ResearchArticle …downloads.hindawi.com/journals/ace/2018/8417208.pdfcruciform section (a tolerance of±10% is the default tol-erance). If the symmetry about either axis diŒers more

Research ArticleStrength of Flanged and Plain Cruciform Members

Nicholas Harris and Girum Urgessa

Volgenau School of Engineering Sid and Reva Dewberry Department of Civil Environmental and Infrastructure EngineeringGeorge Mason University 4400 University Drive MS 6C1 Fairfax VA 22030 USA

Correspondence should be addressed to Girum Urgessa gurgessagmuedu

Received 22 August 2017 Accepted 3 January 2018 Published 19 February 2018

Academic Editor Li Li

Copyright copy 2018 Nicholas Harris and Girum Urgessa )is is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in anymedium provided the original work isproperly cited

)ere are two different types of cruciform members used in practice Flanged cruciform sections are typically fabricated from twohot-rolled WT sections welded to the web of a standard hot-rolled I section whereas plain cruciform sections are typicallyfabricated from two symmetric rectangular plates welded in the form of a cross Cruciform members that are subjected tocombined compression and bending are typically limited by torsional buckling unlike conventional compression members (suchasW-shapes) that are typically limited by flexural (Euler) buckling about their local weak axis of bending Detailed guidance on theanalysis of flanged and plain cruciform members is scarce in literature Hence this paper presents numerical studies on thestrength capacities of both flanged and plain cruciformmembers that are subjected to combined compression and bending effectsAnalysis results show the ability of flanged and plain cruciform to resist lateral-torsional buckling over longer unbraced lengthsallowing development of efficient plastic resistance

1 Introduction

Flanged cruciform members are used in high-load appli-cations as compression members Flanged cruciform sec-tions are typically fabricated from two hot-rolled WTsections welded to the web of a standard hot-rolled I sectionas shown in Figure 1 Typical applications include columnand lateral bracing members for orthogonal moment frameswith large bending moments about both local axes [1] andfor high-load applications including housing of mechanicaland power equipment [2]

On the contrary plain cruciform sections as shown inFigure 2 are typically fabricated from two symmetricrectangular plates welded in the form of a cross Plaincruciformmembers are used in lower load applications suchas for transmission line tower legs using the built-up con-struction with steel angles

While conventional compression members includingW-shapes are typically limited by flexural (Euler) bucklingabout the local weak axis of bending cruciform membersin combined compression and bending are typically limi-ted by torsional buckling )e American Institute for Steel

Construction (AISC) code [3] does not explicitly addresscruciform members )erefore sound engineering judge-ment and practical assumptions are required to performstrength capacity checks for compression bending andcombined compression and bending of cruciform mem-bers )is paper presents numerical studies on the strengthcapacities of both flanged and plain cruciform membersthat are subjected to combined compression and bendingeffects

2 Literature Review

In this section literature review on the use of both plain andflanged cruciform members is presented particularly high-lighting torsional buckling resistance However we note thatpeer-reviewed research on the behavior of flanged cruciformmembers is scarce compared to plain cruciform members

)e fundamental work of Timoshenko and Gere [4]forms the basis of the evaluation of torsional buckling re-sistance for singly doubly and unsymmetrical membersChajes [5] provided a comprehensive formulation of tor-sional buckling equations and added valuable insights into

HindawiAdvances in Civil EngineeringVolume 2018 Article ID 8417208 7 pageshttpsdoiorg10115520188417208

how design codes modify theoretical equations for use inpractice Chajes [5] concluded that for doubly symmetricopen sections such as flanged and plain cruciforms thetorsional buckling mode is the common mode of failure

Svensson and Plum [6] provided a theoretical basis forincreasing torsional buckling strength of flanged cruciformmembers by using intermediate stiffener plates weldedbetween adjacent flanges of W and WT sections )e in-termediate stiffeners serve as to increase the warping re-sistance of the member which is one component of thetorsional buckling resistance However no experimentalinvestigation into the use of intermediate warping stiffenerplates has been identified to qualify or calibrate this the-oretical work

