鋼筋混凝土單向板肋梁樓蓋課程設計示例 An example of curriculum design of reinforced concrete one-way slab rib beam floor

Anexampleofcurriculumdesignofreinforcedconcreteone-wayslabribbeamfloor

Multiplechoicequestionnumber13istakenasadesignexample,andtheknownconditionsofquestionnumber13are:amulti-storeycivilbuildingwithaplanesizeof19.8m×30madoptsbrick-concretestructure,andthefloorrequiresaone-wayslabribfloor.Thewallthicknessis240mm,andthesectionsizeofpilasteris500mm×500mm.Themiddlecolumnisareinforcedconcretecolumnwithacross-sectionaldimensionof400mm×400mm.

Thevariableloadstandardvalue:QK=6kN/m2,γQ=1.3.

Materialselection:C30concrete;HRB40000-gradehot-rolledsteelbarsareusedforlongitudinalstressedsteelbarsinthebeam,andHPB235-gradehot-rolledsteelbarsareusedforothersteelbars.

Structurallayout

Bylookingupthetable

Bylookingupthetable

GradeHRB400steelbar:

GradeHPB235reinforcement:

Designslab,secondarybeamandmainbeamaccordingtoelasticmethod.

ThelayoutofthestructureisshowninFig.2.11,andthemaingirderishorizontallyarrangedwithaspanof6600mm;Thespacingis6600mm;Secondarybeamsarelongitudinallyarrangedwithaspanof6600mmandaspacingof2200mm.Theratioofthelongsidetotheshortsideofthegridisequalto3,whichisdesignedaccordingtotheone-wayslabribfloor.

Fig.2.11Floorcoverstructurelayout.

2.3.2Designofboard

AccordingtotherequirementsofTable2.2,theslabthicknessis80mm.

1.Loadcalculation

Weightofplate:

Floorsurface:

Ceilingplastering:

Standardvalueofconstantload:

Constantloaddesignvalue:

Standardvalueofliveload:

Liveloaddesignvalue:

Totaldesignload:

Convertedconstantload:

Convertedliveload:

2.Calculationpicture

（1）Thesectionheightofsecondarybeamispreliminarilyestimatedaccordingto(l/18~l/12),andh=500mm;Thecross-sectionwidthispreliminarilyestimatedaccordingto(h/3~h/2),andb=200mm.

ThelayoutofthestructureandthegeometricdimensionsoftheplateareshowninFig2.12.

Fig.2.12Sectionviewofslab.

Take1mplatewidthascalculationunit,andthecalculationspanofeachspanisasfollows

Middlespan:

Sidespan:

ThecalculationdiagramoftheabovevaluesisshowninFigure2.13.

Andthedifferencebetweenthesidespanandthemiddlespan:

Therefore,itcanbecalculatedascontinuousbeamwithequalspan.

Bendingmomentcalculation

Fig.2.13Sketchofthecalculationoftheslab.

AmongthemFromthelook-uptable.

Sidespan:

Middlespan:

Bsupport:

ThebendingmomentcalculationoftheplateisshowninTable2.13.

Table2.13Bendingmomentcalculationofplate

Itemsandtimes

Calculationdiagram

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

Mmin

Combinedvalue

-

-6.84

-

-4.96

-

Mmax

Combinedvalue

4.38

-

2.69

-

3.27

4.Reinforcementcalculation

H=80-20=60mm.

ThereinforcementcalculationofplateisshowninTable2.14.

Table2.14Reinforcementcalculationofplate

Section

1

B

2

C

3

Positioninplanview

A~D

A~D

A~D

A~D

A~D

-

1.25

-

1.25

-

4.38

-5.59

2.69

-3.71

3.27

0.085

0.109

0.052

0.072

0.064

0.089

0.115

0.054

0.075

0.066

364.8

472.0

220.0

306.7

269.0

Optionalreinforcement

120

100

2200

160

180

Practicalreinforcement

419

503

251

314

279

Schematicdiagramofreinforcementforone-wayslabisshowninFigure2.14.

Fig.2.14Reinforcementdrawingofone-wayslab.

Designofsecondarybeam

Thebeamheighthofthemaingirderisestimatedaccordingto(l/15~l/8),takingh=650mm,andthespanisestimatedaccordingto(h/15~h/8),takingb=300mm,sothegeometrysizeandsupportofthesecondarybeamareshowninFigure2.15.

Fig.2.15Geometricdimensionandsupportofsecondarybeam.

1.Loadcalculation

Standardvalueofconstantloadtransmittedfromplate:2.99×2.2=6.578kN/m

Standardvalueofdeadweightofsecondarybeam

Secondarybeamsideplasteringstandardvalue:

Standardvalueofconstantload:

Constantloaddesignvalue:

Standardvalueofliveload:

Liveloaddesignvalue:

Totaldesignload:

And

2.Calculationpicture

Sectionsizeofmaingirder:

Calculatedspanlengthofmiddlespan:

Calculationspanlengthofsidespan:

L=6.6m,spanlength,etc.,shallbecalculatedascontinuousbeamwithequalspan.

