The designer should avoid complicated and costly
fabrication. Welded connections providing full continuity are commonly
used in plastically designed structures, This type of connection can
be expensive because vertical groove welds on beam webs must be made
iLl the field 0 In recent years, A325 and ALI-90 hig11~~strength bolts
have become the most cOtunlonly used fasteners in field constructiona
Connections 'vhich require a combination of welding and bolting are
also used in plastically designed 8tructures~ They have the advantage
of being easier to erect. Also, in areas where welders are not readily
available for field welding, field bolting can be done with relatively
unskilled workers.
Currently little information is available for designing
connections which require a combination of welding and bolting.
There are i~nediate needs for improved design methodS'
developed by research, and based upon theoretical and experimental
investigations of full-size connectionSe It is the intent of this
study. to provide basic information for improved design for beam-to
column connections.
333.20
101 PURP~QSE
The purpose of this study is to develop improved' design
methods for safe, efficient, and economical beam-to~column connec
tions. It is the primary goal to, provide a the~retical analysis
along with experimental evidence to verify the design provisions for
beam-to-column connections~
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Connections were designed incorporating all possible, limiting
cases in practical connection designo Joint details were proportioned
such that balanced failures would occur at the design ultimate load~
This will result in a uniform provision for safety~ The design con
cept is applicable to other types of connections as well,
1.2 PREVIOUS RESEARCH
Reference 7 summarized and discussed the results of some of
the studies of rigid moment connections in building frames~ The
tests reported therein were conducted at Cambridge University, Cornell
University and Lehigh University. The types of connections studied
are: 'fully-we Ided corlnections, we Ided top plate and angle seat connec
tions, bolted top plate and angle seat connections, end plate connec
tions, and T-stub connections~ In addition, the behavior of welded
corner connections', bolted lap splices in beams, and end plate type
beam splices was discussed. The connecting media for these specimens
were welding, riveting, and bolting. Only A325 high-strength bolts
were used, The most important result of the studies reported in Ref, 7
is that for all properly designed and detailed welded and bolted moment
connections, the plastic moment of the adjoining member was reached and
the connections were able to develop large plastic rotation capacity. The
behavior of connections was analyzed by using the simplified plastic
theory~ The stress-strain relationship assumed was elastic-perfectly
plastic according to current plastic analysis (3,6).
A summary of research on conn.ections in.cluding theory, des ign
and experimental results is given in ASCE Manual 41, Plastic Design in
Steel (3)~ It contains design recommendations for the use of stiffeners
in beam~to-column connections~ In addition, the design procedures for
four-way beam-to-column conn~ctions are discussed~
The state of art of current research on connections is
presented in Ref. 18 \vhich was prepared in connection with the Planning
and Design of Tall Buildings Project currently undenqay at Lehigh
University. Included therein are a review of theoretical analysis,
design recommendations, and test results of welded bealTI-to .... column
connections, The current design recommendations concerning bolted
beam-to-column connections are also sUlnmarized.
During rec.ent years a number of major developruents have
taken place in the area of plastic analysis and design (8). Studies
on component behavior, especially the research on connections, are
among some of the areas of research which have received major attention.
Investigation into the behavior of connections subjected to anti
symmetrical loading has been reported. One of the important findings
is that the shear deformation of a panel zone can have a significant
effect on the strength and stiffness of unbraced framed structures.
This shear mode of panel deformation was studied theoretically and
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experimentally under monotonic loading at Lehigh University (13,14,15)~
Experiments were conducted at .the University of California on half-
scale subassemblages of a multi-story unbraced frame (9). These
subassemblages were subjected to simulated gravity and cyclic seismic
loads. In calculating the p~ effect, the shear distortion of the panel
zone was includedD The bending mode of panel deformation has not been
investigated yet and is the subject studied herein~
The current design criteria for the need of column stiffen-
ing for beam-to-column connections stem from results of research report-
ed in Ref. 19. Test specimens were fully-welded connections fabricated
from structural carbon steel~ Results of this investigation form the
basis of provisions in Sec~ 1.15, Connections, of the AISC Specifica~
tion (1).
According to the AISC Specification, horizontal stiffeners
shall be provided on the column web 'opposite the comp~ession flange
or 'tv-hen
C1 Af
t <---t
b+ Sk
d ff"t
c y.<180
(1.1)
Opposite the ten.sian fla.nge when
(1.3)
1V'here
t - thickness of web to be stiffened
k. di.stance from outer >face of flange to \veb toe of fillet
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of member to be stiffened, if a nlember is ,a rolled shape
= flange thickness plus the distance to the farthest toe of
the connecting weld, if a member is a welded section
tb
thickness of flange delivering concentrated load
tf
- thickness of flange of member to be stiffened
Af
area of flange delivering concentrated load
d column web depth clear of filletsc
C1
= ratio of beam flange yield stress to column yield stress
These design rules are based upon investigation of structural
carbon steel (19). There is a need to check these rules on full-size
connection specimens made of high-strength steels.
The problenls of strength and stability of the column '\;veb in
the compression region of beam-to-column connections were further ex-
amined in Refs. 10 and 11. A formula for predicting the load-carrying
capacity of the column web in the compression region with d It exceedingc
180/~was proposed (11):'. :-y
Tcr dc
(1.4)
This formula was compared with test results of 36 ksi, 50 ksi and 100
ksi steels. It was found to be conservative for all grades of steel
and for all shapes tested. Reference 11 also proposed an interaction
equation accoun,tillg for the strength and stability of the column \veb in
the compression region:
(1.5)
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This interaction equation is essentially a straight line fitted to
pertinent test data~ It has the advantage of being a one-step analysis
of the compression region to determine whether or not a horizontal
stiffener is required~ Test data used in Ref. 11 were obtained from
simulated tests~ It is necessary to check this formula with test
data from full-size specimens~
Current design provisions concerning the use of high-strength
bolts are based upon early work with riveted joints (28)~ The deter
mination of allowable shear stress was based upon the so-called IItension
shear ratio"~ This design philosophy required the bolts to develop
the ultimate strength of the net section of the member. Because the
ratio of the yield point to ultimate strength changes for different
steels, this criterion resulted in wide variations in the factor of
safety for bolts and led to a conservative design. A more logical
design approach was proposed, based upon a uniform factor of safety
of 2.0 against the shear strength of the fasteners (16,17). It is
the intent of this study to provide further experimental justification
for the design recommendation.
Recently, a series of eight tests of full-size steel beam
to-column connections was carried out at the University of California
(27). The connections were subjected to cyclic loading simulating
earthquake effects on a building frame~ Among those connections
tested \Vere two fully-welded connections, five flange-welded web
bolted connections, and one flange-welded connection. A325 bolts
were used in fastening the web shear plates~ Beam sections used were
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W18x50 and W24x76; column sections were W12xl06~ The ·connection
specimens \Vere nlade of ASTI1 A36 steel. All connection.s had horizontal
stiffeners which were connected to the columns by groove welds~ Re~
suIts of this series of tests show that the load-deflection hysteresis
loops in all cases were stable in shape under repeated loading eyeless
The failure of connection.s \Vas due to either local buckling of bearn
flanges or to weld fracture, and occurred only after many cycles of
loading beyond yielde In this study, connections were made of AS1~
A572 Gr. 55 steel and were subjected to static monotonic loading~
In addition, horizontal stiffeners were not used o Web attachments
were fastened with A490 high-strength bolts designed using higher
allowable shear stresses, namely 40 ksi in bearing-type joints.
An analytical study on beam-to-column connections using the
finite elemen~ method has been recently performed at the University
of Waterloo (31)~ The column was idealized as a plate in plane stress
loaded by in-plane forces from the connecting beams~ Both buckling
and ultimate strength analyses were performed. Similar work ,vas also
done at Lehigh University (33). The connection was also treated as
a plane stress problem and was discretized using rectangular elements
with two degrees of freedom per node throughout the plane of the webs
of the beam and colunlno
The finite element analysis is a useful tool in dealing \vith
complex structural problems. It gives a betterunderst~nding of the
behavior of connections. However, there were questionable areas of
boundary restraints, loading conditions, convergence and accuracy of
333.20 -9
the solutions~ It is current practice to accept results of physical
experiments coupled with simplified statical analyses as a basis for
design rules~ This is a logical approach, indeede
103 SCOP~~;F THUJ'IV~~~~19J~
This investigation is concerned"with those connection types
that would meet the needs of steel fabricating industry and structural
engineers and yet for which inadequate data are availablee Included
in this study are (1) fully-welded connections, (2) flange-welded
web-bolted.connections having round holes in web shear plates and
(3) flange~welded web-bolted connections having slotted holes in
web shear plates. These connections do not have horizontal stiffeners.
