ACI Shrinkage

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aci shrinkage calculation

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250mmShrinkage strain calculation and creep effects based on "Prediction of creep, shrinkage, and temperature effects in concrete structures" - ACI 209R-92Effects of creep, shrinkage, and temperature in concrete slabsMaterial Propertiesf'c30MPaf't (direct tensile strength)1.85MPaACI 209R-92 - Eqn. 2-4Ec25743MPafy500MPaEs200000MPan7.77alpha0.00001CSpreadsheet version 1.00Temperature range20.0CBased on AE spreadheetT10.0CThickness250mmTypeElevated SlabTable 2.5.4 Correction factors for Relative HumidityTable 2.5.3 Shrinkage correction factors for initial moist curingSteps for Considering Shrinkage and Thermal EffectsRelative humidity (%)Creep Shrinkage Moist curing duration (days)Shrinkage CP1. Determine Relevant Material Properties Type of Cement Type of Aggregate Strength of Concrete Coefficient of Thermal Expansion

2. Determine Environment Properties Ambient Temperature Range Relative Humidity

3. Determine Shrinkage with ACI 209R-92

4. Determine Creep Coefficient with ACI 209R-92

5. Determine methods to reduce or eliminate restraint during early shrinkage Consider length of time Pour strips Pour outward from sources of restraint such as cores.Note: Reducing shrinkage does not reduce reinforcing required unless shrinkage is less than tensile strength of concrete.

6. Determine Steel required to control crack width. Determine maximum acceptable crack width Determine acceptable steel to control crack width, primary variables are cover, spacing, and size of bar.Note: Adding steel does not eliminate cracking. Steel controls crack width. Instead of one large crack, many small cracks form.