Smith [2] considered torsional buckling of four equal-legangles used for composite plain cruciform sections His re-search evaluated the elastic critical loads for flexural tor-sional and plate buckling and considers inelastic bucklingwith respect to residual stress distribution in hot-rolledmembers )e results indicated that the AISC code specifi-cations [3] were not conservative for small to mediumslenderness ratios in four angle cruciform members At the

time the AISC code checks are provided only for local platebuckling and not for torsional buckling which has since beenrefined in later years to include torsional buckling checksSmith [2] alsonoted that there is a direct relationship betweentorsional buckling and local plate buckling validating thefundamental work by Bleich [7]

King [8] prepared a technical brief describing the uniquedesign considerations for plain cruciform and flangedcruciformmembers as they relate to Eurocode provisions forsteel construction )e technical brief provides a basicprimer for code checks for flexural and torsional bucklingresistance of doubly symmetric flexural cruciform membersas well as suggestions for typical flanged cruciform stiffenerdetails He also suggested the use of intermediate gussetplates to improve flexural buckling capacity of flangedcruciform members )e incorporation of the intermediategusset details serves to increase the stiffness of the websubject to primary flexural buckling )e suggested spacingof gussets was taken such that the minor axis slendernessratio does not exceed that of the full-flanged cruciformmember Neither theoretical nor experimental research intothe use of intermediate gusset plates for improvement offlexural buckling resistance of flanged cruciform membershas been identified

Trahair [9] considered strength design of the classic plaincruciform section Similar to Smith [2] Trahair evaluated theelastic critical loads for flexural torsional and plate bucklingand considers inelastic bucklingwith respect to residual stressdistribution in hot-rolled members His interest was iden-tifying differences in design code checks for plain cruciformsections across the world He stated that AISC and Eurocodecodes consider torsional buckling in addition to local andflexural buckling when compared to the Australian codeprovisions which ignore torsional buckling Trahair [9]showed that design of the plain cruciform section for localbuckling typically meets the requirements of torsionalbuckling resistance Furthermore it was shown that theAISCand Eurocode approach to torsional buckling which islimited to the elastic torsional buckling resistance results inreduced load capacity for plain cruciform sections with lowstiffness Hence the AISC and Eurocode approaches werefound to be overly conservative with respect to code checksfor torsional buckling resistance of a plain cruciform sectionand furthermore the Australian code check for local bucklingwas deemed to be sufficient to guard against torsionalbuckling resistance of the plain cruciform section whenpostbuckling and inelastic bucking resistance are consideredMore recently Nasrabadi et al [1] and Kiani et al [10] in-cluded panel zone design detailing for seismic applications offlanged cruciform members using finite element analysis

3 Guidelines for Strength Design

A clear guideline is needed for determining capacity ofcruciform members Basic steel design code checks fortypical building applications in the United States areaccording to AISC [3] )e design of cruciform members isnot explicitly addressed in the AISC specification howeverAISC code checks for members with geometry similar to

Figure 1 Typical flanged cruciform

Figure 2 Typical plain cruciform section

2 Advances in Civil Engineering

flanged and plain cruciform members (built-up doublysymmetric) provide a minimum basis for code checks Basedon this the nominal flexural buckling resistance of cruci-form members Pnf is determined by

Pnf FcrfAg (1)

where Ag is the gross area of the section and Fcrf is thelimiting flexural buckling stress given by (2) depending onthe level of the slenderness ratio KLr

Fcrf 0658FyFe1113960 1113961Fy whenKL

rle 471

E

Fy

1113971

Fcrf 0877Fe whenKL

rle 471

E

Fy

1113971

(2)

where E is the modulus of elasticity of steel Fy is the yieldstrength of steel K is the effective length factor L is thelaterally unbraced length of the member r is the radius ofgyration of the member and Fe is the elastic bucklingstrength given by (3) )e elastic buckling strength can bedetermined from the classical Euler buckling equation givenbelow

Fef π2E

[KLr]2 (3)

)e nominal torsional buckling resistance of cruciformmembers Pnt is determined from

Pnt FcrtAg (4)

)e critical torsional buckling strength Fcrt for a doublysymmetric member is limited to the elastic limit and is givenby

Fcrt π2ECw

KzL1113858 11138592 + GJ1113888 1113889

1Ix + Iy

(5)

where G is the shear modulus of steel Cw is the warpingconstant J is the torsional constant and Ix and Iy aremoment of inertia about the principal axes It is to be notedthat the Eurocode provisions [8] for critical torsionalbuckling stress of a doubly symmetric member is limited tothe elastic limit pe as shown in

pe n2π2EH

L2 + GJ1113888 11138891Io

(6)

where n is the number of half-sine waves along the outstandsof the member For members restrained at both ends thisshould be taken as 10 On comparison when substitutingIo Ix+ Iy and K 1n it is clear that (5) from the AISCprovisions takes similar form as (6) from the Eurocodeprovisions