The flange-welded web-bolted connections are very economical in field
construction. Information is lacking concerning the performance of
this type of connections under monotonic loading. The behavior of
connections under cyclic loading is ~ot considered o
The connections studied herein are part of a research program
on beam-to-column connections currently underway at Lehigh University
(22,23). Specirnens ,vere fastened by A490 high-strength bolts and were
designed for all "at the critical rt condit iOllS e The material used \Vas
ASTM A572 Gr. 55 steel. This type of high-strength steel is commonly
used in multi-story buildingso
A theoretical analysis is performed based upon mathematical
models and physical models~ The stress-strain curve is assumed to
be elastic-plastic-linear strain~hardeningG The deformation of the
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connection panel zone is considered in the analysis$
Predictions by a finite element analysis and current plastic
analysis are also included for comparison with theoryo
In summary, the lnajor questions to be ansvlered for " a l1
conditiolls"""critical tt con.nections (and the c.ol1tributions of this \'lark)
are:
1) Can a simplified method of analysis be developed to predict
the behavior of unstiffened beam-~o-column connections
under symmetrical loading condition?
2) Will the use of a commercial grade high-strength steel in
connections designed for simultaneous critical conditions
of shear, moment and fastener stresses result in premature
failure by fracture, even when the attainment of full plastic
moment requires considerable redistribution due to strain-
11ardening·?
3) Will flanges of moment connections develop the full plastic
moment of the wide-flange shape?
4) Will shear connections develop the shear strength of the
web of the wide-flange shape?
5) Can. the proposed tthigher bolt stresses tl obtained in Refs.
16 and 17 be confirmed in beam-to-column connections under
critical loading conditions?
6) In flange-connected joints will slotted holes perform as
well as round holes?
7) Can the proposed bearing stress for bearing-type connections
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developed in Ref. 17 'be confirmed in beam~to~column connec
tions under critical loading conditions?
8) Are simulated tests for column web stability (Refq 11) a
satisfactory technique for experimental correlation?
9) Are column web stiffener requirements developed for A36
steel equally applicable for higher yield levels (to 55 ksi)?
333 .. 20
2. D E S I G NCO N D I T ION S~--
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Beam-to-column connections playa key role in assuring that
a steel framed building structure can reach the design ultimate loado
Often the connection must transfer large shear forces, and since they
are often located at points of maximum moment, the joints are subjected
to the most severe loading conditions~ Design procedures for details
must, therefore, assure the perfOrtnarlce that is assumed in design,
namely, that the conn.ection '\vill develop and subsequently maintain the
required plastic moment.
It is assumed in design that the plastic moment M of the beamp
section is taken by the flanges and the shear force is resisted by the
web Co Figure 1 shows an interior beam-to-co lurnn connection. under
synlffietrical loads~ It is assumed that the flange force T is approxi-
mated by dividing plastic moment Mp
by beam depth db'
(2.1)
The connecting devices (welds or bolts) are designed to resist this
flange force T as well as the shear force V.' Welding is frequently
used to join members that are proportioned by the plastic design
method. However, this is but one of the methods of fabrication for
which plastic design is suitable. Plastic design is also applicable
to structures with welded and .bolted connections whenever it is demon-
strated that the connections will permit the formation of plastic hinges.
,The principal design criteria for connections are:
I. Sufficient strength,
2 v Adequate rotation capacityo
3. Adequate over-all elastic stiffness for maintaining the
locatio11 of beanls and column relative to eac11 other.
4.. Economical fabrication.
It is the primary goal of this study to develop improved
design methods for connections meeting these criteria~ The design
methods are substantiated by a theoretical analysis and justified by
experimental results.
2.2 DESIGN VARIABLES
Since the elimination of horizontal stiffeners will lead to
saving in fabrication costs, this investigation is mainly concerned
with unstiffened connections.
-13
Connecting media are welds and high-strength bolts. The
bending moment is supplied by beam flange groove welds. The shear
force is resisted by either beam web groove welds or A490 high-strength
bolts.
Joint details consist of round holes or slotted holes in
web attachments. This design variable was selected to examine the
design assumption of bending moment taken by flanges and shear force
resisted by beam web.
The provisions used in this study were intended to examine
the theory for all possible limiting cases. This was accomplished
within the framework of practical connection designs~
The limiting cases for beam sections and column sections
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are plastic design sections and the least column size without requiring
stiffeners, respectively" The plastic design. sectiol1.s are defined as
those sections which satisfy the requirements of Sec J 2.7, Minimum
Thickness (Width~Thickness Ratios), of the AISC Specification~
According to Formula (1.15~3) of the AISC Specification,
stiffeners shall be provided 01'1 t11e colunln. web opposite the te11sion
flange when
where tf
is the thickness of column flange, C1
is the ratio of beam
flange yield stress to column yield stress, and Af
is the area of
beam flange. In deriving this formula, the beam flange was assumed
to be yielded; strain-hardening was not considered (19). In order
to develop the plastic moment of the beron, the flange must carry a
force T which is given in Eq. 2.1 to be Mp/db • An equivalent flange
area Af sustaining yield stress' Fy
can be written as
A' =f
TF
Y
333.20
Substituting Eq~ 2.1 into Eq~ 2.2 gives:
where Z = M IF , which is the plastic section modulus with respectx p y
to the major (x-x) axis. The AISC Forlnllia (1.15-3) beC0111eS
-15
(2.3)
(2.4)
This formula takes into consideration the fact that strain~
hardening occurs in the flanges \vhen the beam attains the plastic
moment 0 It replaces Eq. 1 0 3 for connections made of high-strength
steels.
Connection specimens were designed to resist severe loading
conditions. Joint details were proportioned in such a way that, at the
beam-to-column juncture, the plastic moment and the factored shear
capacity of single shear bolts in the beam web would be reached con-
currently.
The limiting value for shear force is V of the beam section.p
The shear force was supplied by the maximum ulrnber of high-strength
bolts that could be used in the beam web.
The material used \Vas ASTM A572 Gr. 55 steel. This type of
high-strength steel is commonly used in multi-story frames. Knowledge
of its ductile behavior may result in a better design of details and
lead to the saving in fabrication costs.
2 0 Fas,!eners
For flange-welded web-bolted connections, ASTM A490 bolts
were used to fasten the shear plate to beam web~ The allowable shear
stress used in design for A490 bolts in bearing-type connections was
40 ksi instead of 32 ksi as suggested in current Specification (28)~
The use of higher allowable shear stresses reflects the
-16
logical design criterion which would result if a minimum adequate factor
of safety were applied against the shear strength of the fasteners.
This design criterion is based upon the results of a study of A7 and
A440 steel lap and butt joints fastened \vith A325 bolts, and A440
steel joints connected with A490 bolts (16). Tests have been 8ub-
sequently carried out to substantiate the suggested design criterion)
especially the use of A490 bolts in A440 and AS14 joints (24,32).
35 Bearing Stress
Figure 2 shows the safe design region for bearing pressure
on projected area of bolts in bearing-type connections (17). The
region recommended for allowable stress design is bounded by the
fo1101ving lines:
e 1.5D
cre0.5 + 1.4.3 --E.:::::
D a-u
CJ-E 1.5(J
u
(2.5)
(2.6)
(2.7)
Equation 2.5 means that the end distance e may not be less than l~
times the bolt diameter D'. For greater end distance, the bearing
-17
pressure 0 is limited by Eq. 2.6 which was obtained by providingp
an adequate marg~n against failure of lap and butt joints reported in
Ref. 17. The nlaxirnum bearing pressure is proposed to be 1,5 times
the tensile strength of the plate 0 CEq. 2,7)~u
The failure of bearing-type joints usually occurred by tearing
and fracture of the plate. The failure can be predicted by considering
static equilibrium between the force applied to the side of the hole
and the resistance given by the plate material. The bolt force is the
product of the plate thickness t, nominal bolt diameter D and the
bearing pressure a 5
p
Bolt force t D cr~ p
(2.8)
The resistance given by the plate is equal to the area of the plate
being sheared off times the shear strength of the plate (which is
assumed to be 70 per cent of the tensile strength 0 ) (17).u
PI · 2 ( 12.) (0 .7 a )ate res~stance = t e - 2 u(2.9)
Equating Eq. 2.8 to Eq. 2.9 gives an equation which defines the failure
of bearing-type joints:
er~ - 0.5 + 0.715 ~
u(2.10)
This prediction is in good agreement with test results as indicated
in Fig. 2.
333.20 -18
The actual design points of specimens in this study are on
the borderline of the proposed design region as shown in Fig. 2 0 The
test results should provide conclusive justification for the design
recommendation.
3$ THE 0 RET I CAL
-19
One of the important concepts and assumptions with regard
to the plastic behavior of structures according to the simplified
plastic theory is that the connections are rigid; the sizes of the
connections are such that member ends are assumed coincident ,mere
member centerlines intersecte Connections proportioned for full con-
tinuity will transmit the calculated plastic moment, This condition
is idealized as a plastic hinge as a point (3,6).
