Young Modulus and Poisson Ratio
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Transcript of Young Modulus and Poisson Ratio
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Modulus of Elasticity and Poissons Ratio of ConcreteKalia Shibao & Jessica LeSpring 2002Presented in fulfillment of CE 334L : Mechanical Behavior of Materials
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IntroductionWhile the American Society for Testing and Materials (ASTM) continues to provide working standards for the concrete industry, definitive values for the materials elastic behavior are not able to be reported due to the heterogeneous nature of concrete
This uncertainty of Youngs Modulus makes it difficult to predict a concrete specimens deformation under a given load and known stress
The following is an attempt to verify current concrete code standards in addition to better understanding the elastic behavior of uniaxially loaded concrete test cylinders
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Project ObjectiveThe ultimate objective of our testing is to obtain the values for Youngs Modulus and Poissons Ratio of concrete
By graphing and analyzing the data we obtain, we will quantify the actual values of YM and PR of our specimens and shall compare it to the calculated theoretical values
Through comparison, we can identify sources of error in lab procedure or inconsistencies with theoretical calculations
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Materials / Equipment UsedSix Test Cylinders 6 diameter, 12 height12 strain gauges, two per cylindergauge factor 2.055 0.05 12 prepared wires, one wire per strain gaugeTwo Strain Indicatorsto read lateral and longitudinal strainSATEC Universal Testing Machine
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Testing ProcedureCap each end of specimen with sulfurlevels surface to insure accurate data acquisitionAffix two strain gauges to each specimenaffixed in lateral and longitudinal directionSolder wires to strain gauges
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This is what the test cylinders should look like!
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Testing Procedure (cont)Check wire connection with ohmmetershould read approximately 120 ohms to insure proper reading from strain indicatorSet up strain indicator and connect wires to apparatus in a quarter bridge orientation
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Test Set UpStrain IndicatorsSATEC Testing MachineTest Specimen
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Testing Procedure (cont)Compress each cylinder until failureRecord strain and plot dataAnalyze results to quantify Youngs Modulus and Poissons Ratio
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Equations - Calculations Area: pr2 = p(3)2 = 9p = 28.27 Stress: Load / Area = Load / 28.27 Yield Stress: 0.4 fc Theoretical Youngs Modulus: E = 57,000 *(fc)^1/2 psi Different values of E are experimentally determined by:Secant Modulus from the graph, draw a line from the origin to 0.4 fc the slope of this line is the secant modulus Chord Modulus E = S2 S1 e2 0.00005 where S2 = 0.4 fc e2 = longitudinal strain at 0.4 fc S1 = stress at 0.00005 long. straine1 = 50.0 x 10-6
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Equations Calculations (cont)Theoretical Poissons Ratio: n = lateral strain ex longitudinal straineyDesirable Range : 0.20 0.21 0.15 0.25 (for concrete aged 50 years)Poissons ratio is experimentally determined by:n = et2 et1 e2 0.00005where et2 = lateral strain at 0.4 fce2 = longitudinal strain at 0.4 fc et1= lateral strain at S1e1 = 50.0 x 10-6=
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Experimental Calculation
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Results: Test Cylinder #1Graph longitudinal strainlateral strainE = 3.9454 x 106Yield strength = 0.4 fclongitudinal strainUltimate strength = fc
Chart1
000
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6487.08878669976487.0887866997
6534.48885744616534.4888574461
6436.85886098346436.8588609834
lateral strain vs. stress
longitudinal strain vs. stress
linear
Elastic Behavior Line (Secant)
Strain (10-6)
