crack width (eurocode)

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Project Spreadsheets to EC2 The Concrete Centre Client Advisory Group Made by Date Page Location Grid line 1 rmw ### 202 FLEXURAL CRACK WIDTH CALCULATION to BS EN 1992-1 : 2004 Checked Revisio Job No v3.0 on CD © 2002-2005 BCA for RCC RECTANGULAR chg - FB625 LEGEND INPUT 30 565 500 129 mm 1000 mm 314 160 mm 31 mm 24.9 KNm 200 mm Age at cracking = 14 days 12 mm Cement type = N (S, N, R or RS) Short term or long term ? L (S or L) 2.0 25 mm CALCULATIONS 32.8 Gpa moduli of elasticity of steel 200.0 Gpa Modular ratio 18.27 0.0024 0.0044 mean concrete strength at cracking 34.26 Mpa mean concrete tensile strength 2.61 Mpa uncracked neutral axis depth 81.21 mm 378 12.51 kNm < 24.9 kNm section is CRACKED 41.19 mm 9.939 Mpa 387.2 Mpa effective tension area = min[2.5(h-d), (h-x)/3, h/2]b 39605 0.0143 154.5 mm average strain for crack width calculation 1474.6 μstrain CALCULATED CRACK WIDTH 0.228 mm Originated from TCC14.xls fck = N/mm 2 Area of tension steel, As = mm 2 fyk = N/mm 2 d = b = Area of compression steel, As2 = mm 2 h = d2 = QP moment, M = Maxmum tension bar spacing, S = Max tension bar dia, Øeq = Creep factor, φ = Cover to As, c = modulus of elasticity of concrete = 22[(fck+8)/10] 0.3 Ecm = Es = αe = ρ' = ρ = fcm,t = fct,eff = [bh²/2+(αe-1)(Asd+As2d2)]/[bh+(αe-1)(As+As2)] xu = uncracked 2 nd moment of area bh³/12+bh(h/2-x)²+(αe-1)[As(d-x)²+As2(x-d2)²] Iu = mm 4 10 6 cracking moment = fctI/(h-x) Mcr = fully cracked x = d[-αe(ρ-ρ') + {αe²(ρ-ρ')²+2αe(ρ+ρ'd2/d)} ½ ] xc = concrete stress = M/[bx(d-x/3)/2+(αe-1)As2(x-d2)/x(d-d2)] σc = stress in tension steel = σc∙αe(d-x)/x σs = Ac,eff = mm 2 As /Ac,eff ρp,eff = max final crack spacing = min[1.3/(h-x),3.4c+0.17Ø/ρ p,eff)] sr,max = εsm-εcm = Wk =

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Calculation crack according to Eurocode 2

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Rectangular3.0ProjectSpreadsheets to EC2The Concrete CentreClientAdvisory GroupMade byDatePageLocationGrid line 1rmw22-May-14202FLEXURAL CRACK WIDTH CALCULATION to BS EN 1992-1 : 2004CheckedRevisionJob NoOriginated from TCC14.xlsv3.0 on CD 2002-2005 BCA for RCCRECTANGULARchg-FB625LEGENDINPUTfck =30N/mm2Area of tension steel, As =565mm2fyk =500N/mm2d =129mmb =1000mmArea of compression steel, As2 =314mm2h =160mmd2 =31mmQP moment, M =24.9KNmMaxmum tension bar spacing, S =200mmAge at cracking =14daysMax tension bar dia, eq =12mmCement type =N(S, N, R or RS)Short term or long term ?L(S or L)Creep factor, =2.0Cover to As, c =25mmCALCULATIONSmodulus of elasticity of concrete = 22[(fck+8)/10]0.3Ecm =32.8GpaTable 3.1moduli of elasticity of steelEs =200.0GpaModular ratioe =18.27' =0.0024 =0.0044mean concrete strength at crackingfcm,t =34.26MpaTable 3.1 & equation (3.4)mean concrete tensile strengthfct,eff =2.61MpaTable 3.1uncracked neutral axis depth[bh/2+(e-1)(Asd+As2d2)]/[bh+(e-1)(As+As2)]xu =81.21mmuncracked 2nd moment of areabh/12+bh(h/2-x)+(e-1)[As(d-x)+As2(x-d2)]Iu =378mm4 106cracking moment = fctI/(h-x)Mcr =12.51kNm< 24.9 kNm section isCRACKEDfully cracked x = d[-e(-') + {e(-')+2e(+'d2/d)}]xc =41.19mmconcrete stress = M/[bx(d-x/3)/2+(e-1)As2(x-d2)/x(d-d2)]c =9.939Mpastress in tension steel = ce(d-x)/xs =387.2Mpaeffective tension area = min[2.5(h-d), (h-x)/3, h/2]bAc,eff =39605mm27.3.2 (3)As /Ac,effp,eff =0.01437.3.4 (2)max final crack spacing = min[1.3/(h-x),3.4c+0.17/p,eff)]sr,max =154.5mmEquations (7.11) & (7.14)average strain for crack width calculationsm-cm =1474.6strainEquation (7.9)CALCULATED CRACK WIDTHWk =0.228mm0Equation (7.8)1