According to plastic analysis, the stress-strain relationship
for structural steels can be described by either elastic-perfectly-
plastic or elastic-plastic-linear strain-hardening. Predictions for
the behavior of structures are usually based upon these two idealizations,
Figure 3 shows the load-midspan deflection curve of a W14x38
beam (12)e The behavior of the bemu was predicted fairly accuratelyo
The shear force at the predicted plastic limit load is 30 per cent of
the shear force that would produce ~ull yielding of the web (V).P
The load-deflection curve of connection ell is shown in
Fig. 4. This connection was a fully-welded connection designed for
a shear capacity at the predicted plastic limit load of 52.5 per cent
of V , thereby simulating the loading condition in a real building.p
Again, the predictions agree with the test curve. The maximum load
is 25 per cent greater tilan the predicted plastic limit load. This
substantial increase in load-carrying capacity is attributed to the
forming of plastic hinges at the jOillts (sho\VD. in Fig. 5) and the
333.20
subsequent strain-hardening that sets in quickly as a consequence of
,the gradient in, moment 0
Another comparison between predictions by the current
-20
plastic analysis and 'test results is shown. in F'igll 6.. CIO is a fully..".
welded connection and Cl is a flange-welded web-bolted connection,
as described in Refs o 22 and 23. Both connections had horizontal stiff-
eners. A good correlation between predictions by plastic analysis and
experimental results is obtained. This is due to the use of horizontal
stiffeners which increase the rigidity of panel zone, meeting the
assumption of the plastic analysis.
The current plastic analysis is also used to predict the
behavior of connection C12 designed according to the provisions in
Chap. 2 0 This conne~tion does not have horizontal stiffeners. In
addition, the shear force at the predicted plastic limit load is very
high, being 95 per cent of V. The test curve deviates substantiallyp
from the prediction as shown in Fig. 7. Two reasons account for
this deviation: (1) the deformation of the connection was increaped
by the high shear force present, (2) the deformation of the panel
zone decreased the rigidity of the connection as a consequence of the
elimination of horizontal stiffeners o These effects are clearly shown
in Fig. 8.
It is the intent of this chapter to develop a theory whereby
the behavior of this particular connection \vithout stiffening can be
predicted.
333,,20 -21
The theory is based upon a postulation that at the predicted
plastic limit load, the bending moment is carried by flanges and the
shear force is resisted by the web~ The stress distribution in
Figs. 9 and 10 are computed from the strain gages located at the
beam-to-column juncture as indicated in Figo 28 Section A-A. The
assumption of plane section remaining plane is satisfactory for loads
below 450 kips (which is slightly higher than the working load P =Til
440 kips). The non-linear stress distribution was observed beginning
at a load of 450 kips, a fact indicating that the flanges carried
most of the bending moment. Also, at the predicted plastic limit load
P 748 kips, the bending moment could be carried by the flanges alonep
due to strain-hardening.
The following derivation is based upon this concept to
predict the over-all load~deflection behavior.
The deflection components of a connection are diagrammatically
sho\vu in Fig. 11 0 The total deflection 6 can be expressed by
ill which
61= deflection of beam due to bending
~2 deflection of beam due to shear
6.3 = deflection d1..16 to rigid body motioll of beam induced by
the panel zone deformationt
(3.1)
333 .. 20
Assumptions luade in predictil1g the bending defortuation f)1
are t11at:
1. the whole section is effective in the elastic range up to
the yield moment M , andy
2. in the strain~hardening range resistance to bending is
given by the flanges only. The \\feb is neglected,
-22
Figure 12 shows an idealized stress-strain CUl-ve for ASTM A572
Gr. 55 steel as obtained from tension tests (29)~ Based upon this
stress-strain curve, a moment-curvature relationship can be obtained
as sho\vu in Fig. 13. In the elastic range the relationship between
bending moment M and curvature ~ is
M -.. Elq:>
where
E Young's modulus of elasticity
I - moment of inertia of the whole section
In the, strain-hardening range, the bending moment is given by
M:= o'A d. f f
(3.2)
(3.3)
where Af
is the area of one flange, df
is the distance between centroids
of flanges and the stress cr is assumed to be uniform across the thick-
ness of the flanges.
The curvature ~ is
2e'P-= d
f
(3. ~.)
(3.5)
333~20
in which € is the strain at 'the centroids of flanges.
Using this moment~curvature relationship ·the deflection at
the tip of the cantilever can be readily obtained by means of the
-23
moment~area method~ This was conveniently performed through a computer
program and the result is plotted in Fig~ 14~
The moment-curvature relationship used herein is different
from the one used in current plastic analysis (3,6), The moment-
curvature relationship in the strain-hardening range in current plastic
analysis is based upon the whole wide-flange section~
where 2est
CfJst = -d-
(3.6)
(3.7)
The raOlllent-curvature relationship based upon the whole \vide .....
flange section was also applied in an analysis of beams under moment
gradient (25). It has been one of the basic concepts in the plastic
analysis. The proposed theory assumes that only flanges are effective
in the strain-hardening range. "This new theory is applicable to con-
ditions when high shear force is present.
3.2 DEFORMATION OF BEAM DUE TO SHEAR-----~---~~-~-_.~ ~~---
Figure 15 shows the shear stress-strain curve for ASTM A572
Gr. 55 steel. It was computed by using the effective stress-strain
concept in the theory of plasticity (26). This procedure was also
applied in a study concerni.ng the shear deformation of a connection
panel zone (14,15)&
The shear deformation is given by the product of shear
strain y and beam span L.
~ := 'Y L2
For a g~ven shear force V, the shear stress T is
V'f :::: A
\'1
where A is the area of the beam web.\'1
-24
(3.8)
(3.9)
Equation 3.9 implies that (1) the shear force is resisted by the beam
web only, and (2) the shear stress distribution in the beam web is
uniform. The relationship bet\veen ~ and y is defined in Fig. 15, and
can be described as follows:
In the elastic range,
Gy
and in the ?train-hardening range,
where
G ::= modulus of elasticity in shear
Gst strain-hardening modulus of elasticity in shear
'f :=. sllear yield stressy
Y shear strain at onset of strain-hardeningst
For a given shear strain, both the shear deformation and
(3.10)
(3.11)
shear stress could be determined by Eq. 3.8 and Eqs. 3010 and 3~11,
333.20 -25
respectivelyw Furthermore, shear force could be calculated by Eq. 3.9.
Thus, the shear deformation corresponding to each applied shear force
could be determined, The predicted shear deformation is also plotted
in Fig. 140
In calculating the shear deformation for shear forces
exceeding V , the strain-hardening part of the shear stress-strainp\
curve was used (Fig. 15). This procedure assumed that once the shear
force exceeded V , the ov~r-al1 shear deformation of the beam was duep
to shear strain-hardening of the beam web~ Similar observations were
reported in a study concerning the deflection of wide-flange beams
subjected to high shear forces (20).
When a wide-flange section is subjected to a high shear force,
inelastic shear buckling may occur in the web. A theoretical prediction
was developed in connection with a study of welded plate girders (5).
The theory was used to explain 'the s'hear bllckling of the panel zone of
beam-to-column connections under antisymmetrical loading (14).
The theoretical reference curves are indicated in Fig. 16.
These are for L/db ratios of 1.0 and 2.0. The actual L/db ratio is
1.52, lying between these two curves. The theoretical buckling curve
for L/db
= 2.0 may be used conservatively for connections here.
Of the tests C2, C3 and C12 studied herein, no failures due
to shear buckling were observed. Indeed, test points plotted in Fig.
16 indicated that there was an adequate margin against shear buckling.
The shear deformation then may be, computed by considering the in-plane
behavior.
-26
3.3 DEFORMATION OF PANEL ZONE
The response of the connection panel zone can be described
by fOllY stages as illustrated in Fi.g. 17. In the elastic range OA,
the deformation is predicted by the analysis of the bending of beams
(column flanges) on art elastic foundation" The panel zone is rnodel1ed
as a system of springs supporting the column flanges~ It is assumed
that the elastic response terminates when yielding spreads to a width
of (tb
+ 5k) in the column web opposite to the beam flanges 0 The in~
elastic behavior of the panel zone is analyzed by assuming the column
flanges to be acting as continuous beams in stage AB~ The subsequent
load-deformation behavior is predicted according to plastic analysis
by considering the formation of plastic hinges at supports (stage Be)
and at load points (stage CD)o Finally, the ultimate load is reached
when a mechanism is developed.
1. Elastic Behavior
The analytical model used in predicting the elastic behavior
is shown in Fig. 18(a). This model utilizes springs to simulate the
deformable panel zone, The column flange is treated as a beam supported
by an elastic"mediuffio Due to symnletry only half of the panel zone is
analyzed. A procedure for solving this type' of problem was discussed
in Ref. 21. It is applied to the connection problem hereo
The differential equation for a beam on an elastic foundation
is expressed by
(3.12)
-27
where p is the spring COllstant and If is the n10ment of inertia. of each
flange. The spring constant is defined as the force required to cause
a unit shortening of a unit strip of web plate. In this case,
p2Etd
c
The general solution for the differential equation, Eqo 3.12, can be
'Written as
(3.14)
i11 ,mich(3.15)
The factor A is called the characteristic of the system.
In solving this problem, it is assumed that the column is of
unlimited length. Figure 18(b) shows the elastic foundation subjected
to a concentrated force T. Because ,of the sy~netry of the ~eflection
curve, only the half to the right of point 0 will be considered. The
constants in the general solution can be determined by considering
boundary conditions.
Since the deflection must approach zero in an infinite
distance away from the application of the load, the terms in Eq. 3.14
containing eAX
must vanish which implies C1
= 0 and C2
= O. The
general solution becomes
(3.16 )
The condition of S~Mletry indicates that the slope of the deflection
curve directly under the load must be zerOe
~28
(3.17)
This condition leads to C3
~ C4 = c.
