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 f't (direct tensile strength) Ec fy Es n alpha Temperature range ΔT Thickness Type
Shrinkage Effects (ACI 209R-92) Ultimate strain Initial moist curing duration Curing correction factor Relative humidity Humidity correction factor
Creep Effects (ACI 209R-92) Creep Factor Humidity correction factor
30 1.85 25743 500 200000 7.77 0.00001 20.0 10.0 250 Elevated Slab
0.00078 7 1 60% 0.8
MPa MPa MPa MPa MPa
Effects of creep, shrinkage, and temperature in concrete slabs
ACI 209R-92 - Eqn. 2-4
°C °C °C mm
Spreadsheet version 1.00 Based on AE spreadheet
Table 2.5.4 Correction factors for Relative Humidity
(2-6) days Table 2.5.3 Table 2.5.4
Relative humidity (%) 0% 40% 50% 60% 70% 80% 90% 100%
3 250 mm 2 2 mm 125
0.71 (2-21a) 0.67 (2-22a)
Factored creep Factored shrinkage
1.46 0.53 0.000415
Correction factors for relative humidity
Shrinkage γλ 1 1 0.9 0.8 0.7 0.6 0.3 0
1 3 7 14 28 90
1 0.8 0.6 Creep
0.4
γλ
0 7 14 28 56 100 500 1000 5000 10000
(2-9) 0.000000 0.000069 0.000119 0.000184 0.000255 0.000307 0.000388 0.000401 0.000412 0.000414
Equivalent temperature change ° C 0.00 -6.92 -11.86 -18.45 -25.54 -30.75 -38.79 -40.10 -41.22 -41.36
Restraint Temperature 10,000 day temperature Total Temperature Equivalent Imposed Strain Creep Coefficient Linear Elastic Restraint Calculations Fully Restrained Stress (MPa) Design Strain Fully Released Shortening (mm) Design Strain
50 m 28 days -18.448 °C -51.363 °C -32.915 °C -0.000329 0.782
20%
Total temp Creep factor vt °C -10.00 -16.92 -21.86 -28.45 -35.54 -40.75 -48.79 -50.10 -51.22 -51.36
(2-8) 0.000 0.354 0.477 0.618 0.769 0.893 1.174 1.257 1.373 1.400
40%
60%
-8.47 -0.000329 -16 0.000000
80%
Dry air or protective membrane Humidity, moist air, soil Deicing chemicals Seawater and seawater spray, wetting & drying Water-retaining structures
1.4 1.2
3. Determine Shrinkage with ACI 209R-92
0.00040 0.00035 0.00030 Shrinkage Strain (ϵsh)t
0.00010 0.00005 0.00000
Crack width (mm) 0.41 0.3 0.18 0.15 0.1
* 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.
4000
6000
8000
Days
4. Determine Creep Coefficient with ACI 209R-92
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.
0.00025
2000
50
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.
0.00045
0.00020 0.00015
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
1
0
100%
Shrinkage Strain (ϵsh)t
ACI 224R-01 -Table 4.1 Guide to reasonable* crack widths, reinforced concrete under service loads Exposure condition
Correction factor for initial curing γCP
0.6 0%
Shrinkage Strain (ϵsh)t
1.2 1.1 1 0.93 0.86 0.75
Steps for Considering Shrinkage and Thermal Effects
0.8
Shrinkage γλ
0.2
0 Length Time to restraint
Moist curing Shrinkage γCP duration (days)
1.2 1 1 0.94 0.87 0.8 0.73 0.67 0.6
2.35 (2-6) 0.87 Table 2.5.4
Creep Shrinkage
Corrected ultimate strain
γλ
0
Days Volume Surface v/s
Creep
Table 2.5.3 Shrinkage correction factors for initial moist curing
10000
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. Spreadsheet version 1.00 Based on AE spreadheet
Cracking calculation based on "Shrinkage Cracking in Fully Restrained Concrete Members" by R. Ian Gilbert - March-April 1992 ACI Structural Journal
w vs. restrain 0.06
0.04
0.03
0.02 Crack width 50%
0.01
0.00 0%
20%
40%
60%
80%
100%
0.10 0.08 0.06
Crack width
0.050
200
0.04
0.02 0.00 25
125
225
325
As/m (T+B)
Ag
ρ
Design Strain
Approx so
Th
Bar Ø
100% 95% 90% 85% 80% 75% 70% 65% 60% 55% 50% 45% 40% 35% 30% 25% 20% 15% 10% 5% 0%
mm 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250
mm 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25
mm 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200
mm2 491 491 491 491 491 491 491 491 491 491 491 491 491 491 491 491 491 491 491 491 491
mm2/m 4,909 4,909 4,909 4,909 4,909 4,909 4,909 4,909 4,909 4,909 4,909 4,909 4,909 4,909 4,909 4,909 4,909 4,909 4,909 4,909 4,909
mm2 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000
1.96% 1.96% 1.96% 1.96% 1.96% 1.96% 1.96% 1.96% 1.96% 1.96% 1.96% 1.96% 1.96% 1.96% 1.96% 1.96% 1.96% 1.96% 1.96% 1.96% 1.96%
-0.000329 -0.000313 -0.000296 -0.000280 -0.000263 -0.000247 -0.000230 -0.000214 -0.000197 -0.000181 -0.000165 -0.000148 -0.000132 -0.000115 -0.000099 -0.000082 -0.000066 -0.000049 -0.000033 -0.000016 0.000000
Eqn. 1 mm 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127
Custom restrain 50%
250
25
200
491
4,909
250,000
1.96%
-0.000165
127
Spacing
Area Bar Ab
As/m (T+B)
Ag
ρ
Design Strain
Approx so
w vs. reinf spacing 0.12
Area Bar Ab
Restrain 0.050
0.05
Spacing
Restrain
Th
Bar Ø
50% 50% 50% 50% 50% 50% 50% 50% 50% 50% 50%
mm 250 250 250 250 250 250 250 250 250 250 250
mm 25 25 25 25 25 25 25 25 25 25 25
mm 50 75 100 125 150 175 200 225 250 275 300
mm2 491 491 491 491 491 491 491 491 491 491 491
mm2/m 19,635 13,090 9,817 7,854 6,545 5,610 4,909 4,363 3,927 3,570 3,272
mm2 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000
7.85% 5.24% 3.93% 3.14% 2.62% 2.24% 1.96% 1.75% 1.57% 1.43% 1.31%
-0.000165 -0.000165 -0.000165 -0.000165 -0.000165 -0.000165 -0.000165 -0.000165 -0.000165 -0.000165 -0.000165
Eqn. 1 mm 32 48 64 80 95 111 127 143 159 175 191
Custom reinforcement spacing 250 50% 25
200
491
4,909
250,000
1.96%
-0.000165
127
Creep Adjusted Creep Adjusted Modular Ratio, Mod. E'c n* Eqn. 22 MPa 14,449 14 14,449 14 14,449 14 14,449 14 14,449 14 14,449 14 14,449 14 14,449 14 14,449 14 14,449 14 14,449 14 14,449 14 14,449 14 14,449 14 14,449 14 14,449 14 14,449 14 14,449 14 14,449 14 14,449 14 14,449 14
14,449
14
Creep Adjusted Creep Adjusted Modular Ratio, Mod. E'c n* Eqn. 22 MPa 14,449 14 14,449 14 14,449 14 14,449 14 14,449 14 14,449 14 14,449 14 14,449 14 14,449 14 14,449 14 14,449 14
14,449
14
C1
Ncr
Conc. Stress c1
Avg. Conc. Stress
ξ
s
Quantity of cracks
C2
N
stress s2*
stress s1*
stress c1*
Crack width
Eqn. 6
Eqn. 12
Eqn. 19 MPa 1.841 1.841 1.841 1.841 1.841 1.841 1.841 1.841 1.841 1.841 1.841 1.841 1.841 1.841 1.841 1.841 1.841 1.841 1.841 1.841 1.841
Eqn. 25
0.748 0.647 0.558 0.477 0.405 0.339 0.279 0.225 0.175 0.128 0.086 0.046 0.009 -0.025 -0.057 -0.087 -0.116 -0.142 -0.167 -0.191 -0.213
Eqn. 27 mm 198 216 237 263 295 335 389 463 571 747 1,078 1,935 9,470 -3,272 -1,395 -886 -650 -513 -423 -361 -314
Eqn. 16
456,994 456,994 456,994 456,994 456,994 456,994 456,994 456,994 456,994 456,994 456,994 456,994 456,994 456,994 456,994 456,994 456,994 456,994 456,994 456,994 456,994
Eqn. 9 MPa 1.831 1.831 1.831 1.831 1.831 1.831 1.831 1.831 1.831 1.831 1.831 1.831 1.831 1.831 1.831 1.831 1.831 1.831 1.831 1.831 1.831
Eqn. 28
0.001701 0.001701 0.001701 0.001701 0.001701 0.001701 0.001701 0.001701 0.001701 0.001701 0.001701 0.001701 0.001701 0.001701 0.001701 0.001701 0.001701 0.001701 0.001701 0.001701 0.001701
m 252 231 211 190 170 149 129 108 88 67 46 26 5 -15 -36 -56 -77 -98 -118 -139 -159
0.748 0.647 0.558 0.477 0.405 0.339 0.279 0.225 0.175 0.128 0.086 0.046 0.009 -0.025 -0.057 -0.087 -0.116 -0.142 -0.167 -0.191 -0.213
264,830 280,988 297,145 313,302 329,459 345,617 361,774 377,931 394,088 410,246 426,403 442,560 458,717 474,874 491,032 507,189 523,346 539,503 555,661 571,818 587,975
Eqn. 17 MPa 53.95 57.24 60.53 63.83 67.12 70.41 73.70 76.99 80.28 83.57 86.87 90.16 93.45 96.74 100.03 103.32 106.62 109.91 113.20 116.49 119.78
Eqn. 15 MPa -40.34 -37.05 -33.76 -30.47 -27.18 -23.89 -20.59 -17.30 -14.01 -10.72 -7.43 -4.14 -0.85 2.45 5.74 9.03 12.32 15.61 18.90 22.20 25.49
