how2 foundations final

IntroductionTheintroductionofEuropeanstandardstoUK

constructionisasignificantevent.Thetendesign

standards,knownastheEurocodes,willaffect

alldesignandconstructionactivitiesascurrent

Britishstandardsfordesignareduetobe

withdrawnin2010.

Thispublicationispartoftheseriesofguides

entitledHow to design concrete structures using

Eurocode 2.Theiraimistomakethetransitionto

Eurocode2: Design of concrete structuresaseasy

aspossiblebydrawingtogetherinoneplacekey

informationandcommentaryrequiredforthe

designoftypicalconcreteelements.

Thecementandconcreteindustryrecognisedthat

asubstantialeffortwasrequiredtoensurethat

theUKdesignprofessionwouldbeabletouse

Eurocode2quickly,effectively,efficientlyand

withconfidence.Withsupportfromgovernment,

consultantsandrelevantindustrybodies,the

ConcreteIndustryEurocode2Group(CIEG)was

formedin1999andthisGrouphasprovidedthe

guidanceforaco-ordinatedandcollaborative

approachtotheintroductionofEurocode2.As

aresult,arangeofresourcesistobemade

availablethroughTheConcreteCentretohelp

designersduringthetransitionperiod(seeback

coverfordetails).

Eurocode 7: Geotechnical designScopeAllfoundationsshouldbedesignedsothatthesoilsafelyresiststhe

actionsappliedtothestructure.Thedesignofanyfoundationconsistsof

twocomponents;thegeotechnicaldesignandthestructuraldesignofthe

foundationitself.However,forsomefoundations(e.g.flexiblerafts)theeffect

oftheinteractionbetweenthesoilandstructuremaybecriticalandmust

alsobeconsidered.GeotechnicaldesigniscoveredbyEurocode71,whichsupersedesseveralcurrentBritishStandardsincludingBS59302,BS80023andBS80044.ThenewEurocodemarksasignificantchangeingeotechnicaldesigninthatlimitstateprinciplesareusedthroughoutandthisshould

ensureconsistencybetweentheEurocodes.TherearetwopartstoEurocode7,

Part1:General rulesandPart2: Ground investigation and testing.

TheessentialfeaturesofEurocode7,Part1relatingtofoundationdesignare

discussedinthisguide.Itshouldbeemphasisedthatthispublicationcovers

onlythedesignofsimplefoundations,whichareasmallpartofthescopeof

Eurocode7.Thereforeitshouldnotbereliedonforgeneralguidanceonthis

Eurocode.AtthetimeofwritingitisanticipatedthattheNationalAnnex(NA)

forPart1willbepublishedinOctober2006.

Limit statesThefollowingultimatelimitstates(ULS)shouldbesatisfiedforgeotechnical

design;theyeachhavetheirowncombinationsofactions.(Foranexplanation

ofEurocodeterminologypleaserefertoHow to design concrete structures

using Eurocode 2: Introduction to Eurocodes5).EQU Lossofequilibriumofthestructure.

STR Internalfailureorexcessivedeformationofthestructureorstructural

member.

GEO Failureduetoexcessivedeformationoftheground.

UPL Lossofequilibriumduetoupliftbywaterpressure.

HYD Failurecausedbyhydraulicgradients.

Inaddition,theserviceabilitylimitstates(SLS)shouldbesatisfied.Itwill

usuallybeclearthatoneofthelimitstateswillgovernthedesignand

thereforeitwillnotbenecessarytocarryoutchecksforallofthem,although

itisconsideredgoodpracticetorecordthattheyhaveallbeenconsidered.

Geotechnical categoriesEurocode7recommendsthreegeotechnicalcategoriestoassistinestablishing

thegeotechnicaldesignrequirementsforastructure(seeTable1).

