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APPENDIX 1 SIEVE ANALYSIS OF AGGREGATESshodhganga.inflibnet.ac.in/bitstream/10603/15807/15/15... ·...
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215 APPENDIX 1 SIEVE ANALYSIS OF AGGREGATES Table A1.1 Sieve analysis of sand IS Sieve size Weight retained, g % weight retained % weight passing Cumulative % weight retained Requirements of IS: 383 - 1970 for grading zone III 4.75 mm 0.00 0.00 100.0 0.00 90 – 100 2.36 mm 7.8 0.78 99.22 0.78 85 - 100 1.18 mm 64.4 6.44 92.78 7.22 75 - 100 600 μ 157.6 15.76 77.02 22.98 60-79 425 μ 510.0 51.0 26.02 73.98 - 300 μ 1.4 0.14 25.88 74.12 12-40 150 μ 217.2 21.72 4.16 95.84 0 - 10 Total 274.92 Fineness modulus = (274.92/100) = 2.75 Table A1.2 Sieve analysis of coarse aggregate IS sieve size Weight retained, g % weight retained % weight passing Cumulative % weight retained 19 mm 0.0 0.0 100.0 0.0 9.5 mm 2145 71.5 28.5 71.5 4.75 mm 675 22.5 6.0 94.0 2.36 mm 127.5 4.25 1.75 98.25 1.18 mm 52.5 1.75 - 100.0 600 μ 0 - - 100.0 300 μ 0 - - 100.0 150 μ 0 - - 100.0 Total 663.75 Fineness modulus = (663.75/100) = 6.64
Transcript of APPENDIX 1 SIEVE ANALYSIS OF AGGREGATESshodhganga.inflibnet.ac.in/bitstream/10603/15807/15/15... ·...
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APPENDIX 1
SIEVE ANALYSIS OF AGGREGATES
Table A1.1 Sieve analysis of sand
IS Sieve size
Weight retained,
g
%weight
retained
%weight passing
Cumulative % weight retained
Requirements of IS: 383 - 1970 for grading zone III
4.75 mm 0.00 0.00 100.0 0.00 90 – 100 2.36 mm 7.8 0.78 99.22 0.78 85 - 100 1.18 mm 64.4 6.44 92.78 7.22 75 - 100
600 µ 157.6 15.76 77.02 22.98 60-79425 µ 510.0 51.0 26.02 73.98 -300 µ 1.4 0.14 25.88 74.12 12-40150 µ 217.2 21.72 4.16 95.84 0 - 10
Total 274.92 Fineness modulus = (274.92/100) = 2.75
Table A1.2 Sieve analysis of coarse aggregate
IS sieve size
Weight retained, g
% weight retained
% weight passing
Cumulative % weight retained
19 mm 0.0 0.0 100.0 0.09.5 mm 2145 71.5 28.5 71.5
4.75 mm 675 22.5 6.0 94.02.36 mm 127.5 4.25 1.75 98.251.18 mm 52.5 1.75 - 100.0
600 µ 0 - - 100.0300 µ 0 - - 100.0150 µ 0 - - 100.0
Total 663.75 Fineness modulus = (663.75/100) = 6.64
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APPENDIX 2
MIX DESIGN OF GEOPOLYMER CONCRETE
Mix design calculations
Let density of Geopolymer Concrete = 2400 kg/m3
Total Aggregate = 77% of 2400 kg/m3
= 1848 kg/m3
Fine Aggregate = 30% of Total Aggregate
= (30/100) x 1848
= 554 kg/m3
Coarse Aggregate = 70% of Total Aggregate
= (70/100) x 1848
= 1294 kg/m3
Fly Ash + Alkaline activator solution = 23% of 2400 kg/m3
= (23/100) x 2400
= 552 kg/m3
Ratio of Alkaline Activator Solution to Fly Ash = 0.4
Alkaline Activator Solution = 0.4x Fly Ash
Alkaline Activator Solution + Fly Ash = 552 kg/m3
(0.4 x Fly Ash) + Fly Ash = 552 kg/m3
1.4 x Fly Ash = 552 kg/m3
Fly Ash = 552/1.4
= 394.3 kg/m3
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Alkaline Activator Solution = 552-394.3
= 157.7 kg/m3
Ratio of Na2Sio3 to NaOH Solution = 2.5
Na2Sio3 Solution + NaOH Solution = 157.7 kg/m3
2.5 x NaOH Solution + NaOH Solution = 157.7 kg/m3
3.5 x NaOH Solution = 157.7 kg/m3
NaOH Solution = 157.7/3.5
= 45.06 kg/m3
Na2Sio3 Solution = 157.7- 45.06
= 112.64 kg/m3
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APPENDIX 3
AXIAL STRESS-STRAIN VALUES
Table A3.1 Axial stress – strain values for GPCC specimen
Load kN
Axial StressMPa
Axial Strain
Spec 1 Spec 2 Spec 3
29.5 1.67 0.000065 0.000055 0.00006059.0 3.34 0.000125 0.000115 0.00012588.5 5.01 0.000195 0.000170 0.000185
118.0 6.68 0.000250 0.000240 0.000235147.5 8.35 0.000310 0.000315 0.000300177.0 10.02 0.000360 0.000370 0.000375206.5 11.69 0.000425 0.000440 0.000415236.0 13.36 0.000495 0.000475 0.000485265.5 15.03 0.000555 0.000535 0.000575295.0 16.70 0.000605 0.000620 0.000625