Stress (psi)
Figure 1. Strain vs. Stress of Cylinder 1
ACI Code
E=57000(f'c)^0.5
f'cEf'cE
0000
50403050.865276332
100570000
200806101.730552664
250901249.133147988
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6500014532205.6137394E1=4238453V1=0.2821440.13639480005098234.98869952
7000015080782.4730682E2=4843294V2=0.15063584005224136.29224966
7500015610092.8888972E3=1238129V3=0.07315088005347073.96619871
8000016122034.6110533E4=1922131V4=0.06807292005467247.9365765
8500016618212.9003091E5=3870464V5=0.10796796005584836.61354565
9000017100000E6=10516068V6=0.545378100005700000
9500017568579.9084616104005812882.24549577
10000018024982.6629598f'c 1=6785108005923613.76188556
10500018470110.9904624f'c 2=6628112006032312.98922727
11000018904761.3050258f'c 3=6537116006139087.88013333
11500019329640.451907f'c 4=6917120006244037.15555889
12000019745379.2062852f'c 5=6817124006347251.37362622
12500020152543.2638166f'c 6=6685128006448813.84442131
13000020551642.2701447132006548801.41705335
13500020943137.3007962136006647285.16012364
14000021327447.1046115140006744330.95273356
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15500022440922.4409337152007027431.96338463
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21500026429812.7121628200008061017.30552664
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26500029342545.901813240008830402.02935291
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28500030429673.0182892256009120000
29000030695439.4006667260009190973.83306035
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31500031991170.6569172280009537924.30248846
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33000032744007.0852668292009740164.26966199
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35000033721654.76366783080010003459.401627
35500033961669.5702673120010068207.3876137
360000342000003160010132541.6357398
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37000034671746.42269993240010260000
37500034905228.83466033280010323139.0574767
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38500035367569.89107393360010448272.5844993
39000035596488.59087093400010510280.6813139
39500035823944.50643313440010571925.0848651
40000036049965.32591953480010633212.1205212
40500036274577.87486993520010694147.9323974
41000036497808.15336723560010754738.4905445
41500036719681.37116663600010814989.5977759
42000036940221.98092483640010874906.8961532
3680010934495.873153
3720010993761.867532
3760011052710.0749092
3800011111345.5530822
ACI Code
11111
Horizontal Strain vs Strength
Vertical Strain vs Strength
0.4f'c
0.4f'c
Slope
Strain (10E-6) Fig 4.
Strength (psi)
Strains vs Strength Sample 4
results
1111
Horizontal Strain vs Strength
Vertical Strain vs Strength
0.4f'c
Slope
Strain (10E-6) Fig 6.
Strength (psi)
Strains vs. Strength Sample 6
graph1
002721.9350
278.7012803282278.70128032822721.9352721.935
497.2766499257497.27664992572721.935
723.2793379076723.27933790762721.935
907.193888378907.1938883782721.935
1054.67921058221054.67921058222721.935
1233.28853363511233.28853363512721.935
1440.19240291431440.19240291432721.935
1659.82881799531659.82881799532721.935
1888.66096059981888.66096059982721.935
2101.93110277992101.93110277992721.935
2331.82429086792331.82429086792721.935
2580.46261583082580.46261583082721.935
2721.93534696192721.93534696192721.935
2942.27912569852942.27912569852721.935
3213.55308764243213.55308764242721.935
3504.98691377243504.98691377242721.935
3744.07582938393744.07582938392721.935
3959.82174435883959.82174435882721.935
4228.61993350784228.61993350782721.935
4634.6466718544634.6466718542721.935
4890.35863337344890.35863337342721.935
5275.87182570565275.87182570562721.935
5558.46360613995558.46360613992721.935
5830.79861356725830.79861356722721.935
6178.82153214976178.82153214972721.935
6376.88335573326376.88335573322721.935
6435.94822098046435.94822098042721.935
2721.935
2721.935
2721.935
2721.935
2721.935
2721.935
2721.935
2721.935
2721.935
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2721.935
2721.935
2721.935
2721.935
2721.935
2721.935
2721.935
2721.935
2721.935
Horizontal Strain vs Strength
Vertical Strain vs Strength
0.4f'c
Slope
Strain (10E-6) Fig 2.