HowtodesignconcretestructuresusingEurocode2

6.FoundationsR WebsterCEng,FIStructEO BrookerBEng,CEng,MICE,MIStructE

2HowtodesignconcretestructuresusingEurocode2

Table 1 Geotechnical categories of structures

Category Description Risk of geotechnical failure Examples from Eurocode 7

1 Smallandrelativelysimplestructures Negligible Nonegiven

2 Conventionaltypesofstructureandfoundationwithnodifficultgroundorloadingconditions

Noexceptionalrisk Spreadfoundations

3 Allotherstructures Abnormalrisks LargeorunusualstructuresExceptionalgroundconditions

Table 2Design values of actions derived for UK design, STR/GEO ultimate limit state persistent and transient design situations

Combination Expression reference from BS EN 1990

Permanent actions Leading variable action

Accompanying variable actions

Unfavourable Favourable Main (if any) Others

Combination 1 (Application of combination 1 (BS EN 1997) to set B (BS EN 1990)

Exp.(6.10) 1.35Gka 1.0Gka 1.5bQk 1.5bco,icQk,i

Exp.(6.10a) 1.35Gka 1.0Gka 1.5co,1cQk 1.5bco,icQk,i

Exp.(6.10b) 0.925dx1.35Gka 1.0Gka 1.5bQk 1.5bco,icQk,i

Combination 2 (Application of combination 2 (BS EN 1997) to set C (BS EN 1990)

Exp.(6.10) 1.0Gka 1.0Gka 1.3bQk,1 1.3bco,ibQk,i

Keya WherethevariationinpermanentactionisnotconsideredsignificantGk,j,supandGk,j,infmaybetakenasGkb Wheretheactionisfavourable,gQ,i=0andthevariableactionsshouldbeignoredc ThevalueofcocanbeobtainedfromTableNA.A1.1oftheUKNAtoBSEN1990(orseeTable3ofIntroduction to Eurocodes5)d ThevalueofjintheUKNAtoBSEN1990is0.925

Table 3Partial factors for geotechnical material properties

Angle of shearing resistance (apply to tan h)

Effective cohesion Undrained shear strength

Unconfined strength Bulk density

Symbol gh gc gcu gqu gg

Combination1 1.0 1.0 1.0 1.0 1.0

Combination2 1.25 1.25 1.4 1.4 1.0

Itisanticipatedthatstructuralengineerswilltakeresponsibilityforthe

geotechnicaldesignofcategory1structures,andthatgeotechnical

engineerswilltakeresponsibilityforcategory3structures.The

geotechnicaldesignofcategory2structuresmaybeundertakenby

membersofeitherprofession.Thisdecisionwillverymuchdependon

individualcircumstances.

Methods of design and combinationsTherehasnotbeenaconsensusamongstgeotechnicalengineers

overtheapplicationoflimitstateprinciplestogeotechnicaldesign.

Therefore,toallowforthesedifferencesofopinion,Eurocode7

providesforthreedesignapproachestobeusedfortheULS.The

decisiononwhichapproachtouseforaparticularcountryisgiven

initsNationalAnnex.IntheUKdesignapproach1willbespecified

intheNationalAnnex.Forthisdesignapproach(excludingpileand

anchoragedesign)therearetwosetsofcombinationstouseforthe

STRandGEOultimatelimitstates.Thevaluesforthepartialfactors

tobeappliedtotheactionsforthesecombinationsofpartialfactors

aregiveninTable2andthepartialfactorsforthegeotechnical

materialpropertiesaregiveninTable3.Combination1willgenerally

governthestructuralresistance,andcombination2willgenerally

governthesizingofthefoundations.

Thepartialfactorsforsoilresistancetoslidingandbearingshouldbe

takenas1.0forbothcombinations.

ThepartialfactorstobeappliedtotheactionsattheEQUlimitstate

aregiveninTable4;thegeotechnicalmaterialpartialfactorsbeingthe

sameasforcombination2inTable3.

FortheSLS,Eurocode7doesnotgiveanyadviceonwhetherthe

characteristic,frequentorquasi-permanentcombinationshouldbe

used.Wheretheprescriptivemethodisusedforspreadfoundations

(seepage3)thenthecharacteristicvaluesshouldbeadopted.For

6.Foundations

3

directmethodsofcalculationthefrequentcombinationcanbeused

forsizingoffoundationsandthequasi-permanentcombinationcanbe

usedforsettlementcalculations.

