behavior steel beam·to·column connectionsdigital.lib.lehigh.edu/fritz/pdf/333_20.pdf · gr 5 55...

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by Joseph S. Huang Wai F. Chen- Lynn s. Beam-fa-Column ·,Connections BEHAVIOR AND DESIGN OF STEEL BEAM· TO·COLUMN MOMENT CONNECTIONS . - Fritz Engineering Laboratory R'eportNo. 3'33.20

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Page 1: BEHAVIOR STEEL BEAM·TO·COLUMN CONNECTIONSdigital.lib.lehigh.edu/fritz/pdf/333_20.pdf · Gr 5 55 steel, with fully-welded or with bolted web attachments having ... bolted connections

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

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;.,

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

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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

i

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333.20

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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333.20

Table

1

2

3

4

LIST OF TABLES...--.-.---.• ~~~*,........",.--..~~~--

Test Specimens

Mechanical Properties ~f Sections

Test Results

Descr~ption of Failure

iii

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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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333.20

22

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31

32

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34

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38

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40

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

v

77

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333 v 20

ABSTRACT--~---,~~~""~--

This investigation is concerned. with bea~~t6-column mome~t

-1

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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333.20 -2

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.

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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~

-3

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

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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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333~20 -5

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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333~20 -6

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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-7

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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333.20 -8

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

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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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-10

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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-11

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)?

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333 .. 20

2. D E S I G NCO N D I T ION S~--

-12

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.

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,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.

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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

-14·

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

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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.

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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)

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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.

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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.

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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

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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.

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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)

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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)

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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

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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,

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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.

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-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)

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-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 )

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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)

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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):

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-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

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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

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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.

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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.

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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

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-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

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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

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-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

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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.

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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

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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

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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

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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

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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

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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

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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.

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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.

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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

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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.

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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 •.

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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

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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

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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

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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

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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

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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.

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333~20

T T

-56

M v v M

T

AI

T'

Fig. 1 Interior Beam-to-Column Connection under Symmetrical Loads

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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

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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)

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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-

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333.20 -60

Pig~-5, Specimen ell after Testing

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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

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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

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333.20 -63

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. - -- -- 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

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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

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-66

(a) Loading

(b) Bending

(c) Shear

(d) Panel ZoneDeformation

Fig. 11 Connection Deflection Components

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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

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333.20

W27 X 9£.+

/45~72 Gr. 55

--Mp

1.0

MMy

- 68

0.5 -I-

Fig. 13 Nondimensional Moment-Curvature Relationship

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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

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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

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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

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333.20

p

p:'g

82

/

1

Q .'

2

-72

o

Fig. 17 Prediction of Panel Zone Deformation

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7/7777

333.20

(a)

-73

y

(b)

y

(c)

Fig., 18 Connection Panel Zone Modelled by an Elastic Foundation

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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

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-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

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333.20

(0)

T

III

T I I~-=t.._.---.~" *--~l

"I

(c)

(b)

-76

Fig. 21 Continuous Beam Models and Mechanism for Ultimate Load·

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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

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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

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-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.

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333.20 -80

Fig. 25 Gaged Bolts (In A490) .

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333,20

//. /1/ -

1/2 Turn

20

____-l L Io 123

S-fRAIN (in. lin.)

Fig. 26 Calibration of Gaged Bolts

-81

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ilt

I

333.20 -82

Fig. 27 Test Setup

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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

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VV27x 94 BearnW J 4 x 176 Colufl1nA572 Gr. 55

1000

-8L~

800

600

o 3

p

Fig. 29 Comparison of Predicted Deflection Components withLoad-Deflection Curve of Specimen C12

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-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

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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

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333.20 -87

,Fig. 32 Deformation at Failure of a Joint Having Slotted Holesin Web Shear Plate (C3)

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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

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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

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333.20 -90

Fig. 35 Fracture of Weld -at Tension Flange of Specimen e12

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333.20 -91

Fig. 36 Fracture along Beam Web Groove Weld of Specimen>C12

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333.20 -92

Fig. 37 Panel Zotte of Specimen e12 After Testing

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333.20 -93

Fig. 38 Tearing' of Column Web Along Web-to-F'lange Junctureof Specimen C2

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333.20

Fig. 39 Fracture at the Heat-Affected Zone of the Groove Weldat the Tension Flange of Specimen C3

-94

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333.20 -95

IJ1

!1

Fig. 40 Panel Zone and Joints of Specimen C3 After Testing

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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.

9. Bertero, V. V., Popov, E, P. and Krawink1er, H.BEAM-COLUMN SUBASSEMBLAGES UNDER REPEATED LOADING, Journal of

the Structural Division, ASCE, Vol. 98, No~ 8T5, Proe. Paper8915, May 1972, p. 1137.

10. Chen, W. F. and Oppenheim, I. J.WEB BUCKLING STRENGTH OF BEAM-TO-COL~rn CONNECTIONS, Fritz

Laboratory Report 333.10, Lehigh University, Bethlehem,Pa., September 1970.

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333.20

11. Chen, w~ F. and Newlin, D. E.COLUMN WEB STRENGTII IN STEEL BEM1-TO-COLUMN CONNECTIONS,

MeetingPreprint 152L~, ASCE Annual and National Environ­mental Engineering Meeting, St. Louis, Missouri, Octoberl8-~2, 1971.

-97

12. Driscoll, G. C., Jr. and Beedle, L. S.THE PLASTIC BEHAVIOR OF STRUCTURAL MEMBERS AND FRAMES, Welding

Journal, Vol. 36, NOe 6, June 1957, po 275-s.

