30
Shrinkage strain calculation and creep effects based on "Prediction of creep, shrinkage, and temperature effects in concrete structures" - ACI 209R-92 Material Properties f'c 30 MPa f't (direct tensile strength) 1.85 MPa ACI 209R-92 - Eqn. 2-4 Ec 25743 MPa fy 500 MPa Es 200000 MPa n 7.77 alpha 0.00001 Spreadsheet ve Temperature range 20.0 Based on AE 10.0 Thickness 250 mm Type Elevated Slab Table 2.5.4 Correction factors for Relative Humidity Table 2.5.3 Shrinkage correction factors for initial moist curing Steps for Considering Shrinkage and Thermal Effects Shrinkage Effects (ACI 209R-92) 0% 1 1 1 1.2 Ultimate strain 0.00078 (2-6) 40% 1 1 3 1.1 Initial moist curing duration 7 days 50% 0.94 0.9 7 1 Curing correction factor 1 Table 2.5.3 60% 0.87 0.8 14 0.93 Relative humidity 60% 70% 0.8 0.7 28 0.86 Humidity correction factor #VALUE! Table 2.5.4 80% 0.73 0.6 90 0.75 90% 0.67 0.3 100% 0.6 0 Creep Effects (ACI 209R-92) Creep Factor 2.35 (2-6) Humidity correction factor #VALUE! Table 2.5.4 Days Volume 250 (2-9) (2-8) Surface 2 0 #VALUE! #VALUE! #VALUE! #VALUE! v/s 125 7 #VALUE! #VALUE! #VALUE! #VALUE! 14 #VALUE! #VALUE! #VALUE! #VALUE! Creep 0.71 (2-21a) 28 #VALUE! #VALUE! #VALUE! #VALUE! Shrinkage 0.67 (2-22a) 56 #VALUE! #VALUE! #VALUE! #VALUE! 100 #VALUE! #VALUE! #VALUE! #VALUE! Factored creep #VALUE! 500 #VALUE! #VALUE! #VALUE! #VALUE! Factored shrinkage #VALUE! 1000 #VALUE! #VALUE! #VALUE! #VALUE! 5000 #VALUE! #VALUE! #VALUE! #VALUE! Corrected ultimate strain #VALUE! 10000 #VALUE! #VALUE! #VALUE! #VALUE! Length 50 m Time to restraint 28 days Restraint Temperature #VALUE! Exposure condition 10,000 day temperature #VALUE! Total Temperature #VALUE! Dry air or protective membrane 0.41 Equivalent Imposed Strain #VALUE! Humidity, moist air, soil 0.3 Creep Coefficient #VALUE! Deicing chemicals 0.18 Seawater and seawater spray, wetting & drying 0.15 Spreadsheet version 1.00 Linear Elastic Restraint Calculations Water-retaining structures 0.1 Based on AE spreadheet Fully Restrained Stress (MPa) #VALUE! Design Strain #VALUE! Fully Released Shortening (mm) #VALUE! Design Strain 0.000000 Effects of creep, shrinkage, and temperature in concrete slabs °C °C ΔT °C Relative humidity (%) Creep γλ Shrinkage γλ Moist curing duration (days) Shrinkage γCP • 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 1992 These 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 Strain (ϵsh)t Equivalent temperature change ° C Total temp ° C Creep factor vt mm 3 mm 2 ACI 224R-01 -Table 4.1 Guide to reasonable* crack widths, reinforced concrete under service loads °C width (mm) °C °C * 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. 0 2000 4000 6000 8000 10000 0.00000 2.00000 4.00000 6.00000 8.00000 10.00000 12.00000 Shrinkage Strain (ϵsh)t Shrinkag e Str... 0 20 40 60 80 0.600000000000001 0.800000000000001 1 1.2 1.4 Correction factor for initial curing γCP Days 0% 10% 20% 30% 40% 50% 60% 70% 80% 90%100% 0 0.2 0.4 0.6 0.8 1 1.2 Correction factors for relative humidity Creep γλ

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Page 1: ACI Shrinkage Calculation.xls

Shrinkage strain calculation and creep effects based on "Prediction of creep, shrinkage, and temperature effects in concrete structures" - ACI 209R-92

Material Propertiesf'c 30 MPa

f't (direct tensile strength) 1.85 MPa ACI 209R-92 - Eqn. 2-4Ec 25743 MPa

fy 500 MPa

Es 200000 MPan 7.77

alpha 0.00001 Spreadsheet version 1.00Temperature range 20.0 Based on AE spreadheet

10.0Thickness 250 mmType Elevated Slab Table 2.5.4 Correction factors for Relative Humidity Table 2.5.3 Shrinkage correction factors for initial moist curing Steps for Considering Shrinkage and Thermal Effects

Shrinkage Effects (ACI 209R-92) 0% 1 1 1 1.2Ultimate strain 0.00078 (2-6) 40% 1 1 3 1.1Initial moist curing duration 7 days 50% 0.94 0.9 7 1Curing correction factor 1 Table 2.5.3 60% 0.87 0.8 14 0.93Relative humidity 60% 70% 0.8 0.7 28 0.86Humidity correction factor #VALUE! Table 2.5.4 80% 0.73 0.6 90 0.75

90% 0.67 0.3100% 0.6 0

Creep Effects (ACI 209R-92)Creep Factor 2.35 (2-6)Humidity correction factor #VALUE! Table 2.5.4

Days

Volume 250 (2-9) (2-8)Surface 2 0 #VALUE! #VALUE! #VALUE! #VALUE!v/s 125 7 #VALUE! #VALUE! #VALUE! #VALUE!

14 #VALUE! #VALUE! #VALUE! #VALUE!Creep 0.71 (2-21a) 28 #VALUE! #VALUE! #VALUE! #VALUE!Shrinkage 0.67 (2-22a) 56 #VALUE! #VALUE! #VALUE! #VALUE!

100 #VALUE! #VALUE! #VALUE! #VALUE!Factored creep #VALUE! 500 #VALUE! #VALUE! #VALUE! #VALUE!Factored shrinkage #VALUE! 1000 #VALUE! #VALUE! #VALUE! #VALUE!

5000 #VALUE! #VALUE! #VALUE! #VALUE!Corrected ultimate strain #VALUE! 10000 #VALUE! #VALUE! #VALUE! #VALUE!

Length 50 mTime to restraint 28 days

Restraint Temperature #VALUE!Exposure condition10,000 day temperature #VALUE!

Total Temperature #VALUE! Dry air or protective membrane 0.41Equivalent Imposed Strain #VALUE! Humidity, moist air, soil 0.3Creep Coefficient #VALUE! Deicing chemicals 0.18

Seawater and seawater spray, wetting & drying 0.15 Spreadsheet version 1.00Linear Elastic Restraint Calculations Water-retaining structures 0.1 Based on AE spreadheetFully RestrainedStress (MPa) #VALUE!Design Strain #VALUE!Fully ReleasedShortening (mm) #VALUE!Design Strain 0.000000

Effects of creep, shrinkage, and temperature in concrete slabs

°C°C

ΔT °C

Relative humidity

(%)Creep γλ Shrinkage γλ

Moist curing duration (days)

Shrinkage γCP

1. 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 Strain (ϵsh)t

Equivalent temperature change ° C

Total temp ° C

Creep factor vt

mm3

mm2

ACI 224R-01 -Table 4.1 Guide to reasonable* crack widths, reinforced concrete under service loads

°C Crack width (mm)°C

°C

* 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.

0 2000 4000 6000 8000 100000.00000

2.00000

4.00000

6.00000

8.00000

10.00000

12.00000Shrinkage Strain (ϵsh)t

Shrinkage Strain (ϵsh)t

0 20 40 60 800.6000000000000010.7000000000000010.8000000000000010.900000000000001

11.11.21.31.4

Correction factor for initial curing γCP

Days0% 10% 20% 30% 40% 50% 60% 70% 80% 90%100%

0

0.2

0.4

0.6

0.8

1

1.2

Correction factors for relative humidity

Creep γλ

Shrinkage γλ

Page 2: ACI Shrinkage Calculation.xls

Cracking calculation based on "Shrinkage Cracking in Fully Restrained Concrete Members" by R. Ian Gilbert - March-April 1992 ACI Structural Journal

Restrain Th

Spacing Area Bar Ab As/m (T+B) Ag ρ Approx so C1 Ncr ξ s C2 N stress s2* stress s1* stress c1* Crack width

Eqn. 1 Eqn. 22 Eqn. 6 Eqn. 12 Eqn. 9 Eqn. 19 Eqn. 28 Eqn. 27 Eqn. 16 Eqn. 25 Eqn. 17 Eqn. 15 Eqn. 23 Eqn. 30mm mm mm mm MPa MPa MPa mm m MPa MPa MPa mm

100% 250 25 200 491 4,909 250,000 1.96% #VALUE! 127 #VALUE! #VALUE! 0.001701 456,994 1.831 1.841 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!95% 250 25 200 491 4,909 250,000 1.96% #VALUE! 127 #VALUE! #VALUE! 0.001701 456,994 1.831 1.841 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!90% 250 25 200 491 4,909 250,000 1.96% #VALUE! 127 #VALUE! #VALUE! 0.001701 456,994 1.831 1.841 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!85% 250 25 200 491 4,909 250,000 1.96% #VALUE! 127 #VALUE! #VALUE! 0.001701 456,994 1.831 1.841 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!80% 250 25 200 491 4,909 250,000 1.96% #VALUE! 127 #VALUE! #VALUE! 0.001701 456,994 1.831 1.841 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!75% 250 25 200 491 4,909 250,000 1.96% #VALUE! 127 #VALUE! #VALUE! 0.001701 456,994 1.831 1.841 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!70% 250 25 200 491 4,909 250,000 1.96% #VALUE! 127 #VALUE! #VALUE! 0.001701 456,994 1.831 1.841 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!65% 250 25 200 491 4,909 250,000 1.96% #VALUE! 127 #VALUE! #VALUE! 0.001701 456,994 1.831 1.841 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!60% 250 25 200 491 4,909 250,000 1.96% #VALUE! 127 #VALUE! #VALUE! 0.001701 456,994 1.831 1.841 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!55% 250 25 200 491 4,909 250,000 1.96% #VALUE! 127 #VALUE! #VALUE! 0.001701 456,994 1.831 1.841 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 250 25 200 491 4,909 250,000 1.96% #VALUE! 127 #VALUE! #VALUE! 0.001701 456,994 1.831 1.841 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!45% 250 25 200 491 4,909 250,000 1.96% #VALUE! 127 #VALUE! #VALUE! 0.001701 456,994 1.831 1.841 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!40% 250 25 200 491 4,909 250,000 1.96% #VALUE! 127 #VALUE! #VALUE! 0.001701 456,994 1.831 1.841 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!35% 250 25 200 491 4,909 250,000 1.96% #VALUE! 127 #VALUE! #VALUE! 0.001701 456,994 1.831 1.841 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!30% 250 25 200 491 4,909 250,000 1.96% #VALUE! 127 #VALUE! #VALUE! 0.001701 456,994 1.831 1.841 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!25% 250 25 200 491 4,909 250,000 1.96% #VALUE! 127 #VALUE! #VALUE! 0.001701 456,994 1.831 1.841 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!20% 250 25 200 491 4,909 250,000 1.96% #VALUE! 127 #VALUE! #VALUE! 0.001701 456,994 1.831 1.841 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!15% 250 25 200 491 4,909 250,000 1.96% #VALUE! 127 #VALUE! #VALUE! 0.001701 456,994 1.831 1.841 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!10% 250 25 200 491 4,909 250,000 1.96% #VALUE! 127 #VALUE! #VALUE! 0.001701 456,994 1.831 1.841 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!5% 250 25 200 491 4,909 250,000 1.96% #VALUE! 127 #VALUE! #VALUE! 0.001701 456,994 1.831 1.841 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!0% 250 25 200 491 4,909 250,000 1.96% #VALUE! 127 #VALUE! #VALUE! 0.001701 456,994 1.831 1.841 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

Custom restrain50% 250 25 200 491 4,909 250,000 1.96% #VALUE! 127 #VALUE! #VALUE! 0.001701 456,994 1.831 1.841 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