Furtherinformationondesigncombinationscanbefoundinanother

guideintheseries,Introduction to Eurocodes5.

Geotechnical design reportAgeotechnicaldesignreportshouldbeproducedforeachproject,

evenifitisonlyasinglesheet.Thereportshouldcontaindetailsof

thesite,interpretationofthegroundinvestigationreport,geotechnical

designrecommendationsandadviceonsupervision,monitoringand

maintenanceoftheworks.Itislikelythatthisreportwillrequireinput

frommorethanoneconsultant,dependingonwhethertheprojectisin

geotechnicalcategory1,2or3.

Thefoundationdesignrecommendationsshouldincludebearing

resistancesandcharacteristicvaluesforsoilparameters.Itshould

alsoclearlystatewhetherthevaluesareapplicabletoSLSorULSand

whethertheyareforcombination1orcombination2.

Spread foundationsThegeotechnicaldesignofspreadfoundations(e.g.stripandpad

foundations)iscoveredbysection6ofEurocode7,Part1andthis

givesthreemethodsfordesign:

Directmethodcalculationiscarriedoutforeachlimitstate. Indirectmethodexperienceandtestingusedtodetermine

serviceabilitylimitstateparametersthatalsosatisfyallrelevant

limitstates(includedinEurocode7mainlytosuitFrenchdesign

methods,andisnotdiscussedfurtherhere).

Prescriptivemethodinwhichapresumedbearingresistanceisused.

FormostspreadfoundationsintheUK,settlementwillbethe

governingcriterion;traditionallyallowablebearingpressureshavebeen

usedtolimitsettlement.Thisconceptofincreasingthefactorofsafety

onbearingresistancestocontrolsettlementmaystillbeusedwiththe

prescriptivemethod.TheexceptionisforsoftclayswhereEurocode7

requiressettlementcalculationstobeundertaken.

Whenusingthedirectmethod,calculationsarecarriedoutforeach

limitstate.AttheULS,thebearingresistanceofthesoilshouldbe

checkedusingpartialfactorsonthesoilpropertiesaswellason

theactions.AttheSLSthesettlementofthefoundationsshouldbe

calculatedandcheckedagainstpermissiblelimits.

Theprescriptivemethodmaybeusedwherecalculationofthesoil

propertiesisnotpossibleornecessaryandcanbeusedprovidedthat

conservativerulesofdesignareused.Thereforereferencecancontinue

tobemadetoTable1ofBS8004(seeTable5)todeterminepresumed

(allowable)bearingpressuresforcategory1structuresandpreliminary

calculationsforcategory2structures.Alternatively,thepresumed

bearingresistancetoallowforsettlementcanbecalculatedbythe

geotechnicaldesignerandincludedinthegeotechnicaldesignreport.

Table 4Design values of actions derived for UK design, EQU ultimate limit state persistent and transient design situations

Combination Expression reference

Permanent actions Leading variable action

Accompanying variable actions

Unfavourable Favourable Main (if any)

Others

Exp.(6.10) 1.0Gka 0.90Gka 1.5bQk 1.5cco,icQk,i

Key

a WherethevariationinpermanentactionisnotconsideredsignificantGk,j,supandGk,j,infmaybetakenasGk

b Wheretheactionisfavourable,gQ,i=0andthevariableactionsshouldbeignored

c ThevalueofcocanbeobtainedfromTableNA.A1.1oftheUKNAtoBSEN1990

Table 5Presumed allowable bearing values under static loading (from BS 8004)

Category Type of soil Presumed allowable bearing value (kN/m2) Remarks

Non-cohesivesoils

Densegravel,ordensesandandgravel >600 Widthoffoundationnotlessthan1m.Groundwaterlevelassumedtobebelowthebaseofthefoundation.Mediumdensegravel,ormedium

densesandandgravel


Partialfactorsforthesoilparametersusedtodeterminetheresistances

canbeobtainedfromTable3above(combination2).