Strength (psi)
Strains vs Strength Sample 2
Cont 1
002721.9350
278.7012803282278.70128032822721.9352721.935
497.2766499257497.27664992572721.935
723.2793379076723.27933790762721.935
907.193888378907.1938883782721.935
1054.67921058221054.67921058222721.935
1233.28853363511233.28853363512721.935
1440.19240291431440.19240291432721.935
1659.82881799531659.82881799532721.935
1888.66096059981888.66096059982721.935
2101.93110277992101.93110277992721.935
2331.82429086792331.82429086792721.935
2580.46261583082580.46261583082721.935
2721.93534696192721.93534696192721.935
2942.27912569852942.27912569852721.935
3213.55308764243213.55308764242721.935
3504.98691377243504.98691377242721.935
3744.07582938393744.07582938392721.935
3959.82174435883959.82174435882721.935
4228.61993350784228.61993350782721.935
4634.6466718544634.6466718542721.935
4890.35863337344890.35863337342721.935
5275.87182570565275.87182570562721.935
5558.46360613995558.46360613992721.935
5830.79861356725830.79861356722721.935
6178.82153214976178.82153214972721.935
6376.88335573326376.88335573322721.935
6435.94822098046435.94822098042721.935
2721.935
2721.935
2721.935
2721.935
2721.935
2721.935
2721.935
2721.935
2721.935
2721.935
2721.935
2721.935
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2721.935
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2721.935
2721.935
2721.935
2721.935
2721.935
2721.935
2721.935
2721.935
2721.935
Horizontal Strain vs Strength
Vertical Strain vs Strength
0.4f'c
Slope
Strain (10E-6) Fig 1.
Strength (psi)
Strains vs Strength Sample 1
002621.490
91.249911579591.24991157952621.492621.49
473.9336492891473.93364928912621.49
658.909245243658.9092452432621.49
813.1145221759813.11452217592621.49
1035.58039187951035.58039187952621.49
1261.58307986141261.58307986142621.49
1489.00049515461489.00049515462621.49
1771.94595741671771.94595741672621.49
2053.12301053972053.12301053972621.49
2157.10546792112157.10546792112621.49
2325.4580179672325.4580179672621.49
2621.48970785882621.48970785882621.49
2884.62898776262884.62898776262621.49
3181.368041313181.368041312621.49
3438.14104831293438.14104831292621.49
3727.4527834763727.4527834762621.49
3992.00679069113992.00679069112621.49
4290.16057154984290.16057154982621.49
4562.49557897724562.49557897722621.49
4887.52917875084887.52917875082621.49
5053.4059560025053.4059560022621.49
5275.87182570565275.87182570562621.49
5513.54601400585513.54601400582621.49
5739.54870198775739.54870198772621.49
5955.29461696265955.29461696262621.49
6178.82153214976178.82153214972621.49
6299.78071726686299.78071726682621.49
2621.49
2621.49
2621.49
2621.49
2621.49
2621.49
2621.49
2621.49
2621.49
2621.49
2621.49
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2621.49
2621.49
2621.49
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2621.49
2621.49
2621.49
2621.49
2621.49
2621.49
2621.49
2621.49
2621.49
2621.49
Horizontal Strain vs Strength
Vertical Strain vs Strength
0.4f'c
Slope
Strain (10E-6) Fig 3.
Strength (psi)
Strains vs. Strength Sample 3
002731.8380
145.0095494094145.00954940942731.8382731.838
331.3998726745331.39987267452731.838
501.1671500318501.16715003182731.838
670.5807455613670.58074556132731.838
828.6765226003828.67652260032731.838
999.504845441999.5048454412731.838
1145.92912216171145.92912216172731.838
1322.06267241991322.06267241992731.838
1476.26794935281476.26794935282731.838
1658.76777251181658.76777251182731.838
1810.49727664991810.49727664992731.838
1992.64341798121992.64341798122731.838
2215.10928768482215.10928768482731.838
2428.37942986492428.37942986492731.838
2654.38211784682654.38211784682731.838
2731.8384381412731.8384381412731.838
2870.48171464952870.48171464952731.838
3095.06967532013095.06967532012731.838
3363.86786446913363.86786446912731.838
3654.24064511563654.24064511562731.838
3881.65806040893881.65806040892731.838
2731.838
2731.838
2731.838
2731.838
2731.838
2731.838
2731.838
2731.838
2731.838
2731.838
2731.838
2731.838
2731.838
2731.838
2731.838
2731.838
2731.838
2731.838
2731.838
2731.838
2731.838
Horizontal Strain vs Strength
Vertical Strain vs Strength
0.4f'c
Slope
Strain (10E-6) Fig 5.