Table A3.2 Axial stress – strain values for S0.25 specimen
Load kN
Axial StressMPa
Axial Strain
Spec 1 Spec 2 Spec 3
32 1.81 0.000060 0.000065 0.000060 64 3.62 0.000125 0.000130 0.000120 96 5.44 0.000185 0.000195 0.000185
128 7.25 0.000245 0.000255 0.000255 160 9.06 0.000315 0.000320 0.000315 192 10.87 0.000385 0.000370 0.000390 224 12.68 0.000445 0.000445 0.000450 256 14.49 0.000515 0.000520 0.000505 288 16.31 0.000580 0.000575 0.000585 320 18.12 0.000645 0.000645 0.000630
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Table A3.3 Axial stress – strain values for S0.5 specimen
Load kN
Axial StressMPa
Axial Strain
Spec 1 Spec 2 Spec 3
33 1.87 0.000055 0.000065 0.000065 66 3.74 0.000120 0.000125 0.000130 99 5.61 0.000185 0.000190 0.000195 132 7.47 0.000245 0.000265 0.000255 165 9.34 0.000320 0.000315 0.000325 198 11.21 0.000385 0.000375 0.000395 231 13.08 0.000455 0.000450 0.000445 264 14.95 0.000525 0.000515 0.000510 297 16.82 0.000590 0.000585 0.000585 330 18.68 0.000660 0.000655 0.000660
Table A3.4 Axial stress – strain values for S0.75 specimen
Load kN
Axial StressMPa
Axial Strain
Spec 1 Spec 2 Spec 3
36 2.04 0.000065 0.000065 0.00006072 4.08 0.000125 0.000130 0.000125
108 6.11 0.000195 0.000190 0.000190144 8.15 0.000270 0.000255 0.000255180 10.19 0.000320 0.000325 0.000340216 12.23 0.000390 0.000400 0.000395252 14.27 0.000470 0.000460 0.000455288 16.31 0.000540 0.000540 0.000540324 18.34 0.000615 0.000605 0.000615360 20.38 0.000680 0.000685 0.000685
220
Table A3.5 Axial stress – strain values for P0.1 specimen
Load kN
Axial StressMPa
Axial Strain
Spec 1 Spec 2 Spec 3
30 1.70 0.000060 0.000055 0.00006060 3.40 0.000115 0.000120 0.000120
90 5.10 0.000175 0.000170 0.000185
120 6.79 0.000240 0.000230 0.000240
150 8.49 0.000295 0.000305 0.000285180 10.19 0.000355 0.000360 0.000360
210 11.89 0.000415 0.000430 0.000420
240 13.59 0.000485 0.000485 0.000480
270 15.29 0.000545 0.000550 0.000535300 16.99 0.000605 0.000610 0.000615
Table A3.6 Axial stress – strain values for P0.2 specimen
Load kN
Axial StressMPa
Axial Strain
Spec 1 Spec 2 Spec 3
30 1.70 0.000060 0.000070 0.00005060 3.40 0.000115 0.000120 0.00012590 5.10 0.000180 0.000185 0.000185
120 6.79 0.000235 0.000250 0.000255150 8.49 0.000305 0.000315 0.000315180 10.19 0.000365 0.000375 0.000385210 11.89 0.000435 0.000425 0.000440240 13.59 0.000505 0.000495 0.000490270 15.29 0.000555 0.000565 0.000555300 16.99 0.000615 0.000610 0.000625
221
Table A3.7 Axial stress – strain values for P0.3 specimen
Load kN
Axial StressMPa
Axial Strain
Spec 1 Spec 2 Spec 3
30 1.70 0.000055 0.000060 0.00007060 3.40 0.000120 0.000120 0.00012590 5.10 0.000185 0.000185 0.000185
120 6.79 0.000240 0.000250 0.000255150 8.49 0.000310 0.000315 0.000315180 10.19 0.000370 0.000375 0.000385210 11.89 0.000435 0.000430 0.000440240 13.59 0.000505 0.000495 0.000495270 15.29 0.000555 0.000565 0.000560300 16.99 0.000615 0.000620 0.000625
Table A3.8 Axial stress – strain values for G0.01 specimen
Load kN
Axial StressMPa
Axial Strain
Spec 1 Spec 2 Spec 3
27.5 1.56 0.000060 0.000050 0.00006555.0 3.11 0.000120 0.000115 0.00011582.5 4.67 0.000175 0.000180 0.000175
110.0 6.23 0.000240 0.000235 0.000235137.5 7.78 0.000300 0.000295 0.000295165.0 9.34 0.000355 0.000360 0.000355192.5 10.90 0.000415 0.000420 0.000415220.0 12.46 0.000475 0.000475 0.000470247.5 14.01 0.000535 0.000540 0.000540275.0 15.57 0.000595 0.000595 0.000595
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Table A3.9 Axial stress – strain values for G0.02 specimen
Load kN
Axial StressMPa
Axial Strain
Spec 1 Spec 2 Spec 3
