question
load-deflection data
formulas
20 Q1) Determine the compressive strength of concrete cylinders (height=150mm diameter=75mm) with different w/c ratios subjected to uniaxial compression according to the ASTM C39/C39M - a. Create a graph in excel for 1. Load (kN) - Deflection (mm) 2. Stress (MPa) - Strain (mm/mm) 6. For the graphs, calculate the parameters using the experimental data: 1. Compressive strength (MPa) 2. Young's Modulus (GPa): Secant Modulus Chord Modulus Tangent Modulus Dynamic Modulus M F 3 1 w/c 0.6 2 Load kN) Deflection (mm) 3 0 0 4 2.94647 0.00817 5 7.15273 0.01616 6 11.85273 0.02426 7 16.58997 0.03224 B 22.1905 0.0403 9 27.5469 0.04812 10 34.59256 0.0566 11 41.93122 0.06437 49.93333 0.07269 13 58 34836 0.08082 14 66.15932 0.08891 15 74.56453 0.09733 16 BL.76339 0.10509 17 89.49264 0.11304 18 97.30911 0.12109 19 105.72042 0.12922 20 114.57101 0.13699 21 124.31406 0.14537 D E w/-0.5 Load (kN) Deflection (mm) 0 0 1.96005161 0.002554902 3.92010323 0.005109803 5.88015484 0.007664705 7.84020646 0.010219606 9.80025807 0.012774508 11.7603097 0.01532941 10.7203613 0.017884311 15.6804129 0.020419213 17.6404645 0.022994115 19.8231925 0.025666608 22.0059204 0.028339102 24.1886484 0.031011595 26.3713764 0.033684089 28.5541043 0.036356582 30.7368323 0.039029076 32.9195602 0.041701560 35.1022882 0.044374063 37 2850162 0.047046556 G H w/c-0.4 Load (kN) Deflection (mm) 0 0 4.44064051 0.00422257 8.88128102 0.00844513 13.3219215 0.0126677 17.762562 0.01689026 22.1213157 0.02083696 26.4800693 0.02478365 30.838823 0.02873034 35.1975766 0.03267704 39.1804744 0.03673538 43.1633722 0.04079372 47.1462701 0.04485207 51.1291679 0.04891041 56.3404339 0.05308013 61.5516999 0.05724985 66.7629659 0.06141957 71.9742319 0.06558929 76.7117212 0.06973361 81.4492105 0.07387793 K w/c-0.3 Load (kN) Deflection (mm) 0 3.39497104 0.0029303 6.78994207 0.0058606 10.1849131 0.0087909 13.5798841 0.01172119 17.5595675 0.01497732 21.5392509 0.01823344 25.5189343 0.02148957 29.4986177 0.02474569 34.1159159 0.02825618 38.7332142 0.03176667 43.3505124 0.03529717 47.9678107 0.03878766 51.7567856 0.04174153 55.5457605 0.0146954 59.3347354 0.04764926 63.1237103 0.05060313 67.1527054 0.05371933 71. 1817005 0.05683552 C B 0.15329 0.16138 0.16945 0.1746 0,17819 A 22 133.42474 23 139.2402 24 133.21462 25 120.3985 26. 105.35588 27 28 29 30 31 32 D 39.6995194 0.019588012 42.1140226 0.052129467 44.5285258 0.054670923 46.943029 0.057212379 49.3575322 0.059753834 517720354 0.06229529 54.1865386 0.064836745 56.6010418 0.067378201 59.015545 0.009919657 61.539092 0.072489879 64,0626391 0.075060102 66.5861862 0.077630325 69.1097332 0.080200548 71.6332803 0.082270721 74.1568274 0.005140993 76.6803744 0.087911216 79.2039215 0_090481439 81.7274636 0.093051662 84.2367173 0.095676524 86.7459656 0.098301386 89.2552141 0.100926248 G 86.1866998 0.07802225 90.924189 0.08216658 95.6029278 0.08634295 100.281666 0.09051932 104,960405 0.09469569 109.639144 0.09887207 114.737404 0.10292452 119.835664 0.10697698 124.933924 0.11102943 130,032184 0.11508189 135.285695 0.11939635 140.539207 0.12371081 145.792718 0.12802527 151,04623 0.13233973 155,560024 0.13627095 160.075018 0.14020217 164.589412 0.1441334 109.103806 0 14806462 173.961614 0.15200788 178.833422 0.15595113 183.69823 0.15989439 75.2106957 0.05995172 79.2396908 0.06306791 83.7956362 0.06645415 88.3515815 0.06984039 92.9075269 0.07322664 97.4634722 0.07651288 101.921065 0.08000274 106.378658 0.083 39261 110.836251 0.08678248 115.293844 0.09012235 118.892253 0.09303652 122.490662 0,09590069 126.089071 0.09876487 129.68748 0.10162904 134.036605 0.1048441 138.38573 0.10805916 142.734856 0.11127423 147.083981 0.11448929 151.686137 0.21794059 156288294 0.12139189 160.89045 0.12484319 30 35 38 39 40 41 42 A c 1 N 43 46 47 49 50 51 52 53 E 91.7644626 0.103551111 94.2737111 0.106175973 96.7829596 0.108800335 99.2922081 0.111425697 101.801457 0.114050559 104,310705 0.116675422 106.75823 0.119173696 109.205751 0.121671971 111.653278 0.124170246 114.100803 0.12666852 116.548327 0.129166795 118.995852 0.13166507 121,443376 0.134163344 123.890901 