NISTIR 88-3849

NEW NIST PUBLICATION

December 21 , 1 988

Experimental Study of

Gusseted Connections

for Laterally Braced

Steel Buildings

John L. Gross and Geraldine Cheok

IJ.S. DEPARTMENT OF COMMERCE

National Institute of Standards and Technology

(Formerly National Bureau of Standards)

Center for Building Technology

Structures Division

Gaithersburg, MD 20899

November 1988

75 Yun Sdvuilidrg Amnti • Prog

NISTIR 88-3849

Experimental Study of

Gusseted Connections

for Laterally Braced

Steel Buildings

John L. Gross and Geraldine Check

U.S. DEPARTMENT OF COMMERCE

National Institute of Standards and Technology

(Formerly National Bureau of Standards)

Center for Building Technology

Structures Division

Gaithersburg, MD 20899

November 1988

National Bureau of Standards became the

National Institute of Standards and Technology

on August 23, 1988, when the Omnibus Trade and

Competitiveness Act was signed. NIST retains

all NBS functions. Its new programs will encourage

improved use of technology by U.S. industry.

U.S. DEPARTMENT OF COMMERCE

C. William Verity, Secretary

NATIONAL INSTITUTE OF STANDARDS

AND TECHNOLOGY

Ernest Ambler, Director

ABSTRACT

The behavior of three diagonally braced steel subassemblages was studied

experimentally. The parameters which were varied included the gusset geometry

and column orientation. The specimens were loaded to failure in their plane

and load-deformation as well as strain data were recorded. The failure mode

for the two strong-axis column connections was gusset buckling. The weak-axis

column connection failed by tearing of the gusset plate. The moment

introduced by the eccentricity in the bracing was distributed to the beam and

column in the strong-axis column connection. This moment was carried almost

entirely by the beam in the weak-axis connection due to the flexibility in the

web connection. The failure loads for all three specimens were found to be

well above those predicted using various analysis methods. Generally,

comparisons of design capacities with the experimental values resulted in a factor of safety in excess of two. The current method of computing gusset

buckling appears to be slightly conservative predicting a buckling capacity of

approximately 65% of the capacity obtained experimentally. The capac ity of

the clip angles, in accordance with AISC, was computed to be very low yet no

distress in the clip angles was observed. This was because frame action

introduced loads in the gusset- to -column bolts which counteracted the load

produced by the bracing.

Braced frames; connections; design; experimental study; gusset

plates; lateral bracing; steel buildings

Key words

:
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ACKNOWLEDGEMENTS

The authors would like to express their appreciation to the many individuals

and organizations that contributed to this project. First, the assistance of

the AISC Task Group on Bracing for Heavy Construction is gratefully

acknowledged. The members of that group include: Roger Brockenbrough , Robert

Disque, John Griffiths, James Holesapple, Nestor Iwankiw, Lawrence Kloiber,

Prof. Ralph Richard, Dr. William Thornton, James Wooten, Jorge Zorilla. The

authors would especially like to express their thanks to Dr. William Thornton

for providing the specimen design capacity calculations and procedure for

distributing diagonal bracing loads and to Prof. Ralph Richard for providing

the computer simulations of the NBS specimens. Finally, the authors would

like to thank Cives Steel Company for providing and fabricating the test

specimens and fixtures.

v
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TABLE OF CONTENTS

LIST OF TABLES ix

LIST OF FIGURES xi

1.0 INTRODUCTION • 1

1 . 1 General 1

1 . 2 Background 1 1.3 Current Design Practice 3

1.4 Objective of the NBS Research ..... 4

1.5 AISC Task Group .................. 4

2.0 EXPERIMENTAL PROGRAM ....... ..... 5

2.1 Experiment Design ....... 5

2.2 Selection of Subassemblage ..... . 5 2.3 Selection of Gusset Configurations 7

2.4 Test Specimens 8

2.5 Test Facility 10

2.6 Instrumentation 11

2.7 Test Procedure 12

3.0 EXPERIMENTAL RESULTS 31

3.1 Test Specimen No . 1 31

3.1.1 Test 1A . . 31

3.1.2 Test IB .... 32

3.2 Test Specimen No . 2 ..... 33

3.2.1 Test 2A . . 33

3.2.2 Test 2B . 34

3.3 Test Specimen No . 3 . . 34

3.3.1 Test 3A 34

3.3.2 Test 3B 35

3.4 Material Properties ..... 36

3.5 Comparisons Between Tests . 36

3.5.1

Concentric vs. Eccentric Bracing Connection

(Test 1A vs. Test 2A) 36

vii
3.5.2

Strong-Axis vs. Weak-Axis Column Connection

(Test 2A vs. Test 3A) 37

4.0 INTERPRETATION AND DISCUSSION OF RESULTS 69

4.1 Whitmore Failure Criterion .... 69

4.2 Comparison of Analytical and Experimental Results 69

4.3 Design Capacities ..... 71

4.3.1 Capacity of Gusset Plate ....... 72

4.3.2 Methods to Distribute Brace Loads .... 72

4.3.3 Capacity of Gusset- to-Beam Attachment 75

4.3.4 Capacity of Gusset- to-Column Attachment ....... 75

4.3.5 Capacity of Beam- to-Column Attachment ... 75

4.4 Comparison Between Experimental and Design Capacities .... 76

4.4.1 Bolt Capacity in Clip Angles - to-Column Connection . . 76

4.4.2 Buckling of the Gusset Plate ..... 77

4.4.3 Yielding of the Whitmore Section .......... 78

4.4.4 Tearout of the Gusset Plate ............. 78

4.5 Comparison Between Experimental and Calculated Capacities . . 80

4.5.1 Buckling of the Gusset Plate ............ 81

4.5.2 Tearout of the Gusset Plate ............. 81

5.0 Summary and Conclusions ........ . 99

5.1 Summary 99

5.2 Conclusions 100

REFERENCES ........................... 103

APPENDIX A ...... .............. 105

APPENDIX B ............ . 123
LIST OF TABLES

Table Page

3.1a Force Components, Elastic Range 38

3.1b Force Components, Inelastic Range ........ 39

3.1c Force Components at Ultimate Frame Capacity ... 40

3.2 Material Properties 41

4.1 Experimental Results vs. Richard's Analytical

Results 82

4.2 Design Brace Load for Specimen No . 1 83

4.3 Design Brace Load for Specimen No . 2 84

4.4 Design Brace Load for Specimen No . 3 85

4.5 Comparison Between Computed Design Capacities and

Measured Capacities for Buckling of Gusset Plate . 86

4.6 Comparison Between Computed Design Capacities and

Measured Capacities for Yielding of Whitmore

Section . 86

4.7a Comparison Between Computed Design Capacities and

Measured Capacities for Tearout of Gusset Plate,

AXSC-ASD Design Method ... 87

4.7b Comparison Between Computed Design Capacities and

Measured Capacities for Tearout of Gusset Plate,

Williams and Richard Method . 87

4.7c Comparison Between Computed Design Capacities and

Measured Capacities for Tearout of Gusset Plate,

Hardash and Bjorhovde Method ... 88

4.7d Comparison Between Computed Design Capacities and

Measured Capacities for Tearout of Gusset Plate,

AISC-LRFD Method ...... .... 88

4.8 Comparison between Computed Buckling Capacity and

Measured Buckling Capacity for Specimens No. 1

and 2 89

4.9 Comparison between Computed Buckling Capacity and

Measured Tearout Capacity (Specimen No. 1) for

Various Methods ...... ...... 89

ix
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.
LIST OF FIGURES

Figure Page

2.1 Schematic of a Typical Braced Connection .... 13

2.2 Prototype Beam Axial Loads 14

2.3 Prototype Diagonal Bracing Loads and Percent

of Total Story Shear Carried by the Bracing . . 15

2.4 Prototype Beam Moments 16

2.5 Prototype Column Moments .... 17

2.6 Boundary Conditions for Test Subassemblages . . 18

2.7 Test Specimen Configuration .......... 19

2.8 Connection Detail for Specimen No . 1 ..... . 20

2.9 Connection Detail for Specimen No . 2 21

2.10 Connection Detail for Specimen No . 3 22

2.11 Upper and Lower Crossheads of TTF 23

2.12 Schematic of NBS Tri-Directional Test Facility . 23

2.13 Tri-Directional Test Facility (TTF) 24

2.14 Roller Support at End of Beam . 25

2.15 Test Specimen Mounted in the TTF ........ 26

2.16 Lateral Support at Column Mid-Height ...... 27

2.17 Strain Gage Locations ............. 28

2.18 Location of Rosette Gages on Gusset Plate ... 29

3.1 Load vs. Deflection, Test 1A 42

3.2 Buckled Lower Gusset Plate, Test 1A ...... 43

3.3 Cracks in Brittle Coating on Lower Gusset,

Test 1A 44

3.4 Lateral Load vs. Axial Loads in Diagonal Bracing,

Test 1A .............. 45

3.5 Load vs. Deflection, Test IB 46

3.6 Buckled Upper Gusset Plate, Test IB 47

3.7 Lateral Load vs. Axial Loads in Diagonal Bracing,

Test IB 48

3.8 Load vs. Deflection, Test 2A ......... . 49

3.9 Lateral Load vs. Axial Loads in Diagonal Bracing,

Test 2A . 50

xi
3.10 Buckled Lower Gusset Plate, Test 2A 51

3.11 View of Closed Gap Between the Lower Gusset and

the Diagonal, Test 2A 52

3.12 Load vs. Deflection, Test 2B 53

3.13 Lateral Load vs. Axial Loads in Diagonal

Bracing, Test 2B 54

3.14 Load vs. Deflection, Test 3A ......... . 55

3.15 Upper Gusset Plate, Test 3A .......... 56

3.16 Lateral Load vs. Axial Loads in Diagonal

Bracing, Test 3A .......... 57

3.17 Tear in Upper Gusset which Occurred in Test 3A . 58

3.18 Load vs. Deflection, Test 3B . . . 59

3.19 Top Edge of Upper Gusset, Test 3B ....... 60

3.20 Lateral Load vs. Axial Loads in Diagonal

Bracing, Test 3B 61

3.21 Diagonal Brace in Contact with Upper Gusset,

Test 3B ...... ....... 62

3.22 Location of Tensile Test Coupons in Gusset

Plates ..................... 63

3.23 Stress - Strain Curve for Upper Gusset,

Specimen No . 1 ........... 64

3.24 Moment Diagram for Test 1A .......... . 65

3.25 Moment Diagram for Test 2A .......... . 65

3.26 Predicted and Experimental Moments for Test 3A . 66

3.27 Moment Diagram for Test 3A ..... 67

4.1 Whitmore Section ................ 90

4.2 Load vs. Deflection Plot for Specimen No . 1 . . 91

4.3 Load vs. Deflection Plot for Specimen No . 2 . . 92

4.4 Load vs. Deflection Plot for Specimen No . 3 . . 93

4.5 Stress Contour Plot for Specimen No. 1 (Ref. [8])

with Experimental Values Superimposed ..... 94

4.6 Stress Contour Plot for Specimen No. 2 (Ref. [8])

with Experimental Values Superimposed ..... 95

4.7 Stress Contour Plot for Specimen No. 3 (Ref. [8])

with Experimental Values Superimposed ..... 96

xn
4.8 Block Shear Failure Mode . 97

A.l T-Section Tearout 115

A. 2 Williams and Richard's Brace Load Distribution . 116

A. 3 Schematic Showing Welds from Gusset to Column

and to Beam 117

A. 4 Gusset- to-Column Connection Detail ....... 118

A. 5 Beam- to-Column Connection Detail 118

A. 6 Schematic Showing AISC Case II 119

A. 7 Schematic Showing AISC Case I 120

A. 8 Force Distribution Using AISC Method for Heavy

Bracing 121

B. l Thornton's Model for Brace Load Distribution . . 127

xiii

1.0 INTRODUCTION

1 . 1 General

Diagonal bracing systems are frequently employed in steel framed structures to

provide stiffness and to resist both wind and seismic loads. It is common in

such bracing systems to use gusset plates to attach the diagonal braces to the

main framing members. The force distribution in a gusseted connection is

extremely complex and designers frequently employ approximate methods to

design the gusset plates and the attachment of the gusset to the beams and

columns. Analytical studies [1] have shown that the force distribution in a gusseted connection depends upon all of the structural components making up

the connection including the gusset plate, diagonal brace, column, beam, and

fasteners (bolts or welds)

.

Experimental work to date has not included the influence of the members

framing into a gusseted connection on the stresses in the gusset and on the

distribution of loads to the framing members. At the suggestion of the AISC

Task Group on Bracing for Heavy Construction, an experimental program was

undertaken at the National Institute of Standards and Technology (NIST--

formerly the National Bureau of Standards) to determine the behavior of

gusseted connections including the influence of the members framing into the

connection. Three nearly full-scale braced frame subassemblages were tested.

Each represented a different connection configuration to investigate the

influence of connection geometry. This report summarizes the findings of the

NIST tests and compares the results obtained with current design practice and

proposed analytical procedures

.

1 . 2 Background

Historically, gusset plates were designed on the basis of ordinary beam

formulas, despite the fact that the validity of such formulas is questionable

for a gusset plate of normal proportions. One of the most significant studies

of gusset plate behavior was that by Whitmore [2] in which he concluded that

beam formulas do not accurately predict the elastic stress distribution in a

- 1 -
gusset plate for a typical bottom chord connection in a Warren truss.

Whitmore proposed an effective width design approach which is widely used in

practice today. On the basis of full-scale tests, Bjorhovde [3] found

acceptable agreement with the Whitmore procedure for the design of gusset

plates in braced frames. These tests included tension loading of full-size

specimens connected to stub beam and column sections. More recently, the

block shear concept has been developed for the prediction of the ultimate

strength of a bolted gusset plate in tension. Richard [4] has shown that the

block shear criteria is identical to the Whitmore criteria when the gross

section is used. On the basis of 28 tests conducted at the University of

Arizona, Hardash [5] proposed a design criteria for gusset plates in tension

using the block shear concept.