24 1.36 0.000050 0.000060 0.00005048 2.72 0.000105 0.000110 0.00010572 4.08 0.000165 0.000160 0.00016096 5.44 0.000210 0.000220 0.000220120 6.79 0.000270 0.000275 0.000270144 8.15 0.000330 0.000320 0.000320168 9.51 0.000390 0.000375 0.000380192 10.87 0.000440 0.000440 0.000435216 12.23 0.000500 0.000495 0.000500240 13.59 0.000555 0.000550 0.000555
Table A3.10 Axial stress – strain values for G0.03 specimen
Load kN
Axial StressMPa
Axial Strain
Spec 1 Spec 2 Spec 3
31 1.76 0.000055 0.000050 0.00005062 3.51 0.000105 0.000110 0.00011093 5.27 0.000170 0.000165 0.000165
124 7.02 0.000225 0.000225 0.000225155 8.78 0.000285 0.000285 0.000290186 10.53 0.000350 0.000345 0.000350217 12.29 0.000415 0.000415 0.000410248 14.04 0.000475 0.000480 0.000475279 15.80 0.000545 0.000545 0.000555310 17.55 0.000625 0.000615 0.000615
223
APPENDIX 4
SORPTIVITY TEST RESULTS
Table A4.1 Sorptivity test results
Spec.Weight of specimens in grams at the time of
0 min 4 min 9 min 16 min 25 min 36 min 49 min 64 min 81 min 100 min 121 min
GPCC2250 2257 2259 2261 2263 2265 2267 2269 2271 2272 2273 2260 2269 2270 2272 2274 2275 2278 2279 2281 2283 2285 2345 2353 2355 2358 2359 2361 2363 2365 2367 2368 2371
S0.25
2370 2378 2379 2380 2382 2384 2386 2387 2388 2389 2390 2305 2312 2313 2316 2317 2318 2321 2323 2324 2325 2327 2331 2342 2344 2345 2347 2349 2350 2352 2353 2354 2356
S0.5
2329 2340 2342 2345 2347 2349 2350 2352 2353 2355 2358 2372 2384 2385 2387 2389 2391 2394 2396 2396 2398 2399 2338 2348 2350 2351 2353 2356 2357 2358 2359 2361 2361
S0.75
2363 2373 2375 2377 2379 2381 2383 2387 2388 2388 2390 2346 2357 2359 2361 2363 2364 2366 2368 2369 2370 2372 2256 2268 2270 2272 2273 2276 2277 2279 2281 2281 2282
P0.1
2374 2381 2383 2384 2385 2386 2389 2390 2391 2391 2392 2296 2304 2305 2306 2307 2307 2309 2310 2310 2312 2313 2334 2343 2344 2345 2347 2348 2349 2350 2351 2352 2353
P0.2
2232 2241 2243 2243 2245 2246 2248 2249 2250 2251 2253 2347 2352 2353 2353 2354 2355 2355 2356 2357 2358 2359 2313 2322 2323 2325 2326 2327 2328 2330 2331 2332 2333
P0.3
2313 2324 2327 2329 2331 2333 2336 2336 2337 2339 2341 2200 2210 2212 2214 2216 2217 2220 2221 2222 2224 2225 2231 2241 2242 2244 2245 2247 2248 2250 2251 2252 2253
G0.01
2303 2309 2310 2311 2312 2313 2314 2315 2316 2317 2318 2330 2335 2336 2337 2338 2339 2340 2341 2342 2343 2343 2329 2333 2335 2337 2338 2339 2340 2342 2343 2344 2344
G0.02
2318 2324 2327 2329 2330 2332 2333 2334 2336 2337 2339 2329 2336 2338 2340 2341 2343 2345 2346 2348 2349 2350 2282 2290 2292 2293 2295 2296 2297 2299 2301 2302 2303
G0.03
2309 2315 2316 2318 2319 2320 2321 2323 2324 2325 2326 2267 2272 2274 2275 2276 2277 2278 2279 2280 2281 2282 2371 2374 2375 2376 2377 2378 2378 2379 2380 2381 2382
224
y = 0.1861x + 0.4339R² = 0.9986
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 2 4 6 8 10 12
Square root of t
Figure A 4.1 AQ Vs t for GPCC specimens
y = 0.1549x + 0.5628R² = 0.9943
0
0.5
1
1.5
2
2.5
0 2 4 6 8 10 12
Square root of t
Figure A 4.2 AQ Vs t for S0.25 specimens
y = 0.1725x + 0.7919R² = 0.9909
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 2 4 6 8 10 12
Square root of t
Figure A 4.3 AQ Vs t for S0.5 Specimens
225
y = 0.1739x + 0.7994R² = 0.9875
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 2 4 6 8 10 12
Square root of t
Figure A 4.4 AQ Vs t for S0.75 Specimens
y = 0.1121x + 0.5945R² = 0.9929
0.00.20.40.60.81.01.21.41.61.82.0
0 2 4 6 8 10 12
Square root of t
Figure A 4.5 AQ Vs t for P0.1 Specimens
y = 0.1121x + 0.5945R² = 0.9929
0.00.20.40.60.81.01.21.41.61.82.0
0 2 4 6 8 10 12
Square root of t
Figure A 4.6 AQ Vs t for P0.2 Specimens
226
y = 0.1618x + 0.7715R² = 0.9909
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 2 4 6 8 10 12
Square root of t
Figure A 4.7 AQ Vs t for P0.3 Specimens
y = 0.1063x + 0.3226R² = 0.9929
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0 2 4 6 8 10 12
Square root of t
Figure A 4.8 AQ Vs t for G0.01 Specimens