ThecalculationdiagramisshowninFigure2.16.

Fig.2.16Calculationdiagramofsecondarybeam.

3.InternalForceCalculation

（1）Calculationofbendingmoment.

CheckthealphavalueundervariousconditionsandcalculatethebendingmomentofsecondarybeamasshowninTable2.15.

Table2.15Calculationtableofsecondarybeambendingmoment

Itemsandtimes

Calculationdiagram

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

Mmin

Combinedvalue

-

-135.55

-

-114.02

-

Mmax

Combinedvalue

107.20

-

65.92

-

77.81

Considertheinfluenceofbearingagain:

（2）Calculationofshearforce.Seetable2.16forshearcalculation.

Itemsandtimes

Calculationdiagram

-

-

-

-

-

-

-

-

-

-

-V

Combinedvalue

-

-112.85

-

-96.01

-

Vmax

Combinedvalue

77.11

-

103.04

-

99.87

Consideringtheinfluenceofbearingwidth:

Then

4.Calculationofsectionreinforcement

Thebearingcapacityofthemid-spansectionofthesecondarybeamiscalculatedaccordingtotheT-shapedsection,andthewidthoftheflangetakesthesmallervalueofthefollowingtwo:

Sotake

Distinguishthetypeoft-sectionineachspan;

Take

Then

Isgreaterthanthebendingmomentvaluesinthetable,sothecross-sectionineachspaniscalculatedaccordingtothefirsttypeofT-section,thebearingcross-sectioniscalculatedaccordingtotherectangularcross-section,andboththebearingandthecross-sectioninthespanareconsideredasarowofsteelbars,withh0=465mm.

ThecalculationofnormalsectionbearingcapacityofsecondarybeamisshowninTable2.17.ThecalculationofinclinedsectionbearingcapacityofsecondarybeamisshowninTable2.18.Schematicdiagramofreinforcementofsecondarybeamisshownin2.17.

Fig.2.17Schematicdiagramofreinforcementofsecondarybeam

Table2.17Calculationofnormalsectionbearingcapacityofsecondarybeam

Section

1

B

2

C

3

107.20

-121.73

65.92

-100.20

77.81

0.016

0.197

0.010

0.162

0.011

0.016

0.221

0.010

0.178

0.012

645.5

817.7

395.7

657.0

467.5

Optionalreinforcement

3C20

4C18

3C14

4C20

3C18

Practicalreinforcement

942

1016

461

942

763

Table2.18Calculationofinclinedsectionbearingcapacityofsecondarybeam

Section

A

B左

B右

C左

C右

72.92

108.22

98.85

91.82

95.68

332475＞V

332475＞V

332475＞V

332475＞V

332475＞V

93093＞V

93093＞V

93093＞V

93093＞V

93093＞V

Numberanddiameterofstirrups

101

101

101

101

101

-

-

-

-

-

Actualstirrupspacing

Designofmaingirder(calculatedaccordingtoelastictheory)

Itisknownfromthetopicthatthecross-sectionaldimensionofthecolumnis400mm×400mm,andthegeometricdimensionandsupportingconditionofthemainbeamareshowninFig.2.18.

Fig.2.18Geometricdimensionandsupportofmainbeam.

1.Loadcalculation

Concentratedloadgfromsecondarybeam:

Self-weightofmaingirder:thedistancebetweensecondarygirdersis2.2m,andevery2.2msectionofmaingirdercanbeconvertedintoconcentratedloadforcalculation:

Beamsideplastering:

Standardvalueofeachconstantload:

Designvalueofeachconstantload:

Standardvalueofeachliveload:

Designvalueforeachliveload:

Totaldesignload:

2.Calculationdiagram

Sincethelinearstiffnessofthemaingirderismuchlargerthanthecolumnstiffness,themiddlesupportofthemaingirderisconsideredashingesupport.Themaingirderissupportedonthebrickwallwithasupportinglengthof370mm.Thecalculationspansare:

（1）Middlespans:

（2）Sidespan:

＜

So,take

ThecalculationdiagramisshowninFigure2.19.

Fig.2.19Calculationdiagramofmainbeam.

3.InternalForceCalculation

（1）CalculationofBendingMomentofMainGirder

ThebendingmomentcalculationofthemaingirderisshowninTable2.19.

（2）Shearforcecalculationofmaingirder:

Lookupthetabletocalculatetheshearforceofthemaingirder,asshowninTable2.20.

Itemsandtimes

Loaddiagram

-

-

-

-

-

-

Mmin

Combinedvalue

-

-379.32

-

Mmax

Combinedvalue

350.22

-

186.35

Table2.20Calculationofmainbeamshearforce

Itemsandtimes

Loaddiagram

Vmin

Combinedvalue

139.12

-254.08

83.33

Vmax

Combinedvalue

159.16

-234.04

211.73

4.Calculationofsectionreinforcement

Themid-spansectionofthemaingirderiscalculatedaccordingtotheT-shapedsectionundertheactionofpositivebendingmoment,anditsflangewidthtakesthesmallerofthefollowingvalues:

Sotake，，Concurrentlytake。

JudgethetypeofT-sectionofeachmid-spansection:

Itislargerthananybendingmomentvalueinthetable,soitbelongstothefirsttypeofsection.