)e controlling compressive resistance of the cruciformmember is then taken as the minimum of the flexuralbuckling resistance and the torsional buckling resistance)e composite cruciform moment of inertias Ix and Iy andsimilarly the elastic and plastic section moduli should bebased on the composite shape for the flanged cruciform (one

W section and two WT sections) )e composite flangedcruciform warping constant Cw is the sum of the Cw valuesfor each ldquoIrdquo shape (taken as that for the selected W shapeplus that of an equivalent W shape composed of the twoselected WT shapes) )e composite flanged cruciformtorsional constant J is the sum of the individual shapes (oneW section and two WT sections)

AISC [3] provides the derivation of torsional bucklingequations from elastic buckling loads using classic theory ofelasticity methods but with modifications for plasticbuckling However for doubly symmetric sections such asthe case in flanged cruciform members the torsionalbuckling stress is limited to the elastic buckling stressInelastic postbuckling strength is usually ignored becauseof difficulty in quantifying its value )e commentary alsoclaims that torsional buckling is an uncommon mode offailure in doubly symmetric compression members withoutslender elements except in cases where torsional unbracedlengths are significantly greater than the weak-axisunbraced lengths and in the case of doubly symmetricmembers However Trahair [9] provides a compelling casefor evaluating local buckling in plain cruciform memberswith or without slender elements Hence we suggest that itis prudent to check local buckling in flanged cruciformmembers as well

)e evaluation of cruciform members under combinedflexural and axial loading can be considered using interactionequations )is requires development of pure bendingstrength of the cruciform member Because no reference toplain or flanged cruciform members is given in code pro-visions caution must be exercised by the designer to selectappropriate and conservative assumptions for the predictionof bending strength for cruciform members before usinginteraction curves )e combined compression and flexureinteraction equationsofAISCapplicable toflanged cruciformmembers take the forms shown in (7) based on the ratio of themagnitude of axial load to axial resistance

Pr

Pc

+89

Mrx

Mcx

+Mry

Mcy

1113888 1113889le 10 whenPr

Pe

ge 020

Pr

2Pc

+Mrx

Mcx

+Mry

Mcy

1113888 1113889le 10 whenPr

Pe

le 020

(7)

where Pr is the required axial strength using LRFD loadcombinations Pc is the available factored axial strength Mris the required flexural strength using LRFD load combi-nations and Mc is the factored flexural strength

4 Numerical Evaluation

A set of analysis programs has been developed in MATLABto determine strength of cruciform members )e firstprogram performs capacity checks for flanged cruciformmembers using W and WT shapes )e second programperforms capacity checks for plain cruciform members )eprograms perform checks based upon a full set of geometricand load inputs However the programs do not utilizeoptimization algorithms

Advances in Civil Engineering 3

41 Independent Assessment of Flanged CruciformSections e anged cruciform program performs strengthchecks for any given anged cruciform member Programinputs to dene the section are simplied to allow the user toenter the desired ldquoWrdquo and ldquoWTrdquo sections For example theuser may input ldquoW16times100rdquo and ldquoWT8times50rdquo as the proposedsections and the program will automatically build andanalyze a anged cruciform member comprised of oneW16times100 and two WT8times50 sections e program also au-tomatically retrieves the required geometric parameters fromthe AISC [3] Shapes Database without the need to get in-dividual section properties Additional inputs to the programinclude unbraced lengths eective length factors materialproperties and design loads (axial load and biaxial exure)

e output of the program is a combined axial andexural interaction ratio (less than 10 is satisfactory) anda text statement indicating whether the input parameterssatisfy AISC code checks Additionally the output includesevaluation of the biaxial symmetry of the proposed angedcruciform section (a tolerance ofplusmn10 is the default tol-erance) If the symmetry about either axis diers more thanthe tolerance a caution message is provided e programdoes not perform local buckling checks