y = 0.1240x + 0.3271R² = 0.9900
0.00.20.40.60.81.01.21.41.61.8
0 2 4 6 8 10 12
Square root of t
Figure A 4.9 AQ Vs t for G0.02 Specimens
227
y = 0.1451x + 0.3638R² = 0.9902
0.0
0.5
1.0
1.5
2.0
2.5
0 2 4 6 8 10 12
Square root of t
Figure A 4.10 AQ Vs t for G0.03 Specimens
228
APPENDIX 5
LOAD – DEFLECTION VALUES
Table A5.1 Experimental load-deflection values for GPCC beam
LoadkN
Deflection mm
LoadkN
Deflection mm
0 0 12.0 1.680.5 0.03 12.5 1.751.0 0.06 13.0 1.821.5 0.09 13.5 1.892.0 0.15 14.0 1.972.5 0.19 14.5 2.043.0 0.25 15.0 2.093.5 0.33 15.5 2.164.0 0.41 16.0 2.224.5 0.51 16.5 2.295.0 0.57 17.0 2.385.5 0.65 17.5 2.466.0 0.74 18.0 2.536.5 0.85 18.5 2.617.0 0.92 19.0 2.7 7.5 1.01 19.5 2.8 8.0 1.09 20.0 2.9 8.5 1.17 20.5 3.019.0 1.24 21.0 3.129.5 1.31 21.5 3.34
10.0 1.39 22.0 4.2410.5 1.46 22.5 5.3911.0 1.53 23.0 6.7411.5 1.6 23.4 8.52
229
Table A5.2 Experimental load-deflection values for SFRGPCC beams
S0.25 S0.5 S0.75
LoadkN
Deflection mm
LoadkN
Deflection mm
LoadkN
Deflection mm
0 0.00 0 0.00 0 0.000.5 0.01 0.5 0.02 0.5 0.021.0 0.02 1.0 0.04 1.0 0.051.5 0.03 1.5 0.06 1.5 0.072.0 0.06 2.0 0.09 2.0 0.112.5 0.12 2.5 0.12 2.5 0.143.0 0.16 3.0 0.14 3.0 0.173.5 0.20 3.5 0.17 3.5 0.214.0 0.24 4.0 0.20 4.0 0.254.5 0.31 4.5 0.24 4.5 0.295.0 0.37 5.0 0.28 5.0 0.345.5 0.45 5.5 0.32 5.5 0.396.0 0.52 6.0 0.37 6.0 0.456.5 0.59 6.5 0.42 6.5 0.517.0 0.65 7.0 0.47 7.0 0.567.5 0.71 7.5 0.51 7.5 0.628.0 0.79 8.0 0.55 8.0 0.678.5 0.88 8.5 0.59 8.5 0.729.0 0.92 9.0 0.65 9.0 0.799.5 0.96 9.5 0.70 9.5 0.8510.0 1.02 10.0 0.75 10.0 0.9110.5 1.08 10.5 0.80 10.5 0.9711.0 1.15 11.0 0.85 11.0 1.0311.5 1.21 11.5 0.91 11.5 1.1012.0 1.27 12.0 0.97 12.0 1.1712.5 1.34 12.5 1.02 12.5 1.2413.0 1.40 13.0 1.08 13.0 1.3113.5 1.48 13.5 1.14 13.5 1.3814.0 1.56 14.0 1.20 14.0 1.4514.5 1.64 14.5 1.25 14.5 1.5215.0 1.71 15.0 1.31 15.0 1.5915.5 1.78 15.5 1.36 15.5 1.6516.0 1.85 16.0 1.42 16.0 1.7216.5 1.89 16.5 1.47 16.5 1.7817.0 1.94 17.0 1.52 17.0 1.85
230
Table A5.2 (Continued)
S0.25 S0.5 S0.75
LoadkN
Deflection mm
LoadkN
Deflection mm
LoadkN
Deflection mm
17.5 2.04 17.5 1.58 17.5 1.9118.0 2.11 18.0 1.65 18.0 1.9618.5 2.17 18.5 1.74 18.5 2.0519.0 2.25 19.0 1.79 19.0 2.1119.5 2.34 19.5 1.85 19.5 2.1720.0 2.40 20.0 1.91 20.0 2.2520.5 2.50 20.5 1.95 20.5 2.3021.0 2.57 21.0 2.01 21.0 2.3621.5 2.66 21.5 2.08 21.5 2.4522.0 2.76 22.0 2.13 22.0 2.5122.5 2.86 22.5 2.19 22.5 2.5823.0 2.95 23.0 2.27 23.0 2.6723.5 3.03 23.5 2.32 23.5 2.7324.0 3.12 24.0 2.40 24.0 2.8224.5 3.25 24.5 2.46 24.5 2.8925.0 3.42 25.0 2.52 25.0 2.9525.5 3.59 25.5 2.59 25.5 3.0526.0 3.82 26.0 2.72 26.0 3.1126.5 4.20 26.5 2.88 26.5 3.1627.0 5.66 27.0 3.02 27.0 3.2227.5 7.94 27.5 3.15 27.5 3.3027.6 10.30 28.0 3.29 28.0 3.36
- - 28.5 3.41 28.5 3.43- - 29.0 3.63 29.0 3.50- - 29.5 4.18 29.5 3.58- - 30.0 4.96 30.0 3.66- - 30.5 6.14 30.5 3.80- - 31.0 8.01 31.0 3.99- - 31.5 10.9 31.5 4.15- - 31.85 14.14 32.0 4.29- - - - 32.5 4.63- - - - 33.0 5.70- - - - 33.5 7.42- - - - 34.0 9.89- - - - 34.5 12.98
231
Table A5.3 Experimental load-deflection values for PFRGPCC beams
P0.1 P0.2 P0.3
LoadkN
Deflection mm
Load kN
Deflection mm
Load kN
Deflection mm
0 0 0.0 0 0 0.000.5 0.02 0.5 0.03 0.5 0.011.0 0.05 1.0 0.06 1.0 0.041.5 0.10 1.5 0.10 1.5 0.062.0 0.16 2.0 0.14 2.0 0.102.5 0.24 2.5 0.18 2.5 0.153.0 0.33 3.0 0.24 3.0 0.193.5 0.41 3.5 0.26 3.5 0.244.0 0.50 4.0 0.35 4.0 0.294.5 0.54 4.5 0.42 4.5 0.345.0 0.60 5.0 0.48 5.0 0.405.5 0.67 5.5 0.57 5.5 0.496.0 0.74 6.0 0.63 6.0 0.596.5 0.81 6.5 0.70 6.5 0.667.0 0.90 7.0 0.77 7.0 0.757.5 0.96 7.5 0.84 7.5 0.848.0 1.03 8.0 0.90 8.0 0.918.5 1.09 8.5 0.96 8.5 0.969.0 1.17 9.0 1.05 9.0 1.029.5 1.25 9.5 1.12 9.5 1.09
10.0 1.32 10.0 1.20 10.0 1.1410.5 1.39 10.5 1.30 10.5 1.2111.0 1.45 11.0 1.34 11.0 1.2811.5 1.53 11.5 1.43 11.5 1.3412.0 1.62 12.0 1.50 12.0 1.4312.5 1.71 12.5 1.58 12.5 1.5113.0 1.78 13.0 1.69 13.0 1.5913.5 1.85 13.5 1.77 13.5 1.67