Strength (psi)
Strains vs. Strength Sample 5
42384534843294123812919221313870464105160680
403050.865276332
570000
806101.730552664
901249.133147988
1066372.35523057
1140000
1612203.46110533
1974537.92062852
2280000
2549117.49434976
2792418.30677282
3016156.49461363
3224406.92221066
3420000
3604996.53259195
3780952.26100516
3949075.84125704
4110328.45402895
4265489.42092229
4415201.01467646
4560000
4700340.41320413
4836610.38331599
4969144.79563637
5098234.98869952
5224136.29224966
5347073.96619871
5467247.9365765
5584836.61354565
5700000
5812882.24549577
5923613.76188556
6032312.98922727
6139087.88013333
6244037.15555889
6347251.37362622
6448813.84442131
6548801.41705335
6647285.16012364
6744330.95273356
6840000
6934349.28453997
7027431.96338463
7119297.71817417
7209993.0651839
7299561.63067345
7388044.39618496
7475479.91770428
7561904.52201031
7647352.48304928
7731856.18076281
7815446.24445719
7898151.68251408
7980000
8061017.30552664
8141228.40853885
8220656.9080579
8299325.27377979
8377254.92031847
8454466.27528905
8530978.84184459
8606811.25620865
8681981.34068486
8756506.15257021
8830402.02935291
8903684.63053359
8976368.97637346
9048469.4838409
9120000
9190973.83306035
9261403.781285
9331302.15993459
9400680.82640827
9469551.2037266
9537924.30248846
9605810.74142105
9673220.76663197
9740164.26966199
9806650.8044286
9872689.6031426
9938289.59127274
10003459.401627
10068207.3876137
10132541.6357398
10196469.977399
Sample 1
Sample 2
Sample 3
Sample 4
Sample 5
Sample 6
ACI Code
Strength (psi) Fig 7.
Young's Modulus (psi)
ACI Code vs Experimental Results
specimen 1
f'c=6534.496534.49f'c=concrete strength (?) [maximum stress]
fy=7348.052613.80fy=yield stress=0.5*f'c
=1000.22*10-6=average longitudinal strain
E=1469286814692867.57
=-0.30
specimen 2
f'c=14439.146347.01
fy=2538.802538.80
=830.77average concrete strength:f'c=6443.46
E=1738043017380430.20
=-0.18
specimen 3average young's modulus:E=14149190.89psi
f'c=14170.256300.67
fy=2520.272520.27
=3055.82
E=46371354637135.04
=-0.10average poisson's ratio:=-0.21in/in
specimen 4
f'c=14797.146579.41
fy=2631.762631.76
=1802.58
E=82088678208867.29HAVE NOT FOUND THE RIGHT VALUE FOR YOUNG'S MODULUS YET!
=-0.06
specimen 5
f'c=14646.786512.56
fy=2605.022605.02
=998.17
E=1467363314673632.75
=-0.11
specimen 6
f'c=14363.566386.63
fy=2554.652554.65
=567.58
E=2530221325302212.51
=-0.53
0.4 f'c
0.4 f'c
0.4 f'c
0.4 f'c
0.4 f'c
0.4 f'c
Vertical Strain
Horizontal Strain
Vertical Strain
Vertical Strain
Vertical Strain
Vertical Strain
Vertical Strain
Horizontal Strain
Horizontal Strain
Horizontal Strain
Horizontal Strain
Horizontal Strain
E
E
E
E
E
E
ACI Code
Sample 1
Sample 4
Sample 2
Sample 3
Sample 6
Sample 5
002613.801009.90449239481009.9
21.577644145721.57764414572613.82613.81054.82844004241009.9
65.440396179765.44039617972613.81116.73151750971009.9
278.7407145384278.74071453842613.81163.07039264241009.9
357.269189954357.2691899542613.81233.46303501951009.9
439.3349840821439.33498408212613.81277.32578705341009.9
497.3470109657497.34701096572613.81322.24973470111009.9
561.3724796604561.37247966042613.81382.73788468341009.9
607.7113547931607.71135479312613.81440.39617969581009.9
670.6756278741670.67562787412613.81494.51715599581009.9
723.3816766891723.38167668912613.81548.28440042451009.9
784.9310222851784.93102228512613.81608.77255040681009.9
837.6370711001837.63707110012613.81660.06367173681009.9
907.3222497347907.32224973472613.81711.70852493811009.9
941.9879731164941.98797311642613.81773.25787053411009.9
1009.90449239481009.90449239482613.81817.12062256811009.9
1054.82844004241054.82844004242613.8
1116.73151750971116.73151750972613.8
1163.07039264241163.07039264242613.8
1233.46303501951233.46303501952613.8
1277.32578705341277.32578705342613.8
1322.24973470111322.24973470112613.8
