##### Document Text Contents

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

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.

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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