232
Table A5.3 (Continued)
P0.1 P0.2 P0.3
LoadkN
Deflection mm
Load kN
Deflection mm
Load kN
Deflection mm
14.0 1.93 14.0 1.85 14.0 1.7414.5 2.01 14.5 1.94 14.5 1.8215.0 2.10 15.0 2.03 15.0 1.9015.5 2.18 15.5 2.09 15.5 1.9816.0 2.25 16.0 2.17 16.0 2.0316.5 2.32 16.5 2.27 16.5 2.1117.0 2.39 17.0 2.35 17.0 2.1917.5 2.47 17.5 2.46 17.5 2.2918.0 2.55 18.0 2.52 18.0 2.3318.5 2.64 18.5 2.63 18.5 2.4319.0 2.71 19.0 2.70 19.0 2.4919.5 2.8 19.5 2.80 19.5 2.5620.0 2.89 20.0 2.89 20.0 2.6320.5 2.97 20.5 2.98 20.5 2.7221.0 3.09 21.0 3.10 21.0 2.8121.5 3.25 21.5 3.21 21.5 2.9822.0 3.57 22.0 3.49 22.0 3.1822.5 4.19 22.5 4.35 22.5 3.7723.0 5.10 23.0 5.64 23.0 4.6223.5 6.65 23.5 7.32 23.5 5.7423.65 8.55 - - 23.85 7.14
233
Table A5.4 Experimental load-deflection values for GFRGPCC beams
G0.01 G0.02 G0.03
LoadkN
Deflection mm
LoadkN
Deflection mm
Load kN
Deflection mm
0 0 0 0.00 0 0.000.5 0.05 0.5 0.03 0.5 0.011.0 0.09 1.0 0.06 1.0 0.011.5 0.14 1.5 0.09 1.5 0.022.0 0.19 2.0 0.13 2.0 0.042.5 0.24 2.5 0.18 2.5 0.083.0 0.29 3.0 0.23 3.0 0.123.5 0.34 3.5 0.29 3.5 0.174.0 0.38 4.0 0.36 4.0 0.224.5 0.43 4.5 0.44 4.5 0.285.0 0.48 5.0 0.51 5.0 0.365.5 0.53 5.5 0.60 5.5 0.426.0 0.61 6.0 0.68 6.0 0.496.5 0.67 6.5 0.78 6.5 0.567.0 0.74 7.0 0.87 7.0 0.637.5 0.82 7.5 0.92 7.5 0.708.0 0.89 8.0 1.02 8.0 0.758.5 0.96 8.5 1.11 8.5 0.809.0 1.02 9.0 1.18 9.0 0.859.5 1.09 9.5 1.23 9.5 0.92
10.0 1.18 10.0 1.30 10.0 0.9910.5 1.26 10.5 1.37 10.5 1.0711.0 1.32 11.0 1.47 11.0 1.1211.5 1.41 11.5 1.58 11.5 1.1812.0 1.51 12.0 1.63 12.0 1.2512.5 1.60 12.5 1.72 12.5 1.3213.0 1.68 13.0 1.80 13.0 1.3813.5 1.76 13.5 1.87 13.5 1.45
234
Table A5.4 (Continued)
G0.01 G0.02 G0.03
LoadkN
Deflection mm
LoadkN
Deflection mm
Load kN
Deflection mm
14.0 1.86 14.0 1.95 14.0 1.5214.5 1.94 14.5 2.03 14.5 1.6315.0 2.02 15.0 2.11 15.0 1.6915.5 2.11 15.5 2.19 15.5 1.7816.0 2.19 16.0 2.27 16.0 1.8816.5 2.29 16.5 2.38 16.5 1.9517.0 2.41 17.0 2.46 17.0 2.0617.5 2.52 17.5 2.53 17.5 2.1518.0 2.60 18.0 2.61 18.0 2.2518.5 2.74 18.5 2.73 18.5 2.3519.0 2.81 19.0 2.81 19.0 2.4719.5 2.90 19.5 2.90 19.5 2.5820.0 3.00 20.0 2.99 20.0 2.6420.5 3.13 20.5 3.08 20.5 2.7421.0 3.24 21.0 3.18 21.0 2.8821.5 3.35 21.5 3.32 21.5 2.9722.0 3.47 22.0 3.49 22.0 3.1222.5 3.68 22.5 3.75 22.5 3.2723.0 3.99 23.0 4.89 23.0 3.6523.5 4.78 23.5 7.02 23.5 4.5124.0 7.11 23.9 9.56 24.0 5.7224.5 9.95 - - 24.5 7.3124.7 13.87 - - 24.865 9.45
235
Table A5.5 Analytical load-deflection values for GPCC beam
Load kN
Deflection mm
Load kN
Deflection mm
Load kN
Deflection mm
0 0 6.30 0.61 14.45 1.770.89 0.03 6.44 0.65 14.47 1.791.79 0.06 6.58 0.66 14.48 1.802.69 0.09 6.78 0.68 14.50 1.803.59 0.12 7.09 0.72 14.52 1.814.49 0.15 7.40 0.77 14.55 1.814.89 0.16 7.43 0.77 14.59 1.825.30 0.17 7.44 0.80 14.65 1.835.35 0.17 7.45 0.81 14.74 1.845.36 0.44 7.47 0.81 14.88 1.865.38 0.44 7.49 0.81 15.08 1.895.39 0.44 7.54 0.82 15.39 1.935.42 0.45 7.60 0.82 15.85 1.995.46 0.45 7.69 0.83 16.54 2.105.52 0.46 7.82 0.85 17.24 2.205.61 0.46 8.03 0.87 18.14 2.335.75 0.48 8.34 0.92 19.04 2.465.77 0.48 8.64 0.96 19.94 2.605.78 0.53 9.11 1.02 20.84 2.745.79 0.53 9.80 1.12 21.74 2.865.81 0.54 10.49 1.21 22.64 3.065.84 0.54 11.39 1.32 23.04 3.895.88 0.54 12.29 1.46 23.22 4.935.94 0.55 13.19 1.59 23.41 6.186.03 0.56 14.09 1.70 23.68 8.946.17 0.58 14.27 1.73 - -
236
Table A5.6 Analytical load-deflection values for S0.25 beam
LoadkN
Deflection mm
LoadkN
Deflection mm
LoadkN
Deflection mm
