Loaded Flat Plates

Loaded Flat Plates

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Home MechanicsIndex Loaded Flat Platess

Introduction..... Introduction ..... Symbols Symbols..... ..... CircularPlates CircularPlates..... ..... RectangularPlates RectangularPlates..... ..... CircularPlateswithcentralholes ..... Introduction Thispageincludessimpleformulaforthecalculationofthemaximumstressanddeflectionforthinflatplatesunderavarietyofsupportand loadingconditons.Theequationsareonlyvalidifthedeflectionissmallcomparedtotheplatethickness.Theplatesareallassumedtobe steelwithapoisson'sratioof0,3.Theequationsarealsoonlyreasonablyaccurateifthethicknessislessthan10%ofthediameter.Theresults canbeusedforinitialestimates-Formoreaccurateresultsitisrecommendedthatqualityreferencebooksareusedi.e"Roark'sFormulasfor StressandStrain".IalsorecommendMitcalc.comseelink1below-asuiteofcalculatorsbasedonExcel. Theloadingscenarioforthesimplysupportedrectangularplatesassumethattheupperedgesoftheloadedsurfacearerestrainedfromlifting suchthatalloftheedgesareincontactduringthetheloadingcondition. Note: IhavecheckedtheresultsfromsomeoftheequationsagainstresultsusingMitcalc.com.Thedeflectionsandstressesresultingaregenerally resonablyaccurate.IhavecheckedmyresultsagainstRoarkandtheyseemtobeOK.Iwouldrecommendthatformorecomprehensive calculationsincludinggreaterdetailwithmoreaccuracystandardreferencetextsareusede.gRoarksbook. Ihavecreatedaexcelcalcsbasedspreadsheetforconvenientaccesstoalloftheequationsonthispage.Thisislocatedat ExcelCalcs.com calculationPlatesTherearealsootherdetailedcalcs/tables/graphsforanumberofdifferentplateconfigurationsontheexcelcalcssiteref. calculationPlates Therearealsootherdetailedcalcs/tables/graphsforanumberofdifferentplateconfigurationsontheexcelcalcssiteref. ExcelcalcsPlates

Symbols / Units r = radiuss of circular plate (m) a = minor length of rectangular plate (m) b = major length of rectangular plate (m) t = plate thickness (m) p = uniform surface pressure on plate (compressive) (N/m P = Single concentrated force (compressive) (N)

2

m = maximum stress(N/m ) y = maximum deflection (m) m



2

E = Young's moudulus of elasticity (N/m )  = Poissan's ratio -Assumed to be 0,3 for steel.

3

2

D = Flexural rigidity = E.t / 12 (1-v )

Circular Plates CircularPlate,uniformload,edgessimplysupported.

2)

Loaded Flat Plates


CircularPlate,uniformload,edgesclamped.

CircularPlate,CentreLoad,edgessimplysupported.

CircularPlate,CentreLoad,edgesclamped.

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Loaded Flat Plates


Rectangular Plates RectangularFlatPlate,uniformload,edgesimplysupported.

RectangularFlatPlate,uniformload,edgeclamped.

RectangularFlatPlate,concentratedloadatcentre,edgesimplysupported.

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Loaded Flat Plates


a/b 1,0

1,1

1,2

1,4

1,6

1,8

2,0

3,0

4 ->

k 1

0,127

0,138

0,148

0,162

0,17

0,177

0,180

0,185

0,185

k 2

0,435

0,565

0,650

0,789

0,875

0,927

0,958

1,000

0,000

RectangularFlatPlate,concentratedloadatcentre,edgeclamped

a/b 1,0

f

1,2

1,4

1,6

1,8

2,0

3 ->

k 1

0,061

0,071

0,076

0,078

0,0786

0,0788

0,0791

k 2

0,754

0,894

0,962

0,991

1,000

1,004

1,008

k 3

-0,238

-0,0078

0,011

0,053

0,068

0,067

0,067

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Loaded Flat Plates


CircularFlatPlatewithcentralhole,concentratedloadathole,simplysupportedatouteredge

a/b 1,25 k 1 0,341

1,5 k 2

0,100

2

k 1 0,519

k 2 1,26

33

k 1

k 2

0,672

k

1,48

4 k 2

1

0,734

1,88

5

k 1

k 2

0,724

2,17

k 1

k 2

0,704

2,34

CircularFlatPlatewithcentralhole,uniformloadoverring,simplysupportedatouteredge

a/b 1,25

1,5

k 1

k

0,184

0,592

2

2

k 1 0,414

k 2 0.976

3

k 1 0,664

k 2

4

k 1

1,44

0,824

k 2 1,88

5

k 1 0,830

k 2 2,08

k 1 0,813

k 2 2,190

CircularFlatPlatewithcentralhole,Concentratedloadathole,clampedatouteredge

a/b 1,25 k 1 0,00504

1,5

2

3

k 2

k 1

k 2

k 1

k 2

k 1

0,194

0,0242

0.320

0,0810

0,454

0,172

4 k 2

0,673

k 1 0,217

5 k

2

1,021

k

1

0,238

k 2 1,305

CircularFlatPlatewithcentralhole,uniformloadoverring,clampedatouteredge

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Loaded Flat Plates


a/b 1,25

1,5

k 1 0,00199

2

3

k 2

k 1

k 2

k 1

k 2

k 1

0,105

0,0139

0.259

0,0575

0,480

0,130

4 k 2

0,657

k 1

5 k 2

0,162

0,710

k

k 2

1

0,175

0,730

CircularFlatPlatewithguidedcentralhole,uniformdistributedload,simplysupportedatouteredge

a/b 1.25 k 1 0,00343

1,5 k 2

k 1

0,122

0,0313

2 k

3

2

k 1

k 2

k

0,336

0,125

0,740

0,221

1

4 k 2

1,210

k 1

5 k

0,417

k 1

2

1,450

k 2

0,492

1,590

CircularFlatPlatewithguidedcentralhole,uniformdistributedload,fixedatouteredge

a/b 10 k 1 0,149

f

3 k 2

0,728

k 0,074

2 k

1 0,58

2

1,5

k 1 0,023

k 2 0,36

k 1 0,003

1,1 k 2

0,151

k 1 -

k 2 0,019

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Loaded Flat Plates


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Relevant Link s 1. Mitcalc.comPlatesDetailedCalculationsforaveryresonablecost 2. Wikipeadia-Platetheory ..Quitedetailed-difficulttofollownotes 3. excelcalcsPlates..Verydetailedacomprehensivecoverageofthesubject.

Steel Plates Pressure Plate

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Loaded Flat Plates

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