1382.73788468341382.73788468342613.8
1440.39617969581440.39617969582613.8
1494.51715599581494.51715599582613.8
1548.28440042451548.28440042452613.8
1608.77255040681608.77255040682613.8
1660.06367173681660.06367173682613.8
1711.70852493811711.70852493812613.8
1773.25787053411773.25787053412613.8
1817.12062256811817.12062256812613.8
1888.92819243011888.92819243012613.8
1921.11779271311921.11779271312613.8
1989.03431199151989.03431199152613.8
2035.37318712422035.37318712422613.8
2102.22851078882102.22851078882613.8
2153.87336399012153.87336399012613.8
2219.31376016982219.31376016982613.8
2262.82278033252262.82278033252613.8
2332.15422709592332.15422709592613.8
2377.43190661482377.43190661482613.8
2441.45737530952441.45737530952613.8
2496.99327909442496.99327909442613.8
2557.12769720552557.12769720552613.8
2611.24867350552611.24867350552613.8
2656.17262115322656.17262115322613.8
2720.55182171912720.55182171912613.8
2773.25787053412773.25787053412613.8
2822.07286876552822.07286876552613.8
2889.98938804392889.98938804392613.8
2942.69543685892942.69543685892613.8
2996.81641315882996.81641315882613.8
3058.36575875493058.36575875492613.8
3108.59568447123108.59568447122613.8
3172.62115316593172.62115316592613.8
3214.00778210123214.00778210122613.8
3280.86310576583280.86310576582613.8
3336.04527767953336.04527767952613.8
3395.11850017693395.11850017692613.8
3449.23947647683449.23947647682613.8
3505.48284400423505.48284400422613.8
3554.29784223563554.29784223562613.8
3623.98302087023623.98302087022613.8
3669.96816413163669.96816413162613.8
3744.60558896363744.60558896362613.8
3785.63848602763785.63848602762613.8
3846.12663600993846.12663600992613.8
3896.35656172623896.35656172622613.8
3960.38203042093960.38203042092613.8
4013.08807923594013.08807923592613.8
4079.94340290064079.94340290062613.8
4117.43898125224117.43898125222613.8
4181.46444994694181.46444994692613.8
4229.21825256464229.21825256462613.8
4294.65864874424294.65864874422613.8
4342.05871949064342.05871949062613.8
4399.00955076054399.00955076052613.8
4456.66784577294456.66784577292613.8
4518.21719136894518.21719136892613.8
4564.55606650164564.55606650162613.8
4635.30244074994635.30244074992613.8
4678.81146091264678.81146091262613.8
4748.1429076764748.1429076762613.8
4790.5907322254790.5907322252613.8
4846.12663600994846.12663600992613.8
4891.05058365764891.05058365762613.8
4951.18500176874951.18500176872613.8
5013.08807923595013.08807923592613.8
5066.85532366475066.85532366472613.8
5213.65405022995213.65405022992613.8
5276.61832331095276.61832331092613.8
5318.71241598875318.71241598872613.8
5380.6154934565380.6154934562613.8
5437.21259285465437.21259285462613.8
5493.80969225335493.80969225332613.8
5559.2500884335559.2500884332613.8
5611.9561372485611.9561372482613.8
5671.02935974535671.02935974532613.8
5717.3682348785717.3682348782613.8
5784.22355854265784.22355854262613.8
5831.6236292895831.6236292892613.8
5937.0357269195937.0357269192613.8
6003.89105058376003.89105058372613.8
6069.33144676346069.33144676342613.8
6119.56137247976119.56137247972613.8
6179.69579059076179.69579059072613.8
6215.77644145746215.77644145742613.8
6288.99893880446288.99893880442613.8
6335.3378139376335.3378139372613.8
6377.7856384866377.7856384862613.8
6434.38273788476434.38273788472613.8
6487.08878669976487.08878669972613.8
6534.48885744616534.48885744612613.8
6436.85886098346436.85886098342613.8
fy=0.4*f'c
lateral strain vs. stress
longitudinal strain vs. stress
f'c
secant
Elastic Behavior Line (Secant)
ym-long
ym-lat
Strain
Stress
Figure 1. Strain vs. Strength of Sample 1
Young's Modulus: y = 3.9454x
Diameter = 6in --> Radius = 3in --> A = Pr2 --> A = 4P = 28.27in2
Stress = Pressure = F/A
E = stress / strainI am columns "D" and "E" multiplied by negative 1
use me!use me!