The remaining constant will be determined by considering the static
equilibrium between the external load T and the reaction forces.
T - 2.t' p y dxo
The final solution can be \vritten as
TI\. -;\xy ~ -- e (COSAX + sinAx)- 2p
(3.18)
~(3.19)
An interesting featu~e of these functions in the solution
given in Eq. 3.19 is the rapidly decreasing amplitude. This means
that the manner in \vhich the beaul is, supported in. a short distance
away from the application of load 'viII have a small effect on the
configuration of the deflection lin~. It is reasonable to treat
this problem as a beam of unlimited length~
The deflection due to a couple of forces T could be obtained
by substituting x = 0 (Fig. 18(b)) and x = df
(Fig. l8Ce» into Eq. 3.19.
It was found that the term corresponding to x ~ df
was very small,
being 0.00085, and could be neglected~ The deflection, then, is given
by
(3,20)
333.20
Finally, the elastic stiffness of the panel zone is obtained by sub-
stituting Yo ~ 5/2 and T = PL/2db
:
-29,
P6
(3.21)
Wl1en a conn.ection panel zone is sub jected to the syrnm.etrical
loading condition indicated in Fig. 1, the buckling of the compression
region due to the concentrated forces delivered by the beam flanges is
apparent. Studies into this problem were reported in Refs Q 10 and 11 •
.TIle theoretical prediction was derived by assuming that the concen....
trated forces delivered to the compression region of the column are
resisted by a square web panel of d x d. In addition, the columnc c
flanges provided simply supported edge conditions.
The theoretical buckling curve is shown in Fig. 19. The
buc~ling equation developed in Ref. 10 can be \rritten as
where
crcr"'(j
y
1d It 2
[Cdeft")]c a
cr = critical buckling stresscr
(j = yield stress levely
d = column web depth clear of filletsc
t thickness of co 1umn. \Veb
The allowable column web depth-to-thickness ratio, (d It) , to precludec a
instability is limited by the AISC Formula (1.15-2):
-30
A test point for the column section used in this study,
W14x176, is plotted in Fig. 19, indicating that yielding (strength)
instead of buckling (stability) of the column web is the governing
factor.
The stren.gtrl of a column web in resisting the cOlupression
forces delivered by beam flanges was investigated in Ref. 19. It
was found that the beam flange force was resisted by an effective
width (tb
+ 5k) of column web.
where
TA
~ beam flange force
tb
~ thickness of beam flange
(3.23)
k = distance from outer face of column flange to web toe of
fillet.
The applied column load PA
is given by
which is the linlit of the elastic range as indicated in Fig. 17.
2. Inelastic Behavior
The inelastic deformation of a connection panel zone is
(3.24)
mainly due to the spread of yielding in the column web. It was ob-
served from the current tests and the tests reported in Ref~ 19 that
the yielding progressed from a width of (tb
+ 5k), which defines the
limit of the elastic stage, to a ~vidth of (tb + 7k) whereupon the
column web failed by excessive lateral deformation (Fig~ 20(a)).
Since the column web was yielded, the additional loading had to be
-31
resisted by the collunn flanges forming the boundary of the connection
panel zone~
The column flanges are treated as continuous beams clamped
at a distance of (tb
+ 7k)/2 away from the application of' load as'
shown in Fig. 20(b). This is equivalent to assuming that the column
above and below the yielded regions could provide a fixed-end condition
to the flanges~ A hinge is located at center of the continuous beam
simulating the restraint to movement provided by the center portion
of the column web.
The prediction of the load-deformation behavior of the con-
tinuous beam model is based upon the' simplified plastic theory (3,6) $
The first hinges will form at the supports~ The behavior of the
continuous beam can be analyzed by c'onsidering the supports as being
replaced by hinges and end moments remaining constant at M of thep
column flange as shown in Fig. 21(a). As further load is added, addi-
tional plastic hinges will form under the load points (Fig,. 21(b)~
The be~l will continue to deform under constant load until it reaches
theoretical ultm1ate load. Figure 21(c) shows the deformed shape
of the connection after a mechanism is formed in each column flange.
Based upon the foregoing theoretical prediction of panel
zone deformation, the angle of rotation of the panel zone shoml in
333020
Fig. 11(d) can be computed from
-J 0e ~ tan . (_.)d
f
6 panel zone deformation
df
distance between centers of two flanges
Since the deformation 6 is very small, it is reasonable to compute
the angle of rotation by
-32
(3 025)
(3 .26)
The deflection of the beam due to the rigid body motion induced by the
deformation of the panel zone is given by
6 = e L3
Substituting Eq. 3~26 into Eq. 3 0 27 gives:
(3.27)
(3.28)
The prediction of over-all deflection including 63
is plotted
in Fig. 14 for a connection that was tested. The comparison of test
results with theory will be discussed in Chap. 5.
333.20
40 E X PER I MEN TAL PRO G RAM
-33
Specimens were designed accord~g to the design provisions
presented in Chap. 2. Joint details were proportioned for a combination
of M and 95 per cent of V of the beam sectiono The shear force wasp p
obtained as the factored shear capacity of the maximum number of one
in. dianleter A490 bolts that could be used in the beam web~ This resulted
in a beam span of 3'-Srt. At the predicted plastic limit load, the bend-
ing moment was assumed to be carried by flanges due to strain~hardening
and the shear force was assumed to be resisted by the \veb attacmnent.
This assumption is examined considering the joint details used: (1)
bemu web connected. to column flange by groove weld, (2) beam web shear
plate fastened by high-strength bolts in round holes, and (3) beam web
shear plate fastened by high-strength bolts in slotted holes. Results
of these tests along with comparison with theory are presented in Chap, 5,
Table 1 sunwarizes test specimens included in this studYe
4.1 DESCRIPTION AND FABRICATION OF SPECIMENS
The connection specimens each consisted of a W27x94 beam
section and a W14x176 column section and represented the practical
interior beam-to-column connections in a multi-story frame.
The W27x94 beam was a plastic design section and also was
one of the economical shapes, being the lightest in weight in its
particular group as given in the Plastic Design Selection Table of
the AISC Manual. The \v14x176 column was the least colUmn size which did
not need horizontal stiffeners.
333.20 -34
A fully-welded connection C12 is shown in Fige 22. Beam
flanges and beam web ~vere connected to the column flanges by groove
welds. An erection plate was tack welded to the column flange, and
was used as the backing strip for the beam web groove weldo This
connection was used as a control test.
The joint details of specimen C2 are ShO\~1 in Fig~ 23. Beam
flanges were directly welded to the column flanges providing for plastic
moment capacity. A one-sided shear plate fastened with seven one in.
diameter A490-X bolts was used to resist vertical shear. The fillet
weld connecting the shear plate to the column flange was sized for
vertical shear only; the moment due to the eccentricity of the applied
load was neglectede The shear plate and beam web had round holes 1/16
inG larger than the nominal diameter of the bolt.
Specimen C3 is shown in Fig. 24. Its connection type is
similar to C2, the only difference being that the one-sided shear plate
of C3 had slotted holeso
The use of slotted holes is desirable to permit erection
adjustments, and also may better facilitate the assumed distribution
of shear and moment at the connections. Previous research has indicated
that slotted holes, placed perpendicular to the line of loading, did
not affect the strength of bearing-type joints (2). Based upon this
finding holes slotted normal to the line of loading may be used in
enclosed parts of statically loaded bearing-type shear connections
provided the width of the slot is not more than 1/16 in. greater than
-35
the bolt diameter and its length is not more than 2~ times the bolt
diameter (28)~ The dimensions of the slots in C3 conform to this
provisiono
A continuous bar with 5/16 in~ in thickness and having
a width equal to the length of the slot was attached on the side
of the slotted shear plateo (The addition of continuous bars for
single shear connections was approved by the Research Council on
Riveted and Bolted Structural Joints at its annual meeting on May 12,
1971,)
The slotted holes were formed by punching two adjacent holes
in the plate and then removing the metal bet~veen them. Round holes
in the beam webs of C2 and C3 were drilled, ~iliereas the round holes
in shear plates of C2 and in the continuous bar of C3 were punched.
The connection specimens were welded according to the AWS
Building Code (4). The welding process used for groove welds was
the innershield procedure; the electrodes were E70TG (flux cored arc
welding with no auxiliary gas shielding)o The types of filler metal
for beam flange groove welds in the flat position and beam web groove
welds in the vertical-up position were NR-311 and NR-202, respectivelyo
The electrodes for fillet welds were E7028. In dete~~ining the size
of fillet weld, the allowable shear stress used on the effective throat
was 21 ksi (1).
Nondestructive testing methods were employed to inspect the
welds before testing of the specimens. Groove welds were inspected
333.20 -36
by ultrasonic testing and fillet welds by magnetic particle~ Results
of weld inspection were evaluated according to the AWS Code, Rejected
welds were repaired and subsequently inspected prior to testing.