Restrain Th

Spacing Area Bar Ab As/m (T+B) Ag ρ Approx so C1 Ncr ξ s C2 N stress s2* stress s1* stress c1* Crack width

Eqn. 1 Eqn. 22 Eqn. 6 Eqn. 12 Eqn. 9 Eqn. 19 Eqn. 28 Eqn. 27 Eqn. 16 Eqn. 25 Eqn. 17 Eqn. 15 Eqn. 23 Eqn. 30mm mm mm mm MPa MPa MPa mm m MPa MPa MPa mm

50% 250 25 50 491 19,635 250,000 7.85% #VALUE! 32 #VALUE! #VALUE! 0.000425 462,348 1.850 1.851 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 250 25 75 491 13,090 250,000 5.24% #VALUE! 48 #VALUE! #VALUE! 0.000637 461,849 1.849 1.850 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 250 25 100 491 9,817 250,000 3.93% #VALUE! 64 #VALUE! #VALUE! 0.000850 461,190 1.846 1.849 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 250 25 125 491 7,854 250,000 3.14% #VALUE! 80 #VALUE! #VALUE! 0.001062 460,374 1.843 1.847 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 250 25 150 491 6,545 250,000 2.62% #VALUE! 95 #VALUE! #VALUE! 0.001275 459,401 1.840 1.846 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 250 25 175 491 5,610 250,000 2.24% #VALUE! 111 #VALUE! #VALUE! 0.001488 458,274 1.836 1.844 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 250 25 200 491 4,909 250,000 1.96% #VALUE! 127 #VALUE! #VALUE! 0.001701 456,994 1.831 1.841 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 250 25 225 491 4,363 250,000 1.75% #VALUE! 143 #VALUE! #VALUE! 0.001914 455,565 1.826 1.839 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 250 25 250 491 3,927 250,000 1.57% #VALUE! 159 #VALUE! #VALUE! 0.002127 453,990 1.820 1.836 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 250 25 275 491 3,570 250,000 1.43% #VALUE! 175 #VALUE! #VALUE! 0.002340 452,270 1.813 1.832 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 250 25 300 491 3,272 250,000 1.31% #VALUE! 191 #VALUE! #VALUE! 0.002553 450,409 1.806 1.829 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

Custom reinforcement spacing50% 250 25 200 491 4,909 250,000 1.96% #VALUE! 127 #VALUE! #VALUE! 0.001701 456,994 1.831 1.841 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

Bar Ø

Design Strain

Creep Adjusted Mod. E'c

Creep Adjusted

Modular Ratio, n*

Conc. Stress c1

Avg. Conc. Stress

Quantity of cracks

mm2 mm2/m mm2

Bar Ø

Design Strain

Creep Adjusted Mod. E'c

Creep Adjusted

Modular Ratio, n*

Conc. Stress c1

Avg. Conc. Stress

Quantity of cracks

mm2 mm2/m mm2

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%0.00

2.00

4.00

6.00

8.00

10.00

12.00w vs. restrain

Crack width

50%

25 75 125 175 225 275 325 3750.00

2.00

4.00

6.00

8.00

10.00

12.00w vs. reinf spacing

Crack width

200

Page 3: ACI Shrinkage Calculation.xls

Cracking calculation based on "Control of Flexural Cracking in Reinforced Concrete" by R. Ian Gilbert - May-June 2008 ACI Structural Journal

Design momentsService 445 kN.m

Restrain Th

Spacing Area Bar Ab As/m (T+B) Ag ρ Cover d Icr s*

Eqn. 22 Eqn. 8.6c Eqn. 8-7 Eqn. 1 Eqn. 8 Eqn. 9mm mm mm mm MPa mm mm mm mm mm MPa mm mm MPa

100% 250 16 200 201 1,005 250,000 0.40% #VALUE! 25 #VALUE! #VALUE! 217 50.41 -66.03 50.41 2.59E+08 99,794 0.01007 264.71 2,220 #VALUE! 0.30 #VALUE! #VALUE!95% 250 16 200 201 1,005 250,000 0.40% #VALUE! 25 #VALUE! #VALUE! 217 50.41 -66.03 50.41 2.59E+08 99,794 0.01007 264.71 2,220 #VALUE! 0.30 #VALUE! #VALUE!90% 250 16 200 201 1,005 250,000 0.40% #VALUE! 25 #VALUE! #VALUE! 217 50.41 -66.03 50.41 2.59E+08 99,794 0.01007 264.71 2,220 #VALUE! 0.30 #VALUE! #VALUE!85% 250 16 200 201 1,005 250,000 0.40% #VALUE! 25 #VALUE! #VALUE! 217 50.41 -66.03 50.41 2.59E+08 99,794 0.01007 264.71 2,220 #VALUE! 0.30 #VALUE! #VALUE!80% 250 16 200 201 1,005 250,000 0.40% #VALUE! 25 #VALUE! #VALUE! 217 50.41 -66.03 50.41 2.59E+08 99,794 0.01007 264.71 2,220 #VALUE! 0.30 #VALUE! #VALUE!75% 250 16 200 201 1,005 250,000 0.40% #VALUE! 25 #VALUE! #VALUE! 217 50.41 -66.03 50.41 2.59E+08 99,794 0.01007 264.71 2,220 #VALUE! 0.30 #VALUE! #VALUE!70% 250 16 200 201 1,005 250,000 0.40% #VALUE! 25 #VALUE! #VALUE! 217 50.41 -66.03 50.41 2.59E+08 99,794 0.01007 264.71 2,220 #VALUE! 0.30 #VALUE! #VALUE!65% 250 16 200 201 1,005 250,000 0.40% #VALUE! 25 #VALUE! #VALUE! 217 50.41 -66.03 50.41 2.59E+08 99,794 0.01007 264.71 2,220 #VALUE! 0.30 #VALUE! #VALUE!60% 250 16 200 201 1,005 250,000 0.40% #VALUE! 25 #VALUE! #VALUE! 217 50.41 -66.03 50.41 2.59E+08 99,794 0.01007 264.71 2,220 #VALUE! 0.30 #VALUE! #VALUE!55% 250 16 200 201 1,005 250,000 0.40% #VALUE! 25 #VALUE! #VALUE! 217 50.41 -66.03 50.41 2.59E+08 99,794 0.01007 264.71 2,220 #VALUE! 0.30 #VALUE! #VALUE!50% 250 16 200 201 1,005 250,000 0.40% #VALUE! 25 #VALUE! #VALUE! 217 50.41 -66.03 50.41 2.59E+08 99,794 0.01007 264.71 2,220 #VALUE! 0.30 #VALUE! #VALUE!45% 250 16 200 201 1,005 250,000 0.40% #VALUE! 25 #VALUE! #VALUE! 217 50.41 -66.03 50.41 2.59E+08 99,794 0.01007 264.71 2,220 #VALUE! 0.30 #VALUE! #VALUE!40% 250 16 200 201 1,005 250,000 0.40% #VALUE! 25 #VALUE! #VALUE! 217 50.41 -66.03 50.41 2.59E+08 99,794 0.01007 264.71 2,220 #VALUE! 0.30 #VALUE! #VALUE!35% 250 16 200 201 1,005 250,000 0.40% #VALUE! 25 #VALUE! #VALUE! 217 50.41 -66.03 50.41 2.59E+08 99,794 0.01007 264.71 2,220 #VALUE! 0.30 #VALUE! #VALUE!30% 250 16 200 201 1,005 250,000 0.40% #VALUE! 25 #VALUE! #VALUE! 217 50.41 -66.03 50.41 2.59E+08 99,794 0.01007 264.71 2,220 #VALUE! 0.30 #VALUE! #VALUE!25% 250 16 200 201 1,005 250,000 0.40% #VALUE! 25 #VALUE! #VALUE! 217 50.41 -66.03 50.41 2.59E+08 99,794 0.01007 264.71 2,220 #VALUE! 0.30 #VALUE! #VALUE!20% 250 16 200 201 1,005 250,000 0.40% #VALUE! 25 #VALUE! #VALUE! 217 50.41 -66.03 50.41 2.59E+08 99,794 0.01007 264.71 2,220 #VALUE! 0.30 #VALUE! #VALUE!15% 250 16 200 201 1,005 250,000 0.40% #VALUE! 25 #VALUE! #VALUE! 217 50.41 -66.03 50.41 2.59E+08 99,794 0.01007 264.71 2,220 #VALUE! 0.30 #VALUE! #VALUE!10% 250 16 200 201 1,005 250,000 0.40% #VALUE! 25 #VALUE! #VALUE! 217 50.41 -66.03 50.41 2.59E+08 99,794 0.01007 264.71 2,220 #VALUE! 0.30 #VALUE! #VALUE!5% 250 16 200 201 1,005 250,000 0.40% #VALUE! 25 #VALUE! #VALUE! 217 50.41 -66.03 50.41 2.59E+08 99,794 0.01007 264.71 2,220 #VALUE! 0.30 #VALUE! #VALUE!0% 250 16 200 201 1,005 250,000 0.40% #VALUE! 25 #VALUE! #VALUE! 217 50.41 -66.03 50.41 2.59E+08 99,794 0.01007 264.71 2,220 #VALUE! 0.30 #VALUE! #VALUE!

Custom restrain75% 250 16 200 201 1,005 250,000 0.40% #VALUE! 25 #VALUE! #VALUE! 217 50.41 -66.03 50.41 2.59E+08 99,794 0.01007 264.71 2,220 #VALUE! 0.30 #VALUE! #VALUE!

Bar Ø

Design Strain

Creep Adjusted Mod., E'c (EQN

22)

Creep Adjusted

Modular Ratio, nbar

Possible Depth to NA 1, c1

Possible Depth to NA 2, c2

Depth to NA, c (c1 or c2)

Concrete Crack Area, Act (EQN

1)

Reinf. Ratio to Act, rhotc

Actual Steel Stress, fa

Actual crack width

Acceptable crack width

Allowable Service Steel

Stress, fsService

Ratio (fa/fs)

mm2 mm2/m mm2 mm4 mm2

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%0.00

2.00

4.00

6.00

8.00

10.00

12.00w vs. restrain

Crack Width

75%

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%0.00

2.00

4.00

6.00

8.00

10.00

12.00w vs. restrain

Crack Width

75%

Page 4: ACI Shrinkage Calculation.xls

Shrinkage strain calculation and creep effects based on "Prediction of creep, shrinkage, and temperature effects in concrete structures" - ACI 209R-92

Material Propertiesf'c 30 MPa

f't (direct tensile strength) 1.85 MPa ACI 209R-92 - Eqn. 2-4Ec 25743 MPa

fy 500 MPa

Es 200000 MPan 7.77

alpha 0.00001 Spreadsheet version 1.00Temperature range 10.0 Based on AE spreadheet

5.0Thickness 300 mmType Foundation Mat Table 2.5.4 Correction factors for Relative Humidity Table 2.5.3 Shrinkage correction factors for initial moist curing Steps for Considering Shrinkage and Thermal Effects

Shrinkage Effects (ACI 209R-92) 0% 1 1 1 1.2Ultimate strain 0.00078 (2-6) 40% 1 1 3 1.1Initial moist curing duration 7 days 50% 0.94 0.9 7 1Curing correction factor 1 Table 2.5.3 60% 0.87 0.8 14 0.93Relative humidity 60% 70% 0.8 0.7 28 0.86Humidity correction factor #VALUE! Table 2.5.4 80% 0.73 0.6 90 0.75

90% 0.67 0.3100% 0.6 0

Creep Effects (ACI 209R-92)Creep Factor 2.35 (2-6)Humidity correction factor #VALUE! Table 2.5.4

Days

Volume 300 (2-9) (2-8)Surface 1 0 #VALUE! #VALUE! #VALUE! #VALUE!v/s 300 7 #VALUE! #VALUE! #VALUE! #VALUE!

14 #VALUE! #VALUE! #VALUE! #VALUE!Creep 0.66 (2-21a) 28 #VALUE! #VALUE! #VALUE! #VALUE!Shrinkage 0.29 (2-22a) 56 #VALUE! #VALUE! #VALUE! #VALUE!

