calculation of eccentricities in load bearing walls-engineers file note

8/14/2019 CALCULATION OF ECCENTRICITIES IN LOAD BEARING WALLS-ENGINEERS FILE NOTE

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NGIN RS IL NOT NO

Published by The Brick Development Association

eISfB I I I7 I 21 I F I

THE C LCUL TION OFECCENTRICITIES IN

LO D E RING W LLSby Professor A W Hendry BSe ph OSe CEng FI E FIStruetE FRSE

B55628: Part 1 states that theeccentricity of loads on walls shouldpreferably be calculated but doesnot indicate how this may be doneThis note based on recent research

work addresses this problemIt discusses the background work andgives a method ofcalculatingthe eccentricity on loadbearing wallsbetween reinforced concrete floors


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INTRODUCTIONOneofthe basicproblems inthe designofloadbearingbrickwork walls is that ofallowing forthe effects ofslenderness andeccentricityofloading. InBS 5628 Part 1designersare advised to determineeccentricity ofloading bycalculation but,recognising the difficulty ofdoingthis atthe timeofpublication, the Code gives anempirical ruleforassessing eccentricity.Recently, researchworkhas beencompletedwhich permits calculation ofeccentridties on a rationalbasisand it isthe purpose ofthis Note to summarise theproblem and a suitablemethodofcalculating eccentricity for the case ofloadbearingbrickwork wallscompressedbetween reinforced concretefloor slabs.

END FIXITY FROMFLOOR SL S

Where a wall iscompressedbetweenreinforced concretefloor slabs, twointer-relatedaspects ofthe problem can bediscerned.Thefirst is illustratedin Fig 1where the strengthening effect offloorslabs ona wall is suggested.Thus, whenawall is tending to fail inbuckling, the ends

tend to rotate;with floor slabs present,somedegreeofrestraint is introducedbyflexure ofthe floor slabs.Thegreater therelative stiffnessofthe floor slabs, thegreater the restraint and the nearer thesituationapproaches that ofa fixed endedcolumn.W LL END

ECCENTRICITYThesecondaspect ofthe problemrelatesto the effect ofthe floor slabs on theeccentridty ofloading at the wall ends.Loading ona floor slab,as inFig 2,will applya momenttothe top ofawall the magnitudeofwhich will depend on the rigidity ofthewall/floorslab joint. Ifthe load from asectionofwall above that underconsideration is eccentric, itwill introducea bendingmoment intothe slab.Thetotalloadappliedto the top ofthe wall , PcJ willbe the sumofthe load from above Pulplusthe slab reaction Ps and will beappliedat an eccentricity eL such thatPu e,PL eL= MsThe momentsdeveloped, and thus theeccentricities ofloadingat the wall ends,dependon a numberoffactors, includingthe relative stiffnessofthe wall and slaband the jointfixity.

Rg1:Res raining effectof floorslobs onwallbuckling.

g2:Condifions atwall/floor slobjoint

P,

; > estr iningy momentbndrot tionrestr ined by

lloorsabs

0nrestrainedendrot tion


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10

08

I~ 0.6~rr;c 4

02

Ie - ONmm2

I, - O5N/mm2

Ie - Q25N fmm20 -- - - - _Rg3: JointfixityV stillne ralJa n

J O I N T FIXITY L UL TIONOF E ENTRI ITY

1 20 30 40 50 6.0 70 8.0 90 00

1 - r- w/m , IIA EI) Ih El

8 II

h

- -I 1Superimposed load

1 r +2MA- 2- N w2E),l EI).

B

Rg 4:Cal Jlatlan orEccentricityIn Exterior MasonryWa lls

I

1Deed LoadM 1 ,

A 8 0+3) lN - 4 0+ 2) - 0 +1)

-I

g/m II

A E), IEI g/mh

h/2- -

Various methods havebeen developed forthe calculationofeccentricityofloadingata joint.Averyeasilyappliedpartialframeanalysisisshowin Fig 4 for externalwallsfrom which eccentricities resulting fromslab loadsmay becalculated,providedthat the rigid framemoments are reducedto allow forthe joint fixity as defined in thepreceedingparagraph. Formulae arealsoavailable forinternalwalls but inthiscaseeccentricities are generally negligible.Thejoint fixity factormay beobtainedfrom Fig 4 but, as an approximation, thefollowing formula maybeused:F= 10.44ex + IIwhere ex is the slab/wall stiffness ratioasdefinedin Fig 4.