Due to lack of literature on anged cruciform sectionsvalidation of the program has been relatively dicult Weresorted to cross-validation by using the work of Svenssonand Plum [6] which included calculations for the Eulerbuckling loads about both axes and the torsional bucklingload Our anged cruciform program modied with directinputs of the composite section parameters to match theexample inputs yields the same Euler and torsional bucklingloads reported by Svensson and Plum [6]

e anged cruciform program was then used todemonstrate the capacity of these members in applicationswith high axial load with combined biaxial exure making itwell suited for use in orthogonal moment frames In ad-dition the program was used to perform a parametric studyof strength capacities for three proposedmembersW16times100and two WT8times50 sections W10times50 and two WT8times25sections and W10times26 and two WT8times13 sections Figure 3shows the ratio of the torsional buckling resistance toexural buckling resistance of each of the three sections atvarious unbraced lengths In the case of these three cases thetorsional buckling resistance is typically greater than that ofthe exural buckling resistance at low slenderness Howeverwith increasing the anged cruciform member slendernessthe torsional buckling mode becomes critical We note thistrend is contrary to the behavior of plain cruciform sectionswherein low to moderate slenderness promotes the im-portance of torsional buckling

42 IndependentAssessment of PlainCruciform Sections eplain cruciform program performs strength checks for anyproposed plain cruciform member e plain cruciformsection is dened by inputs for the desired total section depthalong each axis and the desired thickness of the cruciformlegs on each axis Additional inputs to the program include

unbraced lengths eective length factorsmaterial propertiesand design loads (axial load and biaxial exure) e plaincruciform program was indirectly calibrated by reproducingthe elastic exural and torsional buckling from Trahair [9]e plain cruciform section used for validation has a legthickness of 10mm and variable leg width to leg thicknessratios of 10 20 and 30 A modied slenderness ratio asshown in (8) is implemented for comparison purposes

λoy Ny

Noy

radic (8)

where Ny is the squash load and Noy is the Euler bucklingload If Noz represents the elastic torsional buckling loadplot depicting the ratios NozNy and NoyNy versus themodied slenderness for the varying values of bt providesan insight into the cruciform behavior e plain cruciformprogram was used to produce the result shown in Figure 4

Our results are consistent for exural buckling whencompared to results from available literature [9 10] For lowmodied slenderness our results for torsional buckling ofplain cruciform sections diverge with results reported inavailable literature [9 11] However the plain cruciformprogram uses a warping coecient Cw equal to zero bydefaultis is because torsional buckling resistance is minorfor practical designs of plain cruciform sections when themembers have moderate to high modied slenderness [12]One recommendation is to incorporate a warping stiness ofrectangular sections using the classical torsional rigiditygiven by

00

1

2

3

4

5

10 20 30 40Unbraced length (for flexure and torsion) ()

W16times100 + (2) WT8times50W16times50 + (2) WT8times25W16times26 + (2) WT8times13

Ratio

of P

n TB

PnFB

Figure 3 Torsional to exural buckling ratio for select angedcruciform members (1 ft 0305m)


Cw b3T3

9 (9)

e plain cruciform program was modied to accountfor this warping stiness (Cwne 0) with results plotted inaddition to results from the program default (Cw 0) WhenCw 0 is used the plain cruciform program yields valuesclose to what is reported in literature [9] with the exceptionof very low modied slenderness values of less than 02 Onthe other hand when the program is modied to add Cw(Cwne 0) it predicts higher torsional buckling resistance forlow to moderate modied slenderness values Results con-verge as the modied slenderness approaches 08e resultsindicate that for very low modied slenderness (very shortmembers) sections with higher leg slenderness given thesame leg thickness have a higher torsional buckling re-sistance Although this result is inconsistent with ndings byTrahair [9] we believe that for very low slendernessmembers the warping component of torsional bucklingresistance becomes highly dominant over St Venant tor-sional resistance Since the warping coecient is a functionof b3 given an equal modied slenderness the section withthe more slender leg (larger b) will produce a higher warpingtorsional resistance

e plain cruciform program was used to demonstratethe signicant limitation of plain cruciform sections whensubjected to exural loading Relative to axial resistance ofa given plain cruciform section the section develops littleexural resistance about either axis As such plain cruciformsections should be limited to purely axial applications such

as space trusses or struts Furthermore the program dem-onstrates the susceptibility of plain cruciform sections withlow to moderate slenderness to fail under torsional bucklingat loads signicantly less than that of exural buckling isis consistent with the conclusion presented by Smith [2] forbuilt-up plain cruciform members

