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Eccentric BracedSteel Frames for

Wind andLow-to-Moderate

Seismic Loads

Stanley D. Lindsey

AuthorPrior to founding Lindsey & As-sociates in 1967, Dr. StanleyLindsey was employed by Volun-teer Structures, Inc. in Nashville,Tennessee, as chief engineer. Hereceived his doctorate in civil en-gineering from Vanderbilt Univer-sity in 1972. He is a registeredstructural engineer in California,Nevada, Illinois and Washingtonand a registered professional en-gineer in more than 40 states.

Lindsey is an active member ofthe AISC, ASCE, the SouthernBuilding Code Congress Interna-tional, ACI, EERI and the StructuralEngineers of Northern California.

He is a frequent speaker atprofessional gatherings and hastaught at the University of Ten-nessee, Vanderbilt University,Clemson University and Ten-nessee State. Awarded a specialcitation by AISC in 1972 for out-standing contributions to thedesign of steel structures, he hasserved on numerous importantcommittees, including the AISCCommittee on Specifications,Specification Task Committee onSeismic Design and the LRFDTask Committee on Stability.

SummaryEccentric braced frames (EBFs)are a proven effective, economicalmethod for resisting seismic forces.The concept of an EBF wasdeveloped so the frame would havethe ductility of a ductile momentresisting space frame and the stiff-ness approaching that of a con-centric braced frame. A vastamount of work has been done atthe University of California atBerkeley on the seismic behaviorand design of EBFs. As a directresult of this work, an entire sectionhas been written that is devoted todesign rules for EBFs in the AISC-LRFD Seismic Specifications duefor release this year.

As early as 1930, it was recog-nized that it could be advantageousfor a building to have wind bracingthat was not concentric. Interest-ingly, almost no work has beendone on EBFs for wind load resis-tance. The work done on the seis-mic behavior of EBFs, however,can serve as the basis for an initialset of design guidelines for EBFssubject to primarily wind and/or lowseismic loads. This paper willpresent a suggested design ap-proach for these types of EBFs.

17-1 2003 by American Institute of Steel Construction, Inc. All rights reserved.

This publication or any part thereof must not be reproduced in any form without permission of the publisher.

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ECCENTRIC BRACED FRAMES:

SUGGESTED DESIGN PROCEDURES

FOR WIND AND LOW SEISMIC FORCES

STANLEY D. LINDSEY AND ARVIND V. GOVERDHAN

Introduction

Eccentric Braced Frames (EBFs) are a proven effective, economical method forresisting seismic forces [1,2]. The concept of an EBF was developed so the framewould have the ductility of a ductile moment resisting space frame and the stiffnessapproaching that of a Concentric Braced Frame (CBF) [2]. A vast amount of workhas been done at the University of California at Berkeley on the seismic behaviorand design of EBFs [3, 4, 5, 6, 7, 8, 9, 10, 11,12, 13, 14]. As a direct result of thiswork, an entire section has been written that is devoted to design rules for EBFsin the AISC-LRFD Seismic Specifications due for release this year [15].

As early as 1930, it was recognized that it could be advantageous for a building tohave wind bracing that was not concentric [16]. Interestingly, almost no work has

been done directly on EBFs for wind load resistance. The work done on theseismic behavior of EBFs can, however, serve as the basis for an initial set ofdesign guidelines for EBFs subject to primarily wind and/or low seismic loads.This paper will present a suggested design approach for these types of EBFs.

Stanley D. Lindsey, Ph.D., S.E., is President of Stanley D. Lindsey & Associates,

Ltd., Nashville, Tennessee.

Arvind V. Goverdhan, Ph.D., Researcher and Structural Engineer at Stanley D.Lindsey&Associates. Ltd..Nashville. Tennessee.________________

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2003 by American Institute of Steel Construction, Inc. All rights reserved.This publication or any part thereof must not be reproduced in any form without permission of the publisher.