100 #VALUE! #VALUE! #VALUE! #VALUE!Factored creep #VALUE! 500 #VALUE! #VALUE! #VALUE! #VALUE!Factored shrinkage #VALUE! 1000 #VALUE! #VALUE! #VALUE! #VALUE!

5000 #VALUE! #VALUE! #VALUE! #VALUE!Corrected ultimate strain #VALUE! 10000 #VALUE! #VALUE! #VALUE! #VALUE!

Length 12 mTime to restraint 28 days

Restraint Temperature #VALUE!Exposure condition10,000 day temperature #VALUE!

Total Temperature #VALUE! Dry air or protective membrane 0.41Equivalent Imposed Strain #VALUE! Humidity, moist air, soil 0.3Creep Coefficient #VALUE! Deicing chemicals 0.18

Seawater and seawater spray, wetting & drying 0.15 Spreadsheet version 1.00Linear Elastic Restraint Calculations Water-retaining structures 0.1 Based on AE spreadheetFully RestrainedStress (MPa) #VALUE!Design Strain #VALUE!Fully ReleasedShortening (mm) #VALUE!Design Strain 0.000000

Effects of creep, shrinkage, and temperature in concrete slabs

°C°C

ΔT °C

Relative humidity

(%)Creep γλ Shrinkage γλ

Moist curing duration (days)

Shrinkage γCP

1. 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 Strain (ϵsh)t

Equivalent temperature change ° C

Total temp ° C

Creep factor vt

mm3

mm2

ACI 224R-01 -Table 4.1 Guide to reasonable* crack widths, reinforced concrete under service loads

°C Crack width (mm)°C

°C

* 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.

0 2000 4000 6000 8000 100000.00000

2.00000

4.00000

6.00000

8.00000

10.00000

12.00000Shrinkage Strain (ϵsh)t

Shrinkage Strain (ϵsh)t

0 20 40 60 800.6000000000000010.7000000000000010.8000000000000010.900000000000001

11.11.21.31.4

Correction factor for initial curing γCP

Days0% 10% 20% 30% 40% 50% 60% 70% 80% 90%100%

0

0.2

0.4

0.6

0.8

1

1.2

Correction factors for relative humidity

Creep γλ

Shrinkage γλ

Page 5: ACI Shrinkage Calculation.xls

Cracking calculation based on "Shrinkage Cracking in Fully Restrained Concrete Members" by R. Ian Gilbert - March-April 1992 ACI Structural Journal

Restrain Th

Spacing Area Bar Ab As/m (T+B) Ag ρ Approx so C1 Ncr ξ s C2 N stress s2* stress s1* stress c1* Crack width

Eqn. 1 Eqn. 22 Eqn. 6 Eqn. 12 Eqn. 9 Eqn. 19 Eqn. 28 Eqn. 27 Eqn. 16 Eqn. 25 Eqn. 17 Eqn. 15 Eqn. 23 Eqn. 30mm mm mm mm MPa MPa MPa mm m MPa MPa MPa mm

100% 300 16 200 201 2,011 300,000 0.67% #VALUE! 239 #VALUE! #VALUE! 0.013441 436,810 1.476 1.664 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!95% 300 16 200 201 2,011 300,000 0.67% #VALUE! 239 #VALUE! #VALUE! 0.013441 436,810 1.476 1.664 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!90% 300 16 200 201 2,011 300,000 0.67% #VALUE! 239 #VALUE! #VALUE! 0.013441 436,810 1.476 1.664 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!85% 300 16 200 201 2,011 300,000 0.67% #VALUE! 239 #VALUE! #VALUE! 0.013441 436,810 1.476 1.664 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!80% 300 16 200 201 2,011 300,000 0.67% #VALUE! 239 #VALUE! #VALUE! 0.013441 436,810 1.476 1.664 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!75% 300 16 200 201 2,011 300,000 0.67% #VALUE! 239 #VALUE! #VALUE! 0.013441 436,810 1.476 1.664 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!70% 300 16 200 201 2,011 300,000 0.67% #VALUE! 239 #VALUE! #VALUE! 0.013441 436,810 1.476 1.664 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!65% 300 16 200 201 2,011 300,000 0.67% #VALUE! 239 #VALUE! #VALUE! 0.013441 436,810 1.476 1.664 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!60% 300 16 200 201 2,011 300,000 0.67% #VALUE! 239 #VALUE! #VALUE! 0.013441 436,810 1.476 1.664 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!55% 300 16 200 201 2,011 300,000 0.67% #VALUE! 239 #VALUE! #VALUE! 0.013441 436,810 1.476 1.664 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 300 16 200 201 2,011 300,000 0.67% #VALUE! 239 #VALUE! #VALUE! 0.013441 436,810 1.476 1.664 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!45% 300 16 200 201 2,011 300,000 0.67% #VALUE! 239 #VALUE! #VALUE! 0.013441 436,810 1.476 1.664 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!40% 300 16 200 201 2,011 300,000 0.67% #VALUE! 239 #VALUE! #VALUE! 0.013441 436,810 1.476 1.664 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!35% 300 16 200 201 2,011 300,000 0.67% #VALUE! 239 #VALUE! #VALUE! 0.013441 436,810 1.476 1.664 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!30% 300 16 200 201 2,011 300,000 0.67% #VALUE! 239 #VALUE! #VALUE! 0.013441 436,810 1.476 1.664 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!25% 300 16 200 201 2,011 300,000 0.67% #VALUE! 239 #VALUE! #VALUE! 0.013441 436,810 1.476 1.664 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!20% 300 16 200 201 2,011 300,000 0.67% #VALUE! 239 #VALUE! #VALUE! 0.013441 436,810 1.476 1.664 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!15% 300 16 200 201 2,011 300,000 0.67% #VALUE! 239 #VALUE! #VALUE! 0.013441 436,810 1.476 1.664 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!10% 300 16 200 201 2,011 300,000 0.67% #VALUE! 239 #VALUE! #VALUE! 0.013441 436,810 1.476 1.664 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!5% 300 16 200 201 2,011 300,000 0.67% #VALUE! 239 #VALUE! #VALUE! 0.013441 436,810 1.476 1.664 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!0% 300 16 200 201 2,011 300,000 0.67% #VALUE! 239 #VALUE! #VALUE! 0.013441 436,810 1.476 1.664 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

Custom restrain50% 300 16 200 201 2,011 300,000 0.67% #VALUE! 239 #VALUE! #VALUE! 0.013441 436,810 1.476 1.664 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

Restrain Th

Spacing Area Bar Ab As/m (T+B) Ag ρ Approx so C1 Ncr ξ s C2 N stress s2* stress s1* stress c1* Crack width

Eqn. 1 Eqn. 22 Eqn. 6 Eqn. 12 Eqn. 9 Eqn. 19 Eqn. 28 Eqn. 27 Eqn. 16 Eqn. 25 Eqn. 17 Eqn. 15 Eqn. 23 Eqn. 30mm mm mm mm MPa MPa MPa mm m MPa MPa MPa mm

50% 300 16 50 201 8,042 300,000 2.68% #VALUE! 60 #VALUE! #VALUE! 0.003327 544,923 1.822 1.837 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 300 16 75 201 5,362 300,000 1.79% #VALUE! 90 #VALUE! #VALUE! 0.004998 533,565 1.787 1.819 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 300 16 100 201 4,021 300,000 1.34% #VALUE! 119 #VALUE! #VALUE! 0.006676 518,724 1.741 1.796 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 300 16 125 201 3,217 300,000 1.07% #VALUE! 149 #VALUE! #VALUE! 0.008359 500,987 1.684 1.768 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 300 16 150 201 2,681 300,000 0.89% #VALUE! 179 #VALUE! #VALUE! 0.010047 480,998 1.619 1.735 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 300 16 175 201 2,298 300,000 0.77% #VALUE! 209 #VALUE! #VALUE! 0.011741 459,402 1.549 1.700 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 300 16 200 201 2,011 300,000 0.67% #VALUE! 239 #VALUE! #VALUE! 0.013441 436,810 1.476 1.664 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 300 16 225 201 1,787 300,000 0.60% #VALUE! 269 #VALUE! #VALUE! 0.015147 413,764 1.400 1.626 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 300 16 250 201 1,608 300,000 0.54% #VALUE! 298 #VALUE! #VALUE! 0.016858 390,724 1.324 1.588 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 300 16 275 201 1,462 300,000 0.49% #VALUE! 328 #VALUE! #VALUE! 0.018575 368,061 1.250 1.551 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 300 16 300 201 1,340 300,000 0.45% #VALUE! 358 #VALUE! #VALUE! 0.020298 346,058 1.177 1.514 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

Custom reinforcement spacing50% 300 16 200 201 2,011 300,000 0.67% #VALUE! 239 #VALUE! #VALUE! 0.013441 436,810 1.476 1.664 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

Bar Ø

Design Strain

Creep Adjusted Mod. E'c

Creep Adjusted

Modular Ratio, n*

Conc. Stress c1

Avg. Conc. Stress

Quantity of cracks

mm2 mm2/m mm2

Bar Ø

Design Strain

Creep Adjusted Mod. E'c

Creep Adjusted

Modular Ratio, n*

Conc. Stress c1

Avg. Conc. Stress

Quantity of cracks

mm2 mm2/m mm2

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%0.00

2.00

4.00

6.00

8.00

10.00

12.00w vs. restrain

Crack width

50%

25 75 125 175 225 275 325 3750.00

2.00

4.00

6.00

8.00

10.00

12.00w vs. reinf spacing

Crack width

200

Page 6: ACI Shrinkage Calculation.xls

Cracking calculation based on "Control of Flexural Cracking in Reinforced Concrete" by R. Ian Gilbert - May-June 2008 ACI Structural Journal

Design momentsService 445 kN.m

Restrain Th

Spacing Area Bar Ab As/m (T+B) Ag ρ Cover d Icr s*

Eqn. 22 Eqn. 8.6c Eqn. 8-7 Eqn. 1 Eqn. 8 Eqn. 9mm mm mm mm MPa mm mm mm mm mm MPa mm mm MPa