Load (kips)Load (lbs)Stress (psi)Lateral Strain (10E-6)Longitudinal Strain (10E-6)Poisson's RatioModulus of ElasticityLateral Strain (10E-6)Longitudinal Strain (10E-6)fy=0.4*f'c (psi)SECANTSECANT
0.000.000.000.000.000.000.000.000.002613.8000.00
0.61610.0021.581.60-4.70-0.344.59-1.604.702613.80662.52613.80
1.851850.0065.444.70-18.80-0.253.48-4.7018.802613.80
7.887880.00278.7418.80-82.80-0.233.37-18.8082.802613.80
10.1010100.00357.2728.10-109.40-0.263.27-28.10109.402613.80
12.4212420.00439.3332.80-128.10-0.263.43-32.80128.102613.80
14.0614060.00497.3535.90-145.30-0.253.42-35.90145.302613.80
15.8715870.00561.3740.60-160.90-0.253.49-40.60160.902613.80
17.1817180.00607.7145.30-175.00-0.263.47-45.30175.002613.80
18.9618960.00670.6850.00-190.60-0.263.52-50.00190.602613.80
20.4520450.00723.3853.10-204.70-0.263.53-53.10204.702613.80
22.1922190.00784.9354.70-218.80-0.253.59-54.70218.802613.80
23.6823680.00837.6459.40-232.80-0.263.60-59.40232.802613.80
25.6525650.00907.3262.50-246.90-0.253.67-62.50246.902613.80
26.6326630.00941.9967.20-257.80-0.263.65-67.20257.802613.80ym-lateralym-longitudinal
28.5528550.001009.9071.90-270.30-0.273.74-71.90270.302613.801009.9465.60
29.8229820.001054.8375.00-282.80-0.273.73-75.00282.802613.801009.9465.60
31.5731570.001116.7378.10-296.90-0.263.76-78.10296.902613.801009.9465.60
32.8832880.001163.0781.30-310.90-0.263.74-81.30310.902613.801009.9465.60
34.8734870.001233.4685.90-323.40-0.273.81-85.90323.402613.801009.9465.60
36.1136110.001277.3389.10-335.90-0.273.80-89.10335.902613.801009.9465.60
37.3837380.001322.2593.80-346.90-0.273.81-93.80346.902613.801009.9465.60
39.0939090.001382.7498.40-360.90-0.273.83-98.40360.902613.801009.9465.60
40.7240720.001440.40100.00-375.00-0.273.84-100.00375.002613.801009.9465.60
42.2542250.001494.52104.70-387.50-0.273.86-104.70387.502613.801009.9465.60
43.7743770.001548.28107.80-400.00-0.273.87-107.80400.002613.801009.9465.60
45.4845480.001608.77110.90-414.10-0.273.88-110.90414.102613.801009.9465.60
46.9346930.001660.06115.60-425.00-0.273.91-115.60425.002613.801009.9465.60
48.3948390.001711.71120.30-439.10-0.273.90-120.30439.102613.801009.9465.60
50.1350130.001773.26125.00-453.10-0.283.91-125.00453.102613.801009.9465.60
51.3751370.001817.12128.10-465.60-0.283.90-128.10465.602613.801009.9465.60
53.4053400.001888.93131.30-479.70-0.273.94-131.30479.702613.80
54.3154310.001921.12135.90-493.80-0.283.89-135.90493.802613.80
56.2356230.001989.03139.10-506.30-0.273.93-139.10506.302613.80
57.5457540.002035.37142.20-520.30-0.273.91-142.20520.302613.80
59.4359430.002102.23146.90-534.40-0.273.93-146.90534.402613.80
60.8960890.002153.87151.60-548.40-0.283.93-151.60548.402613.80
62.7462740.002219.31154.70-562.50-0.283.95-154.70562.502613.80
63.9763970.002262.82159.40-576.60-0.283.92-159.40576.602613.80
65.9365930.002332.15164.10-592.20-0.283.94-164.10592.202613.80
67.2167210.002377.43168.80-604.70-0.283.93-168.80604.702613.80
69.0269020.002441.46173.40-618.80-0.283.95-173.40618.802613.80
70.5970590.002496.99176.60-634.40-0.283.94-176.60634.402613.80
72.2972290.002557.13179.90-648.40-0.283.94-179.90648.402613.80
73.8273820.002611.25185.90-662.50-0.283.94-185.90662.502613.80
75.0975090.002656.17190.60-678.10-0.283.92-190.60678.102613.80
76.9176910.002720.55195.30-692.20-0.283.93-195.30692.202613.80
