Project Calculated by AA Client Checked and Approved by MN Floor title LONG TERM DEFLECTION CALCULATION ACI Width 40 cm 318-08 Service moments Instantanuous deflections Ma- -130 t.m 8.9 mm Ma+ 93 t.m 2.7 mm 9.5.2.5 x 2 years or mor Time dependent factor for sustained load 9.5.2.5 0.97 Sustained live load 20 % Percentage of sustained live load for p 80 % Percentage of intermittent load Midspan cm cm Support cm cm Bottom Reinforcement Ø32 @ 12.5 + Ø32 @ 13 128.6 Ø32 @ 13 + Ø32 @ 13 128.6 Top Reinforcement Ø32 @ 25 + Ø32 @ 25 64.3 Ø32 @ 25 + Ø32 @ 25 64.3 c 4 Concrete cover h 80 Section depth d 76 Effective depth of section f'c 32 Mpa Concrete compressive strength 8.5.1 Ec 265.872 Elastic modulus of concrete 8.5.2 Es 2000 Elastic modulus of steel n 8 Modular ratio 9.5.2.3 fr 35.0725 Modulus of rupture ρ 0.04231 ρ' 0.02115 Ig 1706667 Moment of inertia about centroidal axis neglecting reinforceme At midspan At support k 0.54069 0.42703 Compression members eff. length factor j 0.81977 0.85766 Internal lever arm 1-k/3 Icr 2104100 1373072 Moment of inertia of cracked section 9.5.2.3 Mcr 14.9643 14.9643 t.m Cracking moment 9.5.2.3 Ie 2102444 1373580 Effective moment of inertia 1738012 Additional deflection 8.49449 mm 0.5154 2.12 mm Total deflection 22.7 mm CRACK WIDTH CALCULATION fs 1.16 Tensile stress in reinforcement at service dc 4 cm Concrete cover to center of outer bar 2.4 Least distance from reinf. Surface to teni β 1.124 1+0.031.dc (cm) s 6.25 Bar spacing closest to tension face Frosch w 0.03 mm Maximum width of crack ΔDL ΔLL λ∆ cm 2 cm 2 Asbot = Asbot = Astop = Astop = cm 2 cm 2 cm 2 ton/cm 2 4700√f'c ton/cm 2 Es/Ec kg/cm 2 0.62√f'c cm 4 √[(ρn) 2 +2.ρ.n]-ρ.n cm 4 n.As.(1-k).j.d 2 (fr.Ig)/yt cm 4 Icr+(Mcr/Ma) 3 .(Ig-Icr) Ie,average cm 4 ΔDL,long term λ∆ .(Ig/Ie).ΔDL ΔLL,long term Sustained + ΔLL,Long term intermitten ton/cm 2 M/(As.j.d) cc dc-db/2 380.(280/fs)-2.5.cc 2(fs/Es).β.√(dc 2 +(s/2) -130 93 -130 0 0 MOMENT (ton.m) M Z & P A R TN ER S A RC HITEC TURA L & EN G IN EERIN G C O N SULTA N C Y Tel:43 63 813-Fa x: 43 63 812-PO Box:5785D oha -Q ata r STRU C TU RA L D EPA RTM EN T -22.7 -2.7 -8.9 DL LL Long term Deflection (mm)

Long Term Deflection Design

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Sheet1ProjectCalculated byAAClientChecked and Approved byMNFloor titleLONG TERM DEFLECTION CALCULATIONACIWidth40cm318-08Service momentsInstantanuous deflectionsMa--130t.mDL8.9mmMa+93t.mLL2.7mm

9.5.2.5x25 years or moreTime dependent factor for sustained load9.5.2.50.97Sustained live load20%Percentage of sustained live load for p80%Percentage of intermittent loadMidspancmcmcm2Supportcmcmcm2Bottom [email protected][email protected] = [email protected][email protected] = 128.6Top Reinforcement32@25+32@25Astop =64.332@25+32@25Astop =64.3c4cm2Concrete coverh80cm2Section depthd76cm2Effective depth of sectionf'c32MpaConcrete compressive strength8.5.1Ec 265.8721497261ton/cm2Elastic modulus of concrete4700f'c8.5.2Es2000ton/cm2Elastic modulus of steeln8Modular ratioEs/Ec9.5.2.3fr35.0724963469kg/cm2Modulus of rupture 0.62f'c0.0423073684'0.0211536842Ig1706666.66666667cm4Moment of inertia about centroidal axis neglecting reinforcementAt midspanAt supportk0.54069485220.4270257993Compression members eff. length factor[(n)2+2..n]-.nj0.81976838260.8576580669Internal lever arm1-k/3Icr2104100.14472781373071.57886275cm4Moment of inertia of cracked sectionn.As.(1-k).j.d29.5.2.3Mcr 14.96426510814.964265108t.mCracking moment(fr.Ig)/yt9.5.2.3Ie2102444.444218091373580.38901814cm4Effective moment of inertiaIcr+(Mcr/Ma)3.(Ig-Icr)Ie,average1738012.41661812cm4Additional deflectionDL,long term8.4944860743mm .(Ig/Ie).DLLL,long term Sustained0.5153957843 + LL,Long term intermittent2.121043535mmTotal deflection22.7mm

CRACK WIDTH CALCULATION

fs1.16ton/cm2Tensile stress in reinforcement at service loadsM/(As.j.d)dc4cmConcrete cover to center of outer barcc2.4Least distance from reinf. Surface to tenion facedc-db/21.1241+0.031.dc (cm)s6.25Bar spacing closest to tension face380.(280/fs)-2.5.ccFroschw0.03mmMaximum width of crack2(fs/Es)..(dc2+(s/2)2)

xyxyxy0000000.5-8.90.5-2.70.5-22.7309253936101010

xyxyxyxy0-1300000100.593100-1301-1301-130

bar dia.As (mm)000100.79100.015 years or more2121.131212 months1.4141.54146 months1.2162.01163 months1203.1420254.9125328.04324012.56101216202532

50x^2 + (As-).(x-cover) - (As+).(h-cover-x) = 0x= 0Icr = 0Ig =4266666.66666667cm4Moment of inertia of gross concrete section about centroidal axis ignoring reinforcement

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