Resources ACI 209R-92 "Control of Flexural Cracking in Reinforced concrete" R. Ian Gilbert ACI Structural Journal May-June 2008 "Shrinkage Cracking in Fully Restrained Concrete Members" R. Ian Gilbert ACI Structural Journal March-April 1992These two methods consider either direct tension cracking, or flexural cracking with shrinkage.Flexural cracking with shrinkage is effectively a modified method to add direct tension cracking to flexural cracking. There is some debate whether these truly need to be additive.Shrinkage Effects (ACI 209R-92)0%1111.2Ultimate strain0.00078(2-6)40%1131.1Initial moist curing duration7days50%0.940.971Curing correction factor1Table 2.5.360%0.870.8140.93Relative humidity60%70%0.80.7280.86Humidity correction factor0.8Table 2.5.480%0.730.6900.7590%0.670.3100%0.60Creep Effects (ACI 209R-92)Creep Factor2.35(2-6)Humidity correction factor0.87Table 2.5.4DaysShrinkage Strain (sh)tEquivalent temperature change CTotal temp CCreep factor vtVolume250mm3(2-9)(2-8)Surface2mm200.0000000.00-10.000.000v/s12570.000069-6.92-16.920.354140.000119-11.86-21.860.477Creep0.71(2-21a)280.000184-18.45-28.450.618Shrinkage0.67(2-22a)560.000255-25.54-35.540.7691000.000307-30.75-40.750.893Factored creep1.465000.000388-38.79-48.791.174Factored shrinkage0.5310000.000401-40.10-50.101.25750000.000412-41.22-51.221.373Corrected ultimate strain0.000415100000.000414-41.36-51.361.400Length50mACI 224R-01 -Table 4.1 Guide to reasonable* crack widths, reinforced concrete under service loadsTime to restraint28daysRestraint Temperature-18.448CExposure conditionCrack width (mm)10,000 day temperature-51.363CTotal Temperature-32.915CDry air or protective membrane0.41Equivalent Imposed Strain-0.000329Humidity, moist air, soil0.3Creep Coefficient0.782Deicing chemicals0.18Seawater and seawater spray, wetting & drying0.15Spreadsheet version 1.00Linear Elastic Restraint CalculationsWater-retaining structures0.1Based on AE spreadheetFully RestrainedStress (MPa)-8.47* It should be expected that a portion of the cracks in the structure will exceed these values. With time, a significant portion can exceed these values. These are general guidelines for design to be used in conjunction with sound engineering judgement.Design Strain-0.000329Fully ReleasedShortening (mm)-16Design Strain0.000000Cracking calculation based on "Shrinkage Cracking in Fully Restrained Concrete Members" by R. Ian Gilbert - March-April 1992 ACI Structural JournalRestrainThBar SpacingArea Bar AbAs/m (T+B)AgDesign StrainApprox soCreep Adjusted Mod. E'cCreep Adjusted Modular Ratio, n*C1NcrConc. Stress c1Avg. Conc. StresssQuantity of cracksC2Nstress s2*stress s1*stress c1*Crack widthEqn. 1Eqn. 22Eqn. 6Eqn. 12Eqn. 9Eqn. 19Eqn. 28Eqn. 27Eqn. 16Eqn. 25Eqn. 17Eqn. 15Eqn. 23Eqn. 30mmmmmmmm2mm2/mmm2mmMPaMPaMPammmMPaMPaMPamm100%250252004914,909250,0001.96%-0.00032912714,449140.001701456,9941.8311.8410.7481982520.748264,83053.95-40.341.850.05195%250252004914,909250,0001.96%-0.00031312714,449140.001701456,9941.8311.8410.6472162310.647280,98857.24-37.051.850.05190%250252004914,909250,0001.96%-0.00029612714,449140.001701456,9941.8311.8410.5582372110.558297,14560.53-33.761.850.05185%250252004914,909250,0001.96%-0.00028012714,449140.001701456,9941.8311.8410.4772631900.477313,30263.83-30.471.850.05180%250252004914,909250,0001.96%-0.00026312714,449140.001701456,9941.8311.8410.4052951700.405329,45967.12-27.181.850.05175%250252004914,909250,0001.96%-0.00024712714,449140.001701456,9941.8311.8410.3393351490.339345,61770.41-23.891.850.05170%250252004914,909250,0001.96%-0.00023012714,449140.001701456,9941.8311.8410.2793891290.279361,77473.70-20.591.850.05165%250252004914,909250,0001.96%-0.00021412714,449140.001701456,9941.8311.8410.2254631080.225377,93176.99-17.301.850.05060%250252004914,909250,0001.96%-0.00019712714,449140.001701456,9941.8311.8410.175571880.175394,08880.28-14.011.850.05055%250252004914,909250,0001.96%-0.00018112714,449140.001701456,9941.8311.8410.128747670.128410,24683.57-10.721.850.05050%250252004914,909250,0001.96%-0.00016512714,449140.001701456,9941.8311.8410.0861,078460.086426,40386.87-7.431.850.05045%250252004914,909250,0001.96%-0.00014812714,449