The main focus of previous experimental work has been on tension action with

little attention being paid to compression and the study of gusset plate

buckling. Thornton [6] describes a rational procedure for checking gusset

plate stability based on the Whitmore stress acting on a unit strip of the

gusset plate treated as a column. Recently, Hu and Cheng [7] tested gusset

plates loaded in compression using various thicknesses and sizes of gusset

plate and several different boundary conditions. The gusset plates were

designed to fail by elastic buckling and, as in the tension tests by

Bjorhovde, the full-size specimens were connected to stub beam and column

sections

.

Recent analytical studies conducted by Williams and Richard [4] and Fung and

Richard [8] have demonstrated the importance of "frame action" effects. That

is, a gusset plate becomes part of the beam- to -column moment connection and as

such carries load by frame action. Finite element studies of a braced frame

subassemblage demonstrated that this action loads the gusset significantly.

The influence of framing members on gusset plate behavior has not yet been

studied experimentally and the effects of the stresses produced by frame

action on the joint capacity is not known.

Also, the additional loads due to the eccentricity introduced into a gusseted

connection by the fact that the centroidal axes of the framing members do not

intersect at a point, has not been experimentally verified. The elastic tests

- 2 -
of gusseted connections in trusses by Whitmore [2] and by Vasarhelyi [9], and

the tests to failure of braced frame gusseted connections by Bjorhovde [3],

all used configurations in which the centroidal axes intersected at a single

point

.

1 . 3 Current Design Practice

The size and shape of a gusseted connection is generally dictated by fastener

requirements. The thickness of the plate is selected on the basis of either

the stress on the Whitmore section or by the maximum stress calculated using

beam formulas. Beam formulas continue to be used, despite their apparent

failings, largely because their use has produced designs that perform

satisfactorily. Design of the gusset plate attachments, either bolts or

welds, is dictated by the loads which must be transferred to the beam and

column. However, the distribution of diagonal bracing loads to the framing

members is not well understood. If the line of force in the diagonal passes

through the corner of the gusset plate, a common and simple method for

distributing the brace load [10] is to assume that the vertical component of

the load in the brace goes to the gusset- to-column connection and that the

horizontal component goes to the gusset- to-beam connection. If the line of

force in the diagonal passes through the intersection of the beam and column

centerlines, distribution of the load in the brace could be as suggested in

Reference [10] for heavy bracing connections. This method is illustrated in

Appendix A. Thornton [6] presents an approach to the design of both the

gusset plate and its attachments based on simple statics combined with the

notion of adequate strength path. A conservative procedure for checking

gusset plate buckling, based on the Whitmore effective width, is also

presented. Richard [1] recently proposed a method for determining the

distribution of diagonal bracing loads to the framing members on the basis of

nonlinear finite element analyses of various connection configurations. The

equations for the gusset- to- frame fastener force distributions were found to

depend primarily on gusset plate aspect ratio and the brace angle. These

various design approaches are presented in more detail in Chapter 4 and

comparisons are made between design capacity and experimentally determined

capacity for all three specimens.

3
1.4 Objectives of the NIST Research

The objectives of the NIST research are:

o to obtain experimental results for gusseted connections which include

the members framing into the connection and which are loaded in both

tension and compression, and

o to compare experimental results with predicted values using various

design methods.

1 • 5 AISC Task Group

The experimental research program was developed by NIST in cooperation with

the AISC Task Group on Bracing for Heavy Construction. The Task Group

assisted NIST in developing and carrying out the experimental program by

working with NIST to establish the research objectives, and to define the

specimen configuration, test set-up, loading sequence and instrumentation.

Members of the Task Group representatives from design offices, steel

fabricators, universities and standards writing bodies.

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2.0 EXPERIMENTAL PROGRAM

2 . 1 Experiment Design

To meet the stated objectives, an experimental program was developed to test

three braced frame subassemblages. The following general considerations

guided NIST in designing the experiments:

o The behavior of the subassemblage model should duplicate as closely as

possible prototype braced frame behavior.

o The subassemblage should be as close to full scale as practical.

t o The subassemblage must be accommodated by the existing NIST tridirectional test facility.

o The specimens should represent a realistic gusseted diagonal brace

connection in a frame structure.

o The specimens should be carried well beyond initial distress (i.e.,

buckling, yielding, tearing or fracture) with the loading capacity

provided by the NIST facility.

2 . 2 Selection of Subassemblage

Many different arrangements of lateral bracing are possible. The

configuration selected for study in this project is one having diagonals

alternating in direction from story to story. A schematic of the braced core

of a multistory steel building having such an arrangement of diagonals is

shown in Figure 2.1a. Note that this configuration simulates X-bracing as

well as an alternating pattern of vertical bracing. The subassemblage

selected for this experimental program is shown schematically in Figure 2.1b.

A linear elastic analysis was performed on a prototype braced frame core to

determine the boundary conditions for the subassemblage selected for study.

- 5 -
The structure was loaded at each floor elevation with an equal magnitude 1 lateral load, Pl, as shown in Figure 2.2. It was found that the lateral load

was resisted almost entirely by the diagonal braces. Very little was carried

by frame action as illustrated in Figure 2.3. The beams were found to be in

reverse curvature with the point of zero moment almost exactly at mid- span as

seen in Figure 2.4. Note that the beams were assumed to be rigidly fixed to

the columns, rather than pinned, because a gusseted connection provides a substantial rotational restraint. In addition, the beams in the prototype

corresponding to the beam in the subassemblage were found to carry very little

axial load. This suggests that the subassemblage shown in Figure 2.1b can be

modeled with a pin and roller support at the prototype beam mid- span. The

, columns (except in the first story) were also in reverse curvature as shown in

Figure 2.5 but the point of zero moment was not precisely at the column

mid-height. Nevertheless, the assumption of a pin support at the prototype

column mid-height appears to be reasonable for the subassemblage. Since the

diagonals carry principally an axial load, a pin connection at the mid-point

of the diagonal is appropriate as well. Finally, the vertical displacements

of the joints at a floor elevation were found to be essentially equal

indicating that, for the subassemblage to simulate the behavior of the

corresponding portion of the prototype under lateral loading, the top of the

column and the top of the upper diagonal must be restrained to translate only

in the plane of the frame. The boundary conditions and loading for the braced

frame subassemblage are shown schematically in Figure 2.6.

Next, a comparison of analysis results between the prototype and the

subassemblage model, restrained and loaded as indicated, was made to verify

that the subassemblage replicated prototype behavior. Results showed that the

forces in the diagonals differed by less that 6%. The moment in the beam at

the beam- to-column joint differed by less than 1% between prototype and model.

The axial forces in the columns were found to be different between the

prototype and model. This is because column loads resulting from cantilever

action in the prototype accumulate from the top of the structure to the

bottom; an effect which does not occur in the single story subassemblage. It

was concluded that the braced frame subassemblage selected for study provided

a good representation of prototype behavior when supported and loaded as shown

in Figure 2.6.

- 6 -
The height of the subassemblage was 9'-0" between column pin supports. This

was the largest specimen which could be accommodated in the test facility.

The width from column centerline to beam pin support was 7' -6". This

represents approximately a 3/4-scale structure. The geometry of the

subassemblage and the pin fixtures used to represent the boundary conditions

are shown in Figure 2.7.

2 .

3

Selection of Gusset Configurations

Just as there are many possible arrangements of lateral bracing, so too there

are there are many possible configurations for a gusseted connection. Two

important aspects were investigated in this study:

t

o The relationship between the line of force in the diagonal brace and

the intersection of the centroidal axes of the beam and column.

o The orientation of the strong axis of the column with respect to the

plane of the frame.

If the line of force in the diagonal passes through the intersection of the

axes of the beam and column, no moment is produced in the connection by the

axial force in the diagonal. This configuration is termed "concentric".

While no moment is induced in either the beam or column by the force in the

diagonal, this alternative requires a long gusset plate due to the difference

in depth of the column and beam, and the small angle that the diagonal brace

makes with the horizontal. This is of particular importance when the gusset

is in compression because a long gusset plate has a lower buckling capacity.

Also, the gusset plate in a concentric connection is subjected to complex

loadings at its boundaries which are difficult to calculate.

If the line of force in the diagonal does not pass through the intersection of

the beam and column axes, the force in the diagonal produces a moment which

must be resisted by the beam and column. Thus an eccentricity exists with

respect to the force in the diagonal and, therefore, this configuration is

termed "eccentric". The additional moment is simple to compute but the beam

- 7 -
and/or column may have to be increased in size to accommodate the additional

stresses. If the line of force in the diagonal is made to pass through the

corner of the gusset plate, loadings at the gusset boundaries are simple to

compute as well.

A rolled steel column section (W or HP shape) has a strong bending axis and a weak bending axis. Diagonal bracing may frame into either the strong axis of

a column, "strong-axis connection" or into the weak axis of a column, "weakaxis connection". In a weak-axis connection, the gusset is connected to the

column web which is often more flexible than the flange. No experimental work

to date has resolved the difference in performance between a strong-axis and

weak-axis connection.

f

2 . 4 Test Specimens

Three specimens, each with a different connection detail were tested. They

were as follows:

o Specimen No. 1 - Concentric, strong-axis column connection where the

line of force in the diagonal passes through the Intersection of the

beam and column centroidal axes (Figure 2.8).

o Specimen No. 2 - Eccentric, strong-axis column connection where the

line of force in the diagonal passes through the corner of the gusset

plate (Figure 2.9).

o Specimen No. 3 - Eccentric, weak-axis column connection where the line

of force in the diagonal passes through the corner of the gusset plate

(Figure 2.10).

For Specimen No. 1, the gravity axes of the members framing into the joint

intersected at a common point and thus no eccentricity was introduced into the

connection. As noted earlier, this arrangement produces a long gusset plate

which is more susceptible to buckling than a compact gusset plate would be.

- 8 -
Specimen No. 2 had a much more compact gusset than Specimen No. 1, however, an

eccentricity resulted because the centroidal axes of the members framing into

the connection did not meet at a single point. The gusset plates for Specimen

No. 1 and No. 2 were identical except in length since it was intended to

determine if acceptable performance and ultimate strength are obtained when no

special provisions are made to account for the eccentricity.

For Specimen No. 3, the column was turned so that it acted in its weak

direction and the gusset plate was attached to the column web. No web

stiffening was provided. The gusset plate and clip angles were the same for

Specimen No. 2 and Specimen No. 3 so that a comparison could be made between

the results for a strong-axis and a weak-axis connection.

The framing members for each test specimen were the same. The column was a W 10 x 49, the beam a W 16 x 40 , and the diagonal braces were W 8 x 21 's. The

gussets were attached to the beam flanges with fillet welds and were connected

to the column by clip angles welded to the gusset and bolted to either the

column flange or web. The gusset plates were 1/4" thick and the clip angles

were L 3 x 3-1/2 x 1/4. The beam flanges were coped to allow the clip angles

to run the entire depth of the connection as a single piece thereby

simplifying fabrication and fit-up. The diagonal braces were bolted to the

gusset using WT 5 x 11 sections.

The three test specimens were fabricated using standard shop practices. Since

it is essential that none of the members framing into the connection fails

before all the data from the gusset plate is acquired, the gusset plates and

attachment elements were fabricated from 36 ksi steel while the main framing

members were fabricated from 50 ksi steel. E70 electrodes were used for all

weldments and A325 High Strength Bolts were used for all bolted attachments.

The connection configurations were determined by the advisory panel to

represent practical heavy bracing connections.

- 9 -
2 . 5 Test Facility

The experiments were conducted using the NIST Tri-directional Test Facility

(TTF) [11], a permanent structural testing apparatus located in the NIST

Structures Division Laboratory. The TTF can subject large structural

components to controlled displacements, forces, or both, including

translations and rotations in three orthogonal directions. The facility is

computer-based with all aspects of the loading of test specimens and the

acquisition and reduction of data coordinated and controlled by the operator.

The loads are applied by a closed- loop hydraulic system having six

independently servo-controlled hydraulic actuators. Lateral forces as large

as 200 kips and vertical forces up to 250 kips may be applied to the test

specimen.

The testing apparatus consists essentially of two steel crossheads to which

the test specimen is attached (see Figure 2.11). The reaction system consists

of a structural tie-down floor and two vertical reaction walls (see Figure

2.12). The bottom crosshead is anchored to the tie-down floor and is

stationary. The top crosshead is attached to six hydraulic actuators which

control its movement. The actuators are in turn attached to either the bottom

crosshead or one of the reaction walls. The clear distance between the

crossheads is approximately 12 ft. and the clear distance between the vertical

actuators is approximately 10 ft.

Figure 2.13 shows a photo of the tri-dimensional test facility without a test

specimen mounted in it. A close-up of the roller support system for the end

of the beam is shown in Figure 2.14. A test specimen mounted in the test

facility is shown in Figure 2.15. Also, shown in Figure 2.15 is a free-standing steel frame on which instrumentation for measuring displacements

was mounted. The columns in each test were laterally braced at the column

mid-height (Figure 2.16). Pins at both ends of the lateral brace allowed

unrestrained movement of the subassemblage in its plane while providing no

- 10 -
rotational restraint. The lateral brace was instrumented to determine the

load resisted by the brace.

2 . 6 Instrumentation

The following data were either recorded directly or computed from recorded

data for each of the three tests:

o The applied lateral load

o The lateral frame displacement (top and mid-height of sub-assemblage)

.

o The axial force, bending moment, and shear distributions in all of the

framing members

.

o The distribution of stresses in the gusset plate along those edges

attached to the framing members

.

o The principal mode of failure of each specimen.