13. Fielding, D. J.and Huang, J. S.SHEAR IN STEEL BEAM-TO-COLUMN COm~ECTIO~S, Welding Journal,

Vol. 50, No.7, July 1971, p. 313-8.

14. Fielding, D. J., Chen, W. F. and Beedle, L. S.FRAME ANALYSIS AND CONNECTION SHEAR DEFORMATION, Fritz Labora­

tory Report 333.16, Lehigh University, Bethlehem, Pa.,Jal1.uary 1972.

15. Fielding, D. J. and Chen, W. F.STEEL FRAVill ANALYSIS AND C01~ECTION SHEAR DEFORMATION, Journal

of the Structural Division, ASeE, Vol. 99, No. STI, Proe.Paper 9481, January 1973, p.l.

16. Fisher, J. W. and Beedle, L. S.CRITERIA FOR DESIGN~NG BEARING-TYPE BOLTED JOINTS, Journal of

the Structural Division, ASCE, Vol. 91, No. STS, Froe. Paper4511, October 1965, p. 129.

17. Fisher, J. W. and Struik, J. H.,A. " .GUIDE TO DESIGN CRITERIA FOR BOLTED AND RIVETED :JOINTS, Fritz

Laboratory, Lehigh University, Bethlehe~, Pa~', ·(to bepublished by John Wiley and Sons, i973).

18. Gilligan, J. A. and Chen, W. "F.CONNECTIONS, State-of-Art Report No.5, Conference Preprints,

Vol. 11-15, ASCE-IABS'E International Conference on Planningand Design of Tall Buildings; Lehigh University, Bethlehem,Pa., August 21-26, 1972.

19. Graham, J$ D., Sherbourne, A. N., Khabbaz, R. N., and Jensen, C. D.WELDED INTERIOR BEAM-TO-COLUMN CONNECTIONS, Bulletin 63,

Weldi.ng Research Council, Ne\,v Yorl<:, August ~~,-60'. Also,American Institute of Steel Construction~ 1959.

20. Hall, W. J. and Ne\vmark, N. M.SHEAR DEFLECTION OF WIDE-FLANGE STEEL BE~~S IN THE PLASTIC RANGE,

Trans. ASCE, Vol. 122, Paper No-. 2878, 1957, p. 666.

21. Hetenyi, M.BEAMS ON ELASTIC FO~~ATION, The University of Michigan Press,

Ann Arbor, Michigan, 19460

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333.20 -98

22. Huang, J. S., Chen, W. F. and Regec, J. E.TEST PROGRAM OF 'STEEL BEM1-TO-COLUMN CONNECTIONS, Fritz Labora­

tory Report 333.15, Lehigh University, Bethlehem, Pa., July1971.

23. Huang, J. S. and Chen, We FeSTEEL BEAM-TO-COLUMN MOMENT CONNECTIONS, Meeting Preprint 1920,

ASCE National Structural Engineering Meeting, San Francisco,California, April 9-13, '1973.

24. Kulak., G. L o and Fisher', J.W. , .-.A514 STEEL JOINTS FASTENED BY A490 BOLT$, Journ?-,J.- o'f'·' the

Structural Division, ASCE, Vol. 94, No. STlO, P~bc.·Paper

6163, October 1968, p. 2303.

25. Lay, M. G. and Galambos, T. V.INELASTIC BEAMS UNDER MOMENT GRADIENT) Journal of the Structural

Division, ASeE, Vol~ 93, No. STl, Froc. Paper 5110, February1967, p. 381.

26. Mendelson, A.PLASTICITY: THEORY AND APPLICATION, The Macmillan Company,

New York, 1968.

27. Popov, E. P. and Stephen, R. M.CYCLIC LOADING OF FULL-SIZE STEEL CONNECTIONS, Earthquake

Engineering Research Center Report 70-3, University ofCalifornia, Berkeley, California, July 1970. Also AISIBulletin 21, February 1972.

28. RCRBSJSPECIFICATION FOR 'STRUCTUP~L JOINTS USING ASTM A325 OR A490

BOLTS, Research Council on Riveted and Bolted StructuralJoints of the Engineering Foundation, April 1972.

29. Regec, J. E., Huang, J. S. and Chen, W. F.MECHANICAL PROPERTIES OF C-SERIES CONNECTIONS, Fritz'Laboratory

Report 3330 17, Lehigh Univers ity, Beth.1ehem,· Fa e, April 1972'.

'30. Regec, J. E., Huang, J. S. and Chen, W.. F.TEST OF A FULLY-WELDED BEAM-TO-COLUM:N CONNECTION, Fritz Labora­

tory Report 333.12, Lehigh University, Bethlehem, Fa.,September 1972.

31. Sherbourne, A. N., McNeice, G. M. and Bose, S. K.ANALYSIS AND DESIGN OF COLillm ,mBS IN STEEL BEA1-1-TO-COLU~fN

CONNECTIONS, Department of Civil Engineerin.g, Universftyof Waterloo, Waterloo, Orltario, Canada, March 1970.

32. Sterling, G. H. and Fisher, J. W.A440 STEEL JOINTS CONNECTED BY A490 BOLTS, Journal of the

Structural Division,' ASCE, Vol. 92, No. ST3, Frac. Paper4845, June 1966, p. 101.

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335 Struik, J. H. AoAPPLICATIONS OF FINITE EL~IENT ANALYSIS TO NON-LINEAR PLANE

STRESS PROBLEM:S, Ph.D. Dissertation, Depa.rtment of CivilEngineering, Lehigh University, Bethlehem, Pa., November1972.

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