100% 300 16 200 201 1,005 300,000 0.34% #VALUE! 25 #VALUE! #VALUE! 267 56.77 -72.39 56.77 4.06E+08 121,614 0.00827 322.59 1,789 #VALUE! 0.30 #VALUE! #VALUE!95% 300 16 200 201 1,005 300,000 0.34% #VALUE! 25 #VALUE! #VALUE! 267 56.77 -72.39 56.77 4.06E+08 121,614 0.00827 322.59 1,789 #VALUE! 0.30 #VALUE! #VALUE!90% 300 16 200 201 1,005 300,000 0.34% #VALUE! 25 #VALUE! #VALUE! 267 56.77 -72.39 56.77 4.06E+08 121,614 0.00827 322.59 1,789 #VALUE! 0.30 #VALUE! #VALUE!85% 300 16 200 201 1,005 300,000 0.34% #VALUE! 25 #VALUE! #VALUE! 267 56.77 -72.39 56.77 4.06E+08 121,614 0.00827 322.59 1,789 #VALUE! 0.30 #VALUE! #VALUE!80% 300 16 200 201 1,005 300,000 0.34% #VALUE! 25 #VALUE! #VALUE! 267 56.77 -72.39 56.77 4.06E+08 121,614 0.00827 322.59 1,789 #VALUE! 0.30 #VALUE! #VALUE!75% 300 16 200 201 1,005 300,000 0.34% #VALUE! 25 #VALUE! #VALUE! 267 56.77 -72.39 56.77 4.06E+08 121,614 0.00827 322.59 1,789 #VALUE! 0.30 #VALUE! #VALUE!70% 300 16 200 201 1,005 300,000 0.34% #VALUE! 25 #VALUE! #VALUE! 267 56.77 -72.39 56.77 4.06E+08 121,614 0.00827 322.59 1,789 #VALUE! 0.30 #VALUE! #VALUE!65% 300 16 200 201 1,005 300,000 0.34% #VALUE! 25 #VALUE! #VALUE! 267 56.77 -72.39 56.77 4.06E+08 121,614 0.00827 322.59 1,789 #VALUE! 0.30 #VALUE! #VALUE!60% 300 16 200 201 1,005 300,000 0.34% #VALUE! 25 #VALUE! #VALUE! 267 56.77 -72.39 56.77 4.06E+08 121,614 0.00827 322.59 1,789 #VALUE! 0.30 #VALUE! #VALUE!55% 300 16 200 201 1,005 300,000 0.34% #VALUE! 25 #VALUE! #VALUE! 267 56.77 -72.39 56.77 4.06E+08 121,614 0.00827 322.59 1,789 #VALUE! 0.30 #VALUE! #VALUE!50% 300 16 200 201 1,005 300,000 0.34% #VALUE! 25 #VALUE! #VALUE! 267 56.77 -72.39 56.77 4.06E+08 121,614 0.00827 322.59 1,789 #VALUE! 0.30 #VALUE! #VALUE!45% 300 16 200 201 1,005 300,000 0.34% #VALUE! 25 #VALUE! #VALUE! 267 56.77 -72.39 56.77 4.06E+08 121,614 0.00827 322.59 1,789 #VALUE! 0.30 #VALUE! #VALUE!40% 300 16 200 201 1,005 300,000 0.34% #VALUE! 25 #VALUE! #VALUE! 267 56.77 -72.39 56.77 4.06E+08 121,614 0.00827 322.59 1,789 #VALUE! 0.30 #VALUE! #VALUE!35% 300 16 200 201 1,005 300,000 0.34% #VALUE! 25 #VALUE! #VALUE! 267 56.77 -72.39 56.77 4.06E+08 121,614 0.00827 322.59 1,789 #VALUE! 0.30 #VALUE! #VALUE!30% 300 16 200 201 1,005 300,000 0.34% #VALUE! 25 #VALUE! #VALUE! 267 56.77 -72.39 56.77 4.06E+08 121,614 0.00827 322.59 1,789 #VALUE! 0.30 #VALUE! #VALUE!25% 300 16 200 201 1,005 300,000 0.34% #VALUE! 25 #VALUE! #VALUE! 267 56.77 -72.39 56.77 4.06E+08 121,614 0.00827 322.59 1,789 #VALUE! 0.30 #VALUE! #VALUE!20% 300 16 200 201 1,005 300,000 0.34% #VALUE! 25 #VALUE! #VALUE! 267 56.77 -72.39 56.77 4.06E+08 121,614 0.00827 322.59 1,789 #VALUE! 0.30 #VALUE! #VALUE!15% 300 16 200 201 1,005 300,000 0.34% #VALUE! 25 #VALUE! #VALUE! 267 56.77 -72.39 56.77 4.06E+08 121,614 0.00827 322.59 1,789 #VALUE! 0.30 #VALUE! #VALUE!10% 300 16 200 201 1,005 300,000 0.34% #VALUE! 25 #VALUE! #VALUE! 267 56.77 -72.39 56.77 4.06E+08 121,614 0.00827 322.59 1,789 #VALUE! 0.30 #VALUE! #VALUE!5% 300 16 200 201 1,005 300,000 0.34% #VALUE! 25 #VALUE! #VALUE! 267 56.77 -72.39 56.77 4.06E+08 121,614 0.00827 322.59 1,789 #VALUE! 0.30 #VALUE! #VALUE!0% 300 16 200 201 1,005 300,000 0.34% #VALUE! 25 #VALUE! #VALUE! 267 56.77 -72.39 56.77 4.06E+08 121,614 0.00827 322.59 1,789 #VALUE! 0.30 #VALUE! #VALUE!

Custom restrain75% 300 16 200 201 1,005 300,000 0.34% #VALUE! 25 #VALUE! #VALUE! 267 56.77 -72.39 56.77 4.06E+08 121,614 0.00827 322.59 1,789 #VALUE! 0.30 #VALUE! #VALUE!

Bar Ø

Design Strain

Creep Adjusted Mod., E'c (EQN

22)

Creep Adjusted

Modular Ratio, nbar

Possible Depth to NA 1, c1

Possible Depth to NA 2, c2

Depth to NA, c (c1 or c2)

Concrete Crack Area, Act (EQN

1)

Reinf. Ratio to Act, rhotc

Actual Steel Stress, fa

Actual crack width

Acceptable crack width

Allowable Service Steel

Stress, fsService

Ratio (fa/fs)

mm2 mm2/m mm2 mm4 mm2

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%0.00

2.00

4.00

6.00

8.00

10.00

12.00w vs. restrain

Crack Width

75%

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%0.00

2.00

4.00

6.00

8.00

10.00

12.00w vs. restrain

Crack Width

75%

Page 7: ACI Shrinkage Calculation.xls

Shrinkage strain calculation and creep effects based on "Prediction of creep, shrinkage, and temperature effects in concrete structures" - ACI 209R-92

Material Propertiesf'c 35 MPa

f't (direct tensile strength) 2.00 MPa ACI 209R-92 - Eqn. 2-4Ec 27806 MPa

fy 420 MPa

Es 200000 MPan 7.19

alpha 0.00001 Spreadsheet version 1.00Temperature range 20.0 Based on AE spreadheet

10.0Thickness 1500 mmType Foundation Mat Table 2.5.4 Correction factors for Relative Humidity Table 2.5.3 Shrinkage correction factors for initial moist curing Steps for Considering Shrinkage and Thermal Effects

Shrinkage Effects (ACI 209R-92) 0% 1 1 1 1.2Ultimate strain 0.00078 (2-6) 40% 1 1 3 1.1Initial moist curing duration 7 days 50% 0.94 0.9 7 1Curing correction factor 1 Table 2.5.3 60% 0.87 0.8 14 0.93Relative humidity 60% 70% 0.8 0.7 28 0.86Humidity correction factor #VALUE! Table 2.5.4 80% 0.73 0.6 90 0.75

90% 0.67 0.3100% 0.6 0

Creep Effects (ACI 209R-92)Creep Factor 2.35 (2-6)Humidity correction factor #VALUE! Table 2.5.4

Days

Volume 1500 (2-9) (2-8)Surface 1 0 #VALUE! #VALUE! #VALUE! #VALUE!v/s 1500 7 #VALUE! #VALUE! #VALUE! #VALUE!

14 #VALUE! #VALUE! #VALUE! #VALUE!Creep 0.66 (2-21a) 28 #VALUE! #VALUE! #VALUE! #VALUE!Shrinkage 0.20 (2-22a) 56 #VALUE! #VALUE! #VALUE! #VALUE!

100 #VALUE! #VALUE! #VALUE! #VALUE!Factored creep #VALUE! 500 #VALUE! #VALUE! #VALUE! #VALUE!Factored shrinkage #VALUE! 1000 #VALUE! #VALUE! #VALUE! #VALUE!

5000 #VALUE! #VALUE! #VALUE! #VALUE!Corrected ultimate strain #VALUE! 10000 #VALUE! #VALUE! #VALUE! #VALUE!

Length 245 mTime to restraint 28 days

Restraint Temperature #VALUE!Exposure condition10,000 day temperature #VALUE!

Total Temperature #VALUE! Dry air or protective membrane 0.41Equivalent Imposed Strain #VALUE! Humidity, moist air, soil 0.3Creep Coefficient #VALUE! Deicing chemicals 0.18

Seawater and seawater spray, wetting & drying 0.15 Spreadsheet version 1.00Linear Elastic Restraint Calculations Water-retaining structures 0.1 Based on AE spreadheetFully RestrainedStress (MPa) #VALUE!Design Strain #VALUE!Fully ReleasedShortening (mm) #VALUE!Design Strain 0.000000

Effects of creep, shrinkage, and temperature in concrete slabs

°C°C

ΔT °C

Relative humidity

(%)Creep γλ Shrinkage γλ

Moist curing duration (days)

Shrinkage γCP

1. 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 Strain (ϵsh)t

Equivalent temperature change ° C

Total temp ° C

Creep factor vt

mm3

mm2

ACI 224R-01 -Table 4.1 Guide to reasonable* crack widths, reinforced concrete under service loads

°C Crack width (mm)°C

°C

* 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.

0 1000 2000 3000 4000 5000 6000 7000 8000 9000100000.00000

2.00000

4.00000

6.00000

8.00000

10.00000

12.00000Shrinkage Strain (ϵsh)t

Shrinkage Strain (ϵsh)t

0 20 40 60 800.6000000000000010.7000000000000010.8000000000000010.900000000000001

11.11.21.31.4

Correction factor for initial curing γCP

Days

0% 10% 20% 30% 40% 50% 60% 70% 80% 90%100%0

0.2

0.4

0.6

0.8

1

1.2

Correction factors for relative humidity

Creep γλ

Shrinkage γλ

Page 8: ACI Shrinkage Calculation.xls

Cracking calculation based on "Shrinkage Cracking in Fully Restrained Concrete Members" by R. Ian Gilbert - March-April 1992 ACI Structural Journal

Restrain Th

Spacing Area Bar Ab As/m (T+B) Ag ρ Approx so C1 Ncr ξ s C2 N stress s2* stress s1* stress c1* Crack width

Eqn. 1 Eqn. 22 Eqn. 6 Eqn. 12 Eqn. 9 Eqn. 19 Eqn. 28 Eqn. 27 Eqn. 16 Eqn. 25 Eqn. 17 Eqn. 15 Eqn. 23 Eqn. 30mm mm mm mm MPa MPa MPa mm m MPa MPa MPa mm

100% 1500 12 300 113 754 1,500,000 0.05% #VALUE! 2,387 #VALUE! #VALUE! 0.006539 1,065,607 0.715 1.357 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!95% 1500 12 300 113 754 1,500,000 0.05% #VALUE! 2,387 #VALUE! #VALUE! 0.006539 1,065,607 0.715 1.357 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!90% 1500 12 300 113 754 1,500,000 0.05% #VALUE! 2,387 #VALUE! #VALUE! 0.006539 1,065,607 0.715 1.357 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!85% 1500 12 300 113 754 1,500,000 0.05% #VALUE! 2,387 #VALUE! #VALUE! 0.006539 1,065,607 0.715 1.357 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!80% 1500 12 300 113 754 1,500,000 0.05% #VALUE! 2,387 #VALUE! #VALUE! 0.006539 1,065,607 0.715 1.357 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!75% 1500 12 300 113 754 1,500,000 0.05% #VALUE! 2,387 #VALUE! #VALUE! 0.006539 1,065,607 0.715 1.357 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!70% 1500 12 300 113 754 1,500,000 0.05% #VALUE! 2,387 #VALUE! #VALUE! 0.006539 1,065,607 0.715 1.357 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!65% 1500 12 300 113 754 1,500,000 0.05% #VALUE! 2,387 #VALUE! #VALUE! 0.006539 1,065,607 0.715 1.357 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!60% 1500 12 300 113 754 1,500,000 0.05% #VALUE! 2,387 #VALUE! #VALUE! 0.006539 1,065,607 0.715 1.357 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!55% 1500 12 300 113 754 1,500,000 0.05% #VALUE! 2,387 #VALUE! #VALUE! 0.006539 1,065,607 0.715 1.357 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 1500 12 300 113 754 1,500,000 0.05% #VALUE! 2,387 #VALUE! #VALUE! 0.006539 1,065,607 0.715 1.357 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!45% 1500 12 300 113 754 1,500,000 0.05% #VALUE! 2,387 #VALUE! #VALUE! 0.006539 1,065,607 0.715 1.357 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!40% 1500 12 300 113 754 1,500,000 0.05% #VALUE! 2,387 #VALUE! #VALUE! 0.006539 1,065,607 0.715 1.357 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!35% 1500 12 300 113 754 1,500,000 0.05% #VALUE! 2,387 #VALUE! #VALUE! 0.006539 1,065,607 0.715 1.357 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!30% 1500 12 300 113 754 1,500,000 0.05% #VALUE! 2,387 #VALUE! #VALUE! 0.006539 1,065,607 0.715 1.357 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!25% 1500 12 300 113 754 1,500,000 0.05% #VALUE! 2,387 #VALUE! #VALUE! 0.006539 1,065,607 0.715 1.357 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!20% 1500 12 300 113 754 1,500,000 0.05% #VALUE! 2,387 #VALUE! #VALUE! 0.006539 1,065,607 0.715 1.357 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!15% 1500 12 300 113 754 1,500,000 0.05% #VALUE! 2,387 #VALUE! #VALUE! 0.006539 1,065,607 0.715 1.357 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!10% 1500 12 300 113 754 1,500,000 0.05% #VALUE! 2,387 #VALUE! #VALUE! 0.006539 1,065,607 0.715 1.357 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!5% 1500 12 300 113 754 1,500,000 0.05% #VALUE! 2,387 #VALUE! #VALUE! 0.006539 1,065,607 0.715 1.357 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!0% 1500 12 300 113 754 1,500,000 0.05% #VALUE! 2,387 #VALUE! #VALUE! 0.006539 1,065,607 0.715 1.357 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