43 Comparison of Flanged and Plain Cruciform Sections Acomparative study was conducted to investigate thecomparative behavior of typical anged and plain cruci-form members In the study three anged cruciformmembers W16times100 + 2 WT8times50 W10times50 + 2 WT8times25and W10times26 + 2 WT8times13 were compared to theirplain cruciform counterpart sections (16Prime (406 cm)depth times 0585Prime (15 cm) leg thickness 16Prime (406 cm)depth times 038Prime (1 cm) leg thickness and 16Prime depth(406 cm) times 025Prime (065 cm) leg thickness) e selectedmaterial yield strength for all members was 36 ksi(248MPa) e results for axial and exural resistance atdierent unbraced lengths ranging from 10 feet (333m)to 40 feet (133m) are shown in Figures 5ndash8

Results conrm the exceptional exural performance ofanged cruciform members relative to plain cruciformmembers at all slenderness levels e analysis also conrmsthat anged cruciform members are well suited for appli-cations under large axial compression and biaxial exure Asimilar nding for FRP can be found in [13]

Conversely the analysis shows that plain cruciformsections are very economical under pure axial applicationsResults also demonstrate that the high biaxial exuralstrength of anged and plain cruciform members enables

00

05

10

15

20

25

30

35

40

00 02 04 06 08 10 12

Dim

ensio

nles

s buc

klin

g lo

ad N

o N

y

Modified slenderness λ = radicNyNoy

NozNy Cw = 0 with bt = 10NozNy with bt = 10NozNy Cw = 0 with bt = 20NozNy with bt = 20NozNy Cw = 0 with bt = 30NozNy with bt = 30NozNy with bt = 10

Figure 4 Torsional to exural buckling loads for select plaincruciform members

00

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

10 15 20 25 30 35 40

Nor

mal

ized

axia

l res

istan

ce (k

ip)

Unbraced length ()

Axial resistance

W16times100 + (2) WT8times50Plain 16Prime times 0585PrimeW16times50 + (2) WT8times25Plain 16Prime times 038PrimeW16times26 + (2) WT8times13Plain 16Prime times 025Prime

Figure 5 Axial resistance for comparative plain and angedcruciform members (1 ft 0305m and 1 kip 445 kN)


maintenance of a stable exural resistance across a largerange of unbraced length is is due to the ability of angedand plain cruciform to resist lateral-torsional bucklingallowing development of ecient plastic resistance over

longer unbraced lengths when compared to conventionalshapes As the limitation of this study strength check forconnections and local concentrated end bearings are notincluded here

5 Conclusions

is paper presents numerical studies on the strengthcapacities of both anged and plain cruciform membersthat are subjected to combined compression and bendingeects Two numerical programs were developed and theywere used to conduct a comparative study of the behaviorof three anged cruciform to their plain cruciform coun-terpart sections Analysis results show the ability of angedand plain cruciform to resist lateral-torsional buckling overlonger unbraced lengths allowing development of ecientplastic resistance It is to be noted that required checks forstability service and fatigue should be considered in ad-dition to the member strength analysis presented in thisresearch To enhance the ndings of this paper furthercomparative studies using nite element analysis arerecommended

Conflicts of Interest

e authors declare that there are no conicts of interest

Acknowledgments

e authors gratefully acknowledge Yilak H Desta PE forstriking their interest in conducting this research

00

50

100

150

200

250

300

350

10 15 20 25 30 35 40Unbraced length ()

Normalized axial resistanceN

orm

aliz

ed ax

ial r

esist

ance

(kip

in2 )


Figure 6 Normalized axial resistance for comparative plainand anged cruciform members (1 ft 0305 m and 1 kipin2 6895 MPa)

00

10000

20000

30000

40000

Nor

mal

ized

nom

inal

flex

ural

resis

tanc

e (ki

pmiddotin

)

50000

60000

70000

80000

90000

10 15 20 25 30 35 40Unbraced length ()

Flexural resistance


Figure 7 Flexural resistance for comparative plain and angedcruciform members (1 ft 0305m and 1 kip 445 kN)

00

200

400

600

800

1000

1200

1400

1600

10 15 20 25 30 35 40Unbraced length ()

Normalized flexural resistance

Nor

mal

ized

nom

inal

flex

ural

resis

tanc

e (ki

pmiddotin

in2 )