4 ~ 2 CALIBRATION. P.\.ND I~NSTAbMTIOJL9~-r ..j)01TS
Calibration and installation of high .... strength bolts \'lere
performed at Fritz Engineering Laboratory. The turn-of-nut method
was used. All A~·90 bolts had a hardened washer under the nut which
was turned in tightening. Nut rotation from the snug tight -condition
was 1/2 turn as required by the Specification (28). Since the bolt
length was rather short, being 2~ iUm for bolts of C2 and 2-3/4 in~
for bolts of C3, it was not feasible to perform torqued tension cali
bration by nleans of a conwercial bolt calibrator. Instead, the bolt
tensions were determined through the load~strain relationship of gaged
bolts.
The gaged bolts (shown in Fig. 25) were instrumented with
electrical resistance foil strain gages cemented to their shanks.
Flat areas 1/16 in. deep were milled into the shank under the bolt
head to provide a mounting surface for the gages. The gages were
placed on opposite sides of the shank parallel to the axis of the
bolt. The gage wires passed through two holes drilled through the
bolt head.
Tile gaged bolts ~vere calibrated in direct tension to establish
the relatiollship between the strain readings and the tens ion in the
bolt. It was discovered that ~ linear load-strain relationship existed
-37
as shown in Figo 26, This implies that the shanks of the 1 in.
diameter A490 bolts remained elastic into the range of bolt tension
achieved by the turn-of-nut method of installatione
The tension in A490 bolts induced by one~half turn of nut
from the snug position was 82 kips which was above the specified
proof load of 72.7 kips and the minimum fastener tension of 64 kips
as required by the Specification.
4.3 TEST SETUP
The test setup is shown in Fige 27. The axial load in the
column was applied by a 5,000,000 pound-capacity hydraulic universal
testing machine. The crosshead of the testing machine is shown. The
beams were supported by two pedestals resting on the floor. Rollers
were used to simulate simply supported end conditions. Because the
combination of the short span of th~ beam and the size of shapes
resulted in a compact setup, no lateral bracing was needed to provide
stability.
4.4 INSTRilllENTATION
Strain gages and dial deflection gages were used to measure
strain and displacements under load. Figure 28 shows a layout of
the instrumentation. Strain gages located at Sec. A-A provided in
formation for calculating the stress distribution at the beam-to-column
juncture shown in Figs. 9 and 10. The over-all deflection under the
column centerline and the lateral deflection of the column web in the
compression region were measured by dial gages. Dial gages for measurement
333.20
of the panel zone deformation were also mounted on posts tack welded
-38
normal to the column web. A wire was then stretched between the dial
gage and another post~ The panel zone deformation was the average
value of the movement of two posts on the opposite side of the column
4.5 MECHANICAl! PROPERTIES
The material used for wide-flange shapes was ASTI1 A572 Gre 55
steel. A detailed report of mechanical properties is presented in
Ref. 29. Two coupons were cut from the flanges and two from the webs
of each section. The results of tension tests given in Table 2 are
the mean values for webs, flanges and sections. Also included are the
standard deviation and the coefficient of variation to give a measure
of the dispersion associated with each mean. According to the mill
report, the yield strength a and tensile strength a for the W27x94y u
beam section were 60.3 ksi and 81.1 'ksi, respectively; those for the
W14x176 column section were 60.3 ksi and 84.8 ksi, respectively. The
slight discrepancy of these values from the results of laboratory tension
tests was due to the difference in testing speed as would be expected.
Tension tests were also performed on coupons taken from the
component plates. Due to the small quantity of material needed, it
was difficult· to acquire plates made of ASTIf A572 Gro 55 steel. A
substitute steel was used. The static yield stress level for the
material of the shear plates of C2 and C3 was 4~·.4 ksi which was lower
then the specified minimum yield stress of 55 ksi used in design.
TIIEORY
333.20
5$ COM PAR ISO N
i'l I T 1-1
o F T EST RESUIJT8
-39
The purpose of this chapter is to show that the actual
behavior of connections under test verifies the theoretical predic-
tions developed in Chap. 3. In addition, the design conditions in
Chap 0 2 are justified by experimental datao It is shown that the
plastic moment of the beam section can be supplied by flanges only,
and the shear force can be resisted by the beam web. An important
feature of the experiments is that the connections were subjected to
a very severe loading condition, a combinatton of plastic moment and
a shear force of 95 per cent of V being resisted by the joints. Itp
is demonstrated by tests that the proposed theory is valid for connec-
tions subjected to this severe loading condition.
5.1 LOAD-DEFLECTION CURVES
The load-deflection curve of a fully-welded" connection (C12)
is presented in Fig. 29. Also plotted in Figc 29 are the deflection
components predicted according to the proposed theory. In the elastic
ral1ge, the ben.ding monlentis resisted by the whole wide-flange section
up to a load of 652 kips corresponding to the yield moment M of they
beam sectiono Above this load, the bending moment is assumed to be
carried by flanges only due to strain-hardeninge It is assumed in
the theory that the sh~ar force is carried by the beam \veb. The
elastic shear deformation terminates at a load of 790 kips which is
tIle load that would produce shear yielding of the beam '\veb. The
effect of strain-hardening of the beam web in shear is considered in
333.20
computing the shear deformation beyond the elastic limit of 790 kips.
The third theoretical curve -~L\'i_ + ~2 + ~3) include.s the consideration
of the panel ZOlle defornlation (8ho\\111 diagranlmatically in. Fig ~ 17).
In the elastic range the deflection due. to flexure or shear
is about equal" In the f1intermediate" range, flexure and panel action
have the largest influence e In the following zone of larger plastic
deformation, the rate of increase in deformation is mainly due to the
shear effect and the panel action~
The ,test curve shovm in Fig. 29 is in good agreement with
the total predicted deflection including the effect of panel zone
deformation. Tile elastic stiffness ul1.der working load can be predicted
accurately. Above working load, deviation from elastic behavior was
noted. This is due to localized yielding in the panel zone "and at
the beam-to-column juncture. It was noted that in the column compres-
sian region, the yield pattern distr'iblltion along the toe of t11e fillet
was about 10 in. in length at a load of 620 kipse This agrees with
the assumption made in predicting the limit of elastic behavior of the
panel zone in Sec. 3.3.1. It was assumed that the elastic range
terminated at a load of PA
~ 635 kips which was calculated from an
effective width of (tb + Sk) = 10.747 in," The theoretical ultimate
load P corresponding to the pseudo-mechanism in the column flangesu
(Fig. 21(c» is 804 kips which is slightly lower than the actual
maximum load under test P of 838 kips. However, the theory ism
satisfactory (P Ip ~ \04).m u
333.20
For purpose of comparison the. load-deformation behavior of
the connection predicted by a finite element analysis is shown in
Figo 30 (33). The finite element analysis also accurately predicted
the elastic stiffness under working load. In the inelastic region
(up to 700 kips), the finite element prediction is very good~ The
-41
prediction is higher than test results beginning at a load of 700 kipso
This is due to the assumption made in the finite element analysis
that the connection was treated as a plane. stress problem. Only in-
plane deformation was considered e Actually the test curve in Fig. 30
(solid dots) shows that the column web in the compression region began
to deform laterally at this load. As load was increased, an excessive
lateral deformation was noted e In this load range, the prediction
by the finite element analysis is substantially higher than test results
as would be expected.
The prediction by current plastic analysis is also indicated
in Fige 30. The deflection at the predicted plastic limit load (6 ) wasp
calculated by assuming the connection as a cantilever fixed at the
column centerline.
Figure 31 shows the load-deflection curves of C2, C3 and G12.
Both C2 and C3 showed adequate elastic stiffness under working load.
The deviation of C2 and C3 from C12 was due to slip of the joints that
occurred above the working load. The A490 bolts eventually went into
bearing against the sides of the holes, supporting the shear load and
permitting the connections eventually to develop the predicted plastici
limit load P ~ The A490 bolts ~vere able to deform permitting thep
333.20 -42
complete redistribution of forces at maximum load o This observation
is confirmed by the deformation of the joint C3 at failure shown in
Fig. 32. Also in Fig. 32, one can see how the slots in the connection
plate permitted the beam web to move in flexure, the web holes moving
to the left at the top (tension) and to the right at the bottom (com
pression).
TI~e photograph in Figo 32 combined with that of Fig. 40
represents a notable picture of redistribution of stress and what might
be termed "balanced failure". Flanges are fully yielded artd compression
local buckling ~as occurred. Shear yield has progressed to the point
of tension field development. Both the compression and tension zones
of the column web are yielded. Plastic hinges have £orm~d in both
column flanges. The beam web shear plate is fully yielded. Subsequent
fracture occurred at one beam tension flange. TIle ollly missing "event"
is bol t shear' failure .... -which SllO\vS the merit of the higher safety
factor in shear. A truly remarkable example of redistribution and a
confirnlation of design recornmendation, all "at the critical" conditions.
It was demonstrated from tests that connections having
slotted holes (C3) and round holes (C2) exhibited similar over-all
behavior (Fig. 31). C2 and C3 reached the predicted plastic limit load
at about the same deflection. The presence of the slots in C3 may
account for the somewhat increased deformation of this joint beyond
maxinlum load (Fig. 31) than C2. Also they would permit a redistribu
tion of stress from beam web to flange which could possibly account
for the critical flan.ge failure.-· The round holes in C2 \\7ould transmit
333.20 -43
more flexure through the web--and it is noted that it was in C2 that
the column web fracture developed.