Custom restrain50% 1500 12 300 113 754 1,500,000 0.05% #VALUE! 2,387 #VALUE! #VALUE! 0.006539 1,065,607 0.715 1.357 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

Restrain Th

Spacing Area Bar Ab As/m (T+B) Ag ρ Approx so C1 Ncr ξ s C2 N stress s2* stress s1* stress c1* Crack width

Eqn. 1 Eqn. 22 Eqn. 6 Eqn. 12 Eqn. 9 Eqn. 19 Eqn. 28 Eqn. 27 Eqn. 16 Eqn. 25 Eqn. 17 Eqn. 15 Eqn. 23 Eqn. 30mm mm mm mm MPa MPa MPa mm m MPa MPa MPa mm

50% 1500 12 50 113 4,524 1,500,000 0.30% #VALUE! 398 #VALUE! #VALUE! 0.001084 2,854,024 1.905 1.952 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 1500 12 75 113 3,016 1,500,000 0.20% #VALUE! 597 #VALUE! #VALUE! 0.001627 2,692,487 1.798 1.899 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 1500 12 100 113 2,262 1,500,000 0.15% #VALUE! 796 #VALUE! #VALUE! 0.002170 2,495,102 1.667 1.833 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 1500 12 125 113 1,810 1,500,000 0.12% #VALUE! 995 #VALUE! #VALUE! 0.002714 2,280,293 1.524 1.762 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 1500 12 150 113 1,508 1,500,000 0.10% #VALUE! 1,194 #VALUE! #VALUE! 0.003259 2,063,208 1.380 1.690 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 1500 12 175 113 1,293 1,500,000 0.09% #VALUE! 1,393 #VALUE! #VALUE! 0.003804 1,854,513 1.241 1.620 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 1500 12 200 113 1,131 1,500,000 0.08% #VALUE! 1,592 #VALUE! #VALUE! 0.004350 1,660,626 1.112 1.556 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 1500 12 225 113 1,005 1,500,000 0.07% #VALUE! 1,790 #VALUE! #VALUE! 0.004896 1,484,631 0.995 1.497 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 1500 12 250 113 905 1,500,000 0.06% #VALUE! 1,989 #VALUE! #VALUE! 0.005443 1,327,324 0.890 1.445 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 1500 12 275 113 823 1,500,000 0.05% #VALUE! 2,188 #VALUE! #VALUE! 0.005990 1,188,101 0.797 1.398 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 1500 12 300 113 754 1,500,000 0.05% #VALUE! 2,387 #VALUE! #VALUE! 0.006539 1,065,607 0.715 1.357 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

Custom reinforcement spacing50% 1500 12 200 113 1,131 1,500,000 0.08% #VALUE! 1,592 #VALUE! #VALUE! 0.004350 1,660,626 1.112 1.556 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

Bar Ø

Design Strain

Creep Adjusted Mod. E'c

Creep Adjusted

Modular Ratio, n*

Conc. Stress c1

Avg. Conc. Stress

Quantity of cracks

mm2 mm2/m mm2

Bar Ø

Design Strain

Creep Adjusted Mod. E'c

Creep Adjusted

Modular Ratio, n*

Conc. Stress c1

Avg. Conc. Stress

Quantity of cracks

mm2 mm2/m mm2

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%0.00

2.00

4.00

6.00

8.00

10.00

12.00w vs. restrain

Crack width

50%

25 75 125 175 225 275 325 3750.00

2.00

4.00

6.00

8.00

10.00

12.00w vs. reinf spacing

Crack width

200

Page 9: ACI Shrinkage Calculation.xls

Cracking calculation based on "Control of Flexural Cracking in Reinforced Concrete" by R. Ian Gilbert - May-June 2008 ACI Structural Journal

Design momentsService 445 kN.m

Restrain Th

Spacing Area Bar Ab As/m (T+B) Ag ρ Cover d Icr s*

Eqn. 22 Eqn. 8.6c Eqn. 8-7 Eqn. 1 Eqn. 8 Eqn. 9mm mm mm mm MPa mm mm mm mm mm MPa mm mm MPa

100% 1,500 16 200 201 1,005 1,500,000 0.07% #VALUE! 25 #VALUE! #VALUE! 1,467 138.43 -152.89 138.43 1.36E+10 680,787 0.00148 ### 312 #VALUE! 0.30 #VALUE! #VALUE!95% 1,500 16 200 201 1,005 1,500,000 0.07% #VALUE! 25 #VALUE! #VALUE! 1,467 138.43 -152.89 138.43 1.36E+10 680,787 0.00148 ### 312 #VALUE! 0.30 #VALUE! #VALUE!90% 1,500 16 200 201 1,005 1,500,000 0.07% #VALUE! 25 #VALUE! #VALUE! 1,467 138.43 -152.89 138.43 1.36E+10 680,787 0.00148 ### 312 #VALUE! 0.30 #VALUE! #VALUE!85% 1,500 16 200 201 1,005 1,500,000 0.07% #VALUE! 25 #VALUE! #VALUE! 1,467 138.43 -152.89 138.43 1.36E+10 680,787 0.00148 ### 312 #VALUE! 0.30 #VALUE! #VALUE!80% 1,500 16 200 201 1,005 1,500,000 0.07% #VALUE! 25 #VALUE! #VALUE! 1,467 138.43 -152.89 138.43 1.36E+10 680,787 0.00148 ### 312 #VALUE! 0.30 #VALUE! #VALUE!75% 1,500 16 200 201 1,005 1,500,000 0.07% #VALUE! 25 #VALUE! #VALUE! 1,467 138.43 -152.89 138.43 1.36E+10 680,787 0.00148 ### 312 #VALUE! 0.30 #VALUE! #VALUE!70% 1,500 16 200 201 1,005 1,500,000 0.07% #VALUE! 25 #VALUE! #VALUE! 1,467 138.43 -152.89 138.43 1.36E+10 680,787 0.00148 ### 312 #VALUE! 0.30 #VALUE! #VALUE!65% 1,500 16 200 201 1,005 1,500,000 0.07% #VALUE! 25 #VALUE! #VALUE! 1,467 138.43 -152.89 138.43 1.36E+10 680,787 0.00148 ### 312 #VALUE! 0.30 #VALUE! #VALUE!60% 1,500 16 200 201 1,005 1,500,000 0.07% #VALUE! 25 #VALUE! #VALUE! 1,467 138.43 -152.89 138.43 1.36E+10 680,787 0.00148 ### 312 #VALUE! 0.30 #VALUE! #VALUE!55% 1,500 16 200 201 1,005 1,500,000 0.07% #VALUE! 25 #VALUE! #VALUE! 1,467 138.43 -152.89 138.43 1.36E+10 680,787 0.00148 ### 312 #VALUE! 0.30 #VALUE! #VALUE!50% 1,500 16 200 201 1,005 1,500,000 0.07% #VALUE! 25 #VALUE! #VALUE! 1,467 138.43 -152.89 138.43 1.36E+10 680,787 0.00148 ### 312 #VALUE! 0.30 #VALUE! #VALUE!45% 1,500 16 200 201 1,005 1,500,000 0.07% #VALUE! 25 #VALUE! #VALUE! 1,467 138.43 -152.89 138.43 1.36E+10 680,787 0.00148 ### 312 #VALUE! 0.30 #VALUE! #VALUE!40% 1,500 16 200 201 1,005 1,500,000 0.07% #VALUE! 25 #VALUE! #VALUE! 1,467 138.43 -152.89 138.43 1.36E+10 680,787 0.00148 ### 312 #VALUE! 0.30 #VALUE! #VALUE!35% 1,500 16 200 201 1,005 1,500,000 0.07% #VALUE! 25 #VALUE! #VALUE! 1,467 138.43 -152.89 138.43 1.36E+10 680,787 0.00148 ### 312 #VALUE! 0.30 #VALUE! #VALUE!30% 1,500 16 200 201 1,005 1,500,000 0.07% #VALUE! 25 #VALUE! #VALUE! 1,467 138.43 -152.89 138.43 1.36E+10 680,787 0.00148 ### 312 #VALUE! 0.30 #VALUE! #VALUE!25% 1,500 16 200 201 1,005 1,500,000 0.07% #VALUE! 25 #VALUE! #VALUE! 1,467 138.43 -152.89 138.43 1.36E+10 680,787 0.00148 ### 312 #VALUE! 0.30 #VALUE! #VALUE!20% 1,500 16 200 201 1,005 1,500,000 0.07% #VALUE! 25 #VALUE! #VALUE! 1,467 138.43 -152.89 138.43 1.36E+10 680,787 0.00148 ### 312 #VALUE! 0.30 #VALUE! #VALUE!15% 1,500 16 200 201 1,005 1,500,000 0.07% #VALUE! 25 #VALUE! #VALUE! 1,467 138.43 -152.89 138.43 1.36E+10 680,787 0.00148 ### 312 #VALUE! 0.30 #VALUE! #VALUE!10% 1,500 16 200 201 1,005 1,500,000 0.07% #VALUE! 25 #VALUE! #VALUE! 1,467 138.43 -152.89 138.43 1.36E+10 680,787 0.00148 ### 312 #VALUE! 0.30 #VALUE! #VALUE!5% 1,500 16 200 201 1,005 1,500,000 0.07% #VALUE! 25 #VALUE! #VALUE! 1,467 138.43 -152.89 138.43 1.36E+10 680,787 0.00148 ### 312 #VALUE! 0.30 #VALUE! #VALUE!0% 1,500 16 200 201 1,005 1,500,000 0.07% #VALUE! 25 #VALUE! #VALUE! 1,467 138.43 -152.89 138.43 1.36E+10 680,787 0.00148 ### 312 #VALUE! 0.30 #VALUE! #VALUE!

Custom restrain75% 1,500 16 200 201 1,005 1,500,000 0.07% #VALUE! 25 #VALUE! #VALUE! 1,467 138.43 -152.89 138.43 1.36E+10 680,787 0.00148 ### 312 #VALUE! 0.30 #VALUE! #VALUE!

Bar Ø

Design Strain

Creep Adjusted Mod., E'c (EQN

22)

Creep Adjusted

Modular Ratio, nbar

Possible Depth to NA 1, c1

Possible Depth to NA 2, c2

Depth to NA, c (c1 or c2)

Concrete Crack Area, Act (EQN

1)

Reinf. Ratio to Act, rhotc

Actual Steel Stress, fa

Actual crack width

Acceptable crack width

Allowable Service Steel

Stress, fsService

Ratio (fa/fs)

mm2 mm2/m mm2 mm4 mm2

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%0.00

2.00

4.00

6.00

8.00

10.00

12.00w vs. restrain

Crack Width

75%

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%0.00

2.00

4.00

6.00

8.00

10.00

12.00w vs. restrain

Crack Width

75%

Page 10: ACI Shrinkage Calculation.xls

Shrinkage strain calculation and creep effects based on "Prediction of creep, shrinkage, and temperature effects in concrete structures" - ACI 209R-92

Material Propertiesf'c 50 MPa

f't (direct tensile strength) 2.39 MPa ACI 209R-92 - Eqn. 2-4Ec 33234 MPa

fy 420 MPa

Es 200000 MPan 6.02

alpha 0.00001 Spreadsheet version 1.00Temperature range 1000.0 Based on AE spreadheet

10.0Thickness 300 mmType Elevated Slab Table 2.5.4 Correction factors for Relative Humidity Table 2.5.3 Shrinkage correction factors for initial moist curing Steps for Considering Shrinkage and Thermal EffectsNo allowance for temp influences, slump, cement or air content.