The test specimens were instrumented with resistance- type strain gages to

record strains and with linear variable differential transformers (LVDT) to

record displacements or rotations. A sufficient number of strain gages were

applied to determine the axial force and bending moments in all members and

the distribution of stress along the connected edges of the gusset plates.

The locations of the strain gages are shown in Figures 2.17 and 2.18. LVDT's

were located at the center of the upper support pins and at the column midheight to record lateral frame displacements. LVDTs were also located at the

center of the bottom pin supports to monitor any base movements. A total of

96 data channels were used to record data form the strain gages and LVDTs. In

addition, transducers mounted on the hydraulic actuators were used to measure

loads and displacements of the upper crosshead.

All instrumentation was connected to a computer-based analog- to - digital

converter. Acquired data were stored on magnetic tape for later processing

- 11 -
and selected data channels, converted to engineering units, were displayed

during the course of a test.

2 . 7 Test Procedure

Each specimen was loaded in the plane of the frame as shown in Figure 2.6.

Loading of each specimen was conducted in two separate tests as follows:

o Test A - Lateral load was applied so as to produce tension in the

upper diagonal. The specimen was loaded until failure occurred and

the subassemblage was unable to carry additional load. It was then

unloaded. Since yielding and/or buckling occurred in all instances,

there was a residual lateral frame displacement when the specimen was

fully unloaded.

o Test B - The specimen was loaded in the opposite direction producing

compression in the upper diagonal. As in the first test, loading was

continued until failure occurred and the subassemblage was unable to

carry any additional load. The load was then removed.

All tests were conducted under displacement control. That is, the TTF was

given a command to move (displace) the upper crosshead a prescribed amount and

the forces required to produce the given displacement were computed and

recorded.

12 -
- 13 -

Figure

2.1

Schematic

of

Typical

Braced

Connection
Figure 2,2 - Prototype Beam Axial Loads

- 14
92 %

Figure 2.

95 %

92 %

94 %

92 %

99 %

- Prototype Diagonal Bracing Loads and Percent of

Total Story Shear Carried by Bracing

- 15 -
Note: Diagonals

omitted for

clarity

Beam Moments
Figure 2.5 - Prototype Column Moments

- 17
Figure 2.6 - Boundary Conditions for Test Subassemblages

- 18 -
CM

<DV43

bO

•t—4

£l-l

- 19

Test

Specimen

Configuration
Figure 2.8 - Connection Detaii for Test Specimen No. 1

- 20
Figure 2.9 - Connection Detail for Test Specimen No. 2

- 21 -
W10X49

Figure 2.10 - Connection Detail for Test Specimen No. 3

- 22
Upper

crosshead

(movable)

Lower

crosshead

(stationary)

Figure 2.11 - Upper and Lower Crossheads of TTF

Figure 2.12 - Schematic of NBS Tri -Directional Test Facility

- 23 -
24 -

Figure

2.13

-

Tri

-Directional

Test

Facility

(TTF)
25

tiguie

2.14

Roller

Support

at

End

of

Beam
Figure 2.15 Test Specimen Mounted in the TTF

26
- 27

Figure

2.16

-

Lateral

Support

at

Column

Mid-Height
Figure 2.17 - Strain Gage Locations

- 28 -
Specimen No. 1

Specimen Nos. 2 & 3

Figure 2.18 - Location of Rosette Gages on Gusset Plate

- 29

•

"4

3.0 EXPERIMENTAL RESULTS

3 . 1 Test Specimen No. 1

3.1.1 Test 1A

The gusset plates were coated with a brittle lacquer coating on one side and

with a whitewash on the other. This was done in an attempt to determine the

areas of high stress and patterns of yielding in the gusset plates. The

whitewash coating flaked off in pieces rather than crack because the mill

scale had been removed by grit blasting during fabrication. Cracks were

observed in the brittle coating, however, they were not easily seen due to the

size of the cracks and the reflection of light from the glossy coating. As a result, the gusset plates in the later tests were left uncoated.

The load vs. deflection plot for Test 1A is shown in Figure 3.1. At a lateral

load on the frame of 56 kips, flaking of the whitewash was observed in the

lower gusset at the upper corner of the T-section which connects the gusset to

the diagonal. At approximately 60 kips, first cracking of the brittle coating

was observed. Slip of the lower splice between the gusset and the diagonal

resulted in a loud bang at a lateral load of 90 kips. A drop in lateral load

occurred due to the slip and can be noted in Figure 3.1. A linear regression

analysis was used to obtain the frame stiffness. Data points up to a lateral

load of 50 kips were used and the resulting line was constrained to pass

through the origin. A stiffness of 288 kip/in was found.

Buckling of the lower gusset occurred very suddenly at a lateral load equal to

107 kips. The lateral frame load dropped from 107 kips to 96 kips as shown in

Figure 3.1. Thus, the ultimate frame load for Test 1A was 107 kips and the

mode of failure was buckling of the gusset. The load in the compression

(lower) diagonal was 116 kips and the load in the tension (upper) diagonal was

100 kips when the gusset buckled. The corresponding frame displacement was

0.50 in. The buckled lower gusset is shown in Figure 3.2 and a close-up of

the cracks in the brittle coating is shown in Figure 3.3.

31
Figure 3.4 shows the load in the two diagonals for Test A. From the figure,

it can be seen that the compression diagonal carried a greater load than the

tension diagonal. This slight deviation was attributed to the lower crosshead

being considerably stiffer than the upper crosshead which deflected under load

thereby relieving some of the tension load in the upper diagonal.

As shown in Figure 3.1, the frame was not able to carry any additional load

once the gusset buckled. However, as seen in Figure 3.4, the load in the

compression diagonal decreased while the load in the tension diagonal

increased. Loading was stopped at a maximum load of 96 kips and a corresponding displacement of 0.85 in. Force components in the framing

members, calculated from strain measurements, were calculated for three

lateral loads: 1) 40 kips, which was within the linear elastic range; 2)

70 kips, which was within the inelastic range but below ultimate; and 3)

ultimate load, which was different for each specimen. The force components

for these three cases are given in Tables 3.1a, b and c for the elastic range,

inelastic range and ultimate load, respectively. Strains in the lateral brace

less than 10 microstrain indicated that the load in the brace was less than

one kip which was considered negligible.

3.1.2 Test IB

The load vs. deflection plot for Test IB is shown in Figure 3.5. Significant

slip of the splice between the gusset and diagonals occurred twice in Test IB;

once at a load of approximately 79 kips and again at 92 kips (see Figure 3.5).

Lateral displacement of the upper gusset was first noticed at a lateral frame

load of approximately 92 kips. At a lateral load of 96 kips and a lateral

displacement of 0.72 in, the upper gusset buckled. Thus, the ultimate load

for Test IB was 96 kips and the mode of failure was buckling of the compressed

gusset. Unlike Test 1A, buckling of the gusset was not accompanied by a large

decrease in load. Some relaxation in load took place when the specimen was

held at a fixed displacement for a period of time (such as for data recording

and photography). However, the load quickly returned to its previous value

upon application of additional displacement. This relaxation in load is not

shown in Figure 3.5. The extent of buckling is indicated by the shadow cast

by the straightedge on the gusset in Figure 3.6. Note that the value of load

32
of 91 kips reported in the figure is a result of the relaxation noted above.

The load in the compression (upper) diagonal was 96 kips and the load in the

tension (lower) diagonal was 80 kips (see Figure 3.7) when the upper gusset

buckled. As seen in Figure 3.5, the frame carried almost no additional load

upon further displacement of the frame. Again, the load in the compression

diagonal decreased while the load in the tension diagonal increased after the

gusset buckled. The maximum post-buckling load for Test IB was found to be

100 kips at a displacement of 1.09 in. The load in the lateral brace was less

than one kip

.

3 . 2 Test Specimen No. 2

3.2.1 Test 2A

The load vs. deflection plot for Test 2A is shown in Figure 3.8. The frame

stiffness from the regression analysis was 258 kip/in. No major slip of the

splices occurred in the early part of the test. A sharp drop in lateral load

occurred with a slip of one of the splices at a lateral load of approximately

124 kips . As the frame was displaced further and the lateral load increased,

the lower gusset buckled suddenly (Figure 3.8).

The lateral displacement corresponding to the buckling load was 0.80 in. The

load in the compression (lower) diagonal at buckling was 138 kips and the load

in the tension (upper) diagonal was 113 kips . The loads in the diagonals are

shown in Figure 3.9. The compression diagonal is shown to carry a greater

load than did the tension diagonal. Buckling of the gusset was accompanied by

a sudden drop in lateral load as in Test 1A. The load was 117 kips at a displacement of 1.12 in before the specimen was unloaded. The buckled gusset

for Test 2A is shown in Figure 3.10. The original 0.5 in. gap between the

lower gusset and the lower diagonal had closed at this point (Figure 3.11) as

a result of slip of the splice and rotation of the diagonal. Any further

displacement would have caused the edge of the gusset to be loaded by the

flange of the diagonal brace. Force components in the framing members are

given for the linear elastic range, inelastic range, and ultimate load in

33
Tables 3.1a, b and c, respectively. Again, strain in the lateral brace was

insignificant

.

3.2.2 Test 2B

Slip of the splices with accompanying drop in lateral load occurred several

times during this test with the earliest slip occurring at a lateral load of

83 kips. Incipient buckling of the lower gusset plate was noted at a lateral

load of 132 kips and a frame displacement of 1.54 in. The load in the

compression diagonal was 148 kips and in the tension diagonal 114 kips.

The lateral load had peaked and was decreasing when the testing machine

malfunctioned and the test had to be stopped. The test was not resumed after

repairs were made since it was felt that no further information needed to be

obtained. The load vs. deflection plot for Test 2B is shown in Figure 3.12

and the load in the diagonals is shown in Figure 3.13. The irregularities in

Figure 3.12 and Figure 3.13 are a result of numerous occurrences of slip of

the splices.

3 . 3 Test Specimen No. 3

3.3.1 Test 3A

As in the previous tests, slip of the splices occurred in Test 3A with the

earliest slip occurring at a lateral load of 80 kips. The load vs. deflection

plot is shown in Figure 3.14. The initial slope of load vs. deflection plot

was 240 kip/in as obtained from a regression analysis.

During the test two dial gages were added at mid-height of the column to

measure out-of-plane distortions of the column web. The maximum measured

displacement of the column web was 7 thousandths of an inch and was considered

negligible. The lateral load reached a peak value of 122 kips and then

dropped suddenly to approximately 83 kips. The displacement corresponding to

the maximum lateral load was 1.00 in. The load in the compression diagonal

- 34 -
was 139 kips and the load in the tension diagonal was 125 kips at the maximum

lateral load.

No buckling of the lower (compression) gusset plate was observed. However,

noticeable distortion of the upper (tension) gusset and a widening of the gap

between the upper diagonal and gusset were noted. Figure 3.15 shows the gap

between the end of the upper diagonal and the edge of the gusset plate after

the lateral load had peaked at 122 kips and then fallen to 83 kips. The

lateral load continued to drop without attaining a stable value as the frame

was displaced further. The specimen was unloaded at this point. The maximum

displacement of the frame was 1.18 in. The load vs. deflection plot and

diagonal load plot for Test 3A are shown in Figure 3.14 and Figure 3.16,

respectively

.

After Test 3B had been completed and the diagonals had been removed, the

reason for the inability of the frame to carry additional load in Test 3A was

apparent. The tension gusset was torn along the lower bolt line and the upper

bolt line and lower bolt row showed obvious signs of yielding. The bolt holes

were also elongated (Figure 3.17). Thus, the ultimate load for Test 3A was

122 kips and the mode of failure was tearing of the gusset plate.

3.3.2 Test 3B

Many slips of the splices occurred in this test as indicated by the sudden

drops in load shown in Figure 3.18. The two dial gages measuring lateral

displacement of the column web indicated a maximum movement of 0.07 in.

Buckling of the upper gusset, Figure 3.19, occurred at a lateral load of 103

kips, a frame displacement of 2.26 in and a load in the compression diagonal

of 88 kips. The load in the tension diagonal was equal to 122 kips. A plot

of the lateral load vs. axial loads in the diagonal bracing is shown in Figure

3.20. The frame was displaced to a maximum displacement of 1.17 in before the

specimen was unloaded. It was necessary to unload at this point because the

gap between the upper diagonal and the gusset had closed and the diagonal was

resting against the gusset as seen in Figure 3.21. Further loading of the

frame would not have yielded any relevant results.

35
3.4 Material Properties

After testing of all the specimens, coupons were cut out from each of the

members from all three specimens and tension tests were performed on the

coupons in accordance with ASTM Standard A 370 [12]. The coupons from the

gusset were obtained from the shaded area shown in Figure 3.22 which was

between the legs of the two angles and should have experienced little or no

stress during the tests. The results from the tensile tests are given in

Table 3.2. A typical stress-strain plot for the gusset plate is shown in

Figure 3.23. The average yield stress of the gusset plates was 46.7 ksi.

3 .

5

Comparisons Between Tests

3.5.1 Concentric vs. Eccentric Bracing Connection (Test 1A vs. Test 2A)

The connection with eccentric brace loading and compact gusset plate (Specimen

No. 2) had a capacity of 123 kips as compared to the connection without

eccentric loading (Specimen No. 1) which had a capacity of 107 kips. This is

a 10% increase in buckling load capacity. The stiffness of Specimen No. 1 was

found to be greater than that for Specimen No. 2 (288 vs. 258 kip/in).