0 0 7.21 0.63 14.61 1.570.30 0.01 7.23 0.64 14.91 1.610.60 0.02 7.25 0.64 15.21 1.670.90 0.03 7.29 0.64 15.51 1.701.20 0.04 7.35 0.65 15.81 1.741.50 0.05 7.45 0.66 16.11 1.771.80 0.06 7.58 0.67 16.41 1.822.10 0.07 7.79 0.69 16.71 1.852.40 0.08 7.99 0.71 17.01 1.892.70 0.09 8.29 0.75 17.31 1.933.00 0.10 8.43 0.80 17.61 1.963.30 0.11 8.56 0.81 17.91 2.003.60 0.12 8.76 0.83 18.21 2.053.90 0.13 9.06 0.87 18.51 2.094.20 0.13 9.36 0.91 18.81 2.134.50 0.14 9.66 0.94 19.11 2.174.80 0.15 9.96 0.97 19.41 2.215.10 0.16 10.26 1.00 19.71 2.265.40 0.17 10.28 1.03 20.01 2.315.54 0.18 10.29 1.03 20.31 2.355.56 0.18 10.31 1.03 20.61 2.405.57 0.18 10.33 1.04 20.91 2.445.59 0.18 10.37 1.04 21.21 2.485.60 0.39 10.43 1.05 21.51 2.525.61 0.39 10.53 1.06 21.81 2.565.63 0.39 10.66 1.08 22.11 2.605.66 0.40 10.80 1.09 22.41 2.645.70 0.40 11.00 1.11 22.71 2.685.76 0.41 11.30 1.15 23.01 2.725.85 0.41 11.60 1.18 23.31 2.765.98 0.43 11.90 1.22 23.61 2.806.12 0.45 12.20 1.25 23.91 2.846.33 0.47 12.50 1.29 24.21 2.886.42 0.48 12.80 1.33 24.51 2.926.43 0.53 13.10 1.37 24.81 2.976.44 0.53 13.40 1.40 25.11 3.026.46 0.53 13.42 1.43 25.41 3.066.49 0.53 13.43 1.43 25.71 3.146.53 0.54 13.45 1.43 26.01 3.326.59 0.54 13.47 1.44 26.31 3.636.68 0.55 13.51 1.44 26.61 3.996.82 0.56 13.57 1.45 26.91 4.677.02 0.58 13.67 1.46 27.21 5.777.16 0.59 13.80 1.47 27.51 7.847.18 0.60 14.01 1.50 27.81 11.297.20 0.63 14.31 1.53 - -
237
Table A5.7 Analytical load-deflection values for S0. 5 beam
Load kN
Deflection mm
Load kN
Deflection mm
Load kN
Deflection mm
0 0 9.61 0.77 23.90 2.530.30 0.01 9.74 0.78 24.20 2.570.60 0.02 9.95 0.80 24.50 2.610.90 0.03 10.25 0.83 24.80 2.641.20 0.04 10.55 0.86 25.10 2.701.50 0.05 10.85 0.91 25.40 2.741.80 0.06 10.98 0.92 25.70 2.792.10 0.07 11.12 0.97 26.00 2.832.40 0.08 11.25 0.98 26.30 2.862.70 0.09 11.45 1.00 26.60 2.903.00 0.10 11.75 1.02 26.90 2.943.30 0.10 12.05 1.05 27.20 2.983.60 0.11 12.35 1.08 27.50 3.023.90 0.12 12.49 1.09 27.80 3.064.20 0.13 12.55 1.10 28.10 3.124.50 0.14 12.61 1.12 28.40 3.194.80 0.15 12.67 1.13 28.70 3.265.10 0.16 12.76 1.13 29.00 3.365.40 0.17 12.90 1.15 29.30 3.475.70 0.18 13.10 1.17 29.60 3.706.00 0.19 13.40 1.20 29.90 3.936.30 0.20 13.70 1.23 29.93 3.966.60 0.21 14.00 1.27 29.94 3.976.90 0.22 14.30 1.33 29.96 3.997.20 0.23 14.60 1.37 29.97 3.997.26 0.23 14.90 1.40 29.99 4.017.29 0.23 15.20 1.44 30.00 4.047.30 0.41 15.50 1.47 30.02 4.067.31 0.45 15.80 1.50 30.05 4.08
238
Table A5.7 (Continued)
Load kN
Deflection mm
Load kN
Deflection mm
Load kN
Deflection mm
7.32 0.45 16.10 1.54 30.09 4.117.34 0.46 16.40 1.57 30.15 4.167.37 0.47 16.70 1.61 30.24 4.297.40 0.47 17.00 1.64 30.33 4.397.44 0.47 17.30 1.67 30.47 4.567.50 0.48 17.60 1.70 30.48 4.587.59 0.48 17.90 1.77 30.49 4.587.73 0.50 18.20 1.81 30.51 4.627.86 0.53 18.50 1.84 30.53 4.648.07 0.54 18.80 1.88 30.56 4.688.37 0.57 19.10 1.91 30.60 4.738.38 0.61 19.40 1.94 30.66 4.848.39 0.61 19.70 2.01 30.72 4.968.41 0.62 20.00 2.05 30.81 5.368.44 0.62 20.30 2.09 30.90 5.658.45 0.64 20.60 2.12 30.99 5.888.46 0.64 20.90 2.16 31.13 6.288.48 0.64 21.20 2.19 31.26 6.778.50 0.64 21.50 2.22 31.47 7.828.55 0.64 21.80 2.26 31.67 9.368.61 0.65 22.10 2.29 31.88 11.478.70 0.66 22.40 2.33 32.08 14.318.83 0.67 22.70 2.39 - -9.04 0.68 23.00 2.42 - -9.34 0.72 23.30 2.46 - -9.47 0.74 23.60 2.50 - -
239
Table A5.8 Analytical load-deflection values for S0. 75 beam
LoadkN
Deflection mm
LoadkN
Deflection mm
LoadkN
Deflection mm
0 0 11.17 0.86 20.07 1.870.52 0.02 11.26 0.87 20.11 1.871.03 0.03 11.40 0.88 20.17 1.881.55 0.05 11.60 0.91 20.26 1.882.07 0.06 11.81 0.93 20.40 1.902.58 0.08 12.12 0.95 20.61 1.923.10 0.10 12.33 0.97 20.91 1.953.61 0.11 12.53 0.99 21.37 2.004.13 0.13 12.60 1.00 21.89 2.084.65 0.15 12.61 1.04 22.41 2.145.16 0.16 12.62 1.04 22.92 2.195.68 0.18 12.64 1.04 23.44 2.246.19 0.19 12.66 1.05 23.95 2.306.71 0.21 12.70 1.05 24.47 2.357.23 0.23 12.77 1.05 24.99 2.417.74 0.24 12.86 1.06 25.50 2.508.26 0.49 12.99 1.07 26.02 2.568.77 0.55 13.20 1.10 26.53 2.619.29 0.59 13.40 1.12 27.05 2.679.40 0.60 13.71 1.14 27.57 2.739.50 0.67 14.17 1.19 28.08 2.799.60 0.68 14.63 1.24 28.60 2.859.67 0.68 15.15 1.28 29.11 2.959.75 0.70 15.67 1.35 29.63 3.029.82 0.71 16.18 1.42 30.15 3.089.92 0.72 16.70 1.48 30.66 3.16