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General Discussion

Seismic considerations excluded, an EBF has two major advantages over a CBF.It offers architectural flexibility and it has less complicated, hence less expensive,connections. The ability to offset a brace can make the use of an EBF possible ina given architectural layout where it would be impossible to use a CBF. Figure 1.illustrates just such a case; here the EBF allows a door to be used adjacent to thecolumn. The fact that the brace axis does not have to intersect the center ofgravity of the column and girder greatly simplifies the girder to column connection.Figures 2. and 3., respectively, show a normal CBF girder to column connection,and the simpler girder to column connection with an EBF. If the EBF offers more

architectural freedom and is less expensive, why then has the EBF not receivedmore attention by the design community? Some possible reasons can bepostulated. First, until the research on the seismic behavior of EBF, no one reallycould say with certainty what the actual behavior and collapse mechanisms for anEBF were. Secondly, the EBF was thought to be a much less stiff system than aCBF and was not considered as a good design alternate due to this perception.Finally, it was considered to be "just good design practice" to have all connectionsconcentric; one never purposely had connection eccentricity!

Seismic research for EBFs has answered many of the questions of behavior andcollapse [3, 9, 13]. Stiffness has been studied and shown to be much better thanthought [9]. The research has shown that connection eccentricity is not

detrimental to the EBF, but quite the contrary, if done properly it actually enhancesperformance [3, 9, 13].

Take stiffness for example, Figure 4. shows several arrangements of typical EBFs.For various aspect ratios, an important parameter of an EBF is the brace offset (e)versus the girder span (I). Figure 5. shows a plot of e/l versus relative framestiffness for various aspect ratios of some EBFs. Notice that for a common aspectratio in buildings, 0.5 for the D types, an e/l of 0.1 (3'-0 offset in a 30-0 span)results in no real loss of stiffness and for an e/l = 0.2 the loss is only in the rangeof 10 percent. Practically speaking, given proper design, it means one could offseta brace approximately 6 feet on a 30 foot span girder and only suffer an acceptable

amount of reduction in frame stiffness. The ability to offset with so little loss inframe stiffness is quite useful in accommodating an architectural layout. Even withthe other brace configurations shown in Figure 5., there are similar e/l ratios thatcan be used that will not sacrifice frame stiffness.

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Fundamental Approach

Figure 6. shows a typical collapse mechanism of a D type EBF with the girder, thecolumns, the braces, and the links labeled. The link is fundamental to the EBFperformance in an EBF. For seismic forces the link is designed to behaveinelastically and dissipate energy generally either through shear yielding or momentyielding. In an EBF designed for wind forces, the link remains elastic since the EBFdoes not have to dissipate large amounts of energy since the actual loads are notseveral times higher than the design loads. The design problem for an EBF for

wind is, therefore, essentially an elastic design problem. The EBF must resist thelateral and vertical loads without a damaging drift level and it must have a properstiffness for occupant comfort. A seismically designed EBF, on the other hand,must limit drift, provide occupant comfort as well as absorb energy and resistcollapse at load levels several times higher than design loads.

The link behavior in an EBF needs some discussion. Kasai, Popov and othershave done much work in EBFs performance versus link lengths [5, 6, 7, 8, 10, 11,13]. Both shear and moment yielding of lengths of various lengths have beenstudied. In addition, web buckling and lateral buckling of the link have also beenstudied. Based on the work to-date, it seems best to consider only designingEBFs for wind and low seismic forces with links which are short enough to yield in

shear rather than in moment. Kasai [9] has found that the maximum link length toallow shear yielding at ultimate loading to be:

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where:

e = link length to yield in shear defined as cleardistance between column face and diagonal

(1)


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This value of e is maximum length in the absence of axial force in the link thatshould be used to ensure that the link yield in shear. With axial load >

0.15), Kasai [9] has formulated modifications to this expression, which can resultin a somewhat shorter length.

As part of his work on EBFs, Kasai [9] derived the possible lower bound collapsemechanisms for various configurations of EBFs. He also developed theexpressions for the ultimate capacity in terms of a multiplier on lateral loads ofthese EBFs. He compared his lower bound expressions to a finite element elasto-plastic solution and found excellent agreement between the two methods. Byhaving these lower bound solutions, one can easily check the ultimate capacityof an EBF to see if it has adequate collapse resistance without having to do anelasto-plastic finite element analysis. The ability to do this easy check means thatfor an EBF designed to resist primarily wind loads and remain elastic, a simple

direct method is available to check its ultimate capacity. Thus one can use anelastic LRFD procedure to design an EBF and then ensure it has the properultimate strength without having to use a finite element elasto-plastic solution.

