Loads Calculations
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Loads
Dead loadsImposed loads floor roofDeterminingloadpermandm2Wind
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Structurestransmitloadsfromoneplacetoanother
Wheredoloadscomefrom
Deadloads-permanentandstationary
StructureitselfPlantandequipment
Someroughfigures(notethatvaluesaresubjecttovariationdependingonspecifcmaterialtype)Alsonotevaluesareforcesperunitvolumenotmassperunitvolume.
UnitWeightsofbaiscconstructionmaterials kN/m3Aluminium 24Brick 22Concrete 24Steel 70Timber 6
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Precastconcretebeamlength
1.Calculateweightofbeamperunitlength.2.Calculatetotