Young Modulus and Poisson Ratio

Modulus of Elasticity and Poissons Ratio of ConcreteKalia Shibao & Jessica LeSpring 2002Presented in fulfillment of CE 334L : Mechanical Behavior of Materials

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

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

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

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

This is what the test cylinders should look like!

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

Test Set UpStrain IndicatorsSATEC Testing MachineTest Specimen

Testing Procedure (cont)Compress each cylinder until failureRecord strain and plot dataAnalyze results to quantify Youngs Modulus and Poissons Ratio

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

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=

Experimental Calculation

Results: Test Cylinder #1Graph longitudinal strainlateral strainE = 3.9454 x 106Yield strength = 0.4 fclongitudinal strainUltimate strength = fc

Chart1

000

21.577644145721.57764414572613.8

65.440396179765.4403961797

278.7407145384278.7407145384

357.269189954357.269189954

439.3349840821439.3349840821

497.3470109657497.3470109657

561.3724796604561.3724796604

607.7113547931607.7113547931

670.6756278741670.6756278741

723.3816766891723.3816766891

784.9310222851784.9310222851

837.6370711001837.6370711001

907.3222497347907.3222497347

941.9879731164941.9879731164

1009.90449239481009.9044923948

1054.82844004241054.8284400424

1116.73151750971116.7315175097

1163.07039264241163.0703926424

1233.46303501951233.4630350195

1277.32578705341277.3257870534

1322.24973470111322.2497347011

1382.73788468341382.7378846834

1440.39617969581440.3961796958

1494.51715599581494.5171559958

1548.28440042451548.2844004245

1608.77255040681608.7725504068

1660.06367173681660.0636717368

1711.70852493811711.7085249381

1773.25787053411773.2578705341

1817.12062256811817.1206225681

1888.92819243011888.9281924301

1921.11779271311921.1177927131

1989.03431199151989.0343119915

2035.37318712422035.3731871242

2102.22851078882102.2285107888

2153.87336399012153.8733639901

2219.31376016982219.3137601698

2262.82278033252262.8227803325

2332.15422709592332.1542270959

2377.43190661482377.4319066148

2441.45737530952441.4573753095

2496.99327909442496.9932790944

2557.12769720552557.1276972055

2611.24867350552611.2486735055

2656.17262115322656.1726211532

2720.55182171912720.5518217191

2773.25787053412773.2578705341

2822.07286876552822.0728687655

2889.98938804392889.9893880439

2942.69543685892942.6954368589

2996.81641315882996.8164131588

3058.36575875493058.3657587549

3108.59568447123108.5956844712

3172.62115316593172.6211531659

3214.00778210123214.0077821012

3280.86310576583280.8631057658

3336.04527767953336.0452776795

3395.11850017693395.1185001769

3449.23947647683449.2394764768

3505.48284400423505.4828440042

3554.29784223563554.2978422356

3623.98302087023623.9830208702

3669.96816413163669.9681641316

3744.60558896363744.6055889636

3785.63848602763785.6384860276

3846.12663600993846.1266360099

3896.35656172623896.3565617262

3960.38203042093960.3820304209

4013.08807923594013.0880792359

4079.94340290064079.9434029006

4117.43898125224117.4389812522

4181.46444994694181.4644499469

4229.21825256464229.2182525646

4294.65864874424294.6586487442

4342.05871949064342.0587194906

4399.00955076054399.0095507605

4456.66784577294456.6678457729

4518.21719136894518.2171913689

4564.55606650164564.5560665016

4635.30244074994635.3024407499

4678.81146091264678.8114609126

4748.1429076764748.142907676

4790.5907322254790.590732225

4846.12663600994846.1266360099

4891.05058365764891.0505836576

4951.18500176874951.1850017687

5013.08807923595013.0880792359

5066.85532366475066.8553236647

5213.65405022995213.6540502299

5276.61832331095276.6183233109

5318.71241598875318.7124159887

5380.6154934565380.615493456

5437.21259285465437.2125928546

5493.80969225335493.8096922533

5559.2500884335559.250088433

5611.9561372485611.956137248

5671.02935974535671.0293597453

5717.3682348785717.368234878

5784.22355854265784.2235585426

5831.6236292895831.623629289

5937.0357269195937.035726919

6003.89105058376003.8910505837

6069.33144676346069.3314467634

6119.56137247976119.5613724797

6179.69579059076179.6957905907

6215.77644145746215.7764414574

6288.99893880446288.9989388044

6335.3378139376335.337813937