Shrinkage Effects (ACI 209R-92) 0% 1 1 1 1.2Ultimate strain 0.00078 (2-6) 40% 1 1 3 1.1Initial moist curing duration 7 days 50% 0.94 0.9 7 1Curing correction factor 1 Table 2.5.3 60% 0.87 0.8 14 0.93Relative humidity 60% 70% 0.8 0.7 28 0.86Humidity correction factor #VALUE! Table 2.5.4 80% 0.73 0.6 90 0.75

90% 0.67 0.3100% 0.6 0

Creep Effects (ACI 209R-92)Creep Factor 2.35 (2-6)Humidity correction factor #VALUE! Table 2.5.4

Days

Volume 300 (2-9) (2-8)Surface 2 0 #VALUE! #VALUE! #VALUE! #VALUE!v/s 150 7 #VALUE! #VALUE! #VALUE! #VALUE!

14 #VALUE! #VALUE! #VALUE! #VALUE!Creep 0.69 (2-21a) 28 #VALUE! #VALUE! #VALUE! #VALUE!Shrinkage 0.59 (2-22a) 56 #VALUE! #VALUE! #VALUE! #VALUE!

90 #VALUE! #VALUE! #VALUE! #VALUE!Factored creep #VALUE! 1000 #VALUE! #VALUE! #VALUE! #VALUE!Factored shrinkage #VALUE! 2000 #VALUE! #VALUE! #VALUE! #VALUE!

3000 #VALUE! #VALUE! #VALUE! #VALUE!Corrected ultimate strain #VALUE! 10000 #VALUE! #VALUE! #VALUE! #VALUE!

Length 280 mTime to restraint 28 days

Restraint Temperature #VALUE!Exposure condition10,000 day temperature #VALUE!

Total Temperature #VALUE! Dry air or protective membrane 0.41Equivalent Imposed Strain #VALUE! Humidity, moist air, soil 0.3Creep Coefficient #VALUE! Deicing chemicals 0.18

Seawater and seawater spray, wetting & drying 0.15 Spreadsheet version 1.00Linear Elastic Restraint Calculations Water-retaining structures 0.1 Based on AE spreadheetFully RestrainedStress (MPa) #VALUE!Design Strain #VALUE!Fully ReleasedShortening (mm) #VALUE!Design Strain 0.000000

Effects of creep, shrinkage, and temperature in concrete slabs

°C°C

ΔT °C

Relative humidity

(%)Creep γλ Shrinkage γλ

Moist curing duration (days)

Shrinkage γCP

1. 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 Strain (ϵsh)t

Equivalent temperature change ° C

Total temp ° C

Creep factor vt

mm3

mm2

ACI 224R-01 -Table 4.1 Guide to reasonable* crack widths, reinforced concrete under service loads

°C Crack width (mm)°C

°C

* 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.

0 2000 4000 6000 8000 100000.00000

2.00000

4.00000

6.00000

8.00000

10.00000

12.00000Shrinkage Strain (ϵsh)t

Shrinkage Strain (ϵsh)t

0 20 40 60 800.6000000000000010.7000000000000010.8000000000000010.900000000000001

11.11.21.31.4

Correction factor for initial curing γCP

Days0% 10% 20% 30% 40% 50% 60% 70% 80% 90%100%

0

0.2

0.4

0.6

0.8

1

1.2

Correction factors for relative humidity

Creep γλ

Shrinkage γλ

Page 11: ACI Shrinkage Calculation.xls

Cracking calculation based on "Shrinkage Cracking in Fully Restrained Concrete Members" by R. Ian Gilbert - March-April 1992 ACI Structural Journal

Restrain Th

Spacing Area Bar Ab As/m (T+B) Ag ρ Approx so C1 Ncr ξ s C2 N stress s2* stress s1* stress c1* Crack width

Eqn. 1 Eqn. 22 Eqn. 6 Eqn. 12 Eqn. 9 Eqn. 19 Eqn. 28 Eqn. 27 Eqn. 16 Eqn. 25 Eqn. 17 Eqn. 15 Eqn. 23 Eqn. 30mm mm mm mm MPa MPa MPa mm m MPa MPa MPa mm

100% 300 20 250 314 2,513 300,000 0.84% #VALUE! 239 #VALUE! #VALUE! 0.000569 708,672 2.364 2.377 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!95% 300 20 250 314 2,513 300,000 0.84% #VALUE! 239 #VALUE! #VALUE! 0.000569 708,672 2.364 2.377 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!90% 300 20 250 314 2,513 300,000 0.84% #VALUE! 239 #VALUE! #VALUE! 0.000569 708,672 2.364 2.377 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!85% 300 20 250 314 2,513 300,000 0.84% #VALUE! 239 #VALUE! #VALUE! 0.000569 708,672 2.364 2.377 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!80% 300 20 250 314 2,513 300,000 0.84% #VALUE! 239 #VALUE! #VALUE! 0.000569 708,672 2.364 2.377 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!75% 300 20 250 314 2,513 300,000 0.84% #VALUE! 239 #VALUE! #VALUE! 0.000569 708,672 2.364 2.377 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!70% 300 20 250 314 2,513 300,000 0.84% #VALUE! 239 #VALUE! #VALUE! 0.000569 708,672 2.364 2.377 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!65% 300 20 250 314 2,513 300,000 0.84% #VALUE! 239 #VALUE! #VALUE! 0.000569 708,672 2.364 2.377 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!60% 300 20 250 314 2,513 300,000 0.84% #VALUE! 239 #VALUE! #VALUE! 0.000569 708,672 2.364 2.377 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!55% 300 20 250 314 2,513 300,000 0.84% #VALUE! 239 #VALUE! #VALUE! 0.000569 708,672 2.364 2.377 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 300 20 250 314 2,513 300,000 0.84% #VALUE! 239 #VALUE! #VALUE! 0.000569 708,672 2.364 2.377 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!45% 300 20 250 314 2,513 300,000 0.84% #VALUE! 239 #VALUE! #VALUE! 0.000569 708,672 2.364 2.377 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!40% 300 20 250 314 2,513 300,000 0.84% #VALUE! 239 #VALUE! #VALUE! 0.000569 708,672 2.364 2.377 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!35% 300 20 250 314 2,513 300,000 0.84% #VALUE! 239 #VALUE! #VALUE! 0.000569 708,672 2.364 2.377 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!30% 300 20 250 314 2,513 300,000 0.84% #VALUE! 239 #VALUE! #VALUE! 0.000569 708,672 2.364 2.377 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!25% 300 20 250 314 2,513 300,000 0.84% #VALUE! 239 #VALUE! #VALUE! 0.000569 708,672 2.364 2.377 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!20% 300 20 250 314 2,513 300,000 0.84% #VALUE! 239 #VALUE! #VALUE! 0.000569 708,672 2.364 2.377 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!15% 300 20 250 314 2,513 300,000 0.84% #VALUE! 239 #VALUE! #VALUE! 0.000569 708,672 2.364 2.377 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!10% 300 20 250 314 2,513 300,000 0.84% #VALUE! 239 #VALUE! #VALUE! 0.000569 708,672 2.364 2.377 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!5% 300 20 250 314 2,513 300,000 0.84% #VALUE! 239 #VALUE! #VALUE! 0.000569 708,672 2.364 2.377 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!0% 300 20 250 314 2,513 300,000 0.84% #VALUE! 239 #VALUE! #VALUE! 0.000569 708,672 2.364 2.377 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

Custom restrain50% 300 20 250 314 2,513 300,000 0.84% #VALUE! 239 #VALUE! #VALUE! 0.000569 708,672 2.364 2.377 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

Restrain Th

Spacing Area Bar Ab As/m (T+B) Ag ρ Approx so C1 Ncr ξ s C2 N stress s2* stress s1* stress c1* Crack width

Eqn. 1 Eqn. 22 Eqn. 6 Eqn. 12 Eqn. 9 Eqn. 19 Eqn. 28 Eqn. 27 Eqn. 16 Eqn. 25 Eqn. 17 Eqn. 15 Eqn. 23 Eqn. 30mm mm mm mm MPa MPa MPa mm m MPa MPa MPa mm

50% 300 20 50 314 12,566 300,000 4.19% #VALUE! 48 #VALUE! #VALUE! 0.000114 716,664 2.389 2.390 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 300 20 75 314 8,378 300,000 2.79% #VALUE! 72 #VALUE! #VALUE! 0.000171 716,220 2.388 2.389 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 300 20 100 314 6,283 300,000 2.09% #VALUE! 95 #VALUE! #VALUE! 0.000227 715,615 2.386 2.388 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 300 20 125 314 5,027 300,000 1.68% #VALUE! 119 #VALUE! #VALUE! 0.000284 714,850 2.384 2.387 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 300 20 150 314 4,189 300,000 1.40% #VALUE! 143 #VALUE! #VALUE! 0.000341 713,927 2.381 2.385 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 300 20 175 314 3,590 300,000 1.20% #VALUE! 167 #VALUE! #VALUE! 0.000398 712,846 2.377 2.384 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 300 20 200 314 3,142 300,000 1.05% #VALUE! 191 #VALUE! #VALUE! 0.000455 711,608 2.373 2.382 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 300 20 225 314 2,793 300,000 0.93% #VALUE! 215 #VALUE! #VALUE! 0.000512 710,216 2.369 2.379 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 300 20 250 314 2,513 300,000 0.84% #VALUE! 239 #VALUE! #VALUE! 0.000569 708,672 2.364 2.377 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 300 20 275 314 2,285 300,000 0.76% #VALUE! 263 #VALUE! #VALUE! 0.000626 706,976 2.358 2.374 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 300 20 300 314 2,094 300,000 0.70% #VALUE! 286 #VALUE! #VALUE! 0.000683 705,132 2.352 2.371 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

Custom reinforcement spacing50% 300 20 200 314 3,142 300,000 1.05% #VALUE! 191 #VALUE! #VALUE! 0.000455 711,608 2.373 2.382 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

Bar Ø

Design Strain

Creep Adjusted Mod. E'c

Creep Adjusted

Modular Ratio, n*

Conc. Stress c1

Avg. Conc. Stress

Quantity of cracks

mm2 mm2/m mm2

Bar Ø

Design Strain

Creep Adjusted Mod. E'c

Creep Adjusted

Modular Ratio, n*

Conc. Stress c1

Avg. Conc. Stress

Quantity of cracks

mm2 mm2/m mm2

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%0.00

2.00

4.00

6.00

8.00

10.00

12.00w vs. restrain

Crack width

50%

25 75 125 175 225 275 325 3750.00

2.00

4.00

6.00

8.00

10.00

12.00w vs. reinf spacing

Crack width

200

Page 12: ACI Shrinkage Calculation.xls

Cracking calculation based on "Control of Flexural Cracking in Reinforced Concrete" by R. Ian Gilbert - May-June 2008 ACI Structural Journal

Design momentsService 445 kN.m

Restrain Th

Spacing Area Bar Ab As/m (T+B) Ag ρ Cover d Icr s*

Eqn. 22 Eqn. 8.6c Eqn. 8-7 Eqn. 1 Eqn. 8 Eqn. 9mm mm mm mm MPa mm mm mm mm mm MPa mm mm MPa