Eqn. 23 MPa 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85
Eqn. 30 mm 0.051 0.051 0.051 0.051 0.051 0.051 0.051 0.050 0.050 0.050 0.050 0.049 0.044 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.001701
456,994
1.831
1.841
0.086
1,078
46
0.086
426,403
86.87
-7.43
1.85
0.050
C1
Ncr
Conc. Stress c1
Avg. Conc. Stress
ξ
s
Quantity of cracks
C2
N
stress s2*
stress s1*
stress c1*
Crack width
Eqn. 6
Eqn. 12
Eqn. 19 MPa 1.851 1.850 1.849 1.847 1.846 1.844 1.841 1.839 1.836 1.832 1.829
Eqn. 25
0.448 0.260 0.184 0.142 0.116 0.098 0.086 0.076 0.068 0.062 0.057
Eqn. 27 mm 69 154 273 426 611 829 1,078 1,357 1,666 2,004 2,370
Eqn. 16
462,348 461,849 461,190 460,374 459,401 458,274 456,994 455,565 453,990 452,270 450,409
Eqn. 9 MPa 1.850 1.849 1.846 1.843 1.840 1.836 1.831 1.826 1.820 1.813 1.806
Eqn. 28
0.000425 0.000637 0.000850 0.001062 0.001275 0.001488 0.001701 0.001914 0.002127 0.002340 0.002553
m 729 325 183 117 82 60 46 37 30 25 21
0.448 0.260 0.184 0.142 0.116 0.098 0.086 0.076 0.068 0.062 0.057
319,607 367,215 390,975 405,197 414,650 421,378 426,403 430,293 433,389 435,908 437,994
Eqn. 17 MPa 16.28 28.05 39.82 51.59 63.35 75.11 86.87 98.62 110.36 122.10 133.84
Eqn. 15 MPa -7.30 -7.31 -7.32 -7.34 -7.37 -7.40 -7.43 -7.47 -7.51 -7.55 -7.60
Eqn. 23 MPa 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85
Eqn. 30 mm 0.005 0.010 0.015 0.022 0.030 0.040 0.050 0.062 0.074 0.088 0.102
0.001701
456,994
1.831
1.841
0.086
1,078
46
0.086
426,403
86.87
-7.43
1.85
0.050
Cracking calculation based on "Control of Flexural Cracking in Reinforced Concrete" by R. Ian Gilbert - May-June 2008 ACI Structural Journal Design moments Service
445 kN.m
w w vs. vs. restrain restrain 3.02 3.02 3.01 3.01 3.00 3.00 2.984
2.99 2.98 2.97 2.97 2.96 2.96 2.95 2.95 2.94 2.94
Crack Width Crack Width 75% 75%
2.93 2.93 2.92 2.92
2.91 2.91 0% 0%
20% 20%
40% 40%
60% 60%
80% 80%
100% 100%
Spacing
Area Bar Ab
As/m (T+B)
Ag
ρ
Restrain
Th
Bar Ø
100% 95% 90% 85% 80% 75% 70% 65% 60% 55% 50% 45% 40% 35% 30% 25% 20% 15% 10% 5% 0%
mm 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250
mm 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
mm 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200
mm2 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201
mm2/m 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005
mm2 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000
0.40% 0.40% 0.40% 0.40% 0.40% 0.40% 0.40% 0.40% 0.40% 0.40% 0.40% 0.40% 0.40% 0.40% 0.40% 0.40% 0.40% 0.40% 0.40% 0.40% 0.40%
Custom restrain 75%
250
16
200
201
1,005
250,000
0.40%
Design Strain
Cover
Creep Adjusted Creep Adjusted Mod., E'c (EQN Modular Ratio, 22) nbar
-0.000329 -0.000313 -0.000296 -0.000280 -0.000263 -0.000247 -0.000230 -0.000214 -0.000197 -0.000181 -0.000165 -0.000148 -0.000132 -0.000115 -0.000099 -0.000082 -0.000066 -0.000049 -0.000033 -0.000016 0.000000
mm 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25
Eqn. 22 MPa 14,449 14,449 14,449 14,449 14,449 14,449 14,449 14,449 14,449 14,449 14,449 14,449 14,449 14,449 14,449 14,449 14,449 14,449 14,449 14,449 14,449
-0.000247
25
14,449
d
Possible Depth Possible Depth Depth to NA, to NA 1, c1 to NA 2, c2 c (c1 or c2)
Icr
14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14
mm 217 217 217 217 217 217 217 217 217 217 217 217 217 217 217 217 217 217 217 217 217
mm 50.41 50.41 50.41 50.41 50.41 50.41 50.41 50.41 50.41 50.41 50.41 50.41 50.41 50.41 50.41 50.41 50.41 50.41 50.41 50.41 50.41
mm -66.03 -66.03 -66.03 -66.03 -66.03 -66.03 -66.03 -66.03 -66.03 -66.03 -66.03 -66.03 -66.03 -66.03 -66.03 -66.03 -66.03 -66.03 -66.03 -66.03 -66.03
Eqn. 8.6c mm 50.41 50.41 50.41 50.41 50.41 50.41 50.41 50.41 50.41 50.41 50.41 50.41 50.41 50.41 50.41 50.41 50.41 50.41 50.41 50.41 50.41
Eqn. 8-7 mm4 2.59E+08 2.59E+08 2.59E+08 2.59E+08 2.59E+08 2.59E+08 2.59E+08 2.59E+08 2.59E+08 2.59E+08 2.59E+08 2.59E+08 2.59E+08 2.59E+08 2.59E+08 2.59E+08 2.59E+08 2.59E+08 2.59E+08 2.59E+08 2.59E+08
14
217
50.41
-66.03
50.41
2.59E+08
Concrete Crack Area, Reinf. Ratio s* Act (EQN to Act, rhotc 1) Eqn. 1 Eqn. 8 mm mm2 99,794 0.01007 264.71 99,794 0.01007 264.71 99,794 0.01007 264.71 99,794 0.01007 264.71 99,794 0.01007 264.71 99,794 0.01007 264.71 99,794 0.01007 264.71 99,794 0.01007 264.71 99,794 0.01007 264.71 99,794 0.01007 264.71 99,794 0.01007 264.71 99,794 0.01007 264.71 99,794 0.01007 264.71 99,794 0.01007 264.71 99,794 0.01007 264.71 99,794 0.01007 264.71 99,794 0.01007 264.71 99,794 0.01007 264.71 99,794 0.01007 264.71 99,794 0.01007 264.71 99,794 0.01007 264.71
99,794
0.01007
264.71
Allowable Service Service Steel Ratio (fa/fs) Stress, fs
Actual Steel Stress, fa
Actual crack width
Acceptable crack width
MPa 2,220 2,220 2,220 2,220 2,220 2,220 2,220 2,220 2,220 2,220 2,220 2,220 2,220 2,220 2,220 2,220 2,220 2,220 2,220 2,220 2,220
mm 3.006 3.001 2.997 2.993 2.988 2.984 2.980 2.975 2.971 2.966 2.962 2.958 2.953 2.949 2.945 2.940 2.936 2.932 2.927 2.923 2.919
mm 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30
Eqn. 9 MPa 176 179 182 185 189 192 195 199 202 205 208 212 215 218 222 225 228 232 235 238 241
12.64 12.41 12.19 11.97 11.76 11.56 11.37 11.18 10.99 10.82 10.65 10.48 10.32 10.17 10.02 9.87 9.73 9.59 9.45 9.32 9.20
2,220
2.984
0.30
192
11.56
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 f't (direct tensile strength) Ec fy Es n alpha Temperature range ΔT Thickness Type
Shrinkage Effects (ACI 209R-92) Ultimate strain Initial moist curing duration Curing correction factor Relative humidity Humidity correction factor
Creep Effects (ACI 209R-92) Creep Factor Humidity correction factor
30 1.85 25743 500 200000 7.77 0.00001 10.0 5.0 300 Foundation Mat
0.00078 7 1 60% 0.8
MPa MPa MPa MPa MPa
Effects of creep, shrinkage, and temperature in concrete slabs
ACI 209R-92 - Eqn. 2-4
°C °C °C mm
Spreadsheet version 1.00 Based on AE spreadheet
Table 2.5.4 Correction factors for Relative Humidity
(2-6) days Table 2.5.3 Table 2.5.4
Relative humidity (%) 0% 40% 50% 60% 70% 80% 90% 100%
3 300 mm 2 1 mm 300
0.66 (2-21a) 0.29 (2-22a)
Factored creep Factored shrinkage
1.35 0.23 0.000182
Correction factors for relative humidity
Shrinkage γλ 1 1 0.9 0.8 0.7 0.6 0.3 0
1 3 7 14 28 90
1 0.8 0.6 Creep
0.4
γλ
0 7 14 28 56 100 500 1000 5000 10000
(2-9) 0.000000 0.000030 0.000052 0.000081 0.000112 0.000135 0.000170 0.000176 0.000180 0.000181
Equivalent temperature change ° C 0.00 -3.03 -5.19 -8.08 -11.18 -13.46 -16.98 -17.56 -18.05 -18.11
Restraint Temperature 10,000 day temperature Total Temperature Equivalent Imposed Strain Creep Coefficient Linear Elastic Restraint Calculations Fully Restrained Stress (MPa) Design Strain Fully Released Shortening (mm) Design Strain
12 m 28 days -8.076 °C -23.109 °C -15.032 °C -0.000150 0.726
20%
Total temp Creep factor vt °C -5.00 -8.03 -10.19 -13.08 -16.18 -18.46 -21.98 -22.56 -23.05 -23.11
(2-8) 0.000 0.329 0.443 0.574 0.714 0.829 1.090 1.167 1.275 1.300
40%
60%
-3.87 -0.000150 -2 0.000000
80%
Dry air or protective membrane Humidity, moist air, soil Deicing chemicals Seawater and seawater spray, wetting & drying Water-retaining structures
1.4 1.2
0.00020 0.00018 0.00016 0.00014 0.00012 0.00010 0.00008 0.00006 0.00004 0.00002 0.00000
3. Determine Shrinkage with ACI 209R-92
Crack width (mm) 0.41 0.3 0.18 0.15 0.1
* 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.
4000
6000
8000
50
Days
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.