The global member force components in the X and Y directions were comparable

for both tests for similar frame loads. The moment diagrams for Tests 1A and

2A are shown in Figures 3.24 and 3.25, respectively. The moments in these

figures correspond to a lateral load of 70 kips. The moments in the diagonals

are not included because they are negligible in comparison with the moments in

the column and beam. Two observations can be made regarding the moments in

the framing members. The first is that the beam carries a significant moment

regardless of the assumed beam end condition (in this case the beam was

assumed to be pinned) . This is because the gusset plates produce a nearly

fixed condition for the beam- to-column connection. The second observation is

that the moment produced by the force in the diagonal bracing members acting

eccentric to the intersection of the framing member centroidal axes is

distributed to the beam and column. This moment is distributed roughly in

- 36
proportion to the ratio of moment of inertia to length (I/L) of the members

framing into the connection as shown in Figure 3.26.

3.5.2 Strong-Axis vs. Weak-Axis Column Connection (Test 2A vs. Test 3A)

While the ultimate load for both tests was practically the same, the failure

mode of the gusset was different for the two tests. The gusset attaching the

compression diagonal buckled in Test 2A while the gusset attaching the tension

diagonal tore in Test 3A. The tearing of the gusset in Test 3A was likely a

result of the rotation allowed by the connection due to the flexibility of the

column web which increased the load in the tension diagonal. From Section

3.3.1, the loads in the compression diagonals were 138 kips and 139 kips for

Test 2A and 3A, respectively. The loads in the tension diagonals were 113.4

kips and 125 kips for Test 2A and Test 3A, respectively. The stiffness of the

frame in Test 2A was 258 kip/in compared with 240 kip/in for Test 3A.

Again, for equal frame loads in the elastic range (Table 3.1a), the member

loads in the X and Y directions and the moments in the beams were comparable

in both tests. Also, in the elastic range, the moment in the compression

diagonal in Test 3A was greater than that in Test 2A. However, at the

buckling load (Table 3.1c), the moment in the beam in Test 3A was larger than

in Test 2A. The moments corresponding to a lateral load of 70 kips for Test

3A are shown in Figure 3.27. As can be seen, the moment produced by frame

action as well as the moment produced by the eccentricity of the bracing loads

was carried almost exclusively by the beam. Apparently, the thin column web

was not sufficiently stiff to mobilize the column flanges in resisting the

moments

.

37 -
Table 3.1a - Force Components, Elastic Range ^

Test 1A 2A 3A

Lateral load (kip) 40.9 38.9 38.8

Frame Stiffness 288 258 240

(kip/inch)

X-Direction (kip) 2

Top Column 7.6 5.6 -0.4

Bottom Column 0.1 1.5 0.5

Top Diagonal 30.4 30.6 35.0

Beam 0.3 -0.2 -0.4

Lower Diagonal -38.8 -35.9 -37.5

Y-Direction (kip) 2

Top Column -14.5 -14.6 -13.7

Bottom Column -31.1 -27.0 -25.7

Top Diagonal 18.5 16.6 18.0

Beam 5.2 6.4 6.3

Lower Diagonal 23.5 19.6 19.6

Moment (kipTM in) 2

Top Column -154.7 -115.0 0.8

Bottom Column 2.4 31.0 1.0

Top Diagonal 10.9 3.3 2.8

Beam 156.3 315.1 303.2

Lower Diagonal 8.1 8.9 17.7

1 Loads at gage location. See Figure 2.14a

2 Sign convention:

+ value = positive X-direction, right hand coordinate system

+ value = positive Y-direction, right hand coordinate system

+ value = counter-clockwise moment

- 38
Table 3.1b Force Components, Inelastic Range 1

Test 1A 2A 3A

Lateral load ^ 70.9 70.5 69.4

X-Direction (kip) ^

Top Column 13.3 9.8 -0.7

Bottom Column 0.1 3.1 0.3

Top Diagonal 53.7 56.3 63.6

Beam 0.5 -0.3 -0.3

Lower Diagonal -68.0 -65.8 -68.0

Y-Direction (kip) ^

Top Column -29.5 -29.5 -27.7

Bottom Column -50.3 -46.6 -43.2

Top Diagonal 32.5 30.6 32.6

Beam 9.1 11.3 11.5

Lower Diagonal 40.9 35.7 35.3

Moment (kip- in) ^

Top Column -271.0 -199.0 1.3

Bottom Column 2.0 63.6 0.7

Top Diagonal 13.9 4.8 -0.4

Beam 272.3 558.5 552.9

Lower Diagonal 2.5 3.0 26.2

1 Loads at gage location. See Figure 2.18a

2 Sign convention:

+ value = positive X-direction, right hand coordinate system

+ value = positive Y-direction, right hand coordinate system

+ value = counter-clockwise moment

- 39
Table 3.1c - Force Components at Ultimate Frame Capacity

Test 1A 2A 3A

Ult. Capacity (kip)

(mode of failure)

107.0

(buckling)

123.0

(buckling)

122.0

( tearing)

X-Direction (kip) 2

Top Column 17.5 17.9 -0.1

Bottom Column - 3.4 11.0 0.0

Top Diagonal 85.6 99.7 111.0

Beam 0.2 -0.5 0.0

Lower Diagonal -99.6 -121.7 -123.8

Y~Direction (kip) 2

Top Column -48.3 -50.7 -46.2

Bottom Column -73.2 -82.4 -80.0

Top Diagonal 51.6 54.1 57.1

Beam 14.5 18.1 21.1

Lower Diagonal 59.4 65.2 62.6

Moment (kip- in) c

Top Column -356.0 -365.0 3.0

Bottom Column -70,2 224.9 1.0

Top Diagonal 11.4 6.8 10.2

Beam 434.7 896.4 1013.0

Lower Diagonal -20.2 -33.8 36.2

1 Loads at the gage locations

.

See Figure 2.18a

2 Sign convention:

+ value = positive X-direction, right hand coordinate system

+ value = positive Y-direction, right hand coordinate system

+ value = counter-clockwise moment.

- 40 -
Table 3.2 Material Properties

Specimen

o

y

(ksi)

Fu

(lbs)

Cross Sectional

Area

(in2

)

% Elongation

Column:

Test 1 63 - 0.281 39.1

Test 2 61 21,400.0 0.281 43.7

Test 3 55 21,350.0 0.278 40.6

Beam:

Test 1 63 19,550.0 0.252 40.6

Test 2 63 19,700.0 0.253 40.6

Test 3 61 18,550.0 0.253 40.6

Diagonal

Test 1 61 15,050.0 0.189 34.4

Test 2 60 15,150.0 0.190 34.4

Test 3 60 15,200.0 0.189 34.4

Top Gusset Plate:

Test 1 47 8,460.0 0.115 34.4

Test 2 41 8,440.0 0.114 34.4

Test 3 47 8,310.0 0.114 28.1

Bottom Gusset Plate:

Test 1 47 8,465.0 0.114 31.3

Test 2 49 8,360.0 0.115 34.4

Test 3 49 8,470.0 0.115 34.4

Tee Sections:

Coupon 1 49 7,100.0 0.103 34.4

Coupon 2 50 7,120.0 0.103 34.4

Coupon 3 49 8,350.0 0.115 34.4

Coupon 4 52 8,380.0 0.115 34.4

41
LRTERAL

LORD

(KIPS)

SPECINEN DISPLACEMENT (IN.

)

Figure 3.1 - Load vs. Deflection, Test 1A

42 -
Figure 3.2 - Buckled Lower Gusset Plate, Test 1A

43

LATERAL

LOAD

(kips)

125

AXIAL LOAD (kips)

Figure 3.4 - Lateral Load vs. Axial Loads in Diagonal Bracing, Test 1A

- 45
LATERAL

LOAD

(KIPS)

o'. 00 0.24 0.48 0.72 0 . 9G 1.20

SPECIMEN DISPLACEMENT ( IN.

)

Figure 3.5 - Load vs. Deflection, Test IB

46
47

Figure

3.6

-

Buckled

Upper

Gusset

Plate,

Test

IB
LATERAL

LOAD

(KIPS)

AXIAL LOAD (KIPS)

Figure 3.7 - Lateral Load vs. Axial Loads in Diagonal Bracing, Test IB

48 -
LATERAL

LOAD

(KIPS)

150 .

120 . -

90

60 . -

30 . -

0 . 0.00 0.24 0.48 0.72 0.96 1.20

SPECIMEN DISPLACEMENT ( IN.

)

Figure 3.8 - Load vs. Deflection, Test 2A

49
-20 12 44 76 108 140

AXIAL LOAD (kips)

Figure 3 . 9 - Lateral Load vs. Axial Loads in Diagonal Bracing, Test 2A

- 50 -
Figure 3.10 Buckled Lower Gusset Plate

,

Test 2A

51

:

<§.v' s

vV
Figure 3.11 View of the Closed Gap Between the Lower Gusset

and the Diagonal

52
LATERAL

LOAD

(KIPS)

150

120 . -

90 . -

60 . -

30 . -

0 . 0.00

Buckling load=132 kip

0.35 0.70 1.05 1.40 1.75

SPECIMEN DISPLACEMENT (IN.)

Figure 3.12 - Load vs. Deflection, Test 2B

53
LATERAL

LOAD

(KIPS)

0. 30. SO. 90. 120. 150.

AXIAL LOAD (KIPS)

Figure 3.13 - Lateral Load vs. Axial Loads in Diagonal Bracing, Test 2B

54
LRTERRL

LORD

(KIPS)

SPECIMEN DISPLACEMENT (IN.)

Figure 3.14 - Load vs. Deflection, Test 3A

55
56

Figure

3.15

-

Upper

Gusset

Plate,

Test

3A
LATERAL

LOAD

(kips)

-20 12 44 76 108 140

AXIAL LOAD (kips)

Figure 3.16 - Lateral Load vs. Axial Loads in Diagonal Bracing, Test 3A

57
58
LATERAL

LOAD

(KIPS)

SPECIMEN DISPLACEMENT (IN.)

Figure 3.18 - Load vs. Deflection, Test 3B

59
60

Figure

3.19

-

Top

Edge

of

Upper

Gusset,

Test

3B
LATERAL

LOAD

(KIPS)

AXIAL LOAD (KIPS)

Figure 3.20 - Lateral Load vs. Axial Loads in Diagonal Bracing, Test

61
62

iigure

3.21

-

Diagonal

Brace

in

Contact

with

Upper

Gusset,

Test

3B
Shaded area on gusset shows location from

which test coupons were obtained

Figure 3.22 - Location of Tensile Test Coupons in Gusset Plates

63
STRESS

(KSI)

STRAIN

Figure 3.23 - Stress - Strain Curve for Upper Gusset, Specimen No. 1

64
MOMENT DIAGRAM FOR TEST 1A

Figure 3.24 - Moment Diagram for Test 1A

MOMENT DIAGRAM FOR TEST 2A

Figure 3.25 - Moment Diagram for Test 2A

65
Test 1A <, Eccentric Moment Predicted for Test 2A

from Test 2A

Measured

values

Predicted

values

NOTE: Values in kip-in.

Figure 3.26 Predicted and Experimental Moments for Test 2A

66 -
MOMENT DIAGRAM FOR TEST 3A

Figure 3.27 - Moment Diagram for Test 3A

67

4.0 INTERPRETATION AND DISCUSSION OF RESULTS

4 . 1 Whitmore Failure Criterion

The Whitmore criterion, mentioned in Section 1.2, will be used in the

discussion of experimental results. The Whitmore criterion, developed in

1952, is applicable to bolted connections in tension. This criterion provides

a means by which a gusset plate may be designed (bolt pattern and plate

thickness chosen) for a given tension load. Application of the Whitmore

criterion involves constructing what is sometimes referred to as the Whitmore

section (see Figure 4.1). This section is defined as the length of the line

„ passing through the last row of fasteners and extending to the intersection of

the lines drawn from the first fasteners at a 30° angle from the line of the

fasteners. The Whitmore criterion states that yielding occurs when the direct

stress on the Whitmore section exceeds the tension yield stress of the gusset

plate material. The direct stress is the tension load divided by the product

of the Whitmore section and the plate thickness.

4 . 2 Comparison of Analytical and Experimental Results

Fung and Richard [8] performed an inelastic finite element analysis of each of

the NBS test specimens using a computer code developed by Richard at the

University of Arizona. A summary of their results is given in Table 4.1. The

results reported are the applied lateral frame load for which three criteria

are met: the Whitmore yield load which is described in Section 4.1, "first

yield" which is the lateral load at which the effective stress in the gusset

first reaches the yield stress of 36 ksi, and "general yield" which is the

lateral load at which the effective stress in the gusset exceeds 36 ksi in

many elements and is representative of the load corresponding to the

relatively flat portion of the load vs. deflection curve. The effective

stress is defined as

a eff = Ol 2 + a 2

2 ~ °1 cr 2)1//2

where

,

a l> °2 ~ Principal stresses
To compare experimental and computed capacities, it is necessary to interpret

the experimental results presented in Chapter 3 to determine the load at which

yielding occurs. Several definitions will be used here. The onset of

yielding will be defined as the point at which the load deflection curve

becomes nonlinear. To establish this point, a linear regression technique was

used to produce a "best fit" straight line through the data points below a lateral load of 50 kips. The resulting line, or initial tangent stiffness,

was then drawn on the experimental load vs. deflection plot, and the point of

departure from linearity chosen by observation. Figures 4.2, 4.3 and 4.4 show

the load vs. deflection plot, initial tangent stiffness and yield load for

Series A tests of Specimens 1, 2 and 3, respectively. The values determined

from this procedure are reported in Table 4.1 and are labeled "Nonlinearity of

Load-deflection Plot." Note that the departure from linearity reported here

should be interpreted as a lower bound on the yield load.

Two alternate definitions of yielding of the gusset plates are reported to

allow direct comparison with analytical results reported by Fung and Richard

[8]. First yield is defined as the lateral load on the test specimen at which

the effective stress in the gusset is computed to be greater than 36 ksi at

any strain rosette. A yield stress value of 36 ksi is used in this

calculation, rather than the measured yield stress of the gusset plates, to

permit a comparison with analytical results which used a value of 36 ksi.