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ENTER DATA IN BLUE CELLS ONLY.RED MESSAGES INDICATE ENTRY ERRORS.

SpanTeeProjectSpreadsheets to EC2The Concrete CentreClientAdvisory GroupMade byDatePageLocationGrid line 2rmw22-May-1433FLEXURAL CRACK WIDTH CALCULATION to BS EN 1992-1 : 2004TEE INCheckedRevisionJob NoOriginated from TCC14.xls v3.0 on CD 2002-2005 BCA for RCCCOMPRESSIONchg-FB625LEGENDINPUTfck =35N/mm2Area of tension steel, As =1473mm2fyk =500N/mm2d =399.5mmbw =300mmArea of compression steel, As2 =236mm2h =450mmd2 =33mmbf =2170mmMaxmum tension bar spacing, S =87mmhf =125mmMax tension bar dia, eq =25mmQP moment, M =114.2KNmShort term or long term ?L(S or L)Age at cracking =14daysCover to As, c =38mmCement type =N(S, N, R or RS)Creep factor, =2.0CALCULATIONSmodulus of elasticity of concrete = 22[(fck+8)/10]0.3Ecm =34.1GpaTable 3.1moduli of elasticity of steelEs =200.0GpaModular ratioe =17.61mean concrete strength at crackingfcm,t =38.77MpaTable 3.1 & equation (3.4)mean concrete tensile strengthfct,eff =2.89MpaTable 3.1uncracked neutral axis depth[bwh/2+(bf-bw)hf/2+(e-1)(Asd+As2d2)]/[bwh+(bf-bw)hf+(e-1)(As+As2)]xu =138.21mmuncracked 2nd moment of areabwh/12+bwh(h/2-x)+(bf-bw)hf/12+(bf-bw)hf(x-hf/2)+(e-1)[As(d-x)+As2(x-d2)]Iu =6653mm4 106cracking moment = fctI/(h-x)Mcr =61.75kNmabc< 114.2 kNm section isCRACKEDBelow-150263604.54789994125099851.670077190.5519413387bx^2/2 - bx^2 - x[(bf-bw)hf + (ae-1)As' + ae.As] + (bf-bw)hf^2/2 + (ae-1)As'd' + ae.As.d = 0fully cracked x (within flange)xc =85.53mmx is within flange0Within-108529854.54789994110490476.670077185.5292059165bf.x^2/2 - bf.x^2 - x[(ae-1)As' + ae.As] + (ae-1)As'd' + ae.As.d = 0concrete stress (x within flange)c =3.234Mpafzmstress in tension steel = ce(d-x)/xs =209.0MpaBelow33.656932842200.57773683125.95947758443.7552682803effective tension area = min[2.5(h-d), (h-x)/3, h/2]bwAc,eff =36447mm27.3.2 (3)Within3.2342301281M/[bfx(d-x/3)/2+(e-1)As2(x-d2)/x(d-d2)]As /Ac,effp,eff =0.04047.3.4 (2)max final crack spacing = min[1.3/(h-x),3.4c+0.17/p,eff)]sr,max =234.4mmEquations (7.11) & (7.14)average strain for crack width calculationsm-cm =800.1strainEquation (7.9)CALCULATED CRACK WIDTHWk =0.188mm0Equation (7.8)1

PRINTOPERATING INSTRUCTIONS

ENTER DATA IN BLUE CELLS ONLY.RED MESSAGES INDICATE ENTRY ERRORS.