Shrinkage Strain (ϵsh)t
2000
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
1
0
100%
Shrinkage Strain (ϵsh)t
ACI 224R-01 -Table 4.1 Guide to reasonable* crack widths, reinforced concrete under service loads Exposure condition
Correction factor for initial curing γCP
0.6 0%
Shrinkage Strain (ϵsh)t
1.2 1.1 1 0.93 0.86 0.75
Steps for Considering Shrinkage and Thermal Effects
0.8
Shrinkage γλ
0.2
0 Length Time to restraint
Moist curing Shrinkage γCP duration (days)
1.2 1 1 0.94 0.87 0.8 0.73 0.67 0.6
2.35 (2-6) 0.87 Table 2.5.4
Creep Shrinkage
Corrected ultimate strain
γλ
0
Days Volume Surface v/s
Creep
Table 2.5.3 Shrinkage correction factors for initial moist curing
10000
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. Spreadsheet version 1.00 Based on AE spreadheet
Cracking calculation based on "Shrinkage Cracking in Fully Restrained Concrete Members" by R. Ian Gilbert - March-April 1992 ACI Structural Journal
w vs. restrain 0.18
0.16
0.14
0.12
0.10
0.08
0.06 Crack width 50%
0.04
0.02 0.000 0.00 0%
20%
40%
60%
80%
100%
0.70 0.60 0.50
Crack width
0.40
200
0.30
0.20 0.10 0.00 25
125
0.000 225
325
As/m (T+B)
Ag
ρ
Design Strain
Approx so
Th
Bar Ø
100% 95% 90% 85% 80% 75% 70% 65% 60% 55% 50% 45% 40% 35% 30% 25% 20% 15% 10% 5% 0%
mm 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300
mm 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
mm 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200
mm2 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201
mm2/m 2,011 2,011 2,011 2,011 2,011 2,011 2,011 2,011 2,011 2,011 2,011 2,011 2,011 2,011 2,011 2,011 2,011 2,011 2,011 2,011 2,011
mm2 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000
0.67% 0.67% 0.67% 0.67% 0.67% 0.67% 0.67% 0.67% 0.67% 0.67% 0.67% 0.67% 0.67% 0.67% 0.67% 0.67% 0.67% 0.67% 0.67% 0.67% 0.67%
-0.000150 -0.000143 -0.000135 -0.000128 -0.000120 -0.000113 -0.000105 -0.000098 -0.000090 -0.000083 -0.000075 -0.000068 -0.000060 -0.000053 -0.000045 -0.000038 -0.000030 -0.000023 -0.000015 -0.000008 0.000000
Eqn. 1 mm 239 239 239 239 239 239 239 239 239 239 239 239 239 239 239 239 239 239 239 239 239
Custom restrain 50%
300
16
200
201
2,011
300,000
0.67%
-0.000075
239
Spacing
Area Bar Ab
As/m (T+B)
Ag
ρ
Design Strain
Approx so
Restrain
Th
Bar Ø
50% 50% 50% 50% 50% 50% 50% 50% 50% 50% 50%
mm 300 300 300 300 300 300 300 300 300 300 300
mm 16 16 16 16 16 16 16 16 16 16 16
mm 50 75 100 125 150 175 200 225 250 275 300
mm2 201 201 201 201 201 201 201 201 201 201 201
mm2/m 8,042 5,362 4,021 3,217 2,681 2,298 2,011 1,787 1,608 1,462 1,340
mm2 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000
2.68% 1.79% 1.34% 1.07% 0.89% 0.77% 0.67% 0.60% 0.54% 0.49% 0.45%
-0.000075 -0.000075 -0.000075 -0.000075 -0.000075 -0.000075 -0.000075 -0.000075 -0.000075 -0.000075 -0.000075
Eqn. 1 mm 60 90 119 149 179 209 239 269 298 328 358
Custom reinforcement spacing 300 50% 16
200
201
2,011
300,000
0.67%
-0.000075
239
0.90 0.80
Area Bar Ab
Restrain
w vs. reinf spacing 1.00
Spacing
Creep Adjusted Creep Adjusted Modular Ratio, Mod. E'c n* Eqn. 22 MPa 14,915 13 14,915 13 14,915 13 14,915 13 14,915 13 14,915 13 14,915 13 14,915 13 14,915 13 14,915 13 14,915 13 14,915 13 14,915 13 14,915 13 14,915 13 14,915 13 14,915 13 14,915 13 14,915 13 14,915 13 14,915 13
14,915
13
Creep Adjusted Creep Adjusted Modular Ratio, Mod. E'c n* Eqn. 22 MPa 14,915 13 14,915 13 14,915 13 14,915 13 14,915 13 14,915 13 14,915 13 14,915 13 14,915 13 14,915 13 14,915 13
14,915
13
C1
Ncr
Conc. Stress c1
Avg. Conc. Stress
ξ
s
Quantity of cracks
C2
N
stress s2*
stress s1*
stress c1*
Crack width
Eqn. 6
Eqn. 12
Eqn. 19 MPa 1.664 1.664 1.664 1.664 1.664 1.664 1.664 1.664 1.664 1.664 1.664 1.664 1.664 1.664 1.664 1.664 1.664 1.664 1.664 1.664 1.664
Eqn. 25
0.029 0.023 0.018 0.012 0.006 0.001 -0.005 -0.010 -0.015 -0.020 -0.026 -0.031 -0.036 -0.041 -0.046 -0.051 -0.056 -0.061 -0.065 -0.070 -0.075
Eqn. 27 mm 5,667 7,029 9,253 13,534 25,190 181,533 -34,866 -15,906 -10,303 -7,619 -6,044 -5,009 -4,277 -3,731 -3,309 -2,973 -2,698 -2,471 -2,278 -2,114 -1,971
Eqn. 16
436,810 436,810 436,810 436,810 436,810 436,810 436,810 436,810 436,810 436,810 436,810 436,810 436,810 436,810 436,810 436,810 436,810 436,810 436,810 436,810 436,810
Eqn. 9 MPa 1.476 1.476 1.476 1.476 1.476 1.476 1.476 1.476 1.476 1.476 1.476 1.476 1.476 1.476 1.476 1.476 1.476 1.476 1.476 1.476 1.476
Eqn. 28
0.013441 0.013441 0.013441 0.013441 0.013441 0.013441 0.013441 0.013441 0.013441 0.013441 0.013441 0.013441 0.013441 0.013441 0.013441 0.013441 0.013441 0.013441 0.013441 0.013441 0.013441
m 2 2 1 1 0 0 0 -1 -1 -2 -2 -2 -3 -3 -4 -4 -4 -5 -5 -6 -6
0.029 0.023 0.018 0.012 0.006 0.001 -0.005 -0.010 -0.015 -0.020 -0.026 -0.031 -0.036 -0.041 -0.046 -0.051 -0.056 -0.061 -0.065 -0.070 -0.075
539,840 542,863 545,885 548,908 551,930 554,952 557,975 560,997 564,020 567,042 570,064 573,087 576,109 579,132 582,154 585,176 588,199 591,221 594,244 597,266 600,288
Eqn. 17 MPa 268.49 270.00 271.50 273.00 274.51 276.01 277.51 279.02 280.52 282.02 283.53 285.03 286.53 288.04 289.54 291.04 292.55 294.05 295.55 297.06 298.56
Eqn. 15 MPa -7.76 -6.26 -4.75 -3.25 -1.75 -0.24 1.26 2.76 4.27 5.77 7.27 8.78 10.28 11.78 13.29 14.79 16.29 17.80 19.30 20.80 22.31
Eqn. 23 MPa 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85
Eqn. 30 mm 0.168 0.151 0.123 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.013441
436,810
1.476
1.664
-0.026
-6,044
-2
-0.026
570,064
283.53
7.27
1.85
0.000
C1
Ncr
Conc. Stress c1
Avg. Conc. Stress
ξ
s
Quantity of cracks
C2
N
stress s2*
stress s1*
stress c1*
Crack width
Eqn. 6
Eqn. 12
Eqn. 19 MPa 1.837 1.819 1.796 1.768 1.735 1.700 1.664 1.626 1.588 1.551 1.514
Eqn. 25
-0.122 -0.083 -0.061 -0.048 -0.038 -0.031 -0.026 -0.021 -0.018 -0.015 -0.013
Eqn. 27 mm -286 -660 -1,214 -1,981 -3,002 -4,333 -6,044 -8,222 -10,974 -14,434 -18,766
Eqn. 16
544,923 533,565 518,724 500,987 480,998 459,402 436,810 413,764 390,724 368,061 346,058
Eqn. 9 MPa 1.822 1.787 1.741 1.684 1.619 1.549 1.476 1.400 1.324 1.250 1.177
Eqn. 28
0.003327 0.004998 0.006676 0.008359 0.010047 0.011741 0.013441 0.015147 0.016858 0.018575 0.020298
m -42 -18 -10 -6 -4 -3 -2 -1 -1 -1 -1
-0.122 -0.083 -0.061 -0.048 -0.038 -0.031 -0.026 -0.021 -0.018 -0.015 -0.013
632,642 605,649 591,834 583,332 577,525 573,289 570,064 567,535 565,508 563,861 562,505
Eqn. 17 MPa 78.66 112.96 147.18 181.33 215.43 249.49 283.53 317.55 351.58 385.61 419.65
Eqn. 15 MPa 9.60 9.36 9.05 8.67 8.24 7.77 7.27 6.77 6.26 5.76 5.27
Eqn. 23 MPa 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85 1.85
Eqn. 30 mm 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.013441
436,810
1.476
1.664
-0.026
-6,044
-2
-0.026
570,064
283.53
7.27
1.85
0.000
Cracking calculation based on "Control of Flexural Cracking in Reinforced Concrete" by R. Ian Gilbert - May-June 2008 ACI Structural Journal Design moments Service
445 kN.m
w w vs. vs. restrain restrain 2.92 2.92
2.91 2.91
2.896
2.90
2.89
2.88 2.88
2.87 2.87
Crack Width Crack Width 75% 75%
2.86 2.86 2.85 2.85 0% 0%
20% 20%
40% 40%
60% 60%
80% 80%
100% 100%
Spacing
Area Bar Ab
As/m (T+B)
Ag
ρ
Restrain
Th
Bar Ø
100% 95% 90% 85% 80% 75% 70% 65% 60% 55% 50% 45% 40% 35% 30% 25% 20% 15% 10% 5% 0%
mm 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300
mm 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
mm 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200
mm2 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201
mm2/m 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005
mm2 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000
0.34% 0.34% 0.34% 0.34% 0.34% 0.34% 0.34% 0.34% 0.34% 0.34% 0.34% 0.34% 0.34% 0.34% 0.34% 0.34% 0.34% 0.34% 0.34% 0.34% 0.34%
Custom restrain 75%
300
16
200
201
1,005
300,000
0.34%
Design Strain
Cover
Creep Adjusted Creep Adjusted Mod., E'c (EQN Modular Ratio, 22) nbar
-0.000150 -0.000143 -0.000135 -0.000128 -0.000120 -0.000113 -0.000105 -0.000098 -0.000090 -0.000083 -0.000075 -0.000068 -0.000060 -0.000053 -0.000045 -0.000038 -0.000030 -0.000023 -0.000015 -0.000008 0.000000
mm 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25
Eqn. 22 MPa 14,915 14,915 14,915 14,915 14,915 14,915 14,915 14,915 14,915 14,915 14,915 14,915 14,915 14,915 14,915 14,915 14,915 14,915 14,915 14,915 14,915
-0.000113
25
14,915
d
Possible Depth Possible Depth Depth to NA, to NA 1, c1 to NA 2, c2 c (c1 or c2)
Icr
13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13
mm 267 267 267 267 267 267 267 267 267 267 267 267 267 267 267 267 267 267 267 267 267
mm 56.77 56.77 56.77 56.77 56.77 56.77 56.77 56.77 56.77 56.77 56.77 56.77 56.77 56.77 56.77 56.77 56.77 56.77 56.77 56.77 56.77