Aconsiderable amount ofexperimentalresearchhas been devoted to the study ofwall/floorslab interaction and inparticular to the evaluationof jointfixityTheresults aresummarised in Fig 3whichshows the joint fixity, definedas the ratioofthe actualmoment transmitted byajoint to that whichwouldexist ifthe jointwas fully rigid,plottedon a baseofslab/wall stiffnessratio.Thejointrigidity alsodepends on the compression on the jointfrom loadingaboveand three curvesareshownforjoint compressivestressesbetweenO25N/mm2 and lON/mm2


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SLENDERNESS R TIOTheslenderness ratio ofa wall isdefinedas the ratio ofthe effective heighttoeffective thickness. For solidwalls theeffective thickness is the same as theactual thicknesswhilstfor a cavitywall itisconventionally taken as twothirds ofthe combinedthicknessof the leaves. Theeffective height theoretically depends onthe eccentridties ofthe loading at the topand bottom ofthe wall .Thus, referring toFig 5, if the eccentridties are ofthe samesign, orzero at one end), the wall willdeflectin singlecurvature Fig 5 all. If theeccentridties are ofoppositesign, the wallwill deflectin double curvature Fig 5 bl).Inthe first case the effective heightisequal to the actual height ofthe wallwhilstin the second case the effectiveheight isless than the actual height. Tosimplify calculations, the effective heightofa wall compressedbetween floor slabsis usuallyassumed to be three quarters ofthe actual height.This isinreasonableagreement with experimental andtheoreticalresults.Also to simplify calculations, itisreasonable to assume that the eccentricity. ofloadingabove a wall/floorslab jointis zero.DESIGN ST RENGTH

OF W LLHaving determined the slenderness ratioand eccentrid ty ofloading, the designstrength per unit lengthofa wall is thencalculatedby multiplying the designstrength ofthe material fkl) bythethickness ofthe wall t and bya capadtyreduction factor p whichis a function ofthe slenderness ratioand eccentridty.Many theories have been produced fordetermining capadty reduction factorsand these give rather disparate values.Fortunately, inthe majorityof practicalcases the eccentridtieswill be rather smalland the reduction factors by allmethodswillbe near to unitywhere the stress inthe brickwork is significan t.

REDU TION F TORSBy way ofillustration, capacity reductionfactors forthe variousstorey heightsections ofthe outer wall ofa buildingFig 61have been calculatedby the methoddescribedin thisNote in conjunctionwithB55628 Part Two wall thicknesses have

0) ngl urv ture

Fig 5:EIIedive heights in single nd In double urwture


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beenconsidered,namelya 280mmcavitywall and a 215 mmsolidwall.Incalculating the rigidity ofthe jointbetween a floor slab and a cavitywallconsisting oftwo 103 mmthickleaves,experimental results haveshown thatsuchawall will behaveas a singleleafwallwhen the jointcompression exceeds 3N mm This isthe case inall but oneofthe jointsin this example.Theresults aresummarised inTable 1from which itwill beseen thateccentricities are generally quitesmall.The reduction in loadbearing capacityresulting from slenderness andeccentricity does not exceed14 per centbelow the third level from the top ofthebuilding.Aspecimencalculation is given inanAppendix to this Note toshowtheprocedureto beadopted incalculatingeccentricities indesign.

Sab:Span 35 0


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ON LUS ONIn855628Part 1paragraph states thatthe eccentridtyofloading inwalls shouldpreferably be calculated. As described inthisNote practical meansarenowavailable for doingthis.As compared withthe conventional rulegiven inthe odethe resulting eccentridtieswill usually behigherwhencalculated bya methodgiving valuesconsistentwithexperimental results. In mostcaseshowever the capadty reduction factor forslendernessand eccentricitywill not begreatlydifferent as betweenthe twomethodswherebrickwork strength iscritical This is becausethe odereductionfactors donotdecreaseuntil theeccentridty ratiois greater than 0.05andinmanycases the correctly calculatedvaluewill not exceed this figure .Notwithstanding this conclusion itisclearly more satisfactory to adopt a rationalmethodofcalculation inpreferenceto aruleof thumb the limitations ofwhichare unknown.