Thepressuredistributionunderthebaseshouldbeassessedtoensure

thatthemaximumpressuredoesnotexceedthebearingresistances

obtainedfromthegeotechnicaldesignreportatbothEQUandGEO

ultimatelimitstates(seeFigure2).Iftheeccentricityisgreaterthan

L/6atSLS,thenthepressuredistributionusedtodeterminethe

settlementshouldbemodifiedbecausetensioncannotoccurbetween

thebaseandthesoil.Inthiscasethedesignershouldsatisfyhimself

thattherewillbenoadverseconsequences(e.g.excessiverotationof

thebase).ItshouldalsobenotedthattheULSpressuredistribution

diagramwillberectangularandnottrapezoidal.

Reinforced concrete padsWherethepadfoundationsrequirereinforcementthefollowingchecks

shouldbecarriedouttoensure:

Sufficientreinforcementtoresistbendingmoments. Punchingshearstrength. Beamshearstrength.

ThemomentsandshearforcesshouldbeassessedusingtheSTR

combination:

1.35Gk+1.5Qk STRcombination1(Exp.(6.10))

However,theremaybeeconomiestomadefromusingExpressions

(6.10a)or(6.10b)fromtheEurocode.

Thecriticalbendingmomentsfordesignofbottomreinforcement

arelocatedatthecolumnfaces.Bothbeamshearandpunching

shearshouldthenbecheckedatthelocationsshowninFigure3.For

punchingshearthegroundreactionwithintheperimetermaybe

deductedfromthecolumnload(Expression(6.48),Eurocode2116).Itisnotusualforapadfoundationtocontainshearreinforcement,

thereforeitisonlynecessarytoensurethattheconcreteshearstress

capacitywithoutshearreinforcement(vRd,cseeTable6)isgreater

thanappliedshearstress(vEd=VEd/(bd)).

Ifthebasicshearstressisexceeded,thedesignermayincreasethe

depthofthebase.Alternatively,theamountofmainreinforcement

couldbeincreasedor,lessdesirably,shearlinkscouldbeprovided.

(SeetheaccompanyingguideHow to design concrete structures

using Eurocode 2: Beamsforanexplanationofhowtodesignshear

reinforcement.)

How to FoundationsFig 2 16.02.06Job No.

MM M

P

PPe

eee = /M P

P

P

L

L

L

L1 +

e6

6e

1

2P

1.5 3L e

L = width of base

SLS pressure distributions ULS pressure distribution

or

Figure 2Pressure Distribution for Pad Foundations

P

2L e

P P P

Figure 2Pressure distributions for pad foundations

Figure 1Procedures for depth of spread foundations

Design foundation (structural design) using the worst of combinations 1 and 2 (ULS) for actions and geotechnical

material properties.

START

Design using direct method?

Obtain soil parameters from Ground Investigation report

Size foundation (geotechnical design) using the worst of combinations

1 or 2 (ULS) for actions and geotechnical material properties. Combination 2

will usually govern.

Use prescriptive method.Size foundation

(geotechnical design) using SLS for actions

and presumed bearing resistance

Is there an overturning moment?

Check overturning using EQU limit state for actions and

GEO combination 2 for material properties.

Yes No

Yes

No

Aflowchartshowingthedesignprocessforshallowfoundationsis

giveninFigure1.

Wherethereisamomentappliedtothefoundation,theEQUlimit

stateshouldalsobechecked.Assumingthepotentialoverturningof

thebaseisduetothevariableactionfromthewind,thefollowing

combinationshouldbeused(thevariableimposedactionisnot

consideredtocontributetothestabilityofthestructure):

0.9Gk+1.5Qk,w EQUcombination

where:

Gkisthestabilisingcharacteristicpermanentaction

(Use1.1Gkforadestabilisingpermanentaction)

Qk,wisthedestabilisingcharacteristicvariablewindaction

6.Foundations

5

Design for punching shearEurocode2providesspecificguidanceonthedesignoffoundationsfor

punchingshear,andthisvariesfromthatgivenforslabs.InEurocode2the

shearperimeterhasroundedcornersandtheforcesdirectlyresistedby

thegroundshouldbededucted(toavoidunnecessarilyconservative

designs).Thecriticalperimetershouldbefounditeratively,butitis

generallyacceptabletocheckatdand2d.Alternatively,aspreadsheet

couldbeused(e.g.spreadsheetTCC81fromSpreadsheets for concrete

design to BS 8110 and Eurocode 27).TheprocedurefordeterminingthepunchingshearrequirementsisshowninFigure4.