100% 300 25 250 491 1,963 300,000 0.65% #VALUE! 25 #VALUE! #VALUE! 263 66.95 -90.58 66.95 5.52E+08 116,527 0.01685 247.28 949 #VALUE! 0.30 #VALUE! #VALUE!95% 300 25 250 491 1,963 300,000 0.65% #VALUE! 25 #VALUE! #VALUE! 263 66.95 -90.58 66.95 5.52E+08 116,527 0.01685 247.28 949 #VALUE! 0.30 #VALUE! #VALUE!90% 300 25 250 491 1,963 300,000 0.65% #VALUE! 25 #VALUE! #VALUE! 263 66.95 -90.58 66.95 5.52E+08 116,527 0.01685 247.28 949 #VALUE! 0.30 #VALUE! #VALUE!85% 300 25 250 491 1,963 300,000 0.65% #VALUE! 25 #VALUE! #VALUE! 263 66.95 -90.58 66.95 5.52E+08 116,527 0.01685 247.28 949 #VALUE! 0.30 #VALUE! #VALUE!80% 300 25 250 491 1,963 300,000 0.65% #VALUE! 25 #VALUE! #VALUE! 263 66.95 -90.58 66.95 5.52E+08 116,527 0.01685 247.28 949 #VALUE! 0.30 #VALUE! #VALUE!75% 300 25 250 491 1,963 300,000 0.65% #VALUE! 25 #VALUE! #VALUE! 263 66.95 -90.58 66.95 5.52E+08 116,527 0.01685 247.28 949 #VALUE! 0.30 #VALUE! #VALUE!70% 300 25 250 491 1,963 300,000 0.65% #VALUE! 25 #VALUE! #VALUE! 263 66.95 -90.58 66.95 5.52E+08 116,527 0.01685 247.28 949 #VALUE! 0.30 #VALUE! #VALUE!65% 300 25 250 491 1,963 300,000 0.65% #VALUE! 25 #VALUE! #VALUE! 263 66.95 -90.58 66.95 5.52E+08 116,527 0.01685 247.28 949 #VALUE! 0.30 #VALUE! #VALUE!60% 300 25 250 491 1,963 300,000 0.65% #VALUE! 25 #VALUE! #VALUE! 263 66.95 -90.58 66.95 5.52E+08 116,527 0.01685 247.28 949 #VALUE! 0.30 #VALUE! #VALUE!55% 300 25 250 491 1,963 300,000 0.65% #VALUE! 25 #VALUE! #VALUE! 263 66.95 -90.58 66.95 5.52E+08 116,527 0.01685 247.28 949 #VALUE! 0.30 #VALUE! #VALUE!50% 300 25 250 491 1,963 300,000 0.65% #VALUE! 25 #VALUE! #VALUE! 263 66.95 -90.58 66.95 5.52E+08 116,527 0.01685 247.28 949 #VALUE! 0.30 #VALUE! #VALUE!45% 300 25 250 491 1,963 300,000 0.65% #VALUE! 25 #VALUE! #VALUE! 263 66.95 -90.58 66.95 5.52E+08 116,527 0.01685 247.28 949 #VALUE! 0.30 #VALUE! #VALUE!40% 300 25 250 491 1,963 300,000 0.65% #VALUE! 25 #VALUE! #VALUE! 263 66.95 -90.58 66.95 5.52E+08 116,527 0.01685 247.28 949 #VALUE! 0.30 #VALUE! #VALUE!35% 300 25 250 491 1,963 300,000 0.65% #VALUE! 25 #VALUE! #VALUE! 263 66.95 -90.58 66.95 5.52E+08 116,527 0.01685 247.28 949 #VALUE! 0.30 #VALUE! #VALUE!30% 300 25 250 491 1,963 300,000 0.65% #VALUE! 25 #VALUE! #VALUE! 263 66.95 -90.58 66.95 5.52E+08 116,527 0.01685 247.28 949 #VALUE! 0.30 #VALUE! #VALUE!25% 300 25 250 491 1,963 300,000 0.65% #VALUE! 25 #VALUE! #VALUE! 263 66.95 -90.58 66.95 5.52E+08 116,527 0.01685 247.28 949 #VALUE! 0.30 #VALUE! #VALUE!20% 300 25 250 491 1,963 300,000 0.65% #VALUE! 25 #VALUE! #VALUE! 263 66.95 -90.58 66.95 5.52E+08 116,527 0.01685 247.28 949 #VALUE! 0.30 #VALUE! #VALUE!15% 300 25 250 491 1,963 300,000 0.65% #VALUE! 25 #VALUE! #VALUE! 263 66.95 -90.58 66.95 5.52E+08 116,527 0.01685 247.28 949 #VALUE! 0.30 #VALUE! #VALUE!10% 300 25 250 491 1,963 300,000 0.65% #VALUE! 25 #VALUE! #VALUE! 263 66.95 -90.58 66.95 5.52E+08 116,527 0.01685 247.28 949 #VALUE! 0.30 #VALUE! #VALUE!5% 300 25 250 491 1,963 300,000 0.65% #VALUE! 25 #VALUE! #VALUE! 263 66.95 -90.58 66.95 5.52E+08 116,527 0.01685 247.28 949 #VALUE! 0.30 #VALUE! #VALUE!0% 300 25 250 491 1,963 300,000 0.65% #VALUE! 25 #VALUE! #VALUE! 263 66.95 -90.58 66.95 5.52E+08 116,527 0.01685 247.28 949 #VALUE! 0.30 #VALUE! #VALUE!

Custom restrain75% 300 25 250 491 1,963 300,000 0.65% #VALUE! 25 #VALUE! #VALUE! 263 66.95 -90.58 66.95 5.52E+08 116,527 0.01685 247.28 949 #VALUE! 0.30 #VALUE! #VALUE!

Bar Ø

Design Strain

Creep Adjusted Mod., E'c (EQN

22)

Creep Adjusted

Modular Ratio, nbar

Possible Depth to NA 1, c1

Possible Depth to NA 2, c2

Depth to NA, c (c1 or c2)

Concrete Crack Area, Act (EQN

1)

Reinf. Ratio to Act, rhotc

Actual Steel Stress, fa

Actual crack width

Acceptable crack width

Allowable Service Steel

Stress, fsService

Ratio (fa/fs)

mm2 mm2/m mm2 mm4 mm2

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%0.00

2.00

4.00

6.00

8.00

10.00

12.00w vs. restrain

Crack Width

75%

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%0.00

2.00

4.00

6.00

8.00

10.00

12.00w vs. restrain

Crack Width

75%

Page 13: ACI Shrinkage Calculation.xls

Shrinkage strain calculation and creep effects based on "Prediction of creep, shrinkage, and temperature effects in concrete structures" - ACI 209R-92

Material Propertiesf'c 45 MPa

f't (direct tensile strength) 2.27 MPa ACI 209R-92 - Eqn. 2-4Ec 31529 MPa

fy 460 MPa

Es 200000 MPan 6.34

alpha 0.000009 Spreadsheet version 1.00Temperature range 30.0 Based on AE spreadheet

15.0Thickness 400 mmType Elevated Slab Table 2.5.4 Correction factors for Relative Humidity Table 2.5.3 Shrinkage correction factors for initial moist curing Steps for Considering Shrinkage and Thermal Effects

Shrinkage Effects (ACI 209R-92) 0% 1 1 1 1.2Ultimate strain 0.00078 (2-6) 40% 1 1 3 1.1Initial moist curing duration 7 days 50% 0.94 0.9 7 1Curing correction factor 1 Table 2.5.3 60% 0.87 0.8 14 0.93Relative humidity 65% 70% 0.8 0.7 28 0.86Humidity correction factor #VALUE! Table 2.5.4 80% 0.73 0.6 90 0.75

90% 0.67 0.3100% 0.6 0

Creep Effects (ACI 209R-92)Creep Factor 2.35 (2-6)Humidity correction factor #VALUE! Table 2.5.4

Days Total temp

Volume 400 (2-9) (2-8)Surface 2 0 #VALUE! #VALUE! #VALUE! #VALUE!v/s 200 7 #VALUE! #VALUE! #VALUE! #VALUE!

14 #VALUE! #VALUE! #VALUE! #VALUE!Creep 0.670532 (2-21a) 28 #VALUE! #VALUE! #VALUE! #VALUE!Shrinkage 0.466882 (2-22a) 56 #VALUE! #VALUE! #VALUE! #VALUE!

100 #VALUE! #VALUE! #VALUE! #VALUE!Factored creep #VALUE! 500 #VALUE! #VALUE! #VALUE! #VALUE!Factored shrinkage #VALUE! 1000 #VALUE! #VALUE! #VALUE! #VALUE!

5000 #VALUE! #VALUE! #VALUE! #VALUE!Ultimate strain #VALUE! 10000 #VALUE! #VALUE! #VALUE! #VALUE!

Length 75 mTime to restraint 28 days

Restraint Temperature #VALUE!Exposure condition10,000 day temperature #VALUE!

Total Temperature #VALUE! Dry air or protective membrane 0.41Equivalent Imposed Strain #VALUE! Humidity, moist air, soil 0.3Creep Coefficient #VALUE! Deicing chemicals 0.18

Seawater and seawater spray, wetting & drying 0.15 Spreadsheet version 1.00Linear Elastic Restraint Calculations Water-retaining structures 0.1 Based on AE spreadheetFully RestrainedStress (Mpa) #VALUE!Design Strain #VALUE!Fully ReleasedShortening (mm) #VALUE!Design Strain 0.000000

Effects of creep, shrinkage, and temperature in concrete slabs

°C°C

ΔT °C

Relative humidity

(%)Creep γλ Shrinkage γλ

Moist curing duration (days)

Shrinkage γCP

1. 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 Strain

Equivalent temperature

change

Creep factor

mm3

mm2

ACI 224R-01 -Table 4.1 Guide to reasonable* crack widths, reinforced concrete under service loads

°C Crack width (mm)°C

°C

* 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.

0 2000 4000 6000 8000 100000.00000

2.00000

4.00000

6.00000

8.00000

10.00000

12.00000Shrinkage Strain

Shrinkage Strain

0 20 40 60 800.60.7

0.8000000000000010.900000000000001

11.11.21.31.4

Correction factor for initial curing γCP

Days0% 10% 20% 30% 40% 50% 60% 70% 80% 90%100%

0

0.2

0.4

0.6

0.8

1

1.2

Correction factors for relative humidity

Creep γλ

Shrinkage γλ

Page 14: ACI Shrinkage Calculation.xls

Cracking calculation based on "Shrinkage Cracking in Fully Restrained Concrete Members" by R. Ian Gilbert - March-April 1992 ACI Structural Journal

Restrain Th

Spacing Area Bar Ab As/m (T+B) Ag ρ Approx so C1 Ncr ξ s C2 N stress s2* stress s1* stress c1* Crack width

Eqn. 1 Eqn. 22 Eqn. 6 Eqn. 12 Eqn. 9 Eqn. 19 Eqn. 28 Eqn. 27 Eqn. 16 Eqn. 25 Eqn. 17 Eqn. 15 Eqn. 23 Eqn. 30mm mm mm mm MPa MPa MPa mm m MPa MPa MPa mm