78.4078400.002773.26201.60-706.30-0.293.93-201.60706.302613.80
79.7879780.002822.07206.30-721.90-0.293.91-206.30721.902613.80
81.7081700.002889.99209.40-737.50-0.283.92-209.40737.502613.80
83.1983190.002942.70215.60-753.10-0.293.91-215.60753.102613.80
84.7284720.002996.82220.30-767.20-0.293.91-220.30767.202613.80
86.4686460.003058.37226.60-784.40-0.293.90-226.60784.402613.80
87.8887880.003108.60229.70-798.40-0.293.89-229.70798.402613.80
89.6989690.003172.62234.40-814.10-0.293.90-234.40814.102613.80
90.8690860.003214.01239.10-829.70-0.293.87-239.10829.702613.80
92.7592750.003280.86243.80-846.90-0.293.87-243.80846.902613.80
94.3194310.003336.05250.00-862.50-0.293.87-250.00862.502613.80
95.9895980.003395.12254.70-878.10-0.293.87-254.70878.102613.80
97.5197510.003449.24259.40-895.30-0.293.85-259.40895.302613.80
99.1099100.003505.48265.60-910.90-0.293.85-265.60910.902613.80
100.48100480.003554.30273.40-926.60-0.303.84-273.40926.602613.80
102.45102450.003623.98275.00-943.80-0.293.84-275.00943.802613.80
103.75103750.003669.97281.30-960.90-0.293.82-281.30960.902613.80
105.86105860.003744.61287.50-978.10-0.293.83-287.50978.102613.80
107.02107020.003785.64293.80-993.80-0.303.81-293.80993.802613.80
108.73108730.003846.13300.00-1010.90-0.303.80-300.001010.902613.80
110.15110150.003896.36307.80-1029.70-0.303.78-307.801029.702613.80
111.96111960.003960.38312.50-1046.90-0.303.78-312.501046.902613.80
113.45113450.004013.09317.20-1065.60-0.303.77-317.201065.602613.80
115.34115340.004079.94323.40-1082.80-0.303.77-323.401082.802613.80
116.40116400.004117.44329.70-1100.00-0.303.74-329.701100.002613.80
118.21118210.004181.46334.40-1117.20-0.303.74-334.401117.202613.80
119.56119560.004229.22342.20-1137.50-0.303.72-342.201137.502613.80
121.41121410.004294.66350.00-1156.30-0.303.71-350.001156.302613.80
122.75122750.004342.06357.80-1175.00-0.303.70-357.801175.002613.80
124.36124360.004399.01365.60-1193.80-0.313.68-365.601193.802613.80
125.99125990.004456.67376.60-1214.10-0.313.67-376.601214.102613.80
127.73127730.004518.22387.50-1234.40-0.313.66-387.501234.402613.80
129.04129040.004564.56403.10-1256.10-0.323.63-403.101256.102613.80
131.04131040.004635.30420.30-1275.00-0.333.64-420.301275.002613.80
132.27132270.004678.81432.80-1295.30-0.333.61-432.801295.302613.80
134.23134230.004748.14450.00-1315.60-0.343.61-450.001315.602613.80
135.43135430.004790.59462.50-1337.50-0.353.58-462.501337.502613.80
137.00137000.004846.13478.10-1357.80-0.353.57-478.101357.802613.80
138.27138270.004891.05490.60-1379.70-0.363.55-490.601379.702613.80
139.97139970.004951.19501.60-1403.10-0.363.53-501.601403.102613.80
141.72141720.005013.09515.60-1428.10-0.363.51-515.601428.102613.80
143.24143240.005066.86528.10-1453.10-0.363.49-528.101453.102613.80
147.39147390.005213.65554.70-1517.20-0.373.44-554.701517.202613.80
149.17149170.005276.62562.50-1546.90-0.363.41-562.501546.902613.80
150.36150360.005318.71571.90-1575.00-0.363.38-571.901575.002613.80
152.11152110.005380.62581.30-1606.30-0.363.35-581.301606.302613.80
153.71153710.005437.21590.60-1639.10-0.363.32-590.601639.102613.80
155.31155310.005493.81603.10-1673.40-0.363.28-603.101673.402613.80
157.16157160.005559.25614.10-1709.40-0.363.25-614.101709.402613.80
158.65158650.005611.96623.40-1748.40-0.363.21-623.401748.402613.80
160.32160320.005671.03632.80-1785.90-0.353.18-632.801785.902613.80