As an example, for the D-brace frame collapse mechanism shown in Figure 7. andusing Figures 7., 8., and 9. for the internal and external work mechanisms, Kasai[9] derived the following lower bound expression for a constant load factor appliedto the lateral loads:

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Thus to check for the multiplier on the lateral loads for this mechanism, all one hasto do is substitute into equation (2). To establish ultimate strength, one must checkall the possible mechanisms of which this is only one of three for a D type EBF.The reader is referred to Kasai [9] for an in-depth treatment of possible collapse

(2)

where:

Load Factor on Lateral LoadsGirder Span (Feet)Plastic Shear Capacity (kips)Load Intensity (K/Ft)

Link Length (Ft)Depth of Column (Ft)Height at Level i (Ft)Lateral Load at Level(i) (kips)


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mechanisms and load factors for the lateral loads associated with each possiblecollapse mechanism for several EBF configurations.

Proposed Design Approach

For EBFs in seismic regions, the AISC LRFD seismic specifications have adoptedan ultimate strength approach. For EBFs used for wind resistance and smallseismic loads, a more familiar elastic approach using LRFD design criteria formember selection and then followed by a check on ultimate capacity isrecommended. Total ultimate strength approach for wind EBFs would certainly

be acceptable, but given the familiarity of more traditional elastic methods byengineers, the recommended approach seems reasonable.

Additionally, based on the research to-date, limiting the link lengths to ensure shearyielding also seems logical as a first design recommendation. As more experienceis gained with actual EBFs, the ultimate strength design approach with lengthseither yielding in shear or moment may be possible.

The recommended basic design approach consists of:

A. Analysis of the structure using a second order linear elastic procedurewith factored loads.

B. Design of members using LRFD equations.

C. A check of ultimate capacity using the sizes from (B.) and the proper Kasaiequations.

D. Check of the structure for serviceability using Unfactored loads.

E. Revising as required and then recycling steps (A.) through (E.).

The choice of a second order linear elastic procedure as the basis of analysis is

done in an effort to get more meaningful analysis results. The analysis shouldinclude axial shortening effects in the columns and braces, frame and membereffects and should include shear as well as bending deflection contributions of thegirders in the EBF. Leaner column effects on the EBFs should also be included in

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Provisions [15]. As more designs are done on EBFs, some of these suggestedguidelines can be liberalized. Additionally, as more work is done on moment links,provisions for them can be added to these guidelines.

1. Links:

A. The specified minimum yield for links shall not exceed Fy= 50 ksi.

All links shall comply with the appropriate limiting width thicknessratios shown in Table B5.1.

B. The shear force in the link produced by the prescribed designforces shall not exceed the design shear strength of the link whichis defined as the lesser of /e where = 0.6

= 0.9 and e = link length or defined as follows in (E).

C. The web of the link shall be single thickness without doubler platereinforcement and without openings.

D. If the required strength, in a link at the prescribed design forcesis equal to or less than 0.15 where = , it is permitted toneglect the effect of axial force on the link design shear strength.

F. The link flanges shall have full penetration welds to the column. Theconnection of the link web to the column shall be welded to havea design strength to develop the design strength of the link web... Where the link is connected to the column web, the link flanges

E. If the required strength, , in a link at the prescribed design forcesexceeds 0.15 Py, the following additional requirements shall be met:


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shall have full penetration welds to connection plates and the webconnection shall be welded to have a design strength to develop thedesign strength of the link web.

G. Link Stiffeners: Full depth web stiffeners shall be provided on bothsides of link web at the diagonal brace ends of the link. Thesestiffeners shall have a combined width not less than anda thickness not less than nor 3/8 inches, whichever is larger,where and are the width of the link flange and link webthickness, respectively.

H. Links shall be provided with intermediate web stiffeners as follows:. .Links of lengths or less shall be provided withintermediate web stiffeners spaced at intervals not exceedingd/5).

I. .. Intermediate link web stiffeners shall be full depth. For links lessthan 24 inches in depth, stiffeners are required on only one side ofthe link web. The thickness of one-sided stiffeners shall not be lessthan or 3/8 inch, whichever is larger, and the width shall be notless than For links 24 inches in depth or greater, similarintermediate stiffeners are required on both sides of the web.