100% 400 16 200 201 2,011 400,000 0.50% #VALUE! 318 #VALUE! #VALUE! 0.002837 830,745 2.083 2.175 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!95% 400 16 200 201 2,011 400,000 0.50% #VALUE! 318 #VALUE! #VALUE! 0.002837 830,745 2.083 2.175 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!90% 400 16 200 201 2,011 400,000 0.50% #VALUE! 318 #VALUE! #VALUE! 0.002837 830,745 2.083 2.175 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!85% 400 16 200 201 2,011 400,000 0.50% #VALUE! 318 #VALUE! #VALUE! 0.002837 830,745 2.083 2.175 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!80% 400 16 200 201 2,011 400,000 0.50% #VALUE! 318 #VALUE! #VALUE! 0.002837 830,745 2.083 2.175 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!75% 400 16 200 201 2,011 400,000 0.50% #VALUE! 318 #VALUE! #VALUE! 0.002837 830,745 2.083 2.175 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!70% 400 16 200 201 2,011 400,000 0.50% #VALUE! 318 #VALUE! #VALUE! 0.002837 830,745 2.083 2.175 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!65% 400 16 200 201 2,011 400,000 0.50% #VALUE! 318 #VALUE! #VALUE! 0.002837 830,745 2.083 2.175 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!60% 400 16 200 201 2,011 400,000 0.50% #VALUE! 318 #VALUE! #VALUE! 0.002837 830,745 2.083 2.175 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!55% 400 16 200 201 2,011 400,000 0.50% #VALUE! 318 #VALUE! #VALUE! 0.002837 830,745 2.083 2.175 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 400 16 200 201 2,011 400,000 0.50% #VALUE! 318 #VALUE! #VALUE! 0.002837 830,745 2.083 2.175 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!45% 400 16 200 201 2,011 400,000 0.50% #VALUE! 318 #VALUE! #VALUE! 0.002837 830,745 2.083 2.175 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!40% 400 16 200 201 2,011 400,000 0.50% #VALUE! 318 #VALUE! #VALUE! 0.002837 830,745 2.083 2.175 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!35% 400 16 200 201 2,011 400,000 0.50% #VALUE! 318 #VALUE! #VALUE! 0.002837 830,745 2.083 2.175 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!30% 400 16 200 201 2,011 400,000 0.50% #VALUE! 318 #VALUE! #VALUE! 0.002837 830,745 2.083 2.175 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!25% 400 16 200 201 2,011 400,000 0.50% #VALUE! 318 #VALUE! #VALUE! 0.002837 830,745 2.083 2.175 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!20% 400 16 200 201 2,011 400,000 0.50% #VALUE! 318 #VALUE! #VALUE! 0.002837 830,745 2.083 2.175 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!15% 400 16 200 201 2,011 400,000 0.50% #VALUE! 318 #VALUE! #VALUE! 0.002837 830,745 2.083 2.175 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!10% 400 16 200 201 2,011 400,000 0.50% #VALUE! 318 #VALUE! #VALUE! 0.002837 830,745 2.083 2.175 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!5% 400 16 200 201 2,011 400,000 0.50% #VALUE! 318 #VALUE! #VALUE! 0.002837 830,745 2.083 2.175 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!0% 400 16 200 201 2,011 400,000 0.50% #VALUE! 318 #VALUE! #VALUE! 0.002837 830,745 2.083 2.175 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

Custom restrain50% 400 16 200 201 2,011 400,000 0.50% #VALUE! 318 #VALUE! #VALUE! 0.002837 830,745 2.083 2.175 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

Restrain Th

Spacing Area Bar Ab As/m (T+B) Ag ρ Approx so C1 Ncr ξ s C2 N stress s2* stress s1* stress c1* Crack width

Eqn. 1 Eqn. 22 Eqn. 6 Eqn. 12 Eqn. 9 Eqn. 19 Eqn. 28 Eqn. 27 Eqn. 16 Eqn. 25 Eqn. 17 Eqn. 15 Eqn. 23 Eqn. 30mm mm mm mm MPa MPa MPa mm m MPa MPa MPa mm

50% 400 16 50 201 8,042 400,000 2.01% #VALUE! 80 #VALUE! #VALUE! 0.000708 901,388 2.255 2.261 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 400 16 75 201 5,362 400,000 1.34% #VALUE! 119 #VALUE! #VALUE! 0.001062 894,899 2.240 2.254 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 400 16 100 201 4,021 400,000 1.01% #VALUE! 159 #VALUE! #VALUE! 0.001417 886,088 2.218 2.243 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 400 16 125 201 3,217 400,000 0.80% #VALUE! 199 #VALUE! #VALUE! 0.001772 875,092 2.192 2.230 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 400 16 150 201 2,681 400,000 0.67% #VALUE! 239 #VALUE! #VALUE! 0.002127 862,074 2.160 2.214 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 400 16 175 201 2,298 400,000 0.57% #VALUE! 279 #VALUE! #VALUE! 0.002482 847,224 2.123 2.195 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 400 16 200 201 2,011 400,000 0.50% #VALUE! 318 #VALUE! #VALUE! 0.002837 830,745 2.083 2.175 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 400 16 225 201 1,787 400,000 0.45% #VALUE! 358 #VALUE! #VALUE! 0.003193 812,852 2.039 2.153 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 400 16 250 201 1,608 400,000 0.40% #VALUE! 398 #VALUE! #VALUE! 0.003549 793,765 1.991 2.130 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 400 16 275 201 1,462 400,000 0.37% #VALUE! 438 #VALUE! #VALUE! 0.003906 773,699 1.942 2.105 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!50% 400 16 300 201 1,340 400,000 0.34% #VALUE! 477 #VALUE! #VALUE! 0.004262 752,864 1.890 2.079 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

Custom reinforcement spacing50% 400 16 200 201 2,011 400,000 0.50% #VALUE! 318 #VALUE! #VALUE! 0.002837 830,745 2.083 2.175 #VALUE! #VALUE! #VALUE! ### #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

Bar Ø

Design Strain

Creep Adjusted Mod. E'c

Creep Adjusted

Modular Ratio, n*

Conc. Stress c1

Avg. Conc. Stress

Quantity of cracks

mm2 mm2/m mm2

Bar Ø

Design Strain

Creep Adjusted Mod. E'c

Creep Adjusted

Modular Ratio, n*

Conc. Stress c1

Avg. Conc. Stress

Quantity of cracks

mm2 mm2/m mm2

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%0.00

2.00

4.00

6.00

8.00

10.00

12.00w vs. restrain

Crack width

50%

25 75 125 175 225 275 325 3750.00

2.00

4.00

6.00

8.00

10.00

12.00w vs. reinf spacing

Crack width

200

Page 15: ACI Shrinkage Calculation.xls

Cracking calculation based on "Control of Flexural Cracking in Reinforced Concrete" by R. Ian Gilbert - May-June 2008 ACI Structural Journal

Design momentsService 445 kN.m

Restrain Th

Spacing Area Bar Ab As/m (T+B) Ag ρ Cover d Icr s*

Eqn. 22 Eqn. 8.6c Eqn. 8-7 Eqn. 1 Eqn. 8 Eqn. 9mm mm mm mm MPa mm mm mm mm mm MPa mm mm MPa

100% 400 16 200 201 1,005 400,000 0.25% #VALUE! 25 #VALUE! #VALUE! 367 62.04 -74.79 62.04 6.73E+08 168,980 0.00595 448.23 1,280 #VALUE! 0.30 #VALUE! #VALUE!95% 400 16 200 201 1,005 400,000 0.25% #VALUE! 25 #VALUE! #VALUE! 367 62.04 -74.79 62.04 6.73E+08 168,980 0.00595 448.23 1,280 #VALUE! 0.30 #VALUE! #VALUE!90% 400 16 200 201 1,005 400,000 0.25% #VALUE! 25 #VALUE! #VALUE! 367 62.04 -74.79 62.04 6.73E+08 168,980 0.00595 448.23 1,280 #VALUE! 0.30 #VALUE! #VALUE!85% 400 16 200 201 1,005 400,000 0.25% #VALUE! 25 #VALUE! #VALUE! 367 62.04 -74.79 62.04 6.73E+08 168,980 0.00595 448.23 1,280 #VALUE! 0.30 #VALUE! #VALUE!80% 400 16 200 201 1,005 400,000 0.25% #VALUE! 25 #VALUE! #VALUE! 367 62.04 -74.79 62.04 6.73E+08 168,980 0.00595 448.23 1,280 #VALUE! 0.30 #VALUE! #VALUE!75% 400 16 200 201 1,005 400,000 0.25% #VALUE! 25 #VALUE! #VALUE! 367 62.04 -74.79 62.04 6.73E+08 168,980 0.00595 448.23 1,280 #VALUE! 0.30 #VALUE! #VALUE!70% 400 16 200 201 1,005 400,000 0.25% #VALUE! 25 #VALUE! #VALUE! 367 62.04 -74.79 62.04 6.73E+08 168,980 0.00595 448.23 1,280 #VALUE! 0.30 #VALUE! #VALUE!65% 400 16 200 201 1,005 400,000 0.25% #VALUE! 25 #VALUE! #VALUE! 367 62.04 -74.79 62.04 6.73E+08 168,980 0.00595 448.23 1,280 #VALUE! 0.30 #VALUE! #VALUE!60% 400 16 200 201 1,005 400,000 0.25% #VALUE! 25 #VALUE! #VALUE! 367 62.04 -74.79 62.04 6.73E+08 168,980 0.00595 448.23 1,280 #VALUE! 0.30 #VALUE! #VALUE!55% 400 16 200 201 1,005 400,000 0.25% #VALUE! 25 #VALUE! #VALUE! 367 62.04 -74.79 62.04 6.73E+08 168,980 0.00595 448.23 1,280 #VALUE! 0.30 #VALUE! #VALUE!50% 400 16 200 201 1,005 400,000 0.25% #VALUE! 25 #VALUE! #VALUE! 367 62.04 -74.79 62.04 6.73E+08 168,980 0.00595 448.23 1,280 #VALUE! 0.30 #VALUE! #VALUE!45% 400 16 200 201 1,005 400,000 0.25% #VALUE! 25 #VALUE! #VALUE! 367 62.04 -74.79 62.04 6.73E+08 168,980 0.00595 448.23 1,280 #VALUE! 0.30 #VALUE! #VALUE!40% 400 16 200 201 1,005 400,000 0.25% #VALUE! 25 #VALUE! #VALUE! 367 62.04 -74.79 62.04 6.73E+08 168,980 0.00595 448.23 1,280 #VALUE! 0.30 #VALUE! #VALUE!35% 400 16 200 201 1,005 400,000 0.25% #VALUE! 25 #VALUE! #VALUE! 367 62.04 -74.79 62.04 6.73E+08 168,980 0.00595 448.23 1,280 #VALUE! 0.30 #VALUE! #VALUE!30% 400 16 200 201 1,005 400,000 0.25% #VALUE! 25 #VALUE! #VALUE! 367 62.04 -74.79 62.04 6.73E+08 168,980 0.00595 448.23 1,280 #VALUE! 0.30 #VALUE! #VALUE!25% 400 16 200 201 1,005 400,000 0.25% #VALUE! 25 #VALUE! #VALUE! 367 62.04 -74.79 62.04 6.73E+08 168,980 0.00595 448.23 1,280 #VALUE! 0.30 #VALUE! #VALUE!20% 400 16 200 201 1,005 400,000 0.25% #VALUE! 25 #VALUE! #VALUE! 367 62.04 -74.79 62.04 6.73E+08 168,980 0.00595 448.23 1,280 #VALUE! 0.30 #VALUE! #VALUE!15% 400 16 200 201 1,005 400,000 0.25% #VALUE! 25 #VALUE! #VALUE! 367 62.04 -74.79 62.04 6.73E+08 168,980 0.00595 448.23 1,280 #VALUE! 0.30 #VALUE! #VALUE!10% 400 16 200 201 1,005 400,000 0.25% #VALUE! 25 #VALUE! #VALUE! 367 62.04 -74.79 62.04 6.73E+08 168,980 0.00595 448.23 1,280 #VALUE! 0.30 #VALUE! #VALUE!5% 400 16 200 201 1,005 400,000 0.25% #VALUE! 25 #VALUE! #VALUE! 367 62.04 -74.79 62.04 6.73E+08 168,980 0.00595 448.23 1,280 #VALUE! 0.30 #VALUE! #VALUE!0% 400 16 200 201 1,005 400,000 0.25% #VALUE! 25 #VALUE! #VALUE! 367 62.04 -74.79 62.04 6.73E+08 168,980 0.00595 448.23 1,280 #VALUE! 0.30 #VALUE! #VALUE!

Custom restrain75% 400 16 200 201 1,005 400,000 0.25% #VALUE! 25 #VALUE! #VALUE! 367 62.04 -74.79 62.04 6.73E+08 168,980 0.00595 448.23 1,280 #VALUE! 0.30 #VALUE! #VALUE!

Bar Ø

Design Strain

Creep Adjusted Mod., E'c (EQN

22)

Creep Adjusted

Modular Ratio, nbar

Possible Depth to NA 1, c1

Possible Depth to NA 2, c2

Depth to NA, c (c1 or c2)

Concrete Crack Area, Act (EQN

1)

Reinf. Ratio to Act, rhotc

Actual Steel Stress, fa

Actual crack width

Acceptable crack width

Allowable Service Steel

Stress, fsService

Ratio (fa/fs)

mm2 mm2/m mm2 mm4 mm2

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%0.00

2.00

4.00

6.00

8.00

10.00

12.00w vs. restrain

Crack Width

75%

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%0.00

2.00

4.00

6.00

8.00

10.00

12.00w vs. restrain

Crack Width

75%


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