Figure 8 Normalized exural resistance for comparative plainand anged cruciform members (1 ft 0305 m and 1 kipin2 6895MPa)


References

[1] M Nasrabadi S Torabian and S Mirghaderi ldquoPanel zonemodelling of flanged cruciform columns an analytical andnumerical approachrdquo Engineering Structures vol 49pp 491ndash507 2012

[2] E Smith ldquoBuckling of four equal leg angle cruciform col-umnsrdquo Journal of Structural Engineering vol 109 no 2pp 439ndash450 1983

[3] AISC 360 Specification for Structural Steel Buildings Amer-ican Institute of Steel Construction Chicago IL USA 2016

[4] S P Timoshenko and J M Gere 5eory of Elastic StabilityMcGraw-Hill New York NY USA 2nd edition 1961

[5] A Chajes Principles of Structural Stability 5eory Prentice-Hall Englewood Cliffs NJ USA 1974

[6] S A Svensson and C M Plum ldquoStiffener effects on torsionalbuckling of columnsrdquo Journal of Structural Engineeringvol 100 no 3 pp 758ndash772 1983

[7] F Bleich Buckling Strength of Metal Structures McGraw-HillNew York NY USA 1952

[8] C King Design of Cruciform Sections using BS 5950-12000)e British Constructional Steelwork Association Ltd LondonUK 2006

[9] N Trahair ldquoStrength design of cruciform steel columnsrdquoEngineering Structures vol 35 pp 307ndash313 2011

[10] B Kiani S Torabian and S Mirghaderi ldquoLocal seismic sta-bility of flanged cruciform sections (FCSs)rdquo EngineeringStructures vol 96 pp 126ndash138 2014

[11] G Urgessa and T Arciszewski ldquoBlast response comparison ofmultiple steel frame connectionsrdquo Finite Elements in Analysisand Design vol 47 no 7 pp 668ndash675 2011

[12] P B Dinis D Camotim and N Silvestre ldquoOn the local andglobal buckling behaviour of angle T-section and cruciformthin-walled membersrdquo5in-Walled Structures vol 48 no 10-11 pp 786ndash797 2010

[13] G Urgessa S Horton M M Reda Taha and A Maji ldquoSig-nificance of Stress-Block Parameters on theMoment Capacity ofSections Under-Reinforced with FRPrdquo ACI Special Publication230 pp 1531ndash1550 American Concrete Institute FarmingtonHills MI USA 2005


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how design codes modify theoretical equations for use inpractice Chajes [5] concluded that for doubly symmetricopen sections such as flanged and plain cruciforms thetorsional buckling mode is the common mode of failure

Svensson and Plum [6] provided a theoretical basis forincreasing torsional buckling strength of flanged cruciformmembers by using intermediate stiffener plates weldedbetween adjacent flanges of W and WT sections )e in-termediate stiffeners serve as to increase the warping re-sistance of the member which is one component of thetorsional buckling resistance However no experimentalinvestigation into the use of intermediate warping stiffenerplates has been identified to qualify or calibrate this the-oretical work

Smith [2] considered torsional buckling of four equal-legangles used for composite plain cruciform sections His re-search evaluated the elastic critical loads for flexural tor-sional and plate buckling and considers inelastic bucklingwith respect to residual stress distribution in hot-rolledmembers )e results indicated that the AISC code specifi-cations [3] were not conservative for small to mediumslenderness ratios in four angle cruciform members At the

time the AISC code checks are provided only for local platebuckling and not for torsional buckling which has since beenrefined in later years to include torsional buckling checksSmith [2] alsonoted that there is a direct relationship betweentorsional buckling and local plate buckling validating thefundamental work by Bleich [7]

King [8] prepared a technical brief describing the uniquedesign considerations for plain cruciform and flangedcruciformmembers as they relate to Eurocode provisions forsteel construction )e technical brief provides a basicprimer for code checks for flexural and torsional bucklingresistance of doubly symmetric flexural cruciform membersas well as suggestions for typical flanged cruciform stiffenerdetails He also suggested the use of intermediate gussetplates to improve flexural buckling capacity of flangedcruciform members )e incorporation of the intermediategusset details serves to increase the stiffness of the websubject to primary flexural buckling )e suggested spacingof gussets was taken such that the minor axis slendernessratio does not exceed that of the full-flanged cruciformmember Neither theoretical nor experimental research intothe use of intermediate gusset plates for improvement offlexural buckling resistance of flanged cruciform membershas been identified

