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Page 1

ENGINEERING JOURNAL / SECOND QUARTER / 2006 / 91

Objective

The objectives of this research were to determine the accu-
racy of the current design method using a statistical analysis
of data from the available research, and to propose appro-
priate effective length factors for use in the current design
procedures.

Procedure

The available experimental and finite element data on the
buckling capacity of gusset plates was collected and re-
viewed. The experimental and finite element capacities were
compared with the calculated nominal loads for each speci-
men, and the most appropriate effective length factor was
selected for each gusset plate configuration. The accuracy of
the design method was determined using the selected effec-
tive length factors.

Gusset Plate Configurations

Gusset plates are fabricated in many different configurations.
The most common configurations are shown in Figure 2.

The corner-brace configuration has a single brace framing
to the gusset plate at the intersection of two other structural
members. The gusset plate is connected to both members.
There are three types of corner-brace configurations that are
considered in this paper: compact, noncompact, and extend-
ed. For compact gusset plates, the free edges of the gusset
plate are parallel to the connected edges and the brace mem-
ber is pulled in close to the other framing members as shown
in Figure 2a. For noncompact gusset plates, the free edges
of the gusset plate are parallel to the connected edges and
the brace member is not pulled in close to the other fram-
ing members. This configuration is shown in Figure 2b. For
the extended corner-brace configuration, the gusset plate is
shaped so the free edges of the gusset plate are cut at an angle
to the connected edges as shown in Figure 2c. The extended
corner-brace configuration is mainly used where high seis-
mic loads are expected. The additional setback is tended to
ensure ductile behavior in extreme seismic events by allow-
ing a plastic hinge to develop in the free length between the
end of the brace and the restrained edges of the gusset plate.

The gusset plate in the single-brace configuration is con-
nected at only one edge of the plate as shown in Figure 2d.

Effective Length Factors for Gusset Plate Buckling

BO DOWSWELL

Gusset plates are commonly used in steel buildings to connect bracing members to other structural members
in the lateral force resisting system. Figure 1 shows a typical
vertical bracing connection at a beam-to-column intersec-
tion.

Problem Statement

Design procedures have previously been developed from the
research on gusset plates in compression. The design proce-
dures to determine the buckling capacity of gusset plates are
well documented (AISC, 2001), but the accuracy of these
procedures is not well established. Uncertainties exist in the
selection of the effective length factor for each gusset plate
configuration.

Bo Dowswell is principal of Structural Design Solutions, LLC,
Birmingham, AL.

Page 2

92 / ENGINEERING JOURNAL / SECOND QUARTER / 2006

For corner gusset plates, the column length, lavg is calculated
as the average of l1, l2 , and l3 as shown in Figure 4. The
buckling capacity is then calculated using the column curve
in the AISC Load and Resistance Factor Design Specifica-
tion for Structural Steel Buildings (AISC, 1999), hereafter
referred to as the AISC Specification.

The AISC Load and Resistance Factor Design Manual
of Steel Construction, Volume II, Connections (AISC, 1995)
provides effective length factors for compact corner gusset
plates, noncompact corner gusset plates, and single-brace
gusset plates. The effective length factors and the suggested
buckling lengths are summarized in Table 1. (Tables begin
on page 99.) Table 1 also shows the average ratio of experi-
mental buckling load to calculated nominal capacity based
on the tests and finite element models in Tables 2, 3, and 5.
The current design method is conservative by 47% for com-
pact corner gusset plates and is conservative by 140%
for single-brace gusset plates. The current design method
for noncompact corner gusset plates appears to be accurate
based on the test-to-predicted ratio of 0.98; however, the
standard deviation is 0.46, and the test-to-predicted ratio was
as low as 0.33 for one of the specimens. There appears to be
a source of improvement in the design procedure for these
three gusset plate configurations by simply selecting an ef-
fective length factor that gives predicted capacities closer to
the test and finite element results.

The chevron-brace configuration has two braces framing
to the gusset plate as shown in Figure 2e. The gusset plate is
connected at only one edge of the plate.

CURRENT DESIGN PROCEDURES

Effective Width

In design, gusset plates are treated as rectangular, axially
loaded members with a cross section Lw × t, where Lw is
the effective width, and t is the gusset plate thickness. The
effective width is calculated by assuming the stress spreads
through the gusset plate at an angle of 30°. The effective
width is shown in Figure 3 for various connection configura-
tions and is defined as the distance perpendicular to the load,
where 30° lines, which project from the first row of bolts or
the start of the weld, intersect at the last row of bolts or the
end of the weld. The effective cross section is commonly
referred to as the “Whitmore Section.”

Buckling Capacity

Thornton (1984) proposed a method to calculate the buckling
capacity of gusset plates. He recommended that the gusset
plate area between the brace end and the framing members
be treated as a rectangular column with a cross section Lw × t.

c. Extendedb. Noncompact a. Compact

e. Chevron-Braced. Single-Brace

Corner-Brace Configurations

Page 6

96 / ENGINEERING JOURNAL / SECOND QUARTER / 2006

The maximum design load that can be carried by the
1-in.-vertical strip in compression is

Pmax = 0.85(1 in.)Fy t

Fy is the yield strength of the plate. Substitute Pmax into
Equation 1 and replace Lb with l1 to get

For a guided cantilever with a point load at the tip, the end
deflection is

Pb is the point load at the end of the cantilever, and E is the
modulus of elasticity. The moment of inertia of the 1-in.-
horizontal strip is

The actual stiffness of the horizontal strip is

Set the actual stiffness equal to the required stiffness.

Solve for the required plate thickness, t .

The gusset plate is compact if t t , and noncompact if
t t .

The model shown in Figure 6 can also be used to deter-
mine the required strength to brace the gusset plate. The
AISC Specification (AISC, 1999) provision for required
strength of relative bracing at a column is

Pbr = 0.004Pu

Substitute Pmax from Equation 2 into Equation 1 to get

Pbr = (0.0034 in.)Fy t

The moment in the horizontal strip in double curvature is

Mu = Pb c/2 = (0.0017 in.)Fy ct

The design moment capacity of the horizontal strip is

Set the applied moment to the moment capacity and solve
for t.

tp = 0.0075c

From Equation 13, it can be seen that the strength require-
ment is insignificant for any practical gusset plate geometry;
therefore, only the stiffness requirement will be used to de-
termine the buckling mode.

Yielding Design for Compact Corner Gusset Plates

Because compact corner gusset plates generally buckle in the
inelastic range as discussed by Cheng and Grondin (1999),
a lower-bound solution to the test data is the yield capac-
ity of the plate at the effective section. The yield capacity
is calculated with an effective width Lw, which is based on
a 30° spread of the load. It is determined with the following
equation,

Py = Fy tLw

Table 2 shows the yield loads of the compact corner-brace
specimens, and compares them with the experimental and
finite element loads. There were eight separate projects with
a total of 68 specimens: 37 were experimental and 31 were
finite element models. The mean ratio of experimental load
to calculated capacity, Pexp /Pcalc is 1.36, and the standard
deviation is 0.23.

Effective Length Factors

Tables 3 through 6 compare the results from the tests and
finite element models with the nominal buckling capaci-
ties. The nominal buckling capacities were calculated with
Thornton’s design model for effective length with the col-
umn curve in the AISC Specification (AISC, 1999). The sta-
tistical results for noncompact corner braces indicated that
lavg is a more accurate buckling length than l1. For the other
gusset plate configurations, l1 is as accurate as lavg. The pro-
posed effective length factors were correlated for use with
lavg at the noncompact corner gusset plates and l1 at the other
configurations.

The results for noncompact corner braces are summarized
in Table 3. There were two projects with a total of 12 ex-
perimental specimens. Using a buckling length, lavg and an
effective length factor of 1.0, the mean ratio of experimental

I
t

=
( )1

12

3 in.
(5)

(2)

βbr
y yF t

l

F t

l
=
( )( )( )

( )
=

2 0 85 1

0 75
2 27

1 1

.

.
.

in.
(3)

δ=
P

EI
cb

12
3

(4)

β
δ

= =







P
E

t

c
b

3

(6)

E
t

c

F t

l
y





 =
3

1

2 27. (7)

t
F c

El
y

β =1 5
3

1

. (8)

(9)

(10)

(11)

φM F
t

t Fn y y= =0 9
1

4
0 225

2
2.

( .)
.

in
(12)

(13)

(14)

Page 7

ENGINEERING JOURNAL / SECOND QUARTER / 2006 / 97

load to calculated capacity, Pexp /Pcalc is 3.08. The standard
deviation is 1.94.

The results for extended corner braces are summarized in
Table 4. There were a total of 13 specimens from two sepa-
rate projects. Only one of the specimens was experimental,
and 12 were finite element models. Using a buckling length
l1, and an effective length factor of 0.60, the mean ratio of
experimental load to calculated capacity, Pexp /Pcalc is 1.45.
The standard deviation is 0.20.

The results for single braces are summarized in Table 5.
There was only one project with nine finite element models.
Using a buckling length, l1 and an effective length factor of
0.70, the mean ratio of experimental load to calculated ca-
pacity, Pexp /Pcalc is 1.45. The standard deviation is 0.20.

The results for chevron braces are summarized in Table 6.
There were two separate projects with a total of 13 speci-
mens—nine were experimental and four were finite element
models. Using a buckling length, l1 and an effective length
factor of 0.75, the mean ratio of experimental load to cal-
culated capacity, Pexp /Pcalc is 1.25. The standard deviation is
0.22.

Using the experimental and finite element data from the pre-
vious studies, the capacity of gusset plates in compression
were compared with the current design procedures. Based on
a statistical analysis, effective length factors were proposed
for use with the design procedures. Table 7 summarizes the
proposed effective length factors.

It was determined that compact corner gusset plates can
be designed without consideration of buckling effects, and
yielding at the effective width is an accurate predictor of
their compressive capacity. Due to the high variability of
the test-to-predicted ratios for the noncompact corner gusset
plates, an effective length factor was proposed that was con-
servative for most of the specimens. For the extended corner
gusset plates, the single brace gusset plates, and the chevron
brace gusset plates, effective length factors were proposed
that resulted in reasonably accurate capacities when com-
pared with the test and finite element capacities.

AISC (2001), Manual of Steel Construction, Load and Re-
sistance Factor Design, Third Edition, American Institute
of Steel Construction, Inc., Chicago, IL.

AISC (1999), Load and Resistance Factor Design Specifica-
tion for Structural Steel Buildings, American Institute of
Steel Construction, Inc., Chicago, IL.

AISC (1995), Manual of Steel Construction, Load and Re-
sistance Factor Design, Volume II, Connections, Ameri-
can Institute of Steel Construction, Chicago, IL.

Astaneh, A. (1992), “Cyclic Behavior of Gusset Plate
Connections in V-Braced Steel Frames,” Stability and
Ductility of Steel Structures Under Cyclic Loading, Y.
Fukomoto and G.C. Lee, editors, CRC Press, Ann Arbor,
MI, pp. 63–84.

ASTM (2004), “Standard Specification for General Require-
ments for Rolled Structural Steel Bars, Plates, Shapes,
and Sheet Piling,” ASTM A6, ASTM International, West
Conshohocken, PA.

Bjorhovde, R. and Chakrabarti, S.K. (1985), “Tests of Full-
Size Gusset Plate Connections,” Journal of Structural En-
gineering, ASCE, Vol. 111, No. 3, March, pp. 667–683.

Brown, V.L. (1988), “Stability of Gusseted Connections in
Steel Structures,” Ph.D. Dissertation, University of Delaware.

Chakrabarti, S.K. and Richard, R.M. (1990), “Inelastic
Buckling of Gusset Plates,” Structural Engineering Re-
view, Vol. 2, pp. 13–29.

Chakrabarti, S.K. (1987), Inelastic Buckling of Gusset
Plates, Ph.D. Dissertation, University of Arizona.

Cheng, J.J.R. and Grondin, G.Y. (1999), “Recent Develop-
ment in the Behavior of Cyclically Loaded Gusset Plate
Connections,” Proceedings, 1999 North American Steel
Construction Conference, American Institute of Steel
Construction, Chicago, IL.

Cheng, J.J.R. and Hu, S.Z. (1987), “Comprehensive Tests
of Gusset Plate Connections,” Proceedings, 1987 Annual
Technical Session, Structural Stability Research Council,
pp. 191–205.

Dowswell, B. (2005), Design of Steel Gusset Plates with
Large Cutouts, Ph.D. Dissertation, University of Alabama
at Birmingham.