Full s le structural lesl on wall/floor slab loin behavIOu r.


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ECCENTRICITIES NDC P CITY REDUCTION

FACTORS FOR T OUTER WALLOF A BUILDING

Level Floar Slob: Span 3.5 m: thickness lSO mmbeiow 280 mm CavityWall 215mm SolidWall tRoofSlob

1 0.13 0.78 0.17 0.732 0.075 0.86 0.16 0.753 0.057 0.88 014 0.794 0046 089 0.11 0.865 0.038 0.89 0.094 0.896 0.034 0.89 0 079 0.927 0.025 0.89 0.060 0.96

Level Floor Slob: Span 4.5 rn; thickness 170mmbeiow 280 mm CavityWoII 215 mm SoidWolltRoofSlob

1 0.22 0.62 0.20 0.662 0088 0.84 01 4 0.803 0.069 0.87 0.12 0.844 0.055 0.88 0.094 0.895 0.047 0.89 0.078 0.936 0.041 089 0.067 0.957 0.031 0.89 0.060 0.96

S1endemess ratio : 14 t Slenderness rolio 9

ccenlridly ratio - ef t Copocify reduction foetor BS 5628 Port )

PPENDIXC LCUL TION OF

ECCENTRICITY AT AWALLFLOOR SLAB JOINT

The load conditions at the fi t floor ievel at the outerwall in a seven storey brickwork bu ilding are asshown in Rg 7 The floor slob baa on the inner ieatof a 280 mm cavity wall. Testshave been shownthat in suc h a case the jo int fixity should becalculated with reference to the loaded leaf on lyReferring to the pa rtial frame formula shown in Fig4and ta king the ratio of elastic moduli for concreteand brickwork as 2:

EQ , _2 .85 . 2 . ( 100 ) ' _ 176L (EQw 3.0 102.5 .N-4 cx + 2)- cx + 1) -4(1.76+2)-(1.76+ 1)- 48.93Moment due to superimposed load :1 cx + 2- . . wL2 N_ ]. . ( 1.76 + 2 ) X32 x3 '2 48.93 . 4 .-0.37 kNmMoment due to dead load :

1 ,8(cx + 3) gL1 x 9 07x 38 1.76 + 3) .

- 0.72 kNmTotal rigid frame moment- 0.37 + 0.72 - 1 09 kNmJoint fiXty foetor

1 1 -0.53(0.44 cx + 1 1 0.44 x 1.76 + Joint moment- 0.53 x 1.09 - 0.58 kNm

0.58 X 10'e - 82.35 - 704 mme 704- - 102.5 - 0.069

load from t o r e O9G + t6Q,- 82 5kN(m

r so n 3 mSlob load: lAG, + t Q- 12.3tkN(mt 4G, - 9.07kN(mt6Q, - 3.24kN(m

m

Fig 7: lo ing atwall/floorslab join


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The ssodation wou ld be interested to hear. from Engineers or Architects of pro jects which theyconsider worthy of inclusion in The BDA Engineers File Note Series .All initial submissions shouldcontain reference to t he particular a re a of the design which. it is c on sidered. would be of interest to

the design profession as a wh ol e.All enquiries should be addressed to The Technical Editor.J orton BSc PhD CEng MICE lnst

The views expressed in this FileNote are those of the Authors. Readers are expressly advised that theydo not necessarily reflect the views of the Association.To demonstrate the initial engineering decisions taken scheme calculations have been included in theNote . They are NOT intended to be full and detailed calculations and they should NOT be read as suc h.

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Woodside House . Winkfield. Windsor Berkshire SL4 DXPlease enclose 2.50 remittance per binder to cover post and packing.Readers are expressly advISed that whilstthe contents of th is publICat ionare behevt d to be accurate OTKt and ccenpiete.norelianceshouldbeplacl duponitsecete nts asbeIngappbcable toany particular drcumstances Any advkeopinionorinformation containt d is publishfonlyon thefootingthatthe Brick

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calculation of eccentricities in load bearing walls-engineers file note

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