5.2 PM~EL ZONE DEFOID1AT!ON
The proposed theory considers the deformation of the panel
zone as a useful source of inelastic deformation of connections. The
panel zone deformation has been neglected in current plastic analysis.
Figure 33 shows the theoretical and experimental panel zone
deformation in the compression region of C12. The load causing yielding
in an effective length of (tb
+ 5k) of the column web is 635 kips which
is the limit of the elastic range. Below this load the elastic
response of the panel zone is predicted quite accurately. In the
inelastic range the prediction is slightly h~her than the test results.
This is ascribed to the fixed-end boundary conditions assumed for the
continuous beam model shown in Fig. 20(b). However, the prediction
gives a good description of the inelastic behavior. A comparison of
the experimental panel zone deformation in the tension region of C2
with the theoretical prediction is sho"WU ill. Fig. 34. Aga-in, a good
correlation was obtained. (The dial gage was removed in the tension
region prior to failure as a precaution.)
5 • 3 MAXIMUM LOAD
A table containing the experimental and predicted loads is
given as Table 3. The experimental maxim-urn load P and the maximumm
deflection prior to failure 6 are indicated in columns 2 and 3.m
Reference or comparison loads are (1) the predicted plastic limit load
333.20 -44
P > (2) the plastic limit load modified to include the effect of shearp
force P ,and (3) the plastic limit load P assuming that the beamps pr
web does not act in flexure. Also included is the predicted deflection
at the plastic limit load 6 .p
The ratios of maximum load to reference loads ~i~en in the
table show the increased load-carrying capacity over the prediction
from simplified plastic theory. The connections C2, C3 and C12
attai.ned a maximum load of about 10 per cent higher than the predicted
plastic limit load as indicated by the ratio P Ip in column 8.m p
The deformation capacity of a connection is usually indicated
by the ratio of total deflection to the predicted deflection at plastic
limit load 6 /6 which is defined as the ductility factor ~e Them p
ductility factors for C2, C3 and C12 are given in column 11 of Table 3.
The deformation capacities of these connections are adequate for design.
5.4 FAILURE MODE
Table 4 presents the desciiptions of failure of connections.
C12 is a fully·~welded connection. The cause for unloading was buckling
of the column web in the compression region. Testing was concluded
due to a combination of excessive column web deformation in the
compression region and fracture at the tension flange groove weld
(Fig. ·35) and along the beam web groove weld (Fig. 36) which occurred
simultaneously. Fracture occurred by ripping out of column flange
material around the weld, and not fracture of the actual weld itself.
Figure 37 shows the panel zone of C12 after testing. A detailed report
of specimen C12 is given in Ref. 30,
C2 is a flange-welded web-bolted connection having round
holes in web shear plates. Failure was due to tearing of the column
web along the ~veb-to-flange juncture as Sh0W11 in Fig. 38.
C3 is a flange-welded web-bolted connection having slotted
-45
holes in web shear plates 0 Unloading was initiated by local buckling
of the compression flange of the beam. Testing was terminated \~1en
fracture occurred at the heat-affected zone of the groove weld at
the tension flange shown in Fig. 39. The panel zone and joints of
C3 after testing are shown in Fig. 40.
It was demonstrated from tests that the flanges were able to
strain harden sufficiently to transmit the full plastic moment of the
beam section even though the beam web connection was required insofar
as flexure was concerned. In Fig. 31 P is the plastic limit loadpr
counting the flanges only; P corresponds to the full section strength.p
Quite evidently both connections C2 and C3 were able to strain harden
sufficiently to accommodate this 30 per cent difference under conditions
that involved full-yield shear development of the web.
The test results presented in this chapter have verified
the predictions of the proposed theory developed in Chap. 3 and also
have confirmed the design provisions given in Chap. 2.
333.:20
6. SUM1'IARY AND CON C L U S ION S
Steel framing costs can be reduced if proper attention is
given to moment~resisting beam-to-colum~ connections. Realistic design
rules for connections should consider not only strength and rigidity
but also economical fabrication and erection.
In this study, a new theory is developed to an~lyze connections
that are subjected to severe loadi.ng conditions. It is assumed that
the bending moment exceeding the yield moment of a beam section is
carried by flanges due .to strain-hardening, and the shear force·is
resisted by the web. The panel zone deformation is also considered
in the analysis. In the elastic range, the panel zone deformation is
predicted by considering column flanges as being supported by a system
of springs. In the inelastic range, the deflection is calculated by
treating the column flanges as continuous beams supported by the
remaining unyielded portion. of the column. The subsequent load-defor
mation relationship of the panel zone is analyzed by considering the
formation of plastic hinges at supports and at ioad points of column
flanges.
The experimental program consiste~ of full-size connection
specimens fabricated from ASTM A572 Gr. 55 steel. A490 bolts were used
to fasten the one-sided web shear plates that \Vere designed as bearing
type joints having round ·holes and slotted holes. These connections
were desigrled for all rlat-the-critical" conditions.. Joint details were
proportioned for a combination of plastic moment and 95 per cent of Vp
of the beam section.
333.20
On the basis of the results in this study, the following
conclusions have been reached e
1. The current plastic analysis is satisfactory in predicting
-47
the behavior of beams and connections tha~ are subjected to
a shear force at the predicted plastic limit load of not more
than 60 per cent of V . If the shear force is approximatelyp
equal to V , the proposed theory may be used.p
2. The bending mode of panel zone deformation can be predicted
by the proposed theory. (Fig. 17)
3. The flanges are able to develop the full plastic moment of
the wide-flange shape by strain-hardening.
4. The shear force may be resisted by web attachments fastened
by welds or bolts.
5. The proposed higher bolt stress (40 ksi for A490) obtained
in Refs. 16 and 17 is confirmed in beam-to-colufun connections
under critical loading conditions~
60 Slotted holes may be used in one-sided shear plates that are
designed as bearing-type joints.
7. The proposed bearing stress for bearing-type connections
developed in Ref. 17 is confirmed in beam-to-column connec-
tiona under critical loading conditions. (Fig. 2)
8. The proposed interaction equation developed in Ref. 11 based
upon simulated tests concerning the strength and stability
of the column web in the compression region is applicable in
full-size connections 0 (Eq. 1.5)
9. Column web stiffener requirements developed for A36 steel
333.20 -48
are applicable for higher yield levels (up to 55 ksi).
10. Fillet welds connecting a shear plate to the column flange
may be sized for vertical shear only; the moment due to the
eccentricity of the applied load may be neglected.
11. Welds approved by ultrasonic inspection were satisfactory.
A careful weld inspection during fabrication was necessary
to ensure the adequate performance of connections.
333 e 20 -49
7. ACIZNOWT-JEDG1-fEl'1TS
This study covers a part of the research project "Beam-to
Column Connections fT which is sponsored jointly by the American Iron
and Steel Institute and the Welding Research Council. The authors are
thankful for their financial support and the technical assistance
provided by the 1~C Task Group, of which Mr. J. A. Gilligan is Chair-
nlan.
The work was carried out at the Fritz Engineering Laboratory,
Department of Civil Engineering, Lehigh University. Dr. L. S. Beedle
is Director of the Laboratory and - Dr. D D A'. Van.Horn is Chairman of
the Departmento
The authors are especially grateful to Dr. J. WD Fisher,
Messrs. J~ A. Gilligan, O. W. Blodgett, C. F. Diefenderfer, W. E.
Edwards and C. L. Kreidler for their valuable suggestions and assis
tance in the fabrication of the specimens, Messrs. J. E. Regec,
J. K. Orben and M. V. Toprani assisted in testing and reduction of
data.
Thanlcs are also due }fr. K e R. Harpel and the laboratory
technicians for their help in preparing the specimens for testing,
and to Mr. R. Sopko for the photography. The manuscript was reviewed
by Dr. G. ·C. Driscoll, Jr. and typed by Miss S. Matlock. The drawings
were prepared by Mr. J. Gera, Their help is appreciated •.