J. Fillet welds connecting link stiffener to the link web shall have adesign strength adequate to resist a force of The designstrength of fillet welds fastening the stiffener to the flanges shall beadequate to resist a force of = bt of the stiffener andb and t are the width and thickness of the stiffener plate,respectively.

K. Lateral supports shall be provided at both the top and bottomflanges of link at the ends of the link. End lateral supports of linksshall have a design strength of 2 percent of the link flange nominalstrength computed as

2. Diagonal Brace and Beam Outside of Link:

A. The nominal strength of each diagonal brace shall be adequate to

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resist the forces generated by at least 1.2 times the design shearstrength of the link.

B. The sum of the nominal flexural strength of the diagonal brace andof the beam segment outside of the link shall exceed the design linkend moment occurring at 1.2 times the design shear strength ofthe link. The nominal flexural strength of these members shall bedetermined using interaction equations for combined axial force, andbending moment, using the axial force in the member generatedby 1.2 times the design shear strength of the link.

C. Diagonal brace to link connections shall develop the nominalstrength of the diagonal brace and transfer this force to the beam.No part of the diagonal brace to beam connection shall extend overthe link length. If the diagonal brace resists a portion of the link end

moment as described above, the diagonal brace to beamconnection shall be designed as fully restrained (Type FR).

D. The beam outside of the link shall be provided with sufficient lateralsupport to maintain the stability of the beam under the forcesgenerated by at least 1.2 times the shear design strength of thelink. Lateral supports shall be provided at both top and bottomflanges of the beam and shall have a strength to resist at least 2percent of the beam flange nominal strength computed as Fybft f.

Following these provisions will ensure shear failure in the link. Thus the behaviorat ultimate loads will be as predicted by the equations derived by Kasai [9].

Conclusions

EBFs can be an economical alternative to a CBF for wind and low seismic loads.They offer a great deal more architectural freedom than a CBF and their

connections are much simpler than a CBF's connections. With properconsideration to EBF configuration, the loss of stiffness due to eccentricity can besmall. By designing to ensure shear rather than moment yielding in the link, anaccurate method is available to predict ultimate capacity of an EBF. Combining

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that ability with the proper analysis and LRFD design rules, a safe and economicalEBF can be obtained.

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TABLE 1.- LATERAL DEFLECTIONS FOR A 10 STORY D-BRACE FRAME

Load Case: +1 .0W + 1.0 D + 1.0 L

SD = Shear Deformation

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10

987

654321

4.544.073.522.982.42

1.93

1.441.020.63

0.30

4.844.343.753.172.582.041.531.070.660.32

5.024.543.973.392.792.231.691.200.750.34

5.424.904.283.652.992.401.811.280.790.36


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[11] Kasai, K. and E.P. Popov, "Cyclic Web Buckling Control for Shear LinkBeams," Journal of the Structural Division, vol. 112, no.3, ASCE, March1986.

[12] Krawinkler, H., V.V. Bertero, and E.P. Popov,Inelastic Behavior of Steel

Beam-to-Column Subassemblages, Report No. UCB/EERC-71/7,Earthquake Engineering Research Center, University of California,Berkeley, CA, 1971.

[13] Engelhardt, M.D., E.P. Popov, Behavior of Long Links in EccentricallyBraced Frames, Report No. UCB/EERC-89/01, Earthquake EngineeringResearch Center, University of California, Berkeley, CA, 1989.

[14] Ricles, J.M. and E.P. Popov,Dynamic Analysis of Seismically ResistantEccentrically Braced Frames, Report No. UCB/EERC-87/07, EarthquakeEngineering Research Center, University of California, Berkeley, CA, 1987.

[15] AISC, Tentative Seismic Provisions, American Institute of SteelConstruction. (To be published 1989)

[16] Spurr, H.V.,Wind Bracing, McGraw Hill, New York, 1930.

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FIGURE 1

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FIGURE 2

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FIGURE 3

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FIGURE

4

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FIGURE 5

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FIGURE 6

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FIGURE 7

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FIGURE 8

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FIGURE 9

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FIGURE 10

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Lindsay 1989