mm -72.39 -72.39 -72.39 -72.39 -72.39 -72.39 -72.39 -72.39 -72.39 -72.39 -72.39 -72.39 -72.39 -72.39 -72.39 -72.39 -72.39 -72.39 -72.39 -72.39 -72.39
Eqn. 8.6c mm 56.77 56.77 56.77 56.77 56.77 56.77 56.77 56.77 56.77 56.77 56.77 56.77 56.77 56.77 56.77 56.77 56.77 56.77 56.77 56.77 56.77
Eqn. 8-7 mm4 4.06E+08 4.06E+08 4.06E+08 4.06E+08 4.06E+08 4.06E+08 4.06E+08 4.06E+08 4.06E+08 4.06E+08 4.06E+08 4.06E+08 4.06E+08 4.06E+08 4.06E+08 4.06E+08 4.06E+08 4.06E+08 4.06E+08 4.06E+08 4.06E+08
13
267
56.77
-72.39
56.77
4.06E+08
Concrete Crack Area, Reinf. Ratio s* Act (EQN to Act, rhotc 1) Eqn. 1 Eqn. 8 mm mm2 121,614 0.00827 322.59 121,614 0.00827 322.59 121,614 0.00827 322.59 121,614 0.00827 322.59 121,614 0.00827 322.59 121,614 0.00827 322.59 121,614 0.00827 322.59 121,614 0.00827 322.59 121,614 0.00827 322.59 121,614 0.00827 322.59 121,614 0.00827 322.59 121,614 0.00827 322.59 121,614 0.00827 322.59 121,614 0.00827 322.59 121,614 0.00827 322.59 121,614 0.00827 322.59 121,614 0.00827 322.59 121,614 0.00827 322.59 121,614 0.00827 322.59 121,614 0.00827 322.59 121,614 0.00827 322.59
121,614
0.00827
322.59
Allowable Service Service Steel Ratio (fa/fs) Stress, fs
Actual Steel Stress, fa
Actual crack width
Acceptable crack width
MPa 1,789 1,789 1,789 1,789 1,789 1,789 1,789 1,789 1,789 1,789 1,789 1,789 1,789 1,789 1,789 1,789 1,789 1,789 1,789 1,789 1,789
mm 2.908 2.906 2.904 2.901 2.899 2.896 2.894 2.892 2.889 2.887 2.884 2.882 2.879 2.877 2.875 2.872 2.870 2.867 2.865 2.862 2.860
mm 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30
Eqn. 9 MPa 172 174 175 177 178 180 181 183 184 186 187 189 190 192 193 195 196 198 199 201 202
10.39 10.30 10.21 10.13 10.04 9.96 9.87 9.79 9.71 9.64 9.56 9.48 9.41 9.33 9.26 9.19 9.12 9.05 8.98 8.91 8.85
1,789
2.896
0.30
180
9.96
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 f't (direct tensile strength) Ec fy Es n alpha Temperature range ΔT Thickness Type
Shrinkage Effects (ACI 209R-92) Ultimate strain Initial moist curing duration Curing correction factor Relative humidity Humidity correction factor
Creep Effects (ACI 209R-92) Creep Factor Humidity correction factor
35 2.00 27806 420 200000 7.19 0.00001 20.0 10.0 1500 Foundation Mat
0.00078 7 1 60% 0.8
MPa MPa MPa MPa MPa
Effects of creep, shrinkage, and temperature in concrete slabs
ACI 209R-92 - Eqn. 2-4
°C °C °C mm
Spreadsheet version 1.00 Based on AE spreadheet
Table 2.5.4 Correction factors for Relative Humidity
(2-6) days Table 2.5.3 Table 2.5.4
Relative humidity (%) 0% 40% 50% 60% 70% 80% 90% 100%
Creep
γλ
1 1 0.94 0.87 0.8 0.73 0.67 0.6
Table 2.5.3 Shrinkage correction factors for initial moist curing Moist curing Shrinkage γCP duration (days)
Shrinkage γλ 1 1 0.9 0.8 0.7 0.6 0.3 0
1 3 7 14 28 90
Shrinkage Strain (ϵsh)t
1.2 1.1 1 0.93 0.86 0.75
Volume Surface v/s
3 1500 mm 2 1 mm 1500
Creep Shrinkage
0.66 (2-21a) 0.20 (2-22a)
Factored creep Factored shrinkage
1.35 0.16
Corrected ultimate strain
0.000150
0 7 14 28 56 100 500 1000 5000 10000
(2-9) 0.000000 0.000025 0.000043 0.000067 0.000092 0.000111 0.000140 0.000145 0.000149 0.000149
0.00 -2.50 -4.29 -6.67 -9.23 -11.11 -14.02 -14.49 -14.90 -14.95
0.00008 Total temp Creep factor vt °C 0.00006 -10.00 -12.50 -14.29 -16.67 -19.23 -21.11 -24.02 -24.49 -24.90 -24.95
(2-8) 0.00004 0.000 0.00002 0.328 0.00000 0.442 0 0.573 0.713 0.827 1.088 1.165 1.273 1.298
Shrinkage Strain (ϵsh)t
2000
4000
6000
8000
10000
Restraint Temperature 10,000 day temperature Total Temperature Equivalent Imposed Strain Creep Coefficient Linear Elastic Restraint Calculations Fully Restrained Stress (MPa) Design Strain Fully Released Shortening (mm) Design Strain
245 m 28 days -6.667 °C -24.948 °C -18.281 °C -0.000183 0.725
-5.08 -0.000183 -45 0.000000
Dry air or protective membrane Humidity, moist air, soil Deicing chemicals Seawater and seawater spray, wetting & drying Water-retaining structures
3. Determine Shrinkage with ACI 209R-92 50
Days
4. Determine Creep Coefficient with ACI 209R-92
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.
0.8 ACI 224R-01 -Table 4.1 Guide to reasonable* crack widths, reinforced concrete under service loads 0.6 Exposure condition
2. Determine Environment Properties • Ambient Temperature Range • Relative Humidity
1
Correction factors for relative humidity 1.2 1
Length Time to restraint
1. Determine Relevant Material Properties • Type of Cement • Type of Aggregate • Strength of Concrete • Coefficient of Thermal Expansion
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.
0.00010 Equivalent temperature change ° C
1.2
0
0.00012 Shrinkage Strain (ϵsh)t
1.4
0.6
0.00014
Days
Correction factor for initial curing γCP
0.8
0.00016
2.35 (2-6) 0.87 Table 2.5.4
Steps for Considering Shrinkage and Thermal Effects
Crack width 0.4 (mm) 0.2 0.41 0.3 0 0.18 0% 0.15 0.1
* 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.
Creep
γλ
Shrinkage γλ
20%
40%
60%
80%
100% Spreadsheet version 1.00 Based on AE spreadheet
Cracking calculation based on "Shrinkage Cracking in Fully Restrained Concrete Members" by R. Ian Gilbert - March-April 1992 ACI Structural Journal
w vs. restrain 1.00
0.70 0.60 0.50 0.40 0.30
Crack width 50%
0.20 0.10 0.000 0.00 0%
20%
40%
60%
80%
100%
0.70 0.60 0.50
Crack width
0.40
200
0.30
0.20 0.10 0.00 25
125
0.000 225
325
Ag
ρ
Design Strain
Approx so
Bar Ø
100% 95% 90% 85% 80% 75% 70% 65% 60% 55% 50% 45% 40% 35% 30% 25% 20% 15% 10% 5% 0%
mm 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500
mm 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12
mm 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300
mm2 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113 113
mm2/m 754 754 754 754 754 754 754 754 754 754 754 754 754 754 754 754 754 754 754 754 754
mm2 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000
0.05% 0.05% 0.05% 0.05% 0.05% 0.05% 0.05% 0.05% 0.05% 0.05% 0.05% 0.05% 0.05% 0.05% 0.05% 0.05% 0.05% 0.05% 0.05% 0.05% 0.05%
-0.000183 -0.000174 -0.000165 -0.000155 -0.000146 -0.000137 -0.000128 -0.000119 -0.000110 -0.000101 -0.000091 -0.000082 -0.000073 -0.000064 -0.000055 -0.000046 -0.000037 -0.000027 -0.000018 -0.000009 0.000000
Eqn. 1 mm 2,387 2,387 2,387 2,387 2,387 2,387 2,387 2,387 2,387 2,387 2,387 2,387 2,387 2,387 2,387 2,387 2,387 2,387 2,387 2,387 2,387
Custom restrain 50%
1500
12
300
113
754
1,500,000
0.05%
-0.000091
2,387
Spacing
Area Bar Ab
As/m (T+B)
Ag
ρ
Design Strain
Approx so
Restrain
Th
Bar Ø
50% 50% 50% 50% 50% 50% 50% 50% 50% 50% 50%
mm 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500
mm 12 12 12 12 12 12 12 12 12 12 12
mm 50 75 100 125 150 175 200 225 250 275 300
mm2 113 113 113 113 113 113 113 113 113 113 113
mm2/m 4,524 3,016 2,262 1,810 1,508 1,293 1,131 1,005 905 823 754
mm2 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000
0.30% 0.20% 0.15% 0.12% 0.10% 0.09% 0.08% 0.07% 0.06% 0.05% 0.05%
-0.000091 -0.000091 -0.000091 -0.000091 -0.000091 -0.000091 -0.000091 -0.000091 -0.000091 -0.000091 -0.000091
Eqn. 1 mm 398 597 796 995 1,194 1,393 1,592 1,790 1,989 2,188 2,387
Custom reinforcement spacing 1500 50% 12
200
113
1,131
1,500,000
0.08%
-0.000091
1,592
0.90 0.80
As/m (T+B)
Th
w vs. reinf spacing 1.00
Area Bar Ab
Restrain
0.90 0.80
Spacing
Creep Adjusted Creep Adjusted Modular Ratio, Mod. E'c n* Eqn. 22 MPa 16,123 12 16,123 12 16,123 12 16,123 12 16,123 12 16,123 12 16,123 12 16,123 12 16,123 12 16,123 12 16,123 12 16,123 12 16,123 12 16,123 12 16,123 12 16,123 12 16,123 12 16,123 12 16,123 12 16,123 12 16,123 12
16,123
12
Creep Adjusted Creep Adjusted Modular Ratio, Mod. E'c n* Eqn. 22 MPa 16,123 12 16,123 12 16,123 12 16,123 12 16,123 12 16,123 12 16,123 12 16,123 12 16,123 12 16,123 12 16,123 12
16,123
12
C1
Ncr
Conc. Stress c1
Avg. Conc. Stress
ξ
s
Quantity of cracks
C2
N
stress s2*
stress s1*
stress c1*
Crack width
Eqn. 6
Eqn. 12
Eqn. 19 MPa 1.357 1.357 1.357 1.357 1.357 1.357 1.357 1.357 1.357 1.357 1.357 1.357 1.357 1.357 1.357 1.357 1.357 1.357 1.357 1.357 1.357
Eqn. 25
0.005 0.005 0.004 0.004 0.003 0.003 0.002 0.002 0.001 0.001 0.000 0.000 -0.001 -0.001 -0.001 -0.002 -0.002 -0.003 -0.003 -0.004 -0.004
Eqn. 27 mm 321,029 353,822 394,078 444,670 510,165 598,287 723,207 914,060 1,241,757 1,935,731 4,388,063 -16,442,316 -2,860,998 -1,566,814 -1,078,810 -822,600 -664,731 -557,701 -480,357 -421,853 -376,052
Eqn. 16
1,065,607 1,065,607 1,065,607 1,065,607 1,065,607 1,065,607 1,065,607 1,065,607 1,065,607 1,065,607 1,065,607 1,065,607 1,065,607 1,065,607 1,065,607 1,065,607 1,065,607 1,065,607 1,065,607 1,065,607 1,065,607