0.135661619 126,338425 0.139159493 128.552053 0.141848546 130.705681 0.144537199 132.97931 0 147225352 135.192938 0.142914505 137.406506 0.157601158 119.62019 0.155291811 G 188 563037 0.16383765 193.230207 0.16795343 197.897377 0.1720692 202 564547 0.17618498 207 231715 0.18030076 211994167 0.18450G32 216.756616 0.18871188 221.519065 0 19291744 226.281514 0.197123 228.788884 0 20118056 231.296253 0.20523813 233.103623 0 20929560 236.310992 0.21335325 236.310992 0.21335325 236 310992 0.21335325 236.081539 0.22154291 235.852085 0.2297325 235 52085 0.22973257 235.852085 0.2297325 225.2494 0 2051 214.645862 0.24644644 K 165,492607 0.12829.449 169.383935 0.13115365 173.275263 0.13401281 177.166591 0.13687197 181.057919 0.11973113 185.512996 0.14320504 189.968072 0.14667895 194.423148 0.15015286 198.878225 0.15362577 202.448564 0.15679938 205.018904 0.159972 209.589243 0.16314461 213.159583 0.16631723 217.256825 016957111 22135006 0.172825 225.44531 0.17607888 229.540552 0.17933277 234 097054 0.10259678 11.1510 243.210057 0.18912401 2016-30 0.192390 55 58 39 60 ul A B c F G 214.645862 0.24644644 214,645862 0.24644644 206.783254 0.25526555 198.921646 0.26408467 65 66 67 68 69 70 71 72 78 74 25 76 72 78 79 80 81 82 83 84 D E 141.833822 0.157980464 144.047451 0.160669117 146.261079 0.163357769 148.182251 0.165920405 150.103424 0.168483041 152.024597 0.171045676 153.94577 0.173608312 155.866942 0.176170948 157.788115 0.178733583 159.709288 0.181296219 161.63046 0.183858855 163,551633 0.18642149 165,3419760.189079233 167.132319 0.191736976 168.922663 0.194394718 170.713006 0.197052461 172.503349 0.199710204 174.293692 0.202367946 176.084035 0.205025689 177.874378 0.207683432 179.664722 0.210341174 252.635511 0.19587575 257.504464 0.19936267 262 373417 0.2028496 267.24237 0.20633652 270.733757 0.20900498 274.225145 0.21167345 277.716532 0.21434191 281.207919 0.21701038 286.903023 0.22095324 292.598127 0.2248961 298.29323 0.22883897 303.988334 0.23278183 308.153296 0.2358174 312.318259 0.23885296 316.483221 0.24188853 320.648183 0.24492409 324.042216 0.24806535 327.436248 0.25120661 330,83028 0.25434787 334.224313 0.25748913 337.722371 0.26155272 Sheet1 0 F . G H 1 M 185 86 87 88 89 90 91 92 93 94 95 95 97 98 199 100 101 102 103 104 105 0 E 180.823945 0.212988288 181.983167 0.215635402 183.14239 0.218282516 184.301613 0.220929629 185.460836 0.223576743 186.620059 0.226223857 187.779282 0.228870971 188.938505 0.231518084 190.097728 0.234165198 190.527276 0.236725449 190.956824 0.239285699 191.386372 0.24184595 191.81592 0.244406201 192.245468 0.246966451 192.675016 0.249526702 193.104564 0.252086953 193.534112 0.254647203 193.96366 0.257207454 193.284249 0.261617393 192.604837 0.266027332 191.925426 0.270437271 341.220429 0.26561632 344.718486 0.26967992 348.216544 0.27374351 344.569112 0.27624186 340.92168 0.27874022 337.2742481 0.28123857 333.626816 0.28373692 329.81689 0.28654297 326.006965 0.28934902 322.19704 0.29215506 318.387115 0.29496111 312.765182 0.29813543 307.14325 0.30130975 301.521318 0.30448407 295.899386 0.3076584 Sheet1 A B C F G H 1 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 D 191.246014 190.566602 189.887191 189.207779 188.528368 187.848956 184.936089 182.023223 179.110356 176.197489 173.284622 170.371755 167.458889 164.546022 161.633155 E 0.27484721 0.279257149 0.283667088 0.288077027 0.292486966 0.296896905 0.301616198 0.306335491 0.311054784 0.315774077 0.32049337 0.325212663 0.329931955 0.334651248 0.339370541 30 T Stress, MPa 0.68 water-cement ratio 15 x 30 cm concrete cylinder cured for 28 days Calculating the Elastic Moduli 4 = 26 MPa 40% f = 10.4 MPa - SO Secant Modulus: Slope of the line corresponding to stress SO 10.4/(417 x 10-5) = 24.9 GPa Chord Modulus: Slope of the line corresponding to stress SC (10.4-16) (417x 10-6-50 x 10-6) = 24.0 GPa Tangent Modulus: Slope of the line TT drawn tangent to any point on the O- Ecurve (30 - 14.6)(1445 x 10-6 - 625 x 10) = 18.8 GPa Dynamic Modulus (Initial Tangent Modulus): Slope of the line OD from the origin 5/143 x 10-6 = 34.9 GPa 50 500 2000 2500 1000 1500 Strain, *10-6