Finally, general yield is defined as the load at which the effective stress,

computed from rosette strains, exceeds 36 ksi at a majority of the rosettes.

It should be pointed out that the rosette gages were located along the bottom

of the gusset (Figure 2.14) and the maximum stress in the gusset is likely to

be at the end of the diagonal brace and not captured by the rosettes. Thus,

the experimental values of first yield and general yield should be considered

to be upper bounds. Values for first yield and general yield are given in

Table 4.1 for all three specimens.

A comparison can be made between the analytical results reported by Fung and

Richard [8] and the experimental results reported herein by referring to Table

4.1. Both the Whitmore yield and first yield determined from the departure

from linearity of the load vs. deflection curve appear to predict the onset of

70 -
yield in Specimen Nos. 2 and 3. The comparison is not as close for Specimen

No. 1. However, the analytically determined yield load, ranging between 65

kips for the Whitmore yield load and 78 kips for first yield, falls between

the values of 45 kips and 87 kips determined from experimental results.

General yield as determined by experiment was higher than that predicted

analytically for all three specimens. Since the actual yield stress of the

gusset plate material was higher than the assumed yield stress, one would

expect a higher observed general yield for all three specimens.

Contour plots of the effective stress in the gussets for the three specimens

were reported in Reference [8]. Reproductions of these plots with the

experimental stress values superimposed on them are shown in Figures 4.5

through 4.7. The stresses in these figures correspond to an applied frame

load equal to the Whitmore yield load; that is 65 kips, 62 kips and 60 kips

for Tests 1A, 2A and 3A, respectively. As seen in the figures, the

experimental values and the analytical values agree very well. It would

therefore appear that the inelastic finite element analyses predict the state

of stress in the gusset accurately.

4 . 3 Design Capacities

The test specimens were designed using standard design practice and the design

guidelines developed by Williams and Richard [4] for the attachment of the

gusset to the beam and column. The gusset plate capacity in tension was

determined by applying the Whitmore criterion which gave a value of 41.4 kips

as shown in Table 4.2. (Design philosophies are discussed in the following

paragraphs and calculations are presented in Appendices A and B) . Buckling of

the gusset was checked using the procedure described by Thornton [6] and was

found to be 30.9 kips. The design of the gusset- to -column attachment was

based on Williams and Richard's equations and the AISC procedure for bolt

capacity in combined shear and tension for the clip angles. The capacity of

the gusset- to-column attachment was 74.8 kips. To allow comparisons to be

made between the test specimens, the gusset plate thickness, clip angles,

bolts, weld size, etc. were the same for all three test specimens.

71
Design capacities of the test specimens using various other methods are

presented here. The calculations were made by Dr. William Thornton. A

summary of Thornton's calculations is presented in this section in Tables 4.2

through 4.4. Detailed calculations for Specimen No. 1 are presented in

Appendix A. This section briefly discusses the methods used in determining

the brace capacities. The capacities were "back-calculated" as the member

sizes, weld and fastener sizes, and number of fasteners were known quantities.

The calculations were based on the material yield strength of Fy = 36 ksi and

ultimate strength of Fu = 58 ksi.

4.3.1 Capacity of Gusset Plate

For a given number of fasteners and gusset plate thickness, the capacities for

the gusset plate were determined using standard methods based on the AISC

Specification [13]. The bolts used to connect the brace to the gusset were

checked for bearing and double shear. The gusset, brace and splice were also

checked for tearout as described in the commentary of Reference [13].

Yielding of the gusset plate was computed using Whitmore's yield criteria as

described in Section 4.1. The buckling capacity of the gusset was determined

using the method outlined in Reference [6] and illustrated in Appendix A.

4.3.2 Methods to Distribute Brace Loads

Three different methods were used to compute the distribution of the load in

the diagonal brace to the beam and column. The first was that of Williams and

Richard [4] using the following equations:

RB = P [1.4 a / (a + b) - 0.1]

0 B = 0.6 9 for 9 < 45°

0 B = 27 + [8.5 - 20 a / (a + b) ] (45 - 9 ) for 9 > 45°

Hb = Rb cos 9 B

VB = Rb sin 0 B

HC = H - HB

VC = V - VB

72
where

,

P = Brace load

H = Horizontal component of the brace load

V = Vertical component of the brace load

9 = Angle that the brace makes with the horizontal axis

Rg = Resultant of the beam forces

Hg = Horizontal force on beam

Vg = Vertical force on beam

He = Horizontal force on column

Vc = Vertical force on column

a = Length of gusset plate

b = Width of gusset plate

A diagram showing these forces is given in Figure A. 2 in Appendix A. Williams

and Richard's method is based on results obtained from inelastic finite

element analyses. The effect of different gusset geometries is included in

this method.

Another method used to distribute the brace load to the beam and column was

proposed by Thornton [14]. Thornton's model is shown in Figure B.l in

Appendix B and his equations are as follows:

where

,

Hg = (a/r) P

Vg = (eg/r) P

VC = (0/r) P

HC = (e c/r) P

MB = VB ( a " a ) MC = HC 00 - b)

r =

a =

J (a + e c ) 2 + (0 + eb ) 2

K' tan 0 + K (a /b)

2

D

0 = K' - K tan 8 D

9 = Angle that the brace makes with the vertical axis

a, b = Centroids of the horizontal and vertical fastener

groups, respectively

73
K = eg tan 9 - e c K' = a [tan 9 + (a / b)

]

D = tan^ 0+(a/b)2

eg = Depth of beam / 2

e c = Depth of column / 2

This method is presented in Appendix B and will therefore not be discussed

here. In general, Thornton's model predicts capacities similar to those

predicted using Williams and Richard's method. However, it has the advantage

that it satisfies moment equilibrium which Williams and Richard's method does

not

.

The AISC procedure to distribute the brace load to the beam and column is that

outlined for heavy bracing connections in Reference [10]. In this procedure,

the gusset- to -column connection is typically designed for the vertical

component of the brace load and the gusset- to-beam connection is designed for

the horizontal component of the brace load (shear) and a moment equal to the

shear multiplied by half the beam depth. The equations for this method are,

then:

HB " » VB = 0

HC = 0

VC = v

MB = V (d/2)

where the above variables have been defined previously with the exception of,

Mg = Moment in the beam

d - Depth of the beam

The working point for this procedure is at the corner of the gusset. Although

this arrangement introduces an eccentric moment to the connection, the design

of the beam and column do not account for this moment as it is considered to

have "secondary" effects for small brace loads.

74
4.3.3

Capacity of Gusset- to-Beara Attachment

Once the forces distributed to the beam are known, using any of the methods

discussed above, the capacity of the attachments can be determined. The

capacity of the gusset- to-beam weld was computed taking into account combined

shear and tension if applicable. The capacity of the gusset plate in shear

and tension was also determined.

4.3.4 Capacity of Gusset- to -Column Attachment

The weld attaching the clip angles to the gusset was subjected to an eccentric

shearing force. The capacity of this weld was found using the tables in

Reference [13]. The clip angles were subjected to prying action, and the

capacity against this mode of failure was determined using the method proposed

by Thornton in Reference [6]. The shear capacity of the clip angles and the

capacity of the gusset plate in shear and tension were also computed.

Capacities of the bolts used to join the gussets to the column were also

determined using AISC's methods. Two such procedures to design fasteners

subjected to shear and tension are outlined in Reference [10] and referred to

as Case I and Case II. The basic assumptions of these two cases are 1) that

the stress in the fasteners varies linearly from the neutral axis of the

fastener group, and 2) that the shear stress is equal for all fasteners in a fastener group. The difference between the two cases is in the location of

the neutral axis. The neutral axis for Case II is assumed to be at the center

of gravity of the fastener group while the neutral axis for Case I is assumed

to be located at a distance equal to one-sixth of the total bracket depth from

the bottom of the bracket. As stated in Reference [10], Case II is a more

conservative approach than in Case I.

4.3.5 Capacity of the Beam- to-Column Attachment

The shear force at the end of the beam was computed by summing the vertical

forces from the upper and lower gusset. The clip- to-beam web weld was

subjected to this same shearing force plus a moment due to the eccentricity of

75
the shear force. Bolts to the column were checked in single shear and

bearing. The capacity of the beam web was checked for shear and bending.

4 . 4 Comparison Between Experimental and Design Capacities

In this section, a comparison is made between the capacities computed using

various design approaches and the experimental results reported herein. Only

the capacities corresponding to the following failure modes are compared:

o Bolt capacity in clip angles- to -column connection

o Buckling of the gusset plate

o Yielding of the Whitmore section .

o Tearout of the gusset plate

These failure modes produced the four lowest design capacities (see Tables 4.2

through 4.4).

The capacities presented are forces in the diagonal member . Margins of safety

are computed by dividing the experimental capacity by the computed capacity.

Note that, if the gusset failed by buckling, then the margins of safety

reported for yielding and tearout are actually lower bounds -- in other words,

the margin of safety is, as a minimum, equal to the reported value. Minimum

margins of safety are identified by an asterisk. Two margins of safety are

given. The first is computed using the yield capacity defined by the

departure from linearity of the load vs. deflection curve. The second is

computed using the measured ultimate capacity. These two factors are useful

in interpreting the experimental results in terms of both strength and

serviceability

.

4.4.1 Bolt Capacity in Clip Angles - to-Column Connection

As seen from Tables 4.2 through 4.4, the capacity of the test specimens was

limited by the axial capacity of the bolts attaching the clip angles to the

column. The brace capacity, as governed by the clip angles, was approximately

18 kips. Compared to measured capacities of 116 kips and 138 kips for Tests

1A and 2A, respectively which failed by gusset buckling, and 125 kips for Test

76
3A which failed by gusset tearing, the design capacity of the brace of 18 kips

for the clip angles is extremely conservative. This finding is further

reinforced by the lack of visible signs of distress or prying of the clip

angles, even after extensive buckling of the gusset. One possible explanation

for this is that forces on the gusset- to-column attachment resulting from

frame action ("rigid" beam- to-column connection provided by the gusset

plates), tended to oppose the forces resulting from the diagonal bracing. For

instance, in Test A, the top brace was in tension which produced tension on

the upper gusset- to-column connection. However, the beam- to-column

connection, being very rigid, produced compression in the upper gusset at the

gusset- to-column attachment as frame action contributed to resisting the

applied lateral load. These two forces tended to cancel. The limiting

capacities of the three specimens tested were not related to failure of the

clip angles. Hence, the capacity due to this mode of failure is not included

in the following discussions.

4.4.2 Buckling of the Gusset Plate

The brace- to-gusset capacity was limited by buckling as computed using

Thornton's method. This can be seen from Tables 4.2 to 4.4 in which the

computed buckling capacity ranges between 30.9 kips and 34.8 kips. Table 4.5

presents a comparison between computed design capacities and measured

capacities for buckling of the gusset plate. For Specimen No. 1, it is seen

that the margin of safety with respect to ultimate capacity is 3.8. If the

yield load is used, the margin of safety is 1.6. Since excessive deflections

can result once yielding begins, this may be regarded as a serviceability

limit. For Specimen No. 2, the buckling capacity was computed to be 34.8

kips. If the buckling load of 138 kips is used as the limiting capacity, the

margin of safety is 4.0. The margin of safety for yielding is 1.9. Since

Specimen No. 3 failed by tearout before it failed by buckling, the buckling

strength was at least as great as the tearout strength. As a result, the

margin of safety computed for buckling should be considered to be a lower

bound or minimum margin of safety. For Specimen No. 3, the value reported in

Table 4.5 for the minimum margin of safety against buckling is 3.6.

77
4.4.3 Yielding of the Whitmore Section

Design of the gusset plate using the Whitmore yield criterion is essentially

the same as design against tearout. Indeed, both design methods are based on

the gusset plate thickness and the arrangement (spacing and pitch) of bolt

holes. In design practice, one would not need to check both the Whitmore

yield criterion and tearout.

Table 4.6 presents a comparison between computed design capacities and

measured capacities for yielding of the Whitmore section. The computed

Whitmore yield load (load in the diagonal brace) is 41.4 kips. It is seen

that, for Specimen No. 3, the margin of safety for ultimate capacity is 3.0.

The margin of safety against yielding for Specimen No. 3 is 1.4.

4.4,4 Tearout of the Gusset Plate

The computed design capacity based on gusset tearout is 45.4 kips which is

close to the capacity of 41.4 computed for yielding of the Whitmore section.

Indeed, Specimen No. 3 failed by gusset tearout. In this section,

experimental results will be compared with several methods for computing

tearout capacity. In addition to the method already presented (AISC-ASD)

,

three methods for block shear tearout will be compared to experimental

results

.

The design of a gusset plate based on the block shear concept is a recent

development. Block shear failure became a concern when the allowable bearing

stress for bolted connections was increased from 1.35 Fy to 1.50 Fu . Hardash

and Bjorhovde [5] conducted a series of tests at the University of Arizona to

determine the ultimate capacity of a tension connection. Based on their work

and on results of similar studies conducted at the University of Alberta and

the University of Illinois, Hardash and Bjorhovde proposed the following

equations

F-n = Fu

S ne £ + 1.15 Fe ff (1) (t)

- 78
where

,

Feff = C 1 " c l) F

y

+ C 1 Fu

Cj_ = 0.95 - 0.047 L

Rn = Nominal ultimate resistance of connection

S ne t = Net gage distance between outside bolts

t = Plate thickness

L = Distance from center of last row of bolts to plate

edge = 1^ (see Figure 4.8)

Fy = Yield stress

Fu = Tensile strength

In a report by Williams and Richard [4] , the following equation for

determining the ultimate block shear load was presented:

RU

= Avg FVu + Atg F tu

where

,

Ru = Nominal ultimate resistance of connection

AVg = gross shear area = 1 2 x s (Figure 4.8)

FVu = ultimate shear stress = Fy /

At g = gross tensile area

F tu = ultimate tensile stress - Fu

Williams and Richard recommend that, for connections with less than six bolts

per row, the net shear area rather than the gross shear area be used in the

above equation.