Eqn. 9 MPa 0.715 0.715 0.715 0.715 0.715 0.715 0.715 0.715 0.715 0.715 0.715 0.715 0.715 0.715 0.715 0.715 0.715 0.715 0.715 0.715 0.715
Eqn. 28
0.006539 0.006539 0.006539 0.006539 0.006539 0.006539 0.006539 0.006539 0.006539 0.006539 0.006539 0.006539 0.006539 0.006539 0.006539 0.006539 0.006539 0.006539 0.006539 0.006539 0.006539
m 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 -1
0.005 0.005 0.004 0.004 0.003 0.003 0.002 0.002 0.001 0.001 0.000 0.000 -0.001 -0.001 -0.001 -0.002 -0.002 -0.003 -0.003 -0.004 -0.004
2,984,843 2,986,222 2,987,600 2,988,978 2,990,357 2,991,735 2,993,114 2,994,492 2,995,870 2,997,249 2,998,627 3,000,005 3,001,384 3,002,762 3,004,140 3,005,519 3,006,897 3,008,275 3,009,654 3,011,032 3,012,411
Eqn. 17 MPa 3,958.77 3,960.60 3,962.43 3,964.26 3,966.08 3,967.91 3,969.74 3,971.57 3,973.40 3,975.22 3,977.05 3,978.88 3,980.71 3,982.54 3,984.36 3,986.19 3,988.02 3,989.85 3,991.68 3,993.51 3,995.33
Eqn. 15 MPa -19.72 -17.90 -16.07 -14.24 -12.41 -10.58 -8.76 -6.93 -5.10 -3.27 -1.44 0.39 2.21 4.04 5.87 7.70 9.53 11.35 13.18 15.01 16.84
Eqn. 23 MPa 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00
Eqn. 30 mm 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.006539
1,065,607
0.715
1.357
0.000
4,388,063
0
0.000
2,998,627
3,977.05
-1.44
2.00
0.000
C1
Ncr
Conc. Stress c1
Avg. Conc. Stress
ξ
s
Quantity of cracks
C2
N
stress s2*
stress s1*
stress c1*
Crack width
Eqn. 6
Eqn. 12
Eqn. 19 MPa 1.952 1.899 1.833 1.762 1.690 1.620 1.556 1.497 1.445 1.398 1.357
Eqn. 25
-0.009 -0.005 -0.003 -0.002 -0.001 -0.001 0.000 0.000 0.000 0.000 0.000
Eqn. 27 mm -29,632 -75,051 -157,704 -307,390 -590,481 -1,184,309 -2,763,548 -12,247,289 12,221,390 5,685,063 4,388,063
Eqn. 16
2,854,024 2,692,487 2,495,102 2,280,293 2,063,208 1,854,513 1,660,626 1,484,631 1,327,324 1,188,101 1,065,607
Eqn. 9 MPa 1.905 1.798 1.667 1.524 1.380 1.241 1.112 0.995 0.890 0.797 0.715
Eqn. 28
0.001084 0.001627 0.002170 0.002714 0.003259 0.003804 0.004350 0.004896 0.005443 0.005990 0.006539
m -8 -3 -2 -1 0 0 0 0 0 0 0
-0.009 -0.005 -0.003 -0.002 -0.001 -0.001 0.000 0.000 0.000 0.000 0.000
3,026,567 3,015,618 3,009,806 3,006,186 3,003,758 3,002,067 3,000,867 3,000,007 2,999,389 2,998,945 2,998,627
Eqn. 17 MPa 669.02 999.90 1,330.63 1,661.28 1,991.93 2,322.61 2,653.35 2,984.16 3,315.05 3,646.02 3,977.05
Eqn. 15 MPa 5.94 5.27 4.46 3.58 2.68 1.82 1.02 0.29 -0.36 -0.94 -1.44
Eqn. 23 MPa 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00
Eqn. 30 mm 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.004350
1,660,626
1.112
1.556
0.000
-2,763,548
0
0.000
3,000,867
2,653.35
1.02
2.00
0.000
Cracking calculation based on "Control of Flexural Cracking in Reinforced Concrete" by R. Ian Gilbert - May-June 2008 ACI Structural Journal Design moments Service
445 kN.m
w w vs. vs. restrain restrain 2.45 2.45 2.40 2.40 2.35
2.309
2.30 2.25 2.25 2.20 2.20 2.15 2.15 Crack Width Crack Width 75% 75%
2.10 2.10 2.05 2.05 2.00 2.00 0% 0%
20% 20%
40% 40%
60% 60%
80% 80%
100% 100%
Spacing
Area Bar Ab
As/m (T+B)
Ag
ρ
Restrain
Th
Bar Ø
100% 95% 90% 85% 80% 75% 70% 65% 60% 55% 50% 45% 40% 35% 30% 25% 20% 15% 10% 5% 0%
mm 1,500 1,500 1,500 1,500 1,500 1,500 1,500 1,500 1,500 1,500 1,500 1,500 1,500 1,500 1,500 1,500 1,500 1,500 1,500 1,500 1,500
mm 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
mm 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200
mm2 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201
mm2/m 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005
mm2 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000 1,500,000
0.07% 0.07% 0.07% 0.07% 0.07% 0.07% 0.07% 0.07% 0.07% 0.07% 0.07% 0.07% 0.07% 0.07% 0.07% 0.07% 0.07% 0.07% 0.07% 0.07% 0.07%
Custom restrain 75%
1,500
16
200
201
1,005
1,500,000
0.07%
Design Strain
Cover
Creep Adjusted Creep Adjusted Mod., E'c (EQN Modular Ratio, 22) nbar
-0.000183 -0.000174 -0.000165 -0.000155 -0.000146 -0.000137 -0.000128 -0.000119 -0.000110 -0.000101 -0.000091 -0.000082 -0.000073 -0.000064 -0.000055 -0.000046 -0.000037 -0.000027 -0.000018 -0.000009 0.000000
mm 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25
Eqn. 22 MPa 16,123 16,123 16,123 16,123 16,123 16,123 16,123 16,123 16,123 16,123 16,123 16,123 16,123 16,123 16,123 16,123 16,123 16,123 16,123 16,123 16,123
-0.000137
25
16,123
d
Possible Depth Possible Depth Depth to NA, to NA 1, c1 to NA 2, c2 c (c1 or c2)
Icr
12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12
mm 1,467 1,467 1,467 1,467 1,467 1,467 1,467 1,467 1,467 1,467 1,467 1,467 1,467 1,467 1,467 1,467 1,467 1,467 1,467 1,467 1,467
mm 138.43 138.43 138.43 138.43 138.43 138.43 138.43 138.43 138.43 138.43 138.43 138.43 138.43 138.43 138.43 138.43 138.43 138.43 138.43 138.43 138.43
mm -152.89 -152.89 -152.89 -152.89 -152.89 -152.89 -152.89 -152.89 -152.89 -152.89 -152.89 -152.89 -152.89 -152.89 -152.89 -152.89 -152.89 -152.89 -152.89 -152.89 -152.89
Eqn. 8.6c mm 138.43 138.43 138.43 138.43 138.43 138.43 138.43 138.43 138.43 138.43 138.43 138.43 138.43 138.43 138.43 138.43 138.43 138.43 138.43 138.43 138.43
Eqn. 8-7 mm4 1.36E+10 1.36E+10 1.36E+10 1.36E+10 1.36E+10 1.36E+10 1.36E+10 1.36E+10 1.36E+10 1.36E+10 1.36E+10 1.36E+10 1.36E+10 1.36E+10 1.36E+10 1.36E+10 1.36E+10 1.36E+10 1.36E+10 1.36E+10 1.36E+10
12
1,467
138.43
-152.89
138.43
1.36E+10
Concrete Crack Area, Reinf. Ratio s* Act (EQN to Act, rhotc 1) Eqn. 1 Eqn. 8 mm mm2 680,787 0.00148 ###### 680,787 0.00148 ###### 680,787 0.00148 ###### 680,787 0.00148 ###### 680,787 0.00148 ###### 680,787 0.00148 ###### 680,787 0.00148 ###### 680,787 0.00148 ###### 680,787 0.00148 ###### 680,787 0.00148 ###### 680,787 0.00148 ###### 680,787 0.00148 ###### 680,787 0.00148 ###### 680,787 0.00148 ###### 680,787 0.00148 ###### 680,787 0.00148 ###### 680,787 0.00148 ###### 680,787 0.00148 ###### 680,787 0.00148 ###### 680,787 0.00148 ###### 680,787 0.00148 ######
680,787
0.00148
######
Allowable Service Service Steel Ratio (fa/fs) Stress, fs
Actual Steel Stress, fa
Actual crack width
Acceptable crack width
MPa 312 312 312 312 312 312 312 312 312 312 312 312 312 312 312 312 312 312 312 312 312
mm 2.392 2.375 2.359 2.342 2.326 2.309 2.293 2.276 2.260 2.243 2.227 2.210 2.194 2.177 2.161 2.144 2.128 2.111 2.095 2.078 2.062
mm 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30
Eqn. 9 MPa 80 82 84 85 87 89 91 93 95 96 98 100 102 104 106 107 109 111 113 115 116
3.90 3.81 3.73 3.65 3.57 3.50 3.43 3.36 3.30 3.23 3.17 3.11 3.06 3.00 2.95 2.90 2.85 2.81 2.76 2.72 2.67
312
2.309
0.30
89
3.50
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 50 2.39 f't (direct tensile strength) Ec 33234 fy 420 Es 200000 6.02 n alpha 0.00001 Temperature range 1000.0 10.0 ΔT Thickness 300 Type Elevated Slab No allowance for temp influences, slump, cement or air content.
Shrinkage Effects (ACI 209R-92) Ultimate strain Initial moist curing duration Curing correction factor Relative humidity Humidity correction factor
Creep Effects (ACI 209R-92) Creep Factor Humidity correction factor
0.00078 7 1 60% 0.8
MPa MPa MPa MPa MPa
Effects of creep, shrinkage, and temperature in concrete slabs
ACI 209R-92 - Eqn. 2-4
°C °C °C mm
Spreadsheet version 1.00 Based on AE spreadheet
Table 2.5.4 Correction factors for Relative Humidity
(2-6) days Table 2.5.3 Table 2.5.4
Relative humidity (%) 0% 40% 50% 60% 70% 80% 90% 100%
3 300 mm 2 2 mm 150
0.69 (2-21a) 0.59 (2-22a)
Factored creep Factored shrinkage
1.41 0.47 0.000369
Correction factors for relative humidity
Shrinkage γλ 1 1 0.9 0.8 0.7 0.6 0.3 0
1 3 7 14 28 90
1 0.8 0.6 Creep
0.4
γλ
0 7 14 28 56 90 1000 2000 3000 10000
(2-9) 0.000000 0.000061 0.000105 0.000164 0.000227 0.000266 0.000356 0.000363 0.000365 0.000368
Equivalent temperature change ° C 0.00 -6.15 -10.54 -16.39 -22.70 -26.56 -35.64 -36.25 -36.46 -36.76
Restraint Temperature 10,000 day temperature Total Temperature Equivalent Imposed Strain Creep Coefficient Linear Elastic Restraint Calculations Fully Restrained Stress (MPa) Design Strain Fully Released Shortening (mm) Design Strain
280 m 28 days -16.395 °C -46.759 °C -30.365 °C -0.000304 0.758
20%
Total temp Creep factor vt °C -10.00 -16.15 -20.54 -26.39 -32.70 -36.56 -45.64 -46.25 -46.46 -46.76
(2-8) 0.000 0.343 0.462 0.600 0.746 0.844 1.219 1.278 1.305 1.358
40%
60%
-10.09 -0.000304 -85 0.000000
80%
Dry air or protective membrane Humidity, moist air, soil Deicing chemicals Seawater and seawater spray, wetting & drying Water-retaining structures
1.4 1.2
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
1
3. Determine Shrinkage with ACI 209R-92 0
100%
50
Days
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.