Trahair [9] considered strength design of the classic plaincruciform section Similar to Smith [2] Trahair evaluated theelastic critical loads for flexural torsional and plate bucklingand considers inelastic bucklingwith respect to residual stressdistribution in hot-rolled members His interest was iden-tifying differences in design code checks for plain cruciformsections across the world He stated that AISC and Eurocodecodes consider torsional buckling in addition to local andflexural buckling when compared to the Australian codeprovisions which ignore torsional buckling Trahair [9]showed that design of the plain cruciform section for localbuckling typically meets the requirements of torsionalbuckling resistance Furthermore it was shown that theAISCand Eurocode approach to torsional buckling which islimited to the elastic torsional buckling resistance results inreduced load capacity for plain cruciform sections with lowstiffness Hence the AISC and Eurocode approaches werefound to be overly conservative with respect to code checksfor torsional buckling resistance of a plain cruciform sectionand furthermore the Australian code check for local bucklingwas deemed to be sufficient to guard against torsionalbuckling resistance of the plain cruciform section whenpostbuckling and inelastic bucking resistance are consideredMore recently Nasrabadi et al [1] and Kiani et al [10] in-cluded panel zone design detailing for seismic applications offlanged cruciform members using finite element analysis

3 Guidelines for Strength Design

A clear guideline is needed for determining capacity ofcruciform members Basic steel design code checks fortypical building applications in the United States areaccording to AISC [3] )e design of cruciform members isnot explicitly addressed in the AISC specification howeverAISC code checks for members with geometry similar to

Figure 1 Typical flanged cruciform

Figure 2 Typical plain cruciform section



Pnf FcrfAg (1)



rle 471

E

Fy

1113971

Fcrf 0877Fe whenKL

rle 471

E

Fy

1113971

(2)


Fef π2E

[KLr]2 (3)


Pnt FcrtAg (4)


Fcrt π2ECw

KzL1113858 11138592 + GJ1113888 1113889

1Ix + Iy

(5)


pe n2π2EH

L2 + GJ1113888 11138891Io

(6)






Pr

Pc

+89

Mrx

Mcx

+Mry

Mcy

1113888 1113889le 10 whenPr

Pe

ge 020

Pr

2Pc

+Mrx

Mcx

+Mry

Mcy

1113888 1113889le 10 whenPr

Pe

le 020

(7)











λoy Ny

Noy

radic (8)



00

1

2

3

4

5



Ratio

of P

n TB

PnFB



Cw b3T3

9 (9)







00

05

10

15

20

25

30

35

40

00 02 04 06 08 10 12

Dim

ensio

nles

s buc

klin

g lo

ad N

o N

y




00

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

10 15 20 25 30 35 40

Nor

mal

ized

axia

l res

istan

ce (k

ip)

Unbraced length ()

Axial resistance






5 Conclusions




Acknowledgments


00

50

100

150

200

250

300

350

10 15 20 25 30 35 40Unbraced length ()


orm

aliz

ed ax

ial r

esist

ance

(kip

in2 )



00

10000

20000

30000

40000

Nor

mal

ized

nom

inal

flex

ural

resis

tanc

e (ki

pmiddotin

)

50000

60000

70000

80000

90000

10 15 20 25 30 35 40Unbraced length ()

Flexural resistance



00

200

400

600

800

1000

1200

1400

1600

10 15 20 25 30 35 40Unbraced length ()


Nor

mal

ized

nom

inal

flex

ural

resis

tanc

e (ki

pmiddotin

in2 )




References

















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Pnf FcrfAg (1)



rle 471

E

Fy

1113971

Fcrf 0877Fe whenKL

rle 471

E

Fy

1113971

(2)


Fef π2E

[KLr]2 (3)


Pnt FcrtAg (4)


Fcrt π2ECw

KzL1113858 11138592 + GJ1113888 1113889

1Ix + Iy

(5)


pe n2π2EH

L2 + GJ1113888 11138891Io

(6)






Pr

Pc

+89

Mrx

Mcx

+Mry

Mcy

1113888 1113889le 10 whenPr

Pe

ge 020

Pr

2Pc

+Mrx

Mcx

+Mry

Mcy

1113888 1113889le 10 whenPr

Pe

le 020

(7)