140.001701456,9941.8311.8410.0461,935260.046442,56090.16-4.141.850.04940%250252004914,909250,0001.96%-0.00013212714,449140.001701456,9941.8311.8410.0099,47050.009458,71793.45-0.851.850.04435%250252004914,909250,0001.96%-0.00011512714,449140.001701456,9941.8311.841-0.025-3,272-15-0.025474,87496.742.451.850.00030%250252004914,909250,0001.96%-0.00009912714,449140.001701456,9941.8311.841-0.057-1,395-36-0.057491,032100.035.741.850.00025%250252004914,909250,0001.96%-0.00008212714,449140.001701456,9941.8311.841-0.087-886-56-0.087507,189103.329.031.850.00020%250252004914,909250,0001.96%-0.00006612714,449140.001701456,9941.8311.841-0.116-650-77-0.116523,346106.6212.321.850.00015%250252004914,909250,0001.96%-0.00004912714,449140.001701456,9941.8311.841-0.142-513-98-0.142539,503109.9115.611.850.00010%250252004914,909250,0001.96%-0.00003312714,449140.001701456,9941.8311.841-0.167-423-118-0.167555,661113.2018.901.850.0005%250252004914,909250,0001.96%-0.00001612714,449140.001701456,9941.8311.841-0.191-361-139-0.191571,818116.4922.201.850.000-0%250252004914,909250,0001.96%0.00000012714,449140.001701456,9941.8311.841-0.213-314-159-0.213587,975119.7825.491.850.000Custom restrain50%250252004914,909250,0001.96%-0.00016512714,449140.001701456,9941.8311.8410.0861,078460.086426,40386.87-7.431.850.050RestrainThBar SpacingArea Bar AbAs/m (T+B)AgDesign StrainApprox soCreep Adjusted Mod. E'cCreep Adjusted Modular Ratio, n*C1NcrConc. Stress c1Avg. Conc. StresssQuantity of cracksC2Nstress s2*stress s1*stress c1*Crack widthEqn. 1Eqn. 22Eqn. 6Eqn. 12Eqn. 9Eqn. 19Eqn. 28Eqn. 27Eqn. 16Eqn. 25Eqn. 17Eqn. 15Eqn. 23Eqn. 30mmmmmmmm2mm2/mmm2mmMPaMPaMPammmMPaMPaMPamm50%250255049119,635250,0007.85%-0.0001653214,449140.000425462,3481.8501.8510.448697290.448319,60716.28-7.301.850.00550%250257549113,090250,0005.24%-0.0001654814,449140.000637461,8491.8491.8500.2601543250.260367,21528.05-7.311.850.01050%250251004919,817250,0003.93%-0.0001656414,449140.000850461,1901.8461.8490.1842731830.184390,97539.82-7.321.850.01550%250251254917,854250,0003.14%-0.0001658014,449140.001062460,3741.8431.8470.1424261170.142405,19751.59-7.341.850.02250%250251504916,545250,0002.62%-0.0001659514,449140.001275459,4011.8401.8460.116611820.116414,65063.35-7.371.850.03050%250251754915,610250,0002.24%-0.00016511114,449140.001488458,2741.8361.8440.098829600.098421,37875.11-7.401.850.04050%250252004914,909250,0001.96%-0.00016512714,449140.001701456,9941.8311.8410.0861,078460.086426,40386.87-7.431.850.05050%250252254914,363250,0001.75%-0.00016514314,449140.001914455,5651.8261.8390.0761,357370.076430,29398.62-7.471.850.06250%250252504913,927250,0001.57%-0.00016515914,449140.002127453,9901.8201.8360.0681,666300.068433,389110.36-7.511.850.07450%250252754913,570250,0001.43%-0.00016517514,449140.002340452,2701.8131.8320.0622,004250.062435,908122.10-7.551.850.08850%250253004913,272250,0001.31%-0.00016519114,449140.002553450,4091.8061.8290.0572,370210.057437,994133.84-7.601.850.102Custom reinforcement spacing50%250252004914,909250,0001.96%-0.00016512714,449140.001701456,9941.8311.8410.0861,078460.086426,40386.87-7.431.850.050Cracking calculation based on "Control of Flexural Cracking in Reinforced Concrete" by R. Ian Gilbert - May-June 2008 ACI Structural JournalDesign momentsService445kN.mRestrainThBar SpacingArea Bar AbAs/m (T+B)AgDesign StrainCoverCreep Adjusted Mod., E'c (EQN 22)Creep Adjusted Modular Ratio, nbardPossible Depth to NA 1, c1Possible Depth to NA 2, c2Depth to NA, c (c1 or c2)IcrConcrete Crack Area, Act (EQN 1)Reinf. Ratio to Act, rhotcs*Actual Steel Stress, faActual crack widthAcceptable crack widthAllowable Service Steel Stress, fsService Ratio (fa/fs)Eqn. 22Eqn. 8.6cEqn. 8-7Eqn. 1Eqn. 8Eqn. 9mmmmmmmm2mm2/mmm2mmMPammmmmmmmmm4mm2mmMPammmmMPa100%250162002011,005250,0000.40%-0.0003292514,4491421750.41-66.0350.412.59E+0899,7940.01007264.712,2203.0060.3017612.6495%250162002011,005250,0000.40%-0.0003132514,4491421750.41-66.0350.412.59E+0899,7940.01007264.712,2203.0010.3017912.4190%250162002011,005250,0000.40%-0.0002962514,4491421750.41-66.0350.412.59E+0899,7940.01007264.712,2202.9970.3018212.1985%250162002011,005250,0000.40%-0.0002802514,4491421750.41-