Block shear strength, by the AISC Load and Resistance Factor Design [15]

approach, is the larger value determined by the following two equations:

Rn = <t> (0.6 Fy Avg + Fu

Ant)

Rn = <t> (0.6 Fu ^ns + F

y

Atg)

where

,

0 = 0.75

AVg = Gross area subjected to shear

At g = Gross area subjected to tension

79
V Ans = Net area subjected to shear

Ant = Net area subjected to tension

Fy = Yield stress

Fu = Tensile strength

In the following section, the capacities computed using the methods described

above are compared with the experimental results. To permit comparison with

allowable stress calculations, a load factor of 1.4 and a resistance factor of

0.75 are used for those equations written in terms of nominal ultimate

resistance

.

* The four methods for computing tearout are seen to give maximum diagonal brace

loads ranging from 34.8 kips to 57.8 kips as shown in Tables 4.7a through

4.7d. The minimum margins of safety based on ultimate capacity range from 2.0

to 4.0 for all three specimens. For Specimen No'. 3, which failed by tearout,

the margins of safety for the various methods ranged between 2.2 and 3.6. The

margins of safety based on the yield capacity for Specimen No. 3 ranged

between 1.1 and 1.8. The AXSC-LRFD method [15] produced the most conservative

estimate of design capacity while the method by Hardash and Bjorhovde [5]

produced the least conservative. A better understanding of how well each of

these methods is able to predict tearout capacity of the gusset is obtained by

using the measured material properties in the calculations. A comparison of

the various methods on this basis is given in the next section.

4 . 5 Comparison Between Experimental and Calculated Capacities

The design capacities reported above were based on assumed material strength

of Fy = 36 ksi and Fu = 58 ksi. To get an idea of how well buckling and

tearout can be predicted, the calculations were repeated using measured

material strength. The yield stress for the gusset was taken as the average

of the six values of yield stress for the gusset plates reported in Table 3.2

and was equal to 46.7 ksi. Similarly, the ultimate strength was computed as the average of the six ultimate load values divided by the respective crosssectional area and was equal to 73.5 ksi. In addition, the factor of safety,

load factor and resistance factor were not used in the calculations. Thus the

80 -
values reported represent the computed nominal capacity of the gusset in terms

of force in the diagonal bracing member. The computed capacities are compared

with the experimental capacities for the applicable mode of failure.

4.5.1 Buckling of the Gusset Plate

A value of K=0 . 5 was used in the calculation of the buckling capacity rather

than the value of K=0.65 suggested by Thornton [6]. This theoretical K-value

was used since ideal end conditions (no rotation) are closely approximated.

The resulting nominal capacities are presented in Table 4.8. It is seen that

for Specimen No. 1, the nominal buckling capacity is 77.5 kips and the

measured buckling capacity was 116 kips. The measured capacity divided by the

computed capacity, or strength ratio, is 1.5. For Specimen No. 2, which also

failed by buckling of the gusset, the nominal capacity is 83.4 kips, the

measured buckling capacity was 138 kips, and the strength ratio is 1.7. Thus

it is seen that Thornton's method for computing buckling capacity is somewhat

conservative predicting capacities roughly 60 to 70 percent of the measured

capacities. Still, the calculations are simple to make and the results are

not so conservative as to render the method impractical.

4.5.2 Tearout of the Gusset Plate

The computed nominal capacities for gusset tearout using the four methods

described above are given in Table 4.9 along with the measured capacity for

Specimen No. 3 which failed by tearout. The margin of safety is also

presented. It is seen that the strength ratio ranges between 0.9 for the

method by Williams and Bjorhovde [5] to 1.4 for the method by Williams and

Richard [4]. The AISC-LRFD method gives a strength ratio of 1.1 and is

relatively simple to apply.

81
Table 4.1 - Experimental Results vs. Richard's Analytical Results^

Specimen No. 1 Specimen No . 2 Specimen No. 3

Analytical Results from Fung and Richard [8]

Whitmore Yield 65 62 60

First Yield

Upper Gusset 78 62 61

Lower Gusset 76 66 61

General Yield

Upper Gusset 90 75 76

Lower Gusset 90 75 60

Experimental Results

Nonlinearity of

Load-defl. plot 45 61 59

First Yield^

Upper Gusset 87 56 68

Lower Gusset 80 36 43

General Yield^

Upper Gusset 102 90 93

Lower Gusset 89 88 93

1 The unit for the load is kips and all values are applied frame load.

2 The first yield load was taken as the load at which the Von Mises stress

was greater than 36 ksi at any rosette.

3 The general yield load was taken as the load at which the Von Mises

stress was greater than 36 ksi at a majority of the rosettes.

82 -
Table 4.2 - Allowable Stress Design Brace Load for Specimen No. 1

Connection Element Limit

State

Common Design Practice

(based on AISC)

Bolts Shear 77.4 kips

Brace Web Tearout 50.8

Bearing 73.1

Brace Gusset Tearout 45.4

to Bearing 65.3

Gusset Whitmore 41.4

Buckling 30.9

WT Tearout 125.0

Conn. Gross- 140.0

Yield

Net- 157.0

Fracture

- Bearing 188.0

AISC

Richard Thornton AISC AISC HEAVY

CASE I CASE II BRACING

Gusset FW1 Yield 90.0 146.5 * * 59.0

to Beam Gusset Yield 85.1 103.6 * * 61.5

Gusset FW2 Yield 125.0 223.1 * * 56.8

to Bolts Shear 211.0 286.3 k * * Column Bearing 355.0 483.3 * * * Clips Net-shear 257.4 350.4 * * * Axial 74.8 20.6 25.1 17.5 20.8

FW3 Yield 106.0 66.8 * * •k Beam Bolts Shear 71.9 57.5 * * k

to Bearing 122.0 96.0 k * k

Column Clips Net- shear 225.0 178.3 •k k k

Beam web Shear 136.0 107.8 ie k •k Bending 90.7 71.8 * k k

* This load will not control

83
Table 4.3 - Allowable Stress Design Brace Load for Specimen No. 2

Connection Element Limit

State

Common Design Practice

(based on AISC)

Brace

to

Gusset

Bolts

Brace Web

Gusset

WT

Conn.

Shear

Tearout

Bearing

Tearout

Bearing

Whitmore

Buckling

Tearout

GrossYield

NetFracture

Bearing

77.4 kips

50.8

73.1

45.4

65.3

41.4

34.8

125.0

140.0

157.0

188.0

Richard Thornton AISC

CASE I

AISC

CASE II

AISC

HEAVY

BRACING

Gusset FW1 Yield 61.8 NA1 * * 69.7

to Beam Gusset Yield 58.5 NA * * 45.1

Gusset FW2 Yield 93.1 NA * k 65.7

to Bolts Shear 191.0 NA k k 108.0

Column Bearing 325.0 NA k k 183.0

Clips Net- 235.0 NA k k 133.0

Shear

Axial 20.4 NA k k NL2

FW3 Yield 109.0 NA * k NL

Beam Bolts Shear 92.3 NA k k NL

to Bearing 157.0 NA k '

NL

Column Clips NetShear

291.0 NA k k NL

Beam web Shear 176.0 NA k k NL

Bending 117.0 NA k k NL

^ NA = Thornton's method is not applicable to this test specimen.

^ NL = No constraint on P due to this limit state.

84 -
Table 4.4 - Allowable Stress Design Brace Load for Specimen No. 3

Connection Element Limit

State

Common Design Practice

(based on AISC)

Bolts Shear 77.4 kips

Brace Web Tearout 50.8

Bearing 73.1

Brace Gusset Tearout 45.4

to Bearing 65.3

Gusset Whitmore 41.4

Buckling 34.4

WT Tearout 125.0

Conn

.

Gross - 140.0

Yield

Net- 157.0

Fracture

Bearing 188.0

Richard Thornton AISC

CASE I

AISC

CASE II

AISC

HEAVY

BRACING

Gusset FW1 Yield 64.7 NA1 * * 73.8

to Beam Gusset Yield 61.0 NA k k 47.7

Gusset FW2 Yield 98.4 NA * k 68.8

to Bolts Shear 203.0 NA * k 113.0

Column Bearing 345.0 NA * * 191.0

Clips Net- 250.0 NA * * 139.0

Shear

Axial 21.2 NA k * NL2

FW3 Yield 112.0 NA * k NL

Beam Bolts Shear 94.6 NA k k NL

to Bearing 161.0 NA k k NL

Column Clips NetShear

299.0 NA * k NL

Beam web Shear 180.0 NA * k NL

Bending 120.0 NA k k NL

NA = Thornton's model not applicable to this test specimen.

2 NL = No constraint on P due to this limit state

- 85
Table 4.5 - Comparison between Computed Design Capacities and Measured

Capacities for Buckling of Gusset Plate (1)

Specimen

No.

Computed

Design

Capacity (2)

Measured Capacity Strength Ratio (4)

Yield (3) Ultimate Yield (3) Ultimate

1 30.9 50 116 1.6 3.8

2 34.8 65 138 1.9 4.0

3 34.4 60 125 1.7* 3.6*

Table 4.6 - Comparison

Capacities

between Computed Design Capacities and

for Yielding of Whitmore Section (1)

Measured

Specimen

No.

Computed

Design

Capacity (2)

Measured Capacity Strength Ratio (4)

Yield (3) Ultimate Yield (3) Ultimate

1 41.4 50 116 1.2* 2.8*

2 41.4 65 138 1.6* 3.3*

3 41.4 60 125 1.4 3.0

* Minimum Strength Ratio

Notes

(1) Reported values are loads in the diagonal brace.

(2) Based on Fy = 36 ksi.

(3) Yield is defined as departure from linearity of load vs. deflection

curve (see Figures 3.4 through 3.6).

(4) Strength Ratio is the measured capacity divided by the computed design

capacity

.

86 -
Table 4.7a - Comparison between Computed Design Capacities and Measured

Capacities for Tearout of Gusset Plate (1)

AISC-ASD Design Method [13]

Specimen

No.

Computed

Design

Capacity (2)

Measured Capacity Strength Ratio (4)

Yield (3) Ultimate Yield (3) Ultimate

1 45.4 50 116 i.i* 2.6*

2 45.4 65 138 1.4* 3.0*

3 45.4 60 125 1.3 2.8

Table 4. 7b - Comparison between Computed Design Capacities and

Capacities for Tearout of Gusset Plate (1)

Measured

Williams and Richard Method [4]

Specimen

No.

Computed

Design

Capacity (2)

Measured Capacity Strength Ratio (4)

Yield (3) Ultimate Yield (3) Ultimate

1 37.9 50 116 1.3* 3.1*

2 37.9 65 138 1.7* 3.6*

3 37.9 60 125 1.6 3.3

* Minimum Strength Ratio

Notes

:

(1) Reported values are loads in the diagonal brace.

(2) Based on Fy = 36 ksi and Fu = 58 ksi.

(3) Yield is defined as departure from linearity of load vs. deflection

curve (see Figures 3.4 through 3.6).

(4) Strength Ratio is the measured capacity divided by the computed design

capacity

.

87
Table 4.7c - Comparison between Computed Design Capacities and Measured

Capacities for Tearout of Gusset Plate (1)

Hardash and Bjorhovde Method [5]

Specimen

No.

Computed

Design

Capacity (2)

Measured Capacity Strength Ratio (4)

Yield (3) Ultimate Yield (3) Ultimate

1 57.8 50 116 0.9* 2.0*

2 57.8 65 138 i.i* 2.4*

3 57.8 60 125 1.0 2.2

Table 4.7d - Comparison between Computed Design Capacities and Measured

Capacities for Tearout of Gusset Plate (1)

AISC-LRFD Method [15]

Specimen

No.

Computed

Design

Capacity (2)

Measured Capacity Strength Ratio (4)

Yield (3) Ultimate Yield (3) Ultimate

1 34.8 50 116 1.4* 3.3*

2 34.8 65 138 1.9* 4.0*

3 34.8 60 125 1.7 3.6

* Minimum Strength Ratio

Notes

(1) Reported values are loads in the diagonal brace.

(2) Based on Fy = 36 ksi and Fu = 58 ksi.

(3) Yield is defined as departure from linearity of load vs. deflection

curve (see Figures 3.4 through 3.6).

(4) Strength Ratio is the measured capacity divided by the computed design

capacity

.

88
Table 4.8 - Comparison between Computed Buckling Capacity and Measured

Buckling Capacity for Specimens No. 1 and 2 (1)

Specimen

No.

Computed Nominal

Capacity (2)

Measured Ultimate

Capacity

Strength

Ratio (3)

1 77.5 116 1.5

2 83.4 138 1.7

Table 4.9 - Comparison between Computed Tearout Capacity and Measured

Tearout Capacity (Specimen No. 3) for Various Methods (1)

Method Computed Nominal Measured Ultimate Strength

Capacity (2) Capacity Ratio (3)

AISC-ASD [13] 115 125 1.1

Williams and Richard [4] 91 125 1.4

Hardash and Bjorhovde [5] 137 125 0.9

AISC-LRFD [15] 111 125 1.1

Notes

:

(1) Reported values are loads in the diagonal brace.

(2) Based on Fy = 46.7 ksi and K=0„5Q.

(3) Strength Ratio is the measured capacity divided by the computed

capacity.