λoy Ny

Noy

radic (8)



00

1

2

3

4

5



Ratio

of P

n TB

PnFB



Cw b3T3

9 (9)







00

05

10

15

20

25

30

35

40

00 02 04 06 08 10 12

Dim

ensio

nles

s buc

klin

g lo

ad N

o N

y




00

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

10 15 20 25 30 35 40

Nor

mal

ized

axia

l res

istan

ce (k

ip)

Unbraced length ()

Axial resistance






5 Conclusions




Acknowledgments


00

50

100

150

200

250

300

350

10 15 20 25 30 35 40Unbraced length ()


orm

aliz

ed ax

ial r

esist

ance

(kip

in2 )



00

10000

20000

30000

40000

Nor

mal

ized

nom

inal

flex

ural

resis

tanc

e (ki

pmiddotin

)

50000

60000

70000

80000

90000

10 15 20 25 30 35 40Unbraced length ()

Flexural resistance



00

200

400

600

800

1000

1200

1400

1600

10 15 20 25 30 35 40Unbraced length ()


Nor

mal

ized

nom

inal

flex

ural

resis

tanc

e (ki

pmiddotin

in2 )




References

















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








λoy Ny

Noy

radic (8)



00

1

2

3

4

5



Ratio

of P

n TB

PnFB



Cw b3T3

9 (9)







00

05

10

15

20

25

30

35

40

00 02 04 06 08 10 12

Dim

ensio

nles

s buc

klin

g lo

ad N

o N

y




00

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

10 15 20 25 30 35 40

Nor

mal

ized

axia

l res

istan

ce (k

ip)

Unbraced length ()

Axial resistance






5 Conclusions




Acknowledgments


00

50

100

150

200

250

300

350

10 15 20 25 30 35 40Unbraced length ()


orm

aliz

ed ax

ial r

esist

ance

(kip

in2 )



00

10000

20000

30000

40000

Nor

mal

ized

nom

inal

flex

ural

resis

tanc

e (ki

pmiddotin

)

50000

60000

70000

80000

90000

10 15 20 25 30 35 40Unbraced length ()

Flexural resistance



00

200

400

600

800

1000

1200

1400

1600

10 15 20 25 30 35 40Unbraced length ()


Nor

mal

ized

nom

inal

flex

ural

resis

tanc

e (ki

pmiddotin

in2 )




References

















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Cw b3T3

9 (9)







00

05

10

15

20

25

30

35

40

00 02 04 06 08 10 12

Dim

ensio

nles

s buc

klin

g lo

ad N

o N

y




00

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

10 15 20 25 30 35 40

Nor

mal

ized

axia

l res

istan

ce (k

ip)

Unbraced length ()

Axial resistance






5 Conclusions




Acknowledgments


00

50

100

150

200

250

300

350

10 15 20 25 30 35 40Unbraced length ()


orm

aliz

ed ax

ial r

esist

ance

(kip

in2 )



00

10000

20000

30000

40000

Nor

mal

ized

nom

inal

flex

ural

resis

tanc

e (ki

pmiddotin

)

50000

60000

70000

80000

90000

10 15 20 25 30 35 40Unbraced length ()

Flexural resistance



00

200

400

600

800

1000

1200

1400

1600

10 15 20 25 30 35 40Unbraced length ()


Nor

mal

ized

nom

inal

flex

ural

resis

tanc

e (ki

pmiddotin

in2 )




References

















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




5 Conclusions




Acknowledgments


00

50

100

150

200

250

300

350

10 15 20 25 30 35 40Unbraced length ()


orm

aliz

ed ax

ial r

esist

ance

(kip

in2 )



00

10000

20000

30000

40000

Nor

mal

ized

nom

inal

flex

ural

resis

tanc

e (ki

pmiddotin

)

50000

60000

70000

80000

90000

10 15 20 25 30 35 40Unbraced length ()

Flexural resistance



00

200

400

600

800

1000

1200

1400

1600

10 15 20 25 30 35 40Unbraced length ()


Nor

mal

ized

nom

inal

flex

ural

resis

tanc

e (ki

pmiddotin

in2 )




References

















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


References

















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Documents

ResearchArticle …downloads.hindawi.com/journals/ace/2018/8417208.pdfcruciform section (a tolerance of±10% is the default tol-erance). If the symmetry about either axis diŒers more