Thesectionofthemaingirderbearingandthemid-spansectionundertheactionofnegativebendingmomentarecalculatedasrectangularsection.

Take

ThecalculationofreinforcementfornormalsectionandinclinedsectionofmaingirderisshowninTable2.21andTable2.22respectively.

Table2.21Calculationofnormalsectionreinforcementofmaingirder.

Section

1

B

2

M(kNm.)

350.22

-379.32

186.35

-

39.32

-

350.22

-340.0

186.35

0.0294

0.210

0.0157

0.0298

0.2384

0.0158

1602.7

1740.5

849.8

Optionalreinforcement

4C22+2C18

4C22+2C18

4C18

Reinforcedsteelbararea

2028

2028

1016

Table2.22Calculationofreinforcementforinclinedsectionofmaingirder

Section

A

B(left)

B(right)

159.16

254.08

221.73

659.6<V

622.06>V

622.06>V

184.7>V

174.2<V

174.2<V

Numberanddiameterofstirrups

2

2

2

101

101

101

Bendupthesteelbar

-

1C18

1C18

Areaofeachbendingrib(mm2)

-

254.3

254.3

-

51.78

51.78

-

-

-

Actualstirrupspacing(mm)

250

250

250

5.Calculationofmaingirdersuspensionbars

Thedesignvalueofallconcentratedloadstransferredfromthesecondarybeamtothemainbeam:

Then

Selectionofliftingbars:

TheschematicdiagramofreinforcementofmaingirderisshowninFig.2.21.

Fig.2.20Envelopediagramofmainbeam.

Fig.2.21Schematicdiagramofmainbeamreinforcement.

Checkingcalculationofcrackwidthofplateandbeam

1.Checkingcalculationofcrackwidthofplate

（1）Theinternalforceoftheplateiscalculatedfromtheloadstandardvalue,asshowninTable2.23.

Table2.23CalculationTableofInternalForceofPlateunderLoadStandardValue

Controlcrosssection

Combinedvalue

M(consideringbearinginfluence)

1

-

3.45

B

0.99

-3.61

2

-

2.10

C

0.99

-2.91

3

-

2.57

CheckingCalculationofCrackWidthofPlate.CheckingcalculationofcrackwidthoftheplateisshowninTable2.24.

Table2.24Checkingofcrackwidthofplate.

Itemsandtimes

1

B

2

C

3

3.45

-3.61

2.1

-2.91

2.57

419

503

251

314

279

8

8

8

8

8

40000

40000

40000

40000

40000

157.7

137.5

160.3

177.5

176.5

0.0105

0.0126

0.0063＜0.01

0.0079＜0.01

0.0070＜0.01

0.309

0.344

0.285

0.364

0.360

99

89

102

102

102

0.048

0.042

0.047

0.066

0.065

Note1.Taketheprotectivelayerthicknessc=20mm.

2.When＜＜When0.01,0.01istakenforcalculation.

3.ThesteelbarsintheslabareallHPB235,soEs=2.1105N/mm2.

4.WSpecificationstipulatesthatitisgenerally0.3mmor0.4mm.

AscanbeseenfromTable2.24,w<wmeetstherequirements.

Sincetheplatethicknessh=80mmisgreaterthanl/35=2200/35=62.9mm,deflectioncheckingcalculationmaynotbedoneaccordingtothespecificationrequirements,i.e.Theplatethicknessisconsideredtobesufficienttomeetthedeflectionrequirements.

2.Checkingcalculationofcrackwidthofsecondarybeam

,

Then

Theinternalforceofthesecondarybeamiscalculatedfromtheloadstandardvalue,andthecalculationisshownintable2.25.

Table2.25Calculationofinternalforceofnextbeamunderloadstandardvalue

Controlcrosssection

Combinedvalue

M(consideringbearinginfluence)

1

-

84.78

B

10.97

-96.42

2

-

51.96

C

10.97

-79.09

3

-

61.22

（2）CheckingCalculationofCrackWidthofSecondaryBeam.CheckingcalculationofcrackwidthofsecondarybeamisshowninTable2.26.

Table2.26Checkingofcrackwidthofsecondarybeam

Itemsandtimes

1

B

2

C

3

84.78

-96.42

51.96

-79.09

61.22

942

1016

461

942

763

2020

18

14

20

18

50000

-

50000

-

50000

-

210000

-

210000

-

222.5

234.6

278.6

207.5

198.3

0.0188

0.0048

0.0092

0.0045

0.0153

0.788

0.534

0.631

0.470

0.668

132

192

160

208

142

0.244

0.256

0.294

0.213

0.197

AscanbeseenfromTable2.26:Conforming.

3.Checkingcalculationofcrackwidthofmai