89
Figure 4.1 - Whitmore Section

90
Determination

of

Nonlinearity

-

Test

1A

(dpi) avoi

CO

a o

eg

o

o

o2

o

a)

Clog

a;

Zj00

ClH

91

DISPLACEMENT

(in.)
Determination

of

Nonlinearity

-

2A

LO

O

o

CO

o o

04

o

o

o o o

CD CD 00

o

ho o o

CD LO

^

(dj>i) avoi

O

CO

O

04

CNJ

o2

<ug

CJ

<y

<U'h3

&£) •r4

92 -

DISPLACEMENT

(in.)
Determination

of

Nonlinearity

-

Test

3A

(dpi) avon

ro

O

<D

O

n

i

<T

Cjh

93

DISPLACEMENT

(in.)
-rr-\-

Figure 4.5 - Stress Contour Plot for Specimen No. 1 (Ref. [8])

with Experimental Values Superimposed

94
Figure 4.6 - Stress Contour Plot for Specimen No. 2 (Ref. [8])

with Experimental Values Superimposed

95
Figure 4.7 - Stress Contour Plot for Specimen No. 3 (Ref. [8j)

with Experimental Values Superimposed

96
BLOCK SHEAR MODEL

Figure 4.8 - Block Shear Failure Mode

97

5.0 SUMMARY AND CONCLUSIONS

5.1 Summary

The behavior of three diagonally braced steel subassemblages was studied

and column orientation. Specimen No. 1 was a strong-axis column connection in

which the axes of the bracing members, beam and column all intersected at a single point. This connection was referred to as having no eccentricity.

Specimen No. 2 was a strong-axis column connection in which the axes of the

connection of this configuration, it was referred to as eccentric. Specimen

No. 3 was similar to Specimen No. 2 except that the column was oriented so

that its weak axis acted in the plane of the bracing. The specimens were

loaded to failure in their plane and load-deformation as well as strain data

was recorded.

The failure mode for both strong-axis column connections was gusset buckling.

The weak-axis column connection failed by tearing of the gusset plate.

Specimen No. 2 with a compact gusset proved to be a stronger connection than

Specimen No. 1. Although the mode of failure differed for Specimen No. 2 and

Specimen No. 3, the failure load for the two specimens was essentially equal.

The moment introduced by the eccentricity in the bracing was distributed to

the beam and column in the strong-axis column connection. This moment was

carried almost entirely by the beam in the weak-axis connection due to the

flexibility in the web connection. The stress distribution in the gusset

plates predicted by Richard's INELAS program, a nonlinear finite element

program, compared very well with experimentally obtained stresses.

The connections were designed in accordance with AISC using Richard's

guidelines for distributing the bracing loads to the main framing members. In

general, all three subassemblages performed well. The failure loads for all

three specimens were found to be well above the capacities predicted using a variety of methods. Generally, comparisons of design capacities with the

experimental values resulted in a factor of safety in excess of 2. The

The parameters which were varied included the gusset geometry

bracing members did not coincide with the intersection of the beam and column

axes. Because forces in the diagonal bracing introduce a moment into a

99
current method of computing gusset buckling capacity appears to be slightly

consrevative predicting a capacity of 60% to 70% of that obtained

experimentally. The capacity of the clip angles was computed to be very low

using the AISC Specification, yet no distress in the clip angles was observed.

One possible explanation for this is that frame action introduced a moment

which loaded the gusset- to-column bolts in the opposite sense to the load

produced by the bracing.

5 . 2 Conclusions

The following conclusions were drawn from the results of the NBS tests:

o Connections designed using the AISC Specification and Richard's

equations for distributing the bracing loads to the framing members

exceeded their design capacity by a factor of at least two.

o Failure of the clip angles, as predicted per the AISC Specification,

was not observed and allowable bolt tension based on this criterion

produces an unrealistically low connection capacity.

o Gusset buckling capacity, as predicted by Thornton's method, compares

well with experimentally determined capacity.

o Gusset tearout capacity is predicted very closely using either Hardash

and Bjorhovde’s method or the AISC-LRFD approach.

o The weak-axis column connection had a capacity which was comparable to

that of the strong-axis column connection despite the connection to a relatively flexible column web. However, the moment introduced by the

eccentric bracing in Specimen No. 3 was resisted mainly by the beam.

o The moment introduced by the eccentricity of the bracing in Specimen

No. 2 was resisted mainly by the beam and column in proportion to I/L.

- 100
o The moments introduced into the beam and column by the eccentric brace

loading were considerably less than the moments resulting from the

rigid beam- to-column connection.

101
'

.

.
REFERENCES

1. Richard, Ralph, "Analysis of Large Bracing Connection Designs for Heavy

Construction", Proceedings of The 1986 National Engineering Conference,

AISC, Nashville, June 12-14, 1986.

2. Whitmore, R. E., "Experimental Investigation of Stresses in Gusset

Plates," Bulletin No. 16, Engineering Experiment Station, University of

Tennessee, May, 1952.

3. Bjorhovde, Reidar, and Chakrabarti, S. K. , "Tests of Full-Size Gusset

Plate Connections," Journal of Structural Engineering, ASCE, Vol, 111,

No. 3, March, 1985, pp . 667-684.

4. Williams, George C., and Richard, Ralph M. , "Steel Connection Designs

Based on Inelastic Finite Element Analysis," The University of Arizona,

1986.

5. Hardash, Steve G., and Bjorhovde, Reidar, "New Design Criteria for Gusset

Plates in Tension", Engineering Journal, Vol. 22, No. 2, AISC, 1985, pp

.

77-94.

6. Thornton, William A., "Bracing Connections for Heavy Construction,"

Engineering Journal, American Institute of Steel Construction, 3rd

Quarter, 1984, Vol. 21, No. 3, pp. 139-148.

7. Hu, S. Z. , and Cheng, J. J. Roger, "Compressive Behavior of Gusset Plate

Connections," Structural Engibeering Report No. 153, University of

Alberta, 1987.

8. Fung, John Y. , Richard, Ralph M. , "Inelastic Finite Element Analysis of

Gusset Plates," The University of Arizona, 1987.

9. Vasarhelyi, Desi D., "Tests of Gusset Plate Models," Journal of the

Structural Division, ASCE, Vol. 97, No. ST2 , February, 1971, pp . 665-678.

10. Engineering for Steel Construction, American Institute of Steel

Construction, Chicago, 1984.

11. Woodward, Kyle, and Rankin, Frank, "The NBS Tri-Directional Test

Facility," NBSIR 84-2879, U.S. Department of Commerce, National Bureau of

Standards, May, 1984.

12. 1984 Annual Book of ASTM Standards -- Section 1, Iron and Steel Products,

American Society for Testing and Materials, Philadelphia, 1984.

13. Manual of Steel Construction, 8 th. ed. , American Institute of Steel

Construction, Inc., 1980.

14. Personal communication with Dr. William Thornton.

15. Manual of Steel Construction - Load & Resistance Factor Design, First

Edition, American Institute of Steel Construction, Inc., 1986.

103
16. Specification for Structural Joints Using ASTM A325 or A490 Bolts,

American Institute of Steel Construction, Inc., 1985.

17. Thornton, William A., "Prying Action - A General Treatment," Engineering

Journal, American Institure of Steel Construction, 2nd Quarter, 1985,

Vol . 22, No. 2, pp. 67-75.

104
APPENDIX A - DESIGN CALCULATIONS FOR SPECIMEN NO. 1

Calculations of the design capacities were done by Dr. William Thornton and

are presented here. The calculations for Specimens No. 2 and No. 3 are

similar to calculations for Specimen No. 1 and are not presented.

Specimen No. 1

A. Brace to gusset

1. Bolts: 6 A325N, 5/8 <t>

rDS = 2 AbFv = 2 (0.3068) 21 = 12.9 k

Allowable Shear = Pv = 6 (12.9) = 77.4 k

Bearing

Pb = 6 (1.2 Fu Db t)

= 6 (1.2) (58) (0.625) (0.25)

= 65.3 k

2. Gusset

:

1/4 in. Plate, A36

Tearout

:

Av = [5 - 2.5 (11/16)] (0.25) (2) = 1.64 in. 2

At = [3 - 1 (11/16)] (0.25) = 0.58 in. 2

P t0 = 0.30 Av Fu + 0.5 At Fu

= 0.3 (1.64) (58) + 0.5 (0.58) (58)

= 45.4 k

AISC MANUAL

Table 1.5. 2.1,

p. 5-24

Ref. [16]

Table 2,

p. 6-269

Commentary

Sect. 1.5. 1.2

p. 5-108

Whitmore

:

lw = 4 (tan 30) 2 + 3 = 7.62 in.

Pw

= l w t Fb = (7.62) (0.25) (0.6) (36) = 41.4 k

Buckling [ 6 ]

:

1^—8 in., I 2 = 14.75 in., I 3 = 1.5 in. (Figure 4.1)

l aVg = 8.08 in.

105
ki/r = 0.65 (8.08)/ (0.25 / 412) = 72

Fa = 16.22 ksi

^buckling = Fa

lw t = 16.22 (7.62) (0.25)

= 30.9 k

3. Brace: W8 x 21, A572, Gr. 50

Tearout

P to = 0.3 (1.64) (65) + 0.5 (0.58) (65) = 50. 8 k

Bearing

Pb = 1.2 (65) (0.625) (0.25) 6 = 73.1 k

Gross Section:

Ag - 6.16 in. 2

pgross = 0.6 FY A

g = °- 6 ( 5 °) (6.16) = 185 k

Net Section:

An = A

g

- 2Dt = 6.16 - 2 (0.75) (0.25)

= 5.78 in. 2

Ae = C t An = 0.85 (5.78) = 4.91 in. 2

pnet = 4 - 91 (0.5) (65) = 160 k

4. Connection

WT 5 x 11, A3

6

Tearout (Figure A.l):

Av = [5 - 2.5 (11/16)] (0.36) (2) = 2.36 in. 2

At = [1.375 - 0.5 (11/16)] (0.36) (2) = 0.74 in. 2

p to = [°- 3 (2.36) (58) + 0.5 (0.74) (58)] 2

= 125 k

Bearing

Pb = 1.2 (58) (0.625) (0.36) (6) (2) = 188 k

Gross Section: Ag = 3.24 in. 2

P

g = 3.24 (0.6) (36) (2) = 140 k

Table 3-36,

p. 5-74

Sect . 1 . 5 . 1 .

p. 5-18

Sect . 1.14.4

p. 5-44

Sect. 1.14.2.2

p. 5-43

- 106
Net Section:

Anet = 3.24 - 2 ( 0 . 75 ) (0.36) = 2.70 in. 2

Check - 0.85 Ag = 2.75 in. 3 > 2.70 in. 2

use 2.70 in. 3

Pne t = 2 * 70 (°- 5 ) ( 58 > (2) = 157 k

B. Gusset to Column and Beam (Column: W 10 x 49, Beam: W 16 x 40)

1. Williams and Richard's Method (Figure A. 2) Ref. [4]

RB = P [1.4 a / (a + b) - 0.1]

0 B = 0.6 9 for 9 < 45°

0 B = 27 + [8.5 - 20 a / (a + b)](45 - 9 ) for 9 > 45°

Hb = RB cos 9 VB = RB sin 9 HC = H - HB

VC = V - VB

for 9 = 30.92°, a = 23 in. , b = 11 in.

Rb = 0.847 P

HB = 0.803 P

VB = 0.269 P

Hc = 0.055 P

Vc = 0.245 P

2. FW1 (Figure A. 3)

fv = Hb/2 1 = 0.803 P / 2 (19) = 0.021 k/in.

f t = Hc/2 1 = 0.269 P / 2 (19) = 0.007 k/in.

f r = (fv

2 + ft 3

) 1 / 3 = 0.022 P

fr = capacity of 3/16 in. weld

0.022 P = 3 (0.928)

P = 126 k

Using the recommended variability ratio [4] to account for

non-uniform force in weld:

P = 126 / 1.4 = 90.0 k

3 . Gusset at FW1

Shear

:

107
av = 0.803 P / [0.25 (19)] < 0.4 F

y

P = 0.4 (36) (0.25) (19) / 0.803

= 85.1 k

Tension:

<7 t = 0.269 P / [0.25 (19)] < 0.6 F

y

P = 0.6 (36) (0.25) (19) / 0.269

= 381 k

4. FW2 (Figure A. 4)

tan <f> = 0.055 / 0.245

<i> = 12.65°

Since <£ is small, treat resultant, R = 0.215 P, as

if it is a vertical shear.

For kl = 2.5, 1 = 10 in., al = 2.75 in., a = 0.275 Table XV

p. 4-82

C - 0.794

R = CCiDl

r = [0.794 ( 1) (3) ( 10) (0 . 25 / 0.38)] 2 Table III

p. 4-31

P = R / 0.251 = 125 k

5. Bolts at Clio Angles . 8 A325N, 5/8 0

Shear

^ss — ^b Fv Sect . 1 . 5 . 2 .

p. 5-24

8 (0 . 3068) (21) = 0.245 P

P = 210 k

Bearing

Fp — 1.2 Fu A

Ref. [16]

Table 2,

p. 6-269

0.245 P = F-P

P = 1.2 (58) [8 (0.625) (0.25)] / 0.245

355 k

108
6 . Axial force on clip angles . L 3 1/2 x 3 x 1/4, A36

Given: b = 2.375 - 0.25 = 2.125 (Figure A. 2) Ref. [17]

a = 3.5 - 2.375 = 1.125

check 1.25 b > 1.125, use a = 1.125

b' = b - d/2 = 2.125 - 5/16 = 1.8125

a' = a + d/2 = 1.125 + 5/16 = 1.4375

p = b'/a' = 1-2608

5=1- d'/P = 1 - (11/16) / 2 = 0.6563

B = 55 Ab

- 1.8 Vb < 44 Ab Table 1.6.3

p. 5-28 = 16.67 - 1.8 Vb < 13.5

Try P = 30.9 k (gusset buckling load controls so far)

Shear: V = 0.245 P = 0.245 (30.9) = 7.57 k

Vb = V / 8 = 7.57 / 8 = 0.946 k/bolt

B = 16.67 - 1.8 (0.946) = 14.97 > 13.5

use B = 13.5 k

1 8Bb '

2

1 5(1 + p) Pt Fy

1 8 (13.5) (1.8125) _ 0.6563 (2.2608) 2 (25)

2

(36)

= 28.64 > 1 angle bending controls

Max. allowable tension per bolt, Tb

Tb (1 + 5a)

Ref. [17]

Since a > 1, use a = 1

2 (0 , 25 2

) (36)

8 (1.8125) (1.6563)

= 0.514 kip/bolt

Max. allowable tension load is

T = 8 (0.514) = 4.11 k

109
0.055 P = 4.11

P = 74.8 k

Re-check shear per bolt

V = 0.245 (74.8) = 18.3 k

Vb = 18.3 / 8 = 2.29 k/bolt

B = 16.67 - 1.8 (2.29) = 12.54

a = 0.6563 (2.2608)

8 (12.54) (1.8125)

2 (0.25)2(36)

- 1

7.