SupportTeeProjectSpreadsheets to EC2The Concrete CentreClientAdvisory GroupMade byDatePageLocationGrid line 2rmw22-May-1433FLEXURAL CRACK WIDTH CALCULATION to BS EN 1992-1 : 2004TEE INCheckedRevisionJob NoOriginated from TCC14.xls v3.0 on CD 2002-2005 BCA for RCCTENSIONchg-FB625LEGENDINPUTfck =35N/mm2Area of tension steel, As =1000mm2fyk =500N/mm2d =417mmbw =300mmArea of compression steel, As2 =236mm2h =450mmd2 =34mmbf =1222mmMaxmum tension bar spacing, S =87.4mmhf =125mmMax tension bar dia, eq =10mmQP moment, M =147KNmShort term or long term ?L(S or L)Age at cracking =14daysCover to As, c =28mmCement type =N(S, N, R or RS)Creep factor, =2.0CALCULATIONSmodulus of elasticity of concrete = 22[(fck+8)/10]0.3Ecm =34.1GpaTable 3.1moduli of elasticity of steelEs =200.0GpaModular ratioe =17.61' =0.0019 =0.0080mean concrete strength at crackingfcm,t =38.77MpaTable 3.1 & equation (3.4)mean concrete tensile strengthfct,eff =2.89MpaTable 3.1uncracked neutral axis depth[bwh/2+(bf-bw)hf(h-hf/2)+(e-1)(Asd+As2d2)]/[bwh+(bf-bw)hf+(e-1)(As+As2)]xu =303.18mmuncracked 2nd moment of areabwh/12+bwh(h/2-x)+(bf-bw)hf/12+(bf-bw)hf(h-x-hf/2)+(e-1)[As(d-x)+As2(x-d2)]Iu =4572mm4 106cracking moment = fctI/(h-x)Mcr =90.12kNm< 147 kNm section isCRACKEDfully cracked x = d[-e(-') + {e(-')+2e(+'d2/d)}]xc =162.30mmconcrete stress = M/[bx(d-x/3)/2+(e-1)As2(x-d2)/x(d-d2)]c =14.668Mpastress in tension steel = ce(d-x)/xs =405.3Mpas > 0.8fykheight of tension zone = min[2.5(h-d), (h-x)/3, h/2]hc,eff =82.50mmeffective tension areaAc,eff =100815mm27.3.2 (3)As /Ac,effp,eff =0.00997.3.4 (2)max final crack spacing = min[1.3/(h-x),3.4c+0.17/p,eff)]sr,max =266.6mmEquations (7.11) & (7.14)average strain for crack width calculationsm-cm =1341.0strainEquation (7.9)CALCULATED CRACK WIDTHWk =0.357mm0Equation (7.8)1

PRINTOPERATING INSTRUCTIONS

ENTER DATA IN BLUE CELLS ONLY.RED MESSAGES INDICATE ENTRY ERRORS.

RefsNational Annex valuesEC2 RefFunctionValue7.2 (2)k10.6stress limit - concrete7.2 (3)k20.45linear creep limit7.2 (5)k30.8stress limit - steel7.3.4 (3)k33.4Equation (7.11) factor7.3.4 (3)k40.425Equation (7.11) factor

NotesDisclaimerAll advice or information from the British Cement Association and/or 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 BCA, TCC or their subcontractors, suppliers or advisors. Users should note that all TCC software and publications are subject to revision from time to time and should therefore ensure that they are in possession of the latest version.

This spreadsheet should be used in compliance with the accompanying publication 'User Guide RC Spreadsheets: v3' available from The Concrete Bookshop, www.concretebookshop.com, Tel +44 (0)700 4 607777 or +44 (0)1276 607140Status of spreadsheetThis spreadsheet is shareware. It may be distributed freely, but may not be used for commercial purposes until the user has registered with the TCC via The Concrete Bookshop.First public releaseRevision history TCC14 Crack WidthDateVersionActionSize (kB)28-Jun-06TCC11 v3.0v3 release. Page nos, User Guide and registration details amended.9183-Feb-05TCC14 v1.0Tee sections added. RE-BADGED92430-Apr-03RCCen14 4Correction to use of equation (7.14).25826-Mar-03RCCen14 3Updatd to November 2002 draft.25821-Dec-01RCCen14 2Updated to final draft.26631-Aug-01RCCen14 1First issue for in-house comment266

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