Table 6vRd,c resistance of members without shear reinforcement, MPa

r l Effective depth, d (mm)

300 400 500 600 700 800 900 1000a

0.25% 0.47 0.43 0.40 0.38 0.36 0.35 0.35 0.34

0.50% 0.54 0.51 0.48 0.47 0.45 0.44 0.44 0.43

0.75% 0.62 0.58 0.55 0.53 0.52 0.51 0.50 0.49

1.00% 0.68 0.64 0.61 0.59 0.57 0.56 0.55 0.54

1.25% 0.73 0.69 0.66 0.63 0.62 0.60 0.59 0.58

1.50% 0.78 0.73 0.70 0.67 0.65 0.64 0.63 0.62

1.75% 0.82 0.77 0.73 0.71 0.69 0.67 0.66 0.65

2.00% 0.85 0.80 0.77 0.74 0.72 0.70 0.69 0.68

2.50% 0.85 0.80 0.77 0.74 0.72 0.70 0.69 0.68

k 1.816 1.707 1.632 1.577 1.535 1.500 1.471 1.447

Key

aFordepthsgreaterthan1000calculatevRd,cdirectly.

Notes

1Tablederivedfrom:vRd,c=0.12k(100r Ifck)(1/3)0.035k1.5fck0.5wherek=1+(200/d)2andr I=(rIy+r Iz)0.02,r Iy=Asy/(bd)andr Iz=Asz/(bd)

2Thistablehasbeenpreparedforfck=30;wherer lexceed0.40%thefollowingfactorsmaybeused:

fck 25 28 32 35 40 45 50

Factor 0.94 0.98 1.02 1.05 1.10 1.14 1.19

Beam shearfaces

2d

Figure 3Shear checks for pad foundations

d

d

h

Bends may berequired

Punching shear perimeters,(load within deducted from V )Ed


Figure 3Shear checks for pad foundations

START

Determine value of factor ( =1.0 when applied moment is zero; refer to Expressions

(6.38) to (6.42) from BS EN 199211 for other cases)

Determine value of vEd,max (design shear stress at face of column) from:

vEd,max = (VEd DVEd) (from Exp. (6.38)) (u0deff)

where u0 is perimeter of column (see Clause 6.4.5 for columns at base edges)

deff = (dy + dz)/2 where dy and dz are the effective depths in orthogonal directions

Determine value of vRd,max (refer to Table 7)

Determine concrete punching shear capacity vRd (without shear reinforcement) from 2dvRd,c/a (Refer to Table 6 for vRd,c)

Yes

Either increase main steel, or provide punching shear

reinforcement required. (Not recommended

for foundations.)

No

No shear reinforcement required. Check complete.

Figure 4Procedure for determining punching shear capacity for pad foundations


bz

2d2d

by

u1

u1

Figure 5Typical basic control perimeters around loaded areas.

Figure 5Typical basic control perimeters around loaded areas

Yes

Redesign foundationIs vEd,max < vRd,max?No

Determine value of vEd, (design shear stress) from:vEd = (VEd DVEd)

(u1deff)where u1 is length of control perimeter (refer to Figure 5). For

eccentrically loaded bases, refer to Exp. (6.51).The control perimeter will have to be found through iteration;

it will usually be between d and 2d

Is vEd < vRd at critical perimeter?


flexurereferenceshouldbemadetoanotherguideinthisseries,How

to design concrete structures using Eurocode 2: Beams8.