= 26.56

Since a still > 1 , Tb max = 0.514 k/bolt

Shear on Clip Angles

OK

0.245 P

P

^ Fu Ane t

257.4 k

Sect. 1.5. 1.2.2

p. 5-19

C. Beam- to-Column - Using Williams and Richard's forces

1. FW3 (Figure A. 5)

For kl = 0, a = 0.25

C = 0.630

R = CCxDL = 2 [0.630 (1) (3) (12)

]

= 45.4 k

0.538 P = 45.4

P = 84.3 k

2 . Beam Web

Shear

av = 0.538 P / Aw < 0.4 Fy

P = 0.4 (50) (0. 305) (12) / 0.538

P = 136 k

Table XXIII

p. 4-80

Sec t . 1 . 5 . 1 .

p. 5-18

- 110 -
Bending: Sect . 1 . 5 . 1 . 4 .

4

S = 1/6 (0.305) 12 2 = 7.32 in2

M = 0.538 P (4.5)

<71-, = M/S < 0.6 Fy

P = 0 . 6 (50) (7 . 32) / 0.538(4.5)

P = 90.7 k

3. Bolts

p. 5-21

Shear

:

0.538 P = 6 Ab

Fv

P = 6 (0 . 3068) (21 ) / 0.538

= 71.9 k

Bearing

:

Sect . 1 . 5 . 2 .

2

0.538 P = 1.2 Fu Db t Ref. [16]

P = 1.2(58)(0.625)(0.25) / 0.538

= 122 k

4. CliD Angles

Shear

:

0.538 P = 2(0.3 Fu) Anet

P = 2(0.3) (58) [16 - 3(11/16)](0.25) / 0.538

P = 225 k

Table 2,

p. 6-269

D . AISC Methods Ref. [10]

1. Case II (Figure A. 6)

Clip Angles:

2T ( 16 2 + 14 2 + 12 2 + 10 2 + 2

2

) 2 = 2V (5)

175 T = 10 V

p. 1-26

From previous analysis, Tmax = 0.514 kip/bolt for 1/4 in. clips

vmax = 175 (0.514) / 10 = 8.99 k

111
0.514 P = 8.99

P = 17.5 k

Since P = 17.5 k is much smaller than any other

capacity so far it will control. No need to

check FW1 , FW2 , etc.

2. Case I (Figure A. 7) Ref. [10]

p. 1-25

Clip Angles:

Neutral axis = 1/6 of the connection length from bottom

= 36 / 6 = 6 in.

S Moment about neutral axis = 0

Eq. 1 2T/28 (28 2 + 26 2 + 24 2 + 22 2 + 14 2 + 12 2 + 10 2 + 2

2

) + 4C = 2V (5)

2 Forces in X-direction = 0

Eq. 2 2T/28 (28 + 26 + 24 + 22 + 14 + 12 + 10 + 2) = C

C = 9.857 T

Substitute Eq. 2 in Eq. 1

211.7 T + 9.857 T (4) = 10 V

Tmax = 0.514 kip/bolt

V = 12.91 k

0.514 P = 12.91 k

P = 25.1 k

This is the controlling load capacity for the

connection using this method.

3. Heavy Bracing Connections Ref. [10]

p. 7-55 to 7-62

Generalizing the method given in these pages for

the connections to column flanges, one obtains (Figure A. 8)

H" V H ' = H - H" , M = H' e 2

The system of gusset forces H'

,

M and H" will provide

translational and rotational equilibrium of the gusset

with no secondary couples in the column or beam.

- 112 -
Given: e ]_ = 5 in. , e 2 = 8 in. , — 5 in.

V = (sin 9) P = (sin 30.92) P = 0.514 P

H = (cos 9) P = (cos 30.92) P = 0.858 P

H" = 5/13 V = 5/13 (0.514 P) = 0.198 P

H' = H - H" = 0.858 P - 0.198 P = 0.660 P

M = H'e 2 = 0.660 P (8) = 5.28 P

FW1 :

fv = 0.660 P / 2(19) = 0.0174 P

fb = 5.28 P (3) / 19 2 = 0.0439 P

fr = 0.0472 P = 3 (0.928) capacity of 3/16 in. weld

P = 59 k

<t> = tan -1 (0.198 / 0.514) = 21.06°

where <f> is the angle of the resultant force

at the column with the vertical axis. Since 0 < 45°,

treat as 0°

.

R = CC^Dl (see B.4 above)

= 0.794 (1) 3 (2) (0.25/0.38) = 31.3 k

0.551 P = 31.3 k

P = 56.8 k

Axial force of clip angles :

Tmax = 0.514 kip/bolt

0.198 P = 8 (0.514) = 4.11

P = 4.11 / 0.198

= 20.8 k

Beam to column : Since no load is transferred to by the

the beam to the column connection by this method, this

connection does not limit the brace load, P.

E. Conclusions

1. Williams and Richard's method - brace capacity is 30.9 k,

buckling controls.

gusset

113
2. AISC Method - brace capacity is 17.5 < P < 25.1 k

Take P ~ 21 k (estimated capacity) . Clip axial

capacity controls.

- 114
T- Section Tearout

Figure A.l - T-Section Tearout

115 -
figure A. 2 - Williams and Richard's Brace Load Distribution

116
FW2

V=Q.514P I

CM

CO

CM

If)

117

Figure

A.

3

-

Schematic

Showing

Welds

from

Gusset

to

Column

and

to

Beam
FW2

Figure A. 4 Gusset to Column Connection Detail

0.269P

Figure A, 5 - Beam to Column Connection Detail
Figure A. 6 - Schematic Showing AISC Case II

119
Figure A. 7 - Schematic Showing AISC Case I

- 120
LO 00

121

Figure

A.

8

-

Force

Distribution

Using

AISC

Method

for

Heavy

Bracing

APPENDIX B - THORNTON'S MODEL

Thornton proposed a model to distribute the force from the brace to the column

and beam. His model is illustrated in Figure B.l. In the model, equilibrium

of the gusset is satisfied.

Definitions of the various parameters are as follows:

a, b Locate the centroids of the horizontal and vertical fastener

groups

.

a, (3 Locate positions of forces acting on the horizontal and vertical

fastener groups. Note that the ideal case is for a and /3 to be

equal to a and b respectively. If this were the case, moments Mg

(on beam edge) and Mq (on column edge) will be equal to zero.

P Brace load.

H, V Horizontal and vertical components of the brace load,

e^ Half of the column depth

eg Half of the beam depth

Geometric requirement: a and 0 must satisfy the following equation:

then

a - (5 tan 0 = K

2 2 r - 'I (a + e^) + (0 + eg)

K = eg (tan 9) - e c

Eq. 1

From geometry:

p cos e = v Eq. 2

P sin © = H Eq. 3

cos 9 - (eg + 0) / r Eq. 4

sin 0 = (eQ + a) / r Eq. 5

VB / HB = e B / a Eq. 6

vc / HC = £ / e C Eq. 7

123
From equilibrium:

2 Fx: V = VB + VC

2 Fyi H = Hg + He

Solving

HB = H - HC = H - Vc

e c / p

p HB = p H - e c (V - VB )

= P H - e c V + e c VB

= P H - e c V + e c

(e B Hg / a)

P hb

" e C

e B Hg / a = P H - e c v

Hg (ap - eg ec ) / a = P H - e c V

Hg = [a / (a p - eg e c ) ] (p H - e c V)

— [a / (a P

- e B e^)] (/3 P sin 9 - e^ P cos 0) from Eqs . 2 & 3

= [a / (a P

- eg e^;) ] (P sin 6 - e^ cos 0) P

= [a / (a £

- eg e c ) ] [p (e c + a) - e c (eg + P)\ (1/r) P

from Eqs . 4 & 5

= [ (a P e c + a

2

p - a eg e c

- a P e c ) P] / [r (a p - eg e c )

]

= a (a P - eg e c ) P / [r (a P - eg e c )

]

Hg = (a / r) P

The equations for the remaining beam and column forces are obtained from

statics. The beam and column forces are as follows:

Hg = (a/r) P VB = (eg/r) P

VC = (p/ r) P HC = (e c/r) P

Mg = Vg (a - a) Me = Hq (p - b)

- 124 -

Eq. 8

Eq. 9

from Eq. 9

from Eq . 7

from Eq . 8

from Eq. 6
Solution:

1. In the above formulas, a and P are unknown and are related by Eq. 1. One

solution is to designate one of them and use Eq . 1 to solve for the other.

Since the horizontal edge is welded to the beam flange, it has a greater

moment stiffness than the vertical edge which generally is connected to

the column with clip angles. Therefore, let the horizontal edge carry Mg

and set the moment M^ on the vertical edge be zero by setting p = b

.

Equation 1 is , then

a = K + b tan 9

and the forces are computed using the above formulas.

2. Another method to determine a and f$ is to minimize the eccentricities, e^

= (

a

-a) and ev = (p -b) , using the following objective function, 4>\

<t> = [(a - a)/a]2 + [(p - b)/b]^ - A (a - ft tan 9 - K)

where A is the Lagrange multiplier. The results of the minimization are

a = K' tan 9 + K (a /b) 2

D

P = K

> - K tan 9

D

where

,

K = eg, tan 8 - e c K' = a [tan 9 + (a / b)]

D = tan^ 9+ (a /b

125 -
The brace load, P, for Specimen No. 1 distributed to the column and beam using

Thornton's method and the second solution is as follows:

Given:

a = (23 - 4)/2 + 4 = 13.5 in.

b = 5 in. (c.g. of fasteners)

0 = 90 - 30.96 = 59.04°

e c = 5 in.

e-j-) = 8 in

.

Solution:

K = eB tan 9 - e c = 8.3 in.

K' = a (tan 0 + a / b) = 59.0 in.

D = tan2 9 + (a / b) 2 = 10.1

a = [K' tan 0 + K (a / b) 2

] / D - 15.7

p = (K' - K tan 0) / D = 4.5

r = [(a + e c ) 2 + (0 + eb ) 2 ]V2 = 24.2

Hb = (a / r) P = 0.65 P

VB = (e B / r) P = 0.33 P

HC = (e c / r) P = 0.21 P

Vc = (0 / r) P = 0.19 P

126
> OQ

CD

<Q.

127

Figure

B.l

Thornton's

Model

of

Brace

Load

Distribution

M BS-1 1 4A 'REV. 2-80

U.S. DEPT. OP COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

.. PUBLICATION OR

REPORT NO.

NISTIR 88-3849

2. Performing Organ. Report No. 3. Publication Date

October 1988

4. TITLE AND SU BTITLE

Experimental Study of Gusseted Connections for Laterally Braced

Steel Buildings

5. AUTHOR(S)

John L. Gross and Geraldine Cheok

6. PERFORMING ORGAN I ZATI ON (If joint or other than N BS. see in struct ion s) 7 . Contract/Grant No.

NATIONAL BUREAU OF STANDARDS

U.S. DEPARTMENT OF COMMERCE

GAITHERSBURG, MD 20899

8. Type of Report & Period Covered

9.

SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State , ZIP)

10.

SUPPLEMENTARY NOTES

Document describes a computer program; S F - 1 8 5 , FlPS Software Summary, is attached.

11.

ABSTRACT (A 200-word or less factual summary of most significant information. I f document includes a significant

bi bl iography or literature survey , mention it here)

The behavior of three diagonally braced steel subassemblages was studied experimentally. The parameters which were varied included the gusset geometry and

column orientation. The specimens were loaded to failure in their plane and loaddeformation as well as strain data were recorded. The failure mode for the two

strong-axis column connections was gusset buckling. The weak-axis column

connection failed by tearing of the gusset plate. The moment introduced by the

eccentricity in the bracing was distributed to the beam and column in the strongaxis column connection. This moment was carried almost entirely by the beam in

the weak-axis connection due to the flexibility in the web connection. The failure

loads for all three specimens were found to be well above those predicted using

various methods. The current method of predicting gusset buckling appears to be

very good giving a margin of safety of approximately three. Generally, comparisons

of design capacities with the experimental values resulted in a factor of safety in

excess of two. The capacity of the clip angles, in accordance with AISC, was

computed to be very low yet no distress in the clip angles was observed. This was

because frame action introduced loads in the gusset-to-column bolts which counteracted the load produced by the bracing.

12.

KEY WORDS (Six to twelve entries; a Iph a beti ca I order; capitali ze only proper names ; and separate key words by semicolon s) Braced frames; connections; design; experimental study; gusset plates;

lateral bracing; steel buildings

13. AVAILABILITY 14. NO. OF

PRINTED PAGES

y U n 1 1 mi ted 133

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Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402. 15. Price

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