8 • N 0 1'1 ENe L A T U R E'
Af
Area of beam flange
A Area of beam webw
b Width of beam flange
bf
Width of column flange
C1
Ratio of beam flange yield stress to column yield stress
D Nominal bolt diameter
db Depth of beam
d Column web depth clear of filletsc
df
Distance between centers of two flanges
d Web depth of wide-flange shapew
E Young's modulus of elasticity
E Strain-hardening modulusst
e End distance
F Specified minimum yield s~ressy
G Modulus of elasticity in shear
Gst
Strain-hardenirig modulus of elasticity in shear
I Moment of inertia
If Moment of inertia of column flange
k Distance from outer face of column' flange to web toe of fillet
L Beam span
M Bending moment
M Moment at which yielding first occurs in flexurey
M Plastic momentp
P Applied column load
P Maximum load of a connection under testm
pp
ppr
pps
pu
pw
T
Tcr
t
tw
v
vp
vu
zx
y
1:1m
-51
Plastic limit load
Plastic limit load assuming the area of beam web is zero
Plastic limit load modified to include the effect of shear force
Theoretical ultimate load
Working load, P ~ P /1.7Til P
Beam flange force
Beam flange force causing the buckling of column web in thecompression region
Thickness
Thickness of beam flange
Thickness or column flange
Thic1<:ness of web
Shear force
Shear force that produces full yielding of web
Maximum shear force under test
Plastic modulus
S11ear strain
. ~"-:9-
Shear strain at onset of ~train-har"derii11g
Deflection"
Maximum deflection
Deflection at plastic limit load
Deflection of beam due to bending
Deflection of beam due to shear
Deflection due to rigid body motion of beam induced by thepanel zone deformation
Panel zone deformation
Strain
est Strain at ons~t of strain-hardening
A factor
-52
Ductility factor, ~
p Spring constant
cr Stress
6 /6m p
a Critical buckling stresscr
o Bearing pressurep
o Tensile strengthu
cr Yield-stress levely
~ Shear stress
r Shear yield stressy
~ Curvature
ep Curvature at strain-hardeningst
333.20 -53
TABLE 1 TEST SPECIMENS
-rrest Beam Beanl :Ho les Bolts Bolt Column
Flanges \~ebs Design(1) (2) (3) (4) (5) (6) (7)
- .-
C2 Welded Bolted Round A490 Bearin.g (40 ksi) Unstiffened
C3 \~elded Bolted Slotted A490 Bearing (~.O ksi) Ull-stiffened
C12 Welded ~\Telded -- ..- -- Unstiffene.d
333*20
TABLE 2 MECHM~ICAL PROPERTIES OF SECTIONS
-54
.,
Static Ul_~imate: Fracture· Elop.- Reduc,tion~~:~... . \~,~ ~'4"."
Yield Stress Stress . g'ation ofStress AreaLevel (%) (%)
a (ksi) (J (1<8 i) crf (1<8 i)ys tl
(1) (2) (3) (4) (5 ) (6)
Web Mean 55.3 78 .. 7 60.8 24~4 51 ~ 1
Flange }lean 54.5 79.3 58~1 25.9 5609
Total Mean 54.9 79.0 59.5 25l>1 53.9
StalldardDeviation 2.75 3.27 4.27 If84 4,55
Coefficientof
Variation(%) 5.0 4.1 7.2 7.3 8.4
Yield Modulus of Strain at StrainStrain. Elasticity Strain Hardening 0- €u st
e E I-Iardening ~1odulus er ey ys y( . / . \ (Its i) e E (1(8 i)In. l.nll /
st st '(in./iD.• )
(7) (8) (9) (10) (11) (12)
Web Mean 0.0019 29,730 0.0165 564 1.42 8.68
Flange Mean 0.0019 29,420 0.0136 599 1.46 7.16
Total 1-1ean 0.0019 29,570 0.0150 581 1.44 7.89
StandardDeviation 0.0001 993 OeOO24 54.9 0.049 1.12
Coeffieientof
Variat~on(%) 5.3 3.4 16.0 9.4 3 .4~ 14.2
333.20 -55
TABLE 3 TES T RESULTS
Test Experinlental Reference P P P 6m nl m ill--
P 6 p p p ~ p p p ~m m p ps pr p p ps pr p
(1) (2) (3) (4) (5 ) (6) (7) (8) (9) (10) (11)
C2 826 2.67 748 590 522 0,276 ItlO It40 1.58 9.71--'
C3 81-8 41126 748 590 522 0.276 1.09 1,39 1,57 15.4·
C12 838 3.63 7Lf'8 590 522 0.276 1.12 l,L,.2 1.61 13~2
~-
a. All loads (P) listed are column loads in kips; all deflections(6) are in inches-.
TABLE 4 DESCRIPTION OF FAILURE
Test Description of Final Failure Mode
C2 Tearing of column web along web-to-flange juncture.
C3 Fracture occurring at the· heat-affected zone of the tension
flange groove weld.
C12 Fratture at tension flange groove weld; excessive column web
~eformation in the compression region.
333~20
T T
-56
M v v M
T
AI
T'
Fig. 1 Interior Beam-to-Column Connection under Symmetrical Loads
l.UWVJ.No
oo
o Failure
6. Beam Web of C I 00
~ Shear Plates of Cf, C2 ~ C3
o Beam \Veb of C2 ~ C3CT
p =1.5o-u
,~
~,..
o 0 00'*",.
v 0,,"e P ;-=0.5+1.43-- 0 ;,0"'0o cru oo~,
~~~~fr\\:.000 cP 0
~~O "
~ ,..'" 0 0~.. e ~~" 0 00 -=O.5+0.715-
P--
,.,../ 0 0 D vu
~~
DesignRegion
2
3
4
eo
_00
-leLo . I
o-p()u
2 ~~
Fig. 2 Design Recommendation for Bearing Stress for Allowable Stress Design (17) JIn-...I
333.20 -58
654
p
3
L1"(in.)
2
Strain Hardening conSidered\_
~-~-~---£; ..o::-\=-_ __ y ~
Stroi'n He rden ing Neg lected
10
o
20
50
40-'
30
60
P(k)
Fig. 3 Load-Midspan Deflection Curve of a W14x38 Beam(A7 Steel) (12)
333.20
1.0
0.5
~Pw
-59
W2L1rX 61 Bearll\1\/14 >t 136 ColumnA5~72 Gr. 55
p
=Y- ~
6I L~5 6
Fig. 4 Load-Deflection Curve of Specimen Cll-
333.20 -60
Pig~-5, Specimen ell after Testing
333.20 .... 61
WIL1~ x~74 Bea rnW10 x 60 ColurrlnA5-r2 Gr. 55
p
'#=L=4="""=1I=HL:=:U====;;
~~~~
~
43o
1.0
0.5
Fig. 6 Load-Defl~ction Curves of Specimens Cl and CIG
333.20 -62
1000-
\!V27x 9,4 Beorn
VV ILlx 176 ColuIT1nA572 Gr. 55
. /77
p~R =4·40,w
CI2
~- -~------_._-------
Pp :: 748
1~=4cl' ~
~-+---.a-..--+~}--l-__t L_-..-_l (_o 234
6. (in.)
200
800-
400
600
Fig. 7 Load-Deflection Curve of Specimen C12
333.20 -63
. - -- -- Tl180retical Pred iction
333.20
P =150 kilJS0'-\
\\\&~
\
\\
\
\
\\
Io
o-x (l\si)
-6LI-
p:: 300- kips€t--~
\ ,\G>~--
"\~~
\\
......t-J_","",,--1_~I'~~j__~I l-30 0 30
(Tx (I<si)P=450 kips
(All Flollge Stresses are
Averaged Over the Flange)
t----- _ .. , ,..
""""-_.-J:'---.--e9 .~L--L_J_L ",,-,,-I~I~_~_J ~I....
-40 -20 0 20 40O"x O~sj)
Fig. 9 .Normal Stress Distribution Along,Beam-to-Column Juncturein Fig. 28 Section A-A
LVWW
No
. YieldedBetvJeen450 and 475 k
TensionCompression
o 75- 300 225 15P=450 .;)75 "
'" ""'... ,"" " \ \ \ ~ N'"", ' .
60~ '"",' . d d Betvveen-- .:~~ I Ytef e----- ~~,,\\ P d 560 k--~~ ..,'..\ 40 an......-. -"':';"">i~l 5 I
'!~~'0Y· Ided Between \\ 'l\:~, ..................e \\\'."".. __
~ \ \"~'" 52°1Or RI \ ' ..... ~'-..... I\ , .............. IIn. \ '\ '"
3 r I !\ \ \ '... 450 \i '\ \ ... 375
6
L
Ip =75 150 225 3,0 I II I I 40o 20
CJ (ksi)X
Yielded Between520 and 540k
Note: All' Flange Points Represent Average Flange Stress
Fig. 10 Normal Stress Distribution Along Beam-to-Column Juncture in Fig. 28.Section A-A
I
0'\l.n
-66
(a) Loading
(b) Bending
(c) Shear
(d) Panel ZoneDeformation
Fig. 11 Connection Deflection Components
333.20
80-
70
Average Values
E =29.6 x 103 I<si
(J"y =54.9 I\si
€y =0.19 X 10-2 in.! in.
-67
Est =0.58 X 103 ksi
I k 10-2 ' I'Est:= .:) X In. I,n.
60
en~ 50
b40en
(j)
~ 30I({')
10
o 0.2 0.5 1.0
STRAIN E (in./in.)·
1.5
do-=E tdE S
2.0 x10-2
Fig. 12 Idealized Stress-Strain Curve of A572 Gr. 55 Steel
333.20
W27 X 9£.+
/45~72 Gr. 55
--Mp
1.0
MMy
- 68
0.5 -I-
Fig. 13 Nondimensional Moment-Curvature Relationship
333.20
W2-(x 9LJ· Beam\/V I 4x r76 ColurnnA572 Gr. 55
1000-
800 (F~e)()ure "\ ~~'- - __ '.• __ul \ ~.,,,,,,,,,,._ ..,-.- ..--- ..