161.63161630.005717.37639.10-1826.60-0.353.13-639.101826.602613.80
163.52163520.005784.22646.90-1867.20-0.353.10-646.901867.202613.80
164.86164860.005831.62653.10-1909.40-0.343.05-653.101909.402613.80
167.84167840.005937.04671.90-1996.90-0.342.97-671.901996.902613.80
169.73169730.006003.89682.80-2042.20-0.332.94-682.802042.202613.80
171.58171580.006069.33698.40-2096.90-0.332.89-698.402096.902613.80
173.00173000.006119.56710.90-2148.40-0.332.85-710.902148.402613.80
174.70174700.006179.70725.00-2207.80-0.332.80-725.002207.802613.80
175.72175720.006215.78735.90-2264.10-0.332.75-735.902264.102613.80
177.79177790.006289.00750.00-2332.80-0.322.70-750.002332.802613.80
179.10179100.006335.34775.00-2406.30-0.322.63-775.002406.302613.80
180.30180300.006377.79798.00-2492.20-0.322.56-798.002492.202613.80
181.90181900.006434.38825.00-2578.10-0.322.50-825.002578.102613.80
183.39183390.006487.09868.80-2678.10-0.322.42-868.802678.102613.80
184.73184730.006534.49918.80-2803.10-0.332.33-918.802803.102613.80
181.97181970.006436.861003.10-2981.30-0.342.16-1003.102981.302613.80
average poisson's ratio:-0.30ave longitudinal strain:1000.22
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lateral strain vs. stress
longitudinal strain vs. stress
linear
Elastic Behavior Line (Secant)
Strain
Stress
Strain vs. Stress
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Results: Test Cylinder #1Data - CalculationsTheor. E = 57,000 *(fc)^1/2 psi= 4,607,490Secant E = 3.9454
Chord E = S2 S1 e2 0.00005 = 4,083,542
Poissons Ratio n = et2 et1 e2 0.00005 = 0.29DATACALCULATIONS
fc = 6534psi0.4fc = 2613 psiS2 = 2613 psiS1 = 169 psi
e2 = 648.5 x 10-6 e1 = 50.0 x 10-6
et2 = - 186 x 10-6 et1= - 11.56 x 10-6
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Project Results
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Project Results / ConclusionAverage Value for Youngs Modulus = 3.886 x 106Average Target Value for Youngs Modulus = 4.517 x 106
Average Value for Poissons Ratio = 0.22Target Range for Poissons Ratio = 0.15 0.25
* From the above results one can conclude that our results were favorable and comparable to theoretical values, proving a successful project
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ConclusionFrom the data table, we can observe inconsistencies in the experimental values for Cylinders 3, 4, and 6 compared to the desired theoretical values
Taking into account only Cylinders 1, 2, and 5 we get:Avg. Youngs Modulus = 4.147 x 106Target Youngs Modulus = 4.592 x 106
Poissons Ratio = 0.20 Target Ranged of Poissons Ratio = 0.15 - 0.25
We feel that this conclusion yields more accurate prediction for the values of Youngs Modulus and Poissons Ratio
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ConclusionFrom our graphs it is apparent that concrete has a certain stress-strain relationship, making the development of standard values for the material feasible
However, since only 3 out of our 6 samples performed to desired theoretical behavior, we conclude that definitive values for Youngs Modulus and Poissons Ratio cannot be discerned
Accurate ranges for Youngs Modulus and Poissons Ratio currently in practice are valid and may be developed further for various strengths and types of concrete.
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THANK YOU