Fisher, J.W., Galambos, T.V., Kulak, G.L., and Ravindra,
M.K. (1978), “Load and Resistance Factor Design Cri-
teria for Connectors,” Journal of the Structural Division,
ASCE, Vol. 104, No. ST9, September, pp. 1427–1441.

Fouad, F.H., Davidson, J.S., Delatte, N., Calvert, E.A.,
Chen, S., Nunez, E., and Abdalla, R. (2003), “Structur-
al Supports for Highway Signs, Luminaries, and Traffic
Signals,” NCHRP Report 494, Transportation Research
Board, Washington, DC.

Gross, J.L. and Cheok, G. (1988), “Experimental Study of
Gusseted Connections for Laterally Braced Steel Build-
ings,” National Institute of Standards and Technology,
Gaithersburg, MD, November.

Irvan, W.G. (1957), “Experimental Study of Primary Stresses
in Gusset Plates of a Double Plane Pratt Truss,” University
of Kentucky, Engineering Research Station Bulletin No.
46, December.

Lavis, C.S. (1967), “Computer Analysis of the Stresses in a
Gusset Plate,” Masters Thesis, University of Washington.

Page 11

ENGINEERING JOURNAL / SECOND QUARTER / 2006 / 101

Table 6. Details and Calculated Capacity of
Chevron Brace Gusset Plates

k = 0.75

Spec.
No.

T
(in.)

wL

(in.)
1l

(in.)
yF

(ksi)
E

(ksi)
calcP

(k)

Pexp
(k)

P

Pcalc

exp

Reference: Chakrabarti and Richard (1990)
1 0.472 14.8 9.8 43.3 29000 252 286 1.14
2 0.315 14.8 6.4 40 29000 158 222 1.41
3 0.315 14.8 6.4 43.2 29000 169 264 1.56
4 0.315 14.8 9.8 72.3 29000 168.7 292 1.73
5 0.315 21.6 11.2 44.7 29000 174.1 175 1.01
6 0.394 14.8 9.6 36.8 29000 173 191 1.11
7 0.512 14.8 8.8 46.7 29000 309 429 1.39
8 0.394 14.8 6.0 82.9 29000 400 477 1.19

1-FE 0.472 14.8 9.8 43.3 29000 252 274 1.09
2-FE 0.315 14.8 6.4 40 29000 158 201 1.27
5-FE 0.315 21.6 11.2 44.7 29000 174.1 228 1.31
8-FE 0.394 14.8 6.0 82.9 29000 400 431 1.08

Reference: Astaneh (1992)
3 0.25 4.96 4.0 36.0 29000 40.8 42.4 1.04

Table 7. Summary of Proposed Effective Length Factors

Gusset Configuration
Effective

Length Factor
Buckling
Length

P

Pcalc

exp

Compact corner � a � a 1.36

Noncompact corner 1.0 avgl 3.08

Extended corner 0.6 1l 1.45

Single-brace 0.7 1l 1.45

Chevron 0.75 1l 1.25

aYielding is the applicable limit state for compact corner gusset plates;
therefore, the effective length factor and the buckling length are not
applicable.

Table 5. Details and Calculated Capacity of
Single Brace Gusset Plates

k = 0.70

Spec.
No.

t
(in.)

wL

(in.)
1l

(in.)
yF

(ksi)
E

(ksi)
calcP

(k)

Pexp
(k)

P

Pcalc

exp

Reference: Sheng et al. (2002)
31 0.524 11.31 8.00 42.78 29000 151.1 216.2 1.43
32 0.524 8.55 9.59 42.78 29000 195.0 246.4 1.26
33 0.524 5.80 11.18 42.78 29000 239.7 332.6 1.39
34 0.389 11.31 8.00 44.22 29000 99.7 157.3 1.58
35 0.389 8.55 9.59 44.22 29000 137.2 181.4 1.32
36 0.389 5.80 11.18 44.22 29000 176.8 246.2 1.39
37 0.256 11.31 8.00 39.88 29000 41.8 80.3 1.92
38 0.256 8.55 9.59 39.88 29000 66.8 96.3 1.44
39 0.256 5.80 11.18 39.88 29000 95.8 124.9 1.30

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