Shrinkage Strain (ϵsh)t 0.00040 0.00035 0.00030
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.
0.00025 0.00020
Shrinkage Strain (ϵsh)t
0.00015 0.00010 0.00005 0.00000 2000
ACI 224R-01 -Table 4.1 Guide to reasonable* crack widths, reinforced concrete under service loads Exposure condition
Correction factor for initial curing γCP
0.6 0%
Shrinkage Strain (ϵsh)t
1.2 1.1 1 0.93 0.86 0.75
Steps for Considering Shrinkage and Thermal Effects
0.8
Shrinkage γλ
0.2
0 Length Time to restraint
Moist curing Shrinkage γCP duration (days)
1.2 1 1 0.94 0.87 0.8 0.73 0.67 0.6
2.35 (2-6) 0.87 Table 2.5.4
Creep Shrinkage
Corrected ultimate strain
γλ
0
Days Volume Surface v/s
Creep
Table 2.5.3 Shrinkage correction factors for initial moist curing
Crack width (mm) 0.41 0.3 0.18 0.15 0.1
* 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.
4000
6000
8000
10000
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. Spreadsheet version 1.00 Based on AE spreadheet
Cracking calculation based on "Shrinkage Cracking in Fully Restrained Concrete Members" by R. Ian Gilbert - March-April 1992 ACI Structural Journal
w vs. restrain 0.30
0.241 0.25
0.20
0.15
0.10 Crack width 50%
0.05
0.00 0%
20%
40%
60%
80%
100%
0.25
0.20
Crack width
0.159
0.15
200
0.10 0.05 0.00 25
125
225
325
As/m (T+B)
Ag
ρ
Design Strain
Approx so
Th
Bar Ø
100% 95% 90% 85% 80% 75% 70% 65% 60% 55% 50% 45% 40% 35% 30% 25% 20% 15% 10% 5% 0%
mm 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300
mm 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20
mm 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250
mm2 314 314 314 314 314 314 314 314 314 314 314 314 314 314 314 314 314 314 314 314 314
mm2/m 2,513 2,513 2,513 2,513 2,513 2,513 2,513 2,513 2,513 2,513 2,513 2,513 2,513 2,513 2,513 2,513 2,513 2,513 2,513 2,513 2,513
mm2 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000
0.84% 0.84% 0.84% 0.84% 0.84% 0.84% 0.84% 0.84% 0.84% 0.84% 0.84% 0.84% 0.84% 0.84% 0.84% 0.84% 0.84% 0.84% 0.84% 0.84% 0.84%
-0.000304 -0.000288 -0.000273 -0.000258 -0.000243 -0.000228 -0.000213 -0.000197 -0.000182 -0.000167 -0.000152 -0.000137 -0.000121 -0.000106 -0.000091 -0.000076 -0.000061 -0.000046 -0.000030 -0.000015 0.000000
Eqn. 1 mm 239 239 239 239 239 239 239 239 239 239 239 239 239 239 239 239 239 239 239 239 239
Custom restrain 50%
300
20
250
314
2,513
300,000
0.84%
-0.000152
239
Spacing
Area Bar Ab
As/m (T+B)
Ag
ρ
Design Strain
Approx so
Restrain
Th
Bar Ø
50% 50% 50% 50% 50% 50% 50% 50% 50% 50% 50%
mm 300 300 300 300 300 300 300 300 300 300 300
mm 20 20 20 20 20 20 20 20 20 20 20
mm 50 75 100 125 150 175 200 225 250 275 300
mm2 314 314 314 314 314 314 314 314 314 314 314
mm2/m 12,566 8,378 6,283 5,027 4,189 3,590 3,142 2,793 2,513 2,285 2,094
mm2 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000
4.19% 2.79% 2.09% 1.68% 1.40% 1.20% 1.05% 0.93% 0.84% 0.76% 0.70%
-0.000152 -0.000152 -0.000152 -0.000152 -0.000152 -0.000152 -0.000152 -0.000152 -0.000152 -0.000152 -0.000152
Eqn. 1 mm 48 72 95 119 143 167 191 215 239 263 286
Custom reinforcement spacing 300 50% 20
200
314
3,142
300,000
1.05%
-0.000152
191
0.35 0.30
Area Bar Ab
Restrain
w vs. reinf spacing 0.40
Spacing
Creep Adjusted Creep Adjusted Modular Ratio, Mod. E'c n* Eqn. 22 MPa 18,903 11 18,903 11 18,903 11 18,903 11 18,903 11 18,903 11 18,903 11 18,903 11 18,903 11 18,903 11 18,903 11 18,903 11 18,903 11 18,903 11 18,903 11 18,903 11 18,903 11 18,903 11 18,903 11 18,903 11 18,903 11
18,903
11
Creep Adjusted Creep Adjusted Modular Ratio, Mod. E'c n* Eqn. 22 MPa 18,903 11 18,903 11 18,903 11 18,903 11 18,903 11 18,903 11 18,903 11 18,903 11 18,903 11 18,903 11 18,903 11
18,903
11
C1
Ncr
Conc. Stress c1
Avg. Conc. Stress
ξ
s
Quantity of cracks
C2
N
stress s2*
stress s1*
stress c1*
Crack width
Eqn. 6
Eqn. 12
Eqn. 19 MPa 2.377 2.377 2.377 2.377 2.377 2.377 2.377 2.377 2.377 2.377 2.377 2.377 2.377 2.377 2.377 2.377 2.377 2.377 2.377 2.377 2.377
Eqn. 25
0.142 0.129 0.115 0.102 0.089 0.077 0.065 0.053 0.041 0.030 0.019 0.008 -0.003 -0.013 -0.024 -0.034 -0.044 -0.053 -0.063 -0.072 -0.081
Eqn. 27 mm 1,276 1,395 1,539 1,715 1,938 2,226 2,615 3,170 4,022 5,502 8,704 20,826 -53,044 -11,666 -6,553 -4,557 -3,492 -2,831 -2,381 -2,054 -1,806
Eqn. 16
708,672 708,672 708,672 708,672 708,672 708,672 708,672 708,672 708,672 708,672 708,672 708,672 708,672 708,672 708,672 708,672 708,672 708,672 708,672 708,672 708,672
Eqn. 9 MPa 2.364 2.364 2.364 2.364 2.364 2.364 2.364 2.364 2.364 2.364 2.364 2.364 2.364 2.364 2.364 2.364 2.364 2.364 2.364 2.364 2.364
Eqn. 28
0.000569 0.000569 0.000569 0.000569 0.000569 0.000569 0.000569 0.000569 0.000569 0.000569 0.000569 0.000569 0.000569 0.000569 0.000569 0.000569 0.000569 0.000569 0.000569 0.000569 0.000569
m 219 201 182 163 145 126 107 88 70 51 32 13 -5 -24 -43 -61 -80 -99 -118 -136 -155
0.142 0.129 0.115 0.102 0.089 0.077 0.065 0.053 0.041 0.030 0.019 0.008 -0.003 -0.013 -0.024 -0.034 -0.044 -0.053 -0.063 -0.072 -0.081
627,643 635,274 642,906 650,537 658,169 665,800 673,432 681,063 688,695 696,326 703,958 711,589 719,221 726,852 734,484 742,115 749,746 757,378 765,009 772,641 780,272
Eqn. 17 MPa 249.73 252.77 255.80 258.84 261.88 264.91 267.95 270.99 274.02 277.06 280.10 283.13 286.17 289.21 292.24 295.28 298.31 301.35 304.39 307.42 310.46
Eqn. 15 MPa -35.58 -32.55 -29.51 -26.47 -23.44 -20.40 -17.36 -14.33 -11.29 -8.25 -5.22 -2.18 0.86 3.89 6.93 9.97 13.00 16.04 19.07 22.11 25.15
Eqn. 23 MPa 2.39 2.39 2.39 2.39 2.39 2.39 2.39 2.39 2.39 2.39 2.39 2.39 2.39 2.39 2.39 2.39 2.39 2.39 2.39 2.39 2.39
Eqn. 30 mm 0.246 0.246 0.246 0.246 0.246 0.245 0.245 0.245 0.244 0.243 0.241 0.232 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000569
708,672
2.364
2.377
0.019
8,704
32
0.019
703,958
280.10
-5.22
2.39
0.241
C1
Ncr
Conc. Stress c1
Avg. Conc. Stress
ξ
s
Quantity of cracks
C2
N
stress s2*
stress s1*
stress c1*
Crack width
Eqn. 6
Eqn. 12
Eqn. 19 MPa 2.390 2.389 2.388 2.387 2.385 2.384 2.382 2.379 2.377 2.374 2.371
Eqn. 25
0.098 0.063 0.047 0.037 0.031 0.026 0.023 0.021 0.019 0.017 0.016
Eqn. 27 mm 357 803 1,425 2,221 3,188 4,324 5,625 7,086 8,704 10,473 12,389
Eqn. 16
716,664 716,220 715,615 714,850 713,927 712,846 711,608 710,216 708,672 706,976 705,132
Eqn. 9 MPa 2.389 2.388 2.386 2.384 2.381 2.377 2.373 2.369 2.364 2.358 2.352
Eqn. 28
0.000114 0.000171 0.000227 0.000284 0.000341 0.000398 0.000455 0.000512 0.000569 0.000626 0.000683
m 783 349 196 126 88 65 50 40 32 27 23
0.098 0.063 0.047 0.037 0.031 0.026 0.023 0.021 0.019 0.017 0.016
653,212 674,438 685,033 691,376 695,593 698,595 700,838 702,575 703,958 705,083 706,015
Eqn. 17 MPa 51.98 80.51 109.03 137.54 166.06 194.57 223.08 251.59 280.10 308.60 337.10
Eqn. 15 MPa -5.08 -5.09 -5.10 -5.11 -5.13 -5.15 -5.17 -5.19 -5.22 -5.25 -5.28
Eqn. 23 MPa 2.39 2.39 2.39 2.39 2.39 2.39 2.39 2.39 2.39 2.39 2.39
Eqn. 30 mm 0.013 0.026 0.044 0.066 0.093 0.124 0.159 0.198 0.241 0.288 0.338
0.000455
711,608
2.373
2.382
0.023
5,625
50
0.023
700,838
223.08
-5.17
2.39
0.159
Cracking calculation based on "Control of Flexural Cracking in Reinforced Concrete" by R. Ian Gilbert - May-June 2008 ACI Structural Journal Design moments Service
445 kN.m
w w vs. vs. restrain restrain 1.25 1.25 1.24 1.24 1.23 1.23
1.219 1.22 1.21 1.20 1.20 1.19 1.19 1.18 1.18 Crack Width Crack Width 75% 75%
1.17 1.17 1.16 1.16 1.15 1.15 0% 0%
20% 20%
40% 40%
60% 60%
80% 80%
100% 100%
Spacing
Area Bar Ab
As/m (T+B)
Ag
ρ
Restrain
Th
Bar Ø
100% 95% 90% 85% 80% 75% 70% 65% 60% 55% 50% 45% 40% 35% 30% 25% 20% 15% 10% 5% 0%
mm 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300
mm 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25
mm 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250
mm2 491 491 491 491 491 491 491 491 491 491 491 491 491 491 491 491 491 491 491 491 491
mm2/m 1,963 1,963 1,963 1,963 1,963 1,963 1,963 1,963 1,963 1,963 1,963 1,963 1,963 1,963 1,963 1,963 1,963 1,963 1,963 1,963 1,963