Alternatively,atrussanalogymaybeused;thisiscoveredinSections5.6.4

and6.5ofEurocode211.Thestrutangleyshouldbeatleast21.8to

thehorizontal;notethatyshouldbemeasuredintheplaneofthecolumn

andpile.

Bothbeamshearandpunchingshearshouldthenbecheckedasshownin

Figure6.Forbeamshear,thedesignresistancesinTable6maybeused.Ifthe

basicshearstressisexceeded,thedesignershouldincreasethedepthofthe

base.Alternatively,theamountofmainreinforcementcouldbeincreasedor,

lessdesirably,shearlinkscouldbeprovided.Careshouldbetakenthatmain

barsarefullyanchored.Asaminimum,afullanchorageshouldbeprovided

fromtheinnerfaceofpiles.Largeradiusbendsmayberequired.

Whenassessingtheshearcapacityinapilecap,onlythetensionsteel

placedwithinthestresszoneshouldbeconsideredascontributingtothe

shearcapacity(seeFigure7).

Raft foundationsThebasicdesignprocessesforraftsaresimilartothoseforisolated

padfoundationsorpilecaps.Theonlydifferenceinapproachliesinthe

selectionofanappropriatemethodforanalysingtheinteractionbetween

theraftandthegroundsoastoachieveareasonablerepresentationof

theirbehaviour.Forstifferrafts(i.e.span-to-thicknessgreaterthan10)with

afairlyregularlayout,simplifiedapproachessuchasyieldlineortheflat

slabequivalentframemethodmaybeemployed,onceanestimationof

thevariationsinbearingpressurehasbeenobtainedfromageotechnical

specialist.Whateversimplificationsaremade,individualelasticraft

reactionsshouldequatetotheappliedcolumnloads.

Thinner,moreflexibleraftsorthosewithacomplexlayoutmayrequire

theapplicationofafiniteelementorgrillageanalysis.Forraftsbearing

ongranularsub-gradesorwhencontiguous-piledwallsordiaphragm

perimeterwallsarepresent,thegroundmaybemodelledasaseries

ofWinklersprings.However,forcohesivesub-grades,thisapproachis

unlikelytobevalid,andspecialistsoftwarewillberequired.

Piled foundationsForthepurposeofthisguideitisassumedthatthepiledesignwillbe

carriedoutbyaspecialistpilingcontractor.Theactionsonthepilesmust

beclearlyconveyedtothepiledesigner,andtheseshouldbebrokendown

intotheunfactoredpermanentactionsandeachoftheapplicablevariable

actions(e.g.imposedandwindactions).Thepiledesignercanthencarry

outthestructuralandgeotechnicaldesignofthepiles.

WheremomentsareappliedtothepilecaptheEQUcombination

shouldalsobeusedtocheckthepilescanresisttheoverturningforces.

TheseEQUloadsmustalsobeclearlyconveyedtothepiledesigner

andproceduresputinplacetoensurethepilesaredesignedforthe

correctforces.

Apilecapmaybetreatedasabeaminbending,wherethecritical

bendingmomentsforthedesignofthebottomreinforcementare

locatedatthecolumnfaces.Forfurtherguidanceondesigningfor

Table 7Values for vRd, max

fck vRd,max

20 3.68

25 4.50

28 4.97

30 5.28

32 5.58

35 6.02

40 6.72

45 7.38

50 8.00


a a

bF

hF

Figure 8Dimensions for plain foundations

Figure 8Dimensions for plain foundations

Stress zone

45o

As contributing to shear capacity

Figure 7Shear reinforcement for pilecaps.


Figure 7Shear reinforcement for pilecaps

Punching shear 5 2d from column face

f /5

f /5

f

Beam shear 5 d from column face

Figure 6Critical shear perimeters for piles


Figure 6Critical shear perimeters for piles

6.Foundations

7

Table 8Minimum percentage of reinforcement required

fck fctm Minimum % (0.26 fctm /fyka )

25 2.6 0.13%

28 2.8 0.14%

30 2.9 0.15%

32 3.0 0.16%

35 3.2 0.17%

40 3.5 0.18%

45 3.8 0.20%

50 4.1 0.21%

Key

a Wherefyk=500MPa.