10.08 0.73 17.21 1.53 31.18 3.2810.32 0.75 17.73 1.58 31.69 3.4410.68 0.78 18.25 1.64 32.21 3.6110.91 0.80 18.76 1.69 32.73 3.8610.95 0.80 19.28 1.74 33.24 4.2711.00 0.81 19.79 1.79 33.76 4.7911.01 0.85 19.90 1.81 34.27 5.4811.03 0.85 20.00 1.82 34.79 6.8311.04 0.85 20.01 1.86 35.31 8.8311.07 0.86 20.03 1.86 35.54 10.6311.11 0.86 20.04 1.86 35.77 13.33
240
Table A5.9 Analytical load-deflection values for P0.1 beam
LoadkN
Deflection mm
LoadkN
Deflection mm
LoadkN
Deflection mm
0 0 6.57 0.64 14.67 1.760.30 0.01 6.87 0.68 14.97 1.800.60 0.02 7.17 0.71 15.27 1.840.90 0.03 7.30 0.73 15.57 1.881.20 0.04 7.44 0.76 15.87 1.951.50 0.05 7.64 0.78 16.17 1.991.80 0.06 7.77 0.80 16.47 2.032.10 0.07 7.83 0.82 16.77 2.072.40 0.08 7.89 0.83 17.07 2.112.70 0.09 7.99 0.84 17.37 2.153.00 0.10 8.12 0.86 17.67 2.193.30 0.11 8.26 0.88 17.97 2.263.60 0.12 8.46 0.91 18.27 2.303.90 0.13 8.67 0.94 18.57 2.344.20 0.14 8.97 0.98 18.87 2.394.50 0.15 9.27 1.02 19.17 2.444.80 0.16 9.57 1.07 19.47 2.485.10 0.17 9.87 1.11 19.77 2.535.40 0.18 10.17 1.14 20.07 2.575.70 0.19 10.47 1.19 20.37 2.615.84 0.19 10.77 1.23 20.67 2.655.90 0.19 11.07 1.26 20.97 2.695.92 0.19 11.37 1.31 21.27 2.735.94 0.47 11.67 1.34 21.57 2.775.95 0.57 11.97 1.38 21.87 2.815.96 0.57 12.27 1.42 22.17 2.865.98 0.57 12.57 1.46 22.47 2.906.00 0.58 12.87 1.50 22.77 3.106.03 0.58 13.17 1.54 23.07 3.746.07 0.59 13.47 1.60 23.37 5.106.13 0.59 13.77 1.64 23.67 6.456.22 0.60 14.07 1.68 23.97 8.736.36 0.62 14.37 1.72 - -
241
Table A5.10 Analytical load-deflection values for P0.2 beam
LoadkN
Deflection mm
LoadkN
Deflection mm
LoadkN
Deflection mm
0 0 6.84 0.63 13.83 1.630.30 0.01 6.90 0.64 14.13 1.680.60 0.02 6.99 0.66 14.43 1.730.90 0.03 7.08 0.68 14.73 1.771.20 0.04 7.22 0.69 15.03 1.811.50 0.05 7.31 0.71 15.33 1.851.80 0.06 7.40 0.74 15.63 1.912.10 0.07 7.50 0.75 15.93 1.962.40 0.08 7.63 0.77 16.23 1.992.70 0.09 7.84 0.79 16.53 2.043.00 0.10 8.14 0.82 16.83 2.083.30 0.11 8.20 0.83 17.13 2.123.60 0.12 8.26 0.85 17.43 2.163.90 0.13 8.32 0.86 17.73 2.204.20 0.14 8.41 0.87 18.03 2.244.50 0.15 8.55 0.89 18.33 2.284.80 0.16 8.76 0.92 18.63 2.325.10 0.17 8.96 0.97 18.93 2.395.40 0.18 9.17 1.00 19.23 2.445.70 0.19 9.47 1.04 19.53 2.486.00 0.20 9.77 1.08 19.83 2.526.14 0.20 10.07 1.12 20.13 2.576.15 0.20 10.37 1.15 20.43 2.626.16 0.50 10.43 1.18 20.73 2.666.17 0.51 10.49 1.19 21.03 2.716.19 0.51 10.58 1.20 21.33 2.766.22 0.51 10.72 1.22 21.63 2.806.26 0.51 10.92 1.25 21.93 2.846.32 0.52 11.13 1.27 22.23 2.906.41 0.53 11.43 1.31 22.53 2.946.55 0.54 11.73 1.35 22.83 3.136.64 0.55 12.03 1.38 23.13 3.706.73 0.57 12.33 1.43 23.43 4.586.74 0.61 12.63 1.47 23.73 5.676.75 0.62 12.93 1.50 24.03 7.476.77 0.63 13.23 1.54 - -6.80 0.63 13.53 1.59 - -
242
Table A5.11 Analytical load-deflection values for P0.3 beam
Load kN
Deflection mm
Load kN
Deflection mm
Load kN
Deflection mm
0 0 7.44 0.69 9.66 1.041.20 0.04 7.53 0.70 9.80 1.072.40 0.08 7.67 0.72 9.94 1.093.60 0.12 7.81 0.73 10.14 1.114.80 0.16 8.01 0.76 10.45 1.156.00 0.20 8.15 0.77 10.76 1.206.54 0.21 8.21 0.80 11.22 1.256.78 0.22 8.28 0.81 11.91 1.366.80 0.55 8.37 0.82 12.60 1.446.81 0.56 8.51 0.84 13.64 1.586.83 0.56 8.72 0.87 14.68 1.716.85 0.56 8.93 0.89 15.22 1.826.89 0.56 9.25 0.93 15.76 1.896.95 0.57 9.34 0.94 16.57 2.007.04 0.58 9.38 0.95 17.77 2.167.18 0.59 9.40 0.97 18.97 2.377.27 0.60 9.42 1.01 20.17 2.527.29 0.66 9.43 1.02 21.37 2.727.30 0.67 9.45 1.02 22.57 2.897.32 0.68 9.47 1.02 23.77 5.157.34 0.68 9.51 1.03 24.31 7.937.38 0.69 9.57 1.03 - -
243
Table A5.12 Analytical load-deflection values for G0.01 beam
Load kN
Deflection mm
Load kN
Deflection mm
Load kN