mm2 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000 300,000
0.65% 0.65% 0.65% 0.65% 0.65% 0.65% 0.65% 0.65% 0.65% 0.65% 0.65% 0.65% 0.65% 0.65% 0.65% 0.65% 0.65% 0.65% 0.65% 0.65% 0.65%
Custom restrain 75%
300
25
250
491
1,963
300,000
0.65%
Design Strain
Cover
Creep Adjusted Creep Adjusted Mod., E'c (EQN Modular Ratio, 22) nbar
-0.000304 -0.000288 -0.000273 -0.000258 -0.000243 -0.000228 -0.000213 -0.000197 -0.000182 -0.000167 -0.000152 -0.000137 -0.000121 -0.000106 -0.000091 -0.000076 -0.000061 -0.000046 -0.000030 -0.000015 0.000000
mm 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25
Eqn. 22 MPa 18,903 18,903 18,903 18,903 18,903 18,903 18,903 18,903 18,903 18,903 18,903 18,903 18,903 18,903 18,903 18,903 18,903 18,903 18,903 18,903 18,903
-0.000228
25
18,903
d
Possible Depth Possible Depth Depth to NA, to NA 1, c1 to NA 2, c2 c (c1 or c2)
Icr
11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
mm 263 263 263 263 263 263 263 263 263 263 263 263 263 263 263 263 263 263 263 263 263
mm 66.95 66.95 66.95 66.95 66.95 66.95 66.95 66.95 66.95 66.95 66.95 66.95 66.95 66.95 66.95 66.95 66.95 66.95 66.95 66.95 66.95
mm -90.58 -90.58 -90.58 -90.58 -90.58 -90.58 -90.58 -90.58 -90.58 -90.58 -90.58 -90.58 -90.58 -90.58 -90.58 -90.58 -90.58 -90.58 -90.58 -90.58 -90.58
Eqn. 8.6c mm 66.95 66.95 66.95 66.95 66.95 66.95 66.95 66.95 66.95 66.95 66.95 66.95 66.95 66.95 66.95 66.95 66.95 66.95 66.95 66.95 66.95
Eqn. 8-7 mm4 5.52E+08 5.52E+08 5.52E+08 5.52E+08 5.52E+08 5.52E+08 5.52E+08 5.52E+08 5.52E+08 5.52E+08 5.52E+08 5.52E+08 5.52E+08 5.52E+08 5.52E+08 5.52E+08 5.52E+08 5.52E+08 5.52E+08 5.52E+08 5.52E+08
11
263
66.95
-90.58
66.95
5.52E+08
Concrete Crack Area, Reinf. Ratio s* Act (EQN to Act, rhotc 1) Eqn. 1 Eqn. 8 mm mm2 116,527 0.01685 247.28 116,527 0.01685 247.28 116,527 0.01685 247.28 116,527 0.01685 247.28 116,527 0.01685 247.28 116,527 0.01685 247.28 116,527 0.01685 247.28 116,527 0.01685 247.28 116,527 0.01685 247.28 116,527 0.01685 247.28 116,527 0.01685 247.28 116,527 0.01685 247.28 116,527 0.01685 247.28 116,527 0.01685 247.28 116,527 0.01685 247.28 116,527 0.01685 247.28 116,527 0.01685 247.28 116,527 0.01685 247.28 116,527 0.01685 247.28 116,527 0.01685 247.28 116,527 0.01685 247.28
116,527
0.01685
247.28
Allowable Service Service Steel Ratio (fa/fs) Stress, fs
Actual Steel Stress, fa
Actual crack width
Acceptable crack width
MPa 949 949 949 949 949 949 949 949 949 949 949 949 949 949 949 949 949 949 949 949 949
mm 1.237 1.234 1.230 1.226 1.222 1.219 1.215 1.211 1.207 1.204 1.200 1.196 1.192 1.189 1.185 1.181 1.177 1.174 1.170 1.166 1.162
mm 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30
Eqn. 9 MPa 191 194 197 200 203 206 209 212 215 218 221 224 227 230 233 236 239 242 245 248 251
4.97 4.90 4.82 4.75 4.68 4.61 4.54 4.48 4.41 4.35 4.29 4.23 4.18 4.12 4.07 4.02 3.96 3.92 3.87 3.82 3.77
949
1.219
0.30
206
4.61
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 f't (direct tensile strength) Ec fy Es n alpha Temperature range ΔT Thickness Type
Shrinkage Effects (ACI 209R-92) Ultimate strain Initial moist curing duration Curing correction factor Relative humidity Humidity correction factor
Creep Effects (ACI 209R-92) Creep Factor Humidity correction factor
45 2.27 31529 460 200000 6.34 0.000009 30.0 15.0 400 Elevated Slab
MPa MPa MPa MPa MPa
Effects of creep, shrinkage, and temperature in concrete slabs
ACI 209R-92 - Eqn. 2-4
°C °C °C mm
0.00078 (2-6) 7 days Table 2.5.3 1 65% 0.75 Table 2.5.4
Spreadsheet version 1.00 Based on AE spreadheet
Table 2.5.4 Correction factors for Relative Humidity Relative humidity (%) 0% 40% 50% 60% 70% 80% 90% 100%
γλ
Creep Shrinkage
0.670532 (2-21a) 0.466882 (2-22a)
Factored creep Factored shrinkage
1.315752 0.350162
Ultimate strain
0.000273
1 1 0.9 0.8 0.7 0.6 0.3 0
1 3 7 14 28 90
1 0.8 0.6 Creep
0.4
γλ
0 7 14 28 56 100 500 1000 5000 10000
(2-9) 0.000000 0.000046 0.000078 0.000121 0.000168 0.000202 0.000255 0.000264 0.000271 0.000272
Restraint Temperature 10,000 day temperature Total Temperature Equivalent Imposed Strain Creep Coefficient Linear Elastic Restraint Calculations Fully Restrained Stress (Mpa) Design Strain Fully Released Shortening (mm) Design Strain
75 m 28 days -13.488 °C -45.241 °C -31.754 °C -0.000286 0.706
Equivalent temperature change
Total temp
0.00 -5.06 -8.67 -13.49 -18.68 -22.48 -28.36 -29.32 -30.14 -30.24
-15.00 -20.06 -23.67 -28.49 -33.68 -37.48 -43.36 -44.32 -45.14 -45.24
20%
40%
60%
-9.01 -0.000286 -21 0.000000
Dry air or protective membrane Humidity, moist air, soil Deicing chemicals Seawater and seawater spray, wetting & drying Water-retaining structures
1.4 1.2
3. Determine Shrinkage with ACI 209R-92
0.00025 0.00020
0.00005 0.00000 2000
Crack width (mm) 0.41 0.3 0.18 0.15 0.1
* 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.
4000
6000
Days
4. Determine Creep Coefficient with ACI 209R-92
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.
Shrinkage Strain
0.00010
50
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.
0.00030
0.00015
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
1
0
100%
Shrinkage Strain
Creep factor (2-8) 0.000 0.320 0.431 0.559 0.695 0.807 1.061 1.136 1.241 1.265
80%
ACI 224R-01 -Table 4.1 Guide to reasonable* crack widths, reinforced concrete under service loads Exposure condition
Correction factor for initial curing γCP
0.6 0%
Shrinkage Strain
1.2 1.1 1 0.93 0.86 0.75
Steps for Considering Shrinkage and Thermal Effects
0.8
Shrinkage γλ
0.2
0 Length Time to restraint
Moist curing Shrinkage γCP duration (days)
1.2 1 1 0.94 0.87 0.8 0.73 0.67 0.6
2.35 (2-6) 0.835 Table 2.5.4
3 400 mm 2 2 mm 200
Correction factors for relative humidity
Shrinkage γλ
0
Days Volume Surface v/s
Creep
Table 2.5.3 Shrinkage correction factors for initial moist curing
8000
10000
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. Spreadsheet version 1.00 Based on AE spreadheet
Cracking calculation based on "Shrinkage Cracking in Fully Restrained Concrete Members" by R. Ian Gilbert - March-April 1992 ACI Structural Journal
w vs. restrain 0.60
0.50 0.409 0.40
0.30
0.20 Crack width 50%
0.10
0.00 0%
20%
40%
60%
80%
100%
2.00 Crack width
1.50
200
1.00 0.50
0.409
0.00 25
125
225
325
As/m (T+B)
Ag
ρ
Design Strain
Approx so
Th
Bar Ø
100% 95% 90% 85% 80% 75% 70% 65% 60% 55% 50% 45% 40% 35% 30% 25% 20% 15% 10% 5% 0%
mm 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
mm 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
mm 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200
mm2 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201
mm2/m 2,011 2,011 2,011 2,011 2,011 2,011 2,011 2,011 2,011 2,011 2,011 2,011 2,011 2,011 2,011 2,011 2,011 2,011 2,011 2,011 2,011
mm2 400,000 400,000 400,000 400,000 400,000 400,000 400,000 400,000 400,000 400,000 400,000 400,000 400,000 400,000 400,000 400,000 400,000 400,000 400,000 400,000 400,000
0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50% 0.50%
-0.000286 -0.000271 -0.000257 -0.000243 -0.000229 -0.000214 -0.000200 -0.000186 -0.000171 -0.000157 -0.000143 -0.000129 -0.000114 -0.000100 -0.000086 -0.000071 -0.000057 -0.000043 -0.000029 -0.000014 0.000000
Eqn. 1 mm 318 318 318 318 318 318 318 318 318 318 318 318 318 318 318 318 318 318 318 318 318
Custom restrain 50%
400
16
200
201
2,011
400,000
0.50%
-0.000143
318
Spacing
Area Bar Ab
As/m (T+B)
Ag
ρ
Design Strain
Approx so
Restrain
Th
Bar Ø
50% 50% 50% 50% 50% 50% 50% 50% 50% 50% 50%
mm 400 400 400 400 400 400 400 400 400 400 400
mm 16 16 16 16 16 16 16 16 16 16 16
mm 50 75 100 125 150 175 200 225 250 275 300
mm2 201 201 201 201 201 201 201 201 201 201 201
mm2/m 8,042 5,362 4,021 3,217 2,681 2,298 2,011 1,787 1,608 1,462 1,340
mm2 400,000 400,000 400,000 400,000 400,000 400,000 400,000 400,000 400,000 400,000 400,000
2.01% 1.34% 1.01% 0.80% 0.67% 0.57% 0.50% 0.45% 0.40% 0.37% 0.34%