6377.7856384866377.785638486

6434.38273788476434.3827378847

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

3501066372.35523057

1005700004001140000

300987268.960314268001612203.46110533

6001396209.1533864112001974537.92062852

12001974537.9206285216002280000

24002792418.3067728220002549117.49434976

48003949075.8412570424002792418.30677282

60004415201.0146764628003016156.49461363

80005098234.9886995232003224406.92221066

10000570000036003420000

150006981045.7669320640003604996.53259195

200008061017.3055266444003780952.26100516

250009012491.3314798848003949075.84125704

300009872689.603142652004110328.45402895

3500010663723.552305756004265489.42092229

400001140000060004415201.01467646

4500012091525.9582964004560000

5000012745587.471748868004700340.41320413

5500013367684.915496872004836610.38331599

6000013962091.533864176004969144.79563637

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

14500021704953.3517121144006840000

15000022076005.0733823148006934349.28453997

15500022440922.4409337152007027431.96338463

16000022800000156007119297.71817417

16500023153509.4532125160007209993.0651839

17000023501702.0660207164007299561.63067345

17500023844810.7562212168007388044.39618496

18000024183051.9165799172007475479.91770428

18500024516627.0110715176007561904.52201031

19000024845723.9781818180007647352.48304928

19500025170518.4690344184007731856.18076281

20000025491174.9434976188007815446.24445719

20500025807847.6436916192007898151.68251408

21000026120681.4612483196007980000

21500026429812.7121628200008061017.30552664

22000026735369.8309935204008141228.40853885

22500027037473.9944396208008220656.9080579

23000027336239.6828825212008299325.27377979

23500027631775.1872731216008377254.92031847

24000027924183.0677282220008454466.27528905

24500028213560.5693432224008530978.84184459

25000028500000228008606811.25620865

25500028783589.0743319232008681981.34068486

26000029064411.2274789236008756506.15257021

26500029342545.901813240008830402.02935291

27000029618068.8094278244008903684.63053359

27500029891052.1728493248008976368.97637346

28000030161564.9461363252009048469.4838409

28500030429673.0182892256009120000

29000030695439.4006667260009190973.83306035

29500030958924.3999206264009261403.781285

30000031220185.7777945268009331302.15993459

30500031479278.8989837272009400680.82640827

31000031736256.8681311276009469551.2037266

31500031991170.6569172280009537924.30248846

32000032244069.2221066284009605810.74142105

32500032494999.6153254288009673220.76663197

33000032744007.0852668292009740164.26966199

33500032991135.1729521296009806650.8044286

34000033236425.8006182300009872689.6031426

34500033479919.3547416304009938289.59127274

35000033721654.76366783080010003459.401627

35500033961669.5702673120010068207.3876137

360000342000003160010132541.6357398

36500034436681.02474453200010196469.977399

37000034671746.42269993240010260000

37500034905228.83466033280010323139.0574767

38000035137159.81692323320010385894.2802245

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



0.4f'c

Slope


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

2721.935

2721.935

2721.935

2721.935

2721.935

2721.935

2721.935

2721.935

2721.935

2721.935

2721.935

2721.935

2721.935

2721.935

2721.935

2721.935

2721.935

2721.935



0.4f'c

Slope


Strength (psi)


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

2721.935

2721.935

2721.935

2721.935

2721.935

2721.935

2721.935

2721.935

2721.935

2721.935

2721.935

2721.935

2721.935

2721.935

2721.935



0.4f'c

Slope


Strength (psi)


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

2621.49

2621.49

2621.49

2621.49

2621.49

2621.49

2621.49

2621.49

2621.49

2621.49

2621.49

2621.49

2621.49

2621.49

2621.49

2621.49



0.4f'c

Slope


Strength (psi)


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



0.4f'c

Slope


Strength (psi)


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



f'c

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

000

000

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00



linear


Strain

Stress

Strain vs. Stress

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

Project Results

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

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

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.

THANK YOU

Young Modulus and Poisson Ratio

Documents