Deflection mm
0 0 5.72 0.52 12.83 1.540.60 0.02 5.76 0.53 13.43 1.621.20 0.04 5.82 0.53 13.70 1.661.80 0.06 5.91 0.54 13.97 1.712.40 0.08 6.05 0.56 14.24 1.753.00 0.10 6.25 0.62 14.64 1.803.60 0.12 6.46 0.65 15.24 1.884.20 0.14 6.77 0.69 15.84 1.974.80 0.16 6.97 0.71 16.44 2.055.07 0.16 7.02 0.73 17.04 2.165.19 0.17 7.06 0.74 17.64 2.255.25 0.17 7.12 0.76 18.24 2.345.30 0.17 7.18 0.77 18.84 2.435.31 0.43 7.28 0.78 19.44 2.515.32 0.43 7.42 0.80 20.04 2.605.34 0.44 7.63 0.82 20.64 2.685.37 0.44 7.95 0.87 21.24 2.775.41 0.44 8.27 0.91 21.84 2.865.47 0.45 8.75 0.99 22.44 2.945.56 0.46 9.23 1.04 23.04 3.585.62 0.46 9.83 1.12 23.64 5.615.64 0.51 10.43 1.20 24.24 9.275.65 0.51 11.03 1.28 24.84 14.435.67 0.51 11.63 1.37 - -5.69 0.52 12.23 1.46 - -
244
Table A5.13 Analytical load-deflection values for G0.02 beam
Load kN
Deflection mm
Load kN
Deflection mm
Load kN
Deflection mm
0 0 5.11 0.46 7.10 0.771.20 0.04 5.20 0.48 7.30 0.802.40 0.08 5.29 0.49 7.51 0.833.60 0.12 5.43 0.51 7.81 0.874.14 0.13 5.63 0.53 8.27 0.934.68 0.15 5.84 0.55 8.74 0.994.75 0.15 5.98 0.59 9.43 1.084.77 0.15 6.12 0.61 10.12 1.174.78 0.39 6.32 0.63 11.16 1.334.79 0.40 6.39 0.66 12.20 1.464.81 0.40 6.45 0.66 13.40 1.654.83 0.40 6.54 0.67 14.60 1.814.85 0.41 6.69 0.69 15.80 2.004.87 0.42 6.70 0.70 17.00 2.174.90 0.43 6.71 0.72 18.20 2.354.94 0.43 6.72 0.73 19.40 2.524.95 0.44 6.74 0.73 20.60 2.694.96 0.45 6.77 0.73 21.80 2.884.98 0.45 6.81 0.74 23.00 3.415.01 0.45 6.87 0.74 24.20 7.145.05 0.46 6.96 0.75 24.74 9.75
245
Table A5.14 Analytical load-deflection values for G0.03 beam
Load kN
Deflection mm
Load kN
Deflection mm
Load kN
Deflection mm
0 0 7.06 0.65 9.27 1.001.20 0.04 7.15 0.65 9.74 1.062.40 0.08 7.29 0.67 10.21 1.133.60 0.12 7.49 0.70 10.67 1.194.80 0.16 7.51 0.70 11.37 1.286.00 0.19 7.53 0.71 11.85 1.366.24 0.20 7.55 0.72 12.32 1.426.27 0.20 7.57 0.73 13.03 1.536.29 0.20 7.60 0.73 13.74 1.626.30 0.51 7.61 0.77 14.80 1.776.31 0.51 7.62 0.78 15.87 1.906.33 0.51 7.64 0.78 16.41 1.986.36 0.52 7.67 0.78 16.95 2.076.40 0.52 7.71 0.79 17.49 2.156.46 0.53 7.77 0.79 18.30 2.266.55 0.54 7.86 0.80 19.50 2.456.69 0.55 7.99 0.82 20.70 2.626.89 0.57 8.20 0.84 21.90 2.796.90 0.63 8.34 0.86 23.10 3.276.91 0.63 8.48 0.89 23.64 4.026.93 0.63 8.61 0.92 24.18 5.456.96 0.64 8.75 0.94 24.72 7.397.00 0.64 8.96 0.96 25.26 9.64
246
APPENDIX 6
THEORETICAL STRESS CALCULATIONS
Figure A6.1 Loading diagram in ANSYS model
First crack load for GPCC beam predicted by ANSYS, W = 5353N
Maximum Moment Mmax = 5353 9003 3
Wl = 1605900N.mm
The gross moment of Inertia, IG = 3 3100 150
12 12bd = 28125000 mm4
The modulus of elasticity of concrete = 25330 MPa
Flexural strength of concrete fr =3.48 MPa
The stresses at the extreme tension fibre are calculated using a transformed
moment of inertia of the concrete and steel reinforcement.
Transformed area of steel , (As)t = m As = 7.9 x 100.48 = 793.37 mm2
distributed on each side of the concrete cross section.
The distance from the top fibre to the neutral axis of the transformed moment
of inertia is given by
1 1 2 2
1 2
(1500 75) (793.37 131)'(1500 793.37)
A y A yyA A
= 77.81mm
W W
300mm 300mm 300mm
247
The transformed moment of inertia is given by
Itr = [Ig +Ad2] concrete + [Ad2] steel
Itr = [28125000 + 15000 x (-2.81)2 ] + [793.37 x (53.19)2]
Itr = 30488018 mm4
The stress at the exreme tension fibre is then calculated using
1605900 72.1930488018
bct
tr
MyfI
fct = 3.80 MPa
Theoretical Deflection calculations
The deflection at the centerline of the concrete beam at a load of 5353N is
given by
2 2
max(3 4 )24 tr
Wa l aEI
2 2
max
5353 300(3 900 4 300 )24 25330 30488018
max 0.16 mm
Theoretical First crack load Calculations
The load at first crack is calculated from
bct
tr
MyfI
3 ct tr
b
f IPl y
3 3.48 30488018900 72.19
P
4899P N