-0.000143 -0.000143 -0.000143 -0.000143 -0.000143 -0.000143 -0.000143 -0.000143 -0.000143 -0.000143 -0.000143
Eqn. 1 mm 80 119 159 199 239 279 318 358 398 438 477
Custom reinforcement spacing 400 50% 16
200
201
2,011
400,000
0.50%
-0.000143
318
3.00 2.50
Area Bar Ab
Restrain
w vs. reinf spacing 3.50
Spacing
Creep Adjusted Creep Adjusted Modular Ratio, Mod. E'c n* Eqn. 22 MPa 18,476 11 18,476 11 18,476 11 18,476 11 18,476 11 18,476 11 18,476 11 18,476 11 18,476 11 18,476 11 18,476 11 18,476 11 18,476 11 18,476 11 18,476 11 18,476 11 18,476 11 18,476 11 18,476 11 18,476 11 18,476 11
18,476
11
Creep Adjusted Creep Adjusted Modular Ratio, Mod. E'c n* Eqn. 22 MPa 18,476 11 18,476 11 18,476 11 18,476 11 18,476 11 18,476 11 18,476 11 18,476 11 18,476 11 18,476 11 18,476 11
18,476
11
C1
Ncr
Conc. Stress c1
Avg. Conc. Stress
ξ
s
Quantity of cracks
C2
N
stress s2*
stress s1*
stress c1*
Crack width
Eqn. 6
Eqn. 12
Eqn. 19 MPa 2.175 2.175 2.175 2.175 2.175 2.175 2.175 2.175 2.175 2.175 2.175 2.175 2.175 2.175 2.175 2.175 2.175 2.175 2.175 2.175 2.175
Eqn. 25
0.081 0.073 0.066 0.059 0.052 0.045 0.038 0.031 0.024 0.018 0.011 0.005 -0.002 -0.008 -0.014 -0.020 -0.026 -0.032 -0.038 -0.044 -0.050
Eqn. 27 mm 2,848 3,113 3,432 3,824 4,316 4,955 5,815 7,036 8,907 12,133 19,024 44,030 -140,036 -27,031 -14,960 -10,341 -7,902 -6,394 -5,369 -4,627 -4,066
Eqn. 16
830,745 830,745 830,745 830,745 830,745 830,745 830,745 830,745 830,745 830,745 830,745 830,745 830,745 830,745 830,745 830,745 830,745 830,745 830,745 830,745 830,745
Eqn. 9 MPa 2.083 2.083 2.083 2.083 2.083 2.083 2.083 2.083 2.083 2.083 2.083 2.083 2.083 2.083 2.083 2.083 2.083 2.083 2.083 2.083 2.083
Eqn. 28
0.002837 0.002837 0.002837 0.002837 0.002837 0.002837 0.002837 0.002837 0.002837 0.002837 0.002837 0.002837 0.002837 0.002837 0.002837 0.002837 0.002837 0.002837 0.002837 0.002837 0.002837
m 26 24 22 20 17 15 13 11 8 6 4 2 -1 -3 -5 -7 -9 -12 -14 -16 -18
0.081 0.073 0.066 0.059 0.052 0.045 0.038 0.031 0.024 0.018 0.011 0.005 -0.002 -0.008 -0.014 -0.020 -0.026 -0.032 -0.038 -0.044 -0.050
839,451 845,197 850,943 856,689 862,435 868,181 873,927 879,673 885,419 891,165 896,911 902,657 908,403 914,149 919,895 925,641 931,387 937,133 942,879 948,625 954,371
Eqn. 17 MPa 417.51 420.37 423.22 426.08 428.94 431.80 434.66 437.51 440.37 443.23 446.09 448.94 451.80 454.66 457.52 460.38 463.23 466.09 468.95 471.81 474.67
Eqn. 15 MPa -33.61 -30.75 -27.89 -25.04 -22.18 -19.32 -16.46 -13.61 -10.75 -7.89 -5.03 -2.17 0.68 3.54 6.40 9.26 12.11 14.97 17.83 20.69 23.55
Eqn. 23 MPa 2.27 2.27 2.27 2.27 2.27 2.27 2.27 2.27 2.27 2.27 2.27 2.27 2.27 2.27 2.27 2.27 2.27 2.27 2.27 2.27 2.27
Eqn. 30 mm 0.490 0.489 0.487 0.485 0.483 0.480 0.475 0.469 0.460 0.444 0.409 0.284 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.002837
830,745
2.083
2.175
0.011
19,024
4
0.011
896,911
446.09
-5.03
2.27
0.409
C1
Ncr
Conc. Stress c1
Avg. Conc. Stress
ξ
s
Quantity of cracks
C2
N
stress s2*
stress s1*
stress c1*
Crack width
Eqn. 6
Eqn. 12
Eqn. 19 MPa 2.261 2.254 2.243 2.230 2.214 2.195 2.175 2.153 2.130 2.105 2.079
Eqn. 25
0.038 0.025 0.019 0.016 0.014 0.012 0.011 0.010 0.010 0.009 0.009
Eqn. 27 mm 1,460 3,218 5,568 8,417 11,668 15,230 19,024 22,986 27,067 31,232 35,459
Eqn. 16
901,388 894,899 886,088 875,092 862,074 847,224 830,745 812,852 793,765 773,699 752,864
Eqn. 9 MPa 2.255 2.240 2.218 2.192 2.160 2.123 2.083 2.039 1.991 1.942 1.890
Eqn. 28
0.000708 0.001062 0.001417 0.001772 0.002127 0.002482 0.002837 0.003193 0.003549 0.003906 0.004262
m 51 23 13 9 6 5 4 3 3 2 2
0.038 0.025 0.019 0.016 0.014 0.012 0.011 0.010 0.010 0.009 0.009
874,059 884,601 889,745 892,736 894,656 895,970 896,911 897,608 898,140 898,555 898,886
Eqn. 17 MPa 108.68 164.99 221.26 277.51 333.72 389.92 446.09 502.24 558.37 614.49 670.60
Eqn. 15 MPa -4.10 -4.18 -4.30 -4.44 -4.62 -4.81 -5.03 -5.27 -5.53 -5.79 -6.07
Eqn. 23 MPa 2.27 2.27 2.27 2.27 2.27 2.27 2.27 2.27 2.27 2.27 2.27
Eqn. 30 mm 0.036 0.075 0.125 0.186 0.255 0.330 0.409 2.519 2.675 2.836 3.000
0.002837
830,745
2.083
2.175
0.011
19,024
4
0.011
896,911
446.09
-5.03
2.27
0.409
Cracking calculation based on "Control of Flexural Cracking in Reinforced Concrete" by R. Ian Gilbert - May-June 2008 ACI Structural Journal Design moments Service
445 kN.m
w w vs. vs. restrain restrain 2.96 2.96 2.94 2.94 2.917 2.917 2.92
2.90
2.88 2.88 2.86 2.86 2.84 2.84
Crack Width Crack Width 75% 75%
2.82 2.82 2.80 2.80 0% 0%
20% 20%
40% 40%
60% 60%
80% 80%
100% 100%
Spacing
Area Bar Ab
As/m (T+B)
Ag
ρ
Restrain
Th
Bar Ø
100% 95% 90% 85% 80% 75% 70% 65% 60% 55% 50% 45% 40% 35% 30% 25% 20% 15% 10% 5% 0%
mm 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
mm 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
mm 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200
mm2 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201 201
mm2/m 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005 1,005
mm2 400,000 400,000 400,000 400,000 400,000 400,000 400,000 400,000 400,000 400,000 400,000 400,000 400,000 400,000 400,000 400,000 400,000 400,000 400,000 400,000 400,000
0.25% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25%
Custom restrain 75%
400
16
200
201
1,005
400,000
0.25%
Design Strain
Cover
Creep Adjusted Creep Adjusted Mod., E'c (EQN Modular Ratio, 22) nbar
-0.000286 -0.000271 -0.000257 -0.000243 -0.000229 -0.000214 -0.000200 -0.000186 -0.000171 -0.000157 -0.000143 -0.000129 -0.000114 -0.000100 -0.000086 -0.000071 -0.000057 -0.000043 -0.000029 -0.000014 0.000000
mm 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25
Eqn. 22 MPa 18,476 18,476 18,476 18,476 18,476 18,476 18,476 18,476 18,476 18,476 18,476 18,476 18,476 18,476 18,476 18,476 18,476 18,476 18,476 18,476 18,476
-0.000214
25
18,476
d
Possible Depth Possible Depth Depth to NA, to NA 1, c1 to NA 2, c2 c (c1 or c2)
Icr
11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
mm 367 367 367 367 367 367 367 367 367 367 367 367 367 367 367 367 367 367 367 367 367
mm 62.04 62.04 62.04 62.04 62.04 62.04 62.04 62.04 62.04 62.04 62.04 62.04 62.04 62.04 62.04 62.04 62.04 62.04 62.04 62.04 62.04
mm -74.79 -74.79 -74.79 -74.79 -74.79 -74.79 -74.79 -74.79 -74.79 -74.79 -74.79 -74.79 -74.79 -74.79 -74.79 -74.79 -74.79 -74.79 -74.79 -74.79 -74.79
Eqn. 8.6c mm 62.04 62.04 62.04 62.04 62.04 62.04 62.04 62.04 62.04 62.04 62.04 62.04 62.04 62.04 62.04 62.04 62.04 62.04 62.04 62.04 62.04
Eqn. 8-7 mm4 6.73E+08 6.73E+08 6.73E+08 6.73E+08 6.73E+08 6.73E+08 6.73E+08 6.73E+08 6.73E+08 6.73E+08 6.73E+08 6.73E+08 6.73E+08 6.73E+08 6.73E+08 6.73E+08 6.73E+08 6.73E+08 6.73E+08 6.73E+08 6.73E+08
11
367
62.04
-74.79
62.04
6.73E+08
Concrete Crack Area, Reinf. Ratio s* Act (EQN to Act, rhotc 1) Eqn. 1 Eqn. 8 mm mm2 168,980 0.00595 448.23 168,980 0.00595 448.23 168,980 0.00595 448.23 168,980 0.00595 448.23 168,980 0.00595 448.23 168,980 0.00595 448.23 168,980 0.00595 448.23 168,980 0.00595 448.23 168,980 0.00595 448.23 168,980 0.00595 448.23 168,980 0.00595 448.23 168,980 0.00595 448.23 168,980 0.00595 448.23 168,980 0.00595 448.23 168,980 0.00595 448.23 168,980 0.00595 448.23 168,980 0.00595 448.23 168,980 0.00595 448.23 168,980 0.00595 448.23 168,980 0.00595 448.23 168,980 0.00595 448.23
168,980
0.00595
448.23
Allowable Service Service Steel Ratio (fa/fs) Stress, fs
Actual Steel Stress, fa
Actual crack width
Acceptable crack width
MPa 1,280 1,280 1,280 1,280 1,280 1,280 1,280 1,280 1,280 1,280 1,280 1,280 1,280 1,280 1,280 1,280 1,280 1,280 1,280 1,280 1,280
mm 2.949 2.943 2.936 2.930 2.923 2.917 2.911 2.904 2.898 2.891 2.885 2.879 2.872 2.866 2.859 2.853 2.847 2.840 2.834 2.827 2.821
mm 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30
Eqn. 9 MPa 98 101 103 106 109 112 115 118 121 123 126 129 132 135 138 141 143 146 149 152 155
13.09 12.72 12.37 12.03 11.72 11.42 11.14 10.87 10.61 10.36 10.13 9.90 9.69 9.49 9.29 9.10 8.92 8.74 8.58 8.42 8.26
1,280
2.917
0.30
112
11.42