Plain concrete foundationsStripandpadfootingsmaybeconstructedfromplainconcrete

providedthefollowingrulesareadheredto.

Incompression,thevalueofacc,thecoefficienttakingaccountoflong-termeffectsappliedtodesigncompressivestrength

(seeCl.3.1.6),shouldbetakenas0.6asopposedto0.85for

reinforcedconcrete.

Theminimumfoundationdepth,hF,(seeFigure8)maybecalculatedfrom:

where:

sgd=thedesignvalueofthegroundbearingpressure

fctd =thedesignconcretetensilestrengthfromExp.(3.16)

Formanysituationsthisisunlikelytoofferanysavingsoverthecurrent

practiceofdesigningforhfa.

Thepossibilityofsplittingforces,asadvisedinClause9.8.4ofEurocode

211,mayneedtobeconsidered.

Eurocode2allowsplainconcretefoundationstocontainreinforcement

forcontrolofcracking.

Rules for spacing and quantity of reinforcementCrack controlRefertoHow to design concrete structures using Eurocode 2: Getting

started 9.

Minimum area of principal reinforcementTheminimumareaofreinforcementisAs,min=0.26fctmbtd/fykbutnot

lessthan0.0013btd(seeTable8).

Maximum area of reinforcementExceptatlaplocations,themaximumareaoftensionorcompression

reinforcement,shouldnotexceedAs,max=0.04Ac

Minimum spacing of reinforcementTheminimumspacingofbarsshouldbethegreaterof:

Bardiameter, Aggregatesizeplus5mm,or 20mm.

Deep elementsFordeepelementstheadviceinEurocode2forthesidefacesofdeep

beamsmaybefollowed.TheUKNationalAnnexrecommendsthat0.2%

isprovidedineachface.Thedistancebetweenbarsshouldnotexceed

thelesseroftwicethebeamdepthor300mm.Forpilecapstheside

facemaybeunreinforcedifthereisnoriskoftensiondeveloping.

Symbol Definition Value

Ac Crosssectionalareaofconcrete bh

As Areaoftensionsteel

As,prov Areaoftensionsteelprovided

As,reqd Areaoftensionsteelrequired

d Effectivedepth

deff Averageeffectivedepth (dy+dz)/2

fcd Designvalueofconcretecompressivestrength accfck/gc

fck Characteristiccylinderstrengthofconcrete

fctm Meanvalueofaxialtensilestrength 0.30fck2/3forfckC50/60 (fromTable3.1,Eurocode2)

Gk Characteristicvalueofpermanentaction

h Overalldepthofthesection

leff Effectivespanofmember SeeSection5.3.2.2(1)

M DesignmomentattheULS

Qk Characteristicvalueofavariableaction

Qk,w Characteristicvalueofavariablewindaction

VEd Designvalueofappliedshearforce

vEd Designvalueofappliedshearstress

VRd,c Designvalueofthepunchingshearresistancewithoutpunchingshearreinforcement

vRd,c Designvalueofthepunchingshearstressresistancewithoutpunchingshearreinforcement

vRd,max Designvalueofthemaximumpunchingshearresistancealongthecontrolsectionconsidered

x Depthtoneutralaxis (dz)/0.4

xmax Limitingvaluefordepthtoneutralaxis (d0.4)dwhered1.0

z Leverarm

acc Coefficienttakingaccountoflongterm 0.85forflexureandeffectsoncompressivestrengthandof axialloads,1.0forunfavourableeffectsresultingfromtheway otherphenomenaloadisapplied(FromUKNationalAnnex)

b Factorfordeterminingpunchingshearstress

d Ratiooftheredistributedmomenttotheelasticbendingmoment

gm Partialfactorformaterialproperties

r0 Referencereinforcementratio fck/1000

r l Requiredtensionreinforcementatmid-span Asl bdtoresistthemomentduetothedesignloads(oratsupportforcantilevers)