~'t~~.-.- --Pp .,,p ~ "
; ~ ~~
600 -- I Parte) Zone:: (L\1+L\2+L\3)I
: -Pw400 1
II 'I
'1II
200 il-
I I
p( 1< )
o 0.5 1.0
L\ (in,)'
1.5
Fig. 14 Predicted Deflection Components
333.20
40
G=II.4x I03ksi
Ty ::: 31. 7 ksi
Yy ::: 0.28 X 10-2 rad
-70
Gst ::: 0.19 x 103 ksi
1St =2.55 X 10-2 rad
~... ~
30 - IIT I I
I I(l{si) I I
I I20 I I
I II II II I
10 I II II IX ~I Yy I sfI I1 I
0 2 3 4 X 10-2
Y (rod.)
Fig. 15 Shear Stress-Strain Curve of A572 Gr. 55 Steel
333.20
\' Shear Buckling
-71
2.0
1.0
Test Values
0 CI2 ~[ ]r]dbA C2G C3 1- L ~
--1 f I L0 20 40 60 80
dvv ~tv, .
Fig. 16 Comparison of Test Values with Theoretical Predictions ofInelastic Shear Buckling of Beam Web
333.20
p
p:'g
82
/
1
Q .'
2
-72
o
Fig. 17 Prediction of Panel Zone Deformation
7/7777
333.20
(a)
-73
y
(b)
y
(c)
Fig., 18 Connection Panel Zone Modelled by an Elastic Foundation
333~20
1.5-
\\\
I.Qt--- ..-----..-(i.~--~\
WI4Xl76J
-74
o 0.5 1.0 1.5
Fig. 19 Comparison of Test Value with Theoretical Prediction ofBuckling of Column Web
-75
T=~-.".".,....,..=-~._.
"'--r-J['?:-I.;..:':;;'~.1.a
A
TRT777l~~.
~_"""'--~E~····~~~ / tb
+71\ ,
v /<1,,£--,/
YieldedZone
~77h/ J>
T .t lr ·'T~":~--= ~t b+7k-J::- .
Yielded - V.LJ_~"'"'Zone WebBucl<led
(0)
·T
(b)
Fig. 20 Column Flanges Modelled by a Continuous Beam
333.20
(0)
T
III
T I I~-=t.._.---.~" *--~l
"I
(c)
(b)
-76
Fig. 21 Continuous Beam Models and Mechanism for Ultimate Load·
333.20 -77
1Sym.
A
-- ----\-
Vv 14 x 176(Fy :: 55 1\ si)
Elevation
--3/-4
..........~-8-,0-,----«r y p.
30 0
10 Y2 II
3/8" X 4" x 23 Y'2 II
Erection ft (A~36)
2 _3/411 ¢ A 307 Erection
Bolts in 13/IGIl Holes
\V27 x 94!-, fJ" I" II (F\I =55 1< s i )+==-=r~~ J ~
~
~3/811 X I" X 12"
Backing Strip (A36)
(Ty p. )
d-26U II- '8
A
Syrn. j
3 Tacl{ Welds to Colurnn
Section A-A
Scale:l-L---1o 5 lOin.
Fig. 22 Joint Details of Specimen C12
333.20
Syrn.
1/ 1I3.12
3/e 2lV2 t~~l
WI4xl76(F =551,si)y
:3 III 1'4
13/4
11
Elevation
31 10-<0Typ.I~ 3/8
30° ~(I
,--=i=-~W2~?x94
(Fy=551\si) d
3@311=9
ft2
t--I II. I II r IIY2 X 5/4 )( 21 Y2
Shear Plate(Fy=55ksi)
II fA7-) 't' A490-)( Bolts
in I VIGil Round Ho les
3/811
X III X 12 11
BacJ<ing Strip (A36)
(Typ.)
-78
7, 11d= 26 Ya
Sym.
Plan ViewScale:
Io 5
JlOin.
Fig. 23 Joint Details of Specimen C2
-79
7-111 ¢ A490-X Bolts
in Slotted Holes
1 ~131 II
~ 4 VV27x94
( Fy:: 55ksi) d
3@3 11 ::9 H 2 7. IId::26~8
------"~~Ck
3@3"::9 11
II II J 111/2 X 6 X 21Y'2Shear Plate(F =55}{si)y
3 II-I /4 !
31 IIR= 14
WI4x 176( Fy :: 55 I<si)
h II I II I II
°/16 X 2 Y2 X21 Y2• (I ItPlate v/ltrr Yl6
Round Holes(A36)
Sym.
Elevation3/a
1iX I" x 12 II
Bacl,ing Strip (A36)
( Typ.)
Syrn. ___lIYI'~IiII."""""" ~ _
.....-...~~~~-----
Pion View
o 5
Scale:I ,
Slot Detail
I ~ IIt- 16 _I
17 lIy '0~~61R= "32 1_ 2 \12 " -I
Fig. 24 Joint Details of Specimen C3
lOin.
333.20 -80
Fig. 25 Gaged Bolts (In A490) .
333,20
//. /1/ -
1/2 Turn
20
____-l L Io 123
S-fRAIN (in. lin.)
Fig. 26 Calibration of Gaged Bolts
-81
ilt
I
333.20 -82
Fig. 27 Test Setup
333 5 20 -83
ette
n Gages
Posts
Io
I ~=-t
GiZ'u. SR-4 Strai
~ Strain Ros,)$1
I
(2) Dial Gages
€) Dial Gage
I
rA
~ g G -~""~,
csm N
~ 0
~ - 1- ~ p - '\~ ~
IQera
mD R
@0Vbl1k$
I LA
U211
Scale:
L t
0 I
B i"n.
Fig. 28 Instrumentation of Test Specimen C12
VV27x 94 BearnW J 4 x 176 Colufl1nA572 Gr. 55
1000
-8L~
800
600
o 3
p
4·
Fig. 29 Comparison of Predicted Deflection Components withLoad-Deflection Curve of Specimen C12
-85 .
W27x 94 Beam
WJ4xl76 ColumnA572 Gr. 55
p
II
1~=4LI'6
~ P =440w
.~---------i-7-\-~-l_---&....-----..l._~_Lo 2 3 4 .
6. (in.)
400~ ~
Fig. 30 Comparison of Proposed Theory with Other M~thods of Analysis
333~20
W27 x 94 8eamW14 x 176 ColurnnA572 Gr. 55
~86
1.0
0.5
o
Fig. 31 Load-Deflection Curves of Specimens C2, C3 and C12
333.20 -87
,Fig. 32 Deformation at Failure of a Joint Having Slotted Holesin Web Shear Plate (C3)
333.20
1000-
800,
8
-88
o 0.5
8 (in.)
1.0
Fig. 33 Panel Zone Deformation in the Compression Region ofSpec.imen C12
333.20
~ p
-89
p( k )
800
600
200
o
Theory, .,..- - \. ---,...,.
~Pp
C 2
8
0.58 (in.)
1.0
Fig. 34 Panel Zone Deformation in the Tension Region ofSpecimen C2
333.20 -90
Fig. 35 Fracture of Weld -at Tension Flange of Specimen e12
333.20 -91
Fig. 36 Fracture along Beam Web Groove Weld of Specimen>C12
333.20 -92
Fig. 37 Panel Zotte of Specimen e12 After Testing
333.20 -93
Fig. 38 Tearing' of Column Web Along Web-to-F'lange Junctureof Specimen C2
333.20
Fig. 39 Fracture at the Heat-Affected Zone of the Groove Weldat the Tension Flange of Specimen C3
-94
333.20 -95
IJ1
!1
Fig. 40 Panel Zone and Joints of Specimen C3 After Testing
333~20 -96
10. R E FER ENe E S
1. AISCMANUAL OF STEEL CONSTRUCTION, SPECIFICATION FOR THE DESIGN,
FABRICATION Al\TD ERECTION OF STRUCTURAL STEEL FOR B1JILDINGS, 7th ed., American Institute of Steel Construction,1970.
2. Allan, R. N. and Fisher, J. WoBOLTED JOINTS WTTH OVERSIZE OR SLOTTED HOLES, Journal of the
Structural Division, ASeE, Vol. 94, No. ST9, Proe. Paper6113, September 1968, p. 2061.
3. ASCE-WRCPLASTIC DESIGN IN srrEEL, ASeE MANUAL 41, 2nd ed., The Welding
Researcll Council and TheAm~ricat1 Societ)T of Civil Engineers,1971.
4. AWSCODE FOR 1~LDING IN BUILDING CONSTRUCTION, AWS D1.0-69, 9th
ed., American Welding Society, 1969.
5. Basler, K.STRENGTH OF PLATE GIRDERS IN SHEAR, Journal of the Structural
Division, ASeE, Vol. 87, No, ST7, Froe. Paper 2967, October1961, p. 151. Also, Trans. ASCE, Vol. 128, Part II, 1963,p. 683.
6. Beedle, L. S.PLASTIC DESIGN OF STEEL FRAMES, John Wiley and Sons, Inc.,
New York, 1958.
7. Beedle, L. S. and Christopher, R.TESTS OF STEEL MOMENT CONNECT'IONS, AISC En.gineering Journal J
Vol. 1, No. ~., October 1964, p. 116.
8. Beedle, L. S., Lu, L. Wo and Lim, L. CoRECENT DEVELOPMENTS IN PLASTIC DESIGN PRACTICE, Journal of
the Structural Division, ASCE, Vol. 95, No. 8T9, Froe. Paper6781, September 1969, p. 1911.
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