c0 Factorforcombinationvalueofavariableaction

c1 Factorforfrequentvalueofavariableaction

c2 Factorforquasi-permanentvalueofavariableaction

Selected symbols

6.Foundations

Alladviceorinformation from The Concrete Centre is intended for those who will evaluate the significance and limitations of its contents and take responsibility for its use and application. No liability (including that for negligence) for any loss resulting from such advice or information is accepted by The Concrete Centre or its subcontractors, suppliers or advisors. Readers should note that publications from The Concrete Centre are subject to revision from time to time and they should therefore ensure that they are in possession of the latest version. This publication has been produced following a contract placed by the Department for Trade and Industry (DTI); the views expressed are not necessarily those of the DTI.

Ref:TCC/03/21ISBN1-904818-31-5PublishedApril2006TheConcreteCentre

Published by The Concrete Centre

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Tel:+44(0)1276606800Fax:+44(0)1276606801

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3 BRITISHSTANDARDSINSTITUTION.BS8002:Code of practice for earth retaining structures.BSI,1994.

4 BRITISHSTANDARDSINSTITUTION.BS8004:Code of practice for foundations.BSI,1986.

5 NARAYANAN,RS&BROOKER,O.How to design concrete structures using Eurocode 2: Introduction to Eurocodes.TheConcreteCentre,2005.

6 BRITISHSTANDARDSINSTITUTION.BSEN199211,Eurocode 2: Design of concrete structures. General rules and rules for buildings.BSI,2004.

7 GOODCHILD,CH&WEBSTERRM.Spreadsheets for concrete design to BS 8110 and Eurocode 2, version3.TheConcreteCentre,2006.

8 MOSS,RM&BROOKER,O.How to design concrete structures using Eurocode 2: Beams.TheConcreteCentre,2006.

9 BROOKER,O.How to design concrete structures using Eurocode 2: Getting started.TheConcreteCentre,2005.

Further guidance and advice Guidesinthisseriescover:Introduction to Eurocodes, Getting started, Slabs, Beams, Columns, Foundations, Flat slabsandDeflection calculations.

Forfreedownloads,detailsofotherpublicationsandmoreinformationonEurocode2visitwww.eurocode2.info

ThisguideistakenfromTheConcreteCentrespublication,How to design concrete structures using Eurocode 2(Ref.CCIP-006)

AcknowledgementsThecontentofthispublicationwasproducedaspartoftheprojectEurocode2:transitionfromUKtoEuropeanconcretedesignstandards.This

projectwaspartfundedbytheDTIunderthePartnersinInnovationscheme.TheleadpartnerwastheBritishCementAssociation.Theworkwas

carriedoutundertheguidanceoftheConcreteIndustryEurocode2Group,whichconsistsofrepresentativesfrom:

AlanBaxterandAssociatesArupBritishCementAssociationBritishPrecastBuildingResearchEstablishmentClarkSmithPartnership

ConcreteInnovationandDesignConstructDepartmentforTradeandIndustryOfficeoftheDeputyPrimeMinisterTheConcreteCentre

TheConcreteSocietyQuarryProductsAssociation.

ThanksareduetoDrAndrewBondofGeocentrixLtdforhisassistancewiththeinterpretationofEurocode7.

The Concrete Centre provides Eurocode 2 seminars and short courses across the UK

Free CPD seminar 9 May, London, 6.00 pm startAn Introduction to Eurocode 2: Design of Concrete StructuresThisseminarintroducesEurocode2andaimstohelpdesignersbecomefamiliarwithanewsetofdocuments,theirterminologyandtheinteractionbetweenthem.

Short course in partnership with IStructE 14 June, Manchester, 9.00 am startDesign to Eurocode 2 including the UK AnnexTheone-daycoursewillincludeanintroductiontothenewcode,followedbyworkedexamplesondesignanddetailingofthemainstructuralelementsusingtheUKsnationallydeterminedparameters.198+VATIStructEmembers;220+VATnon-members

For more information on these events, or alternative dates, venues and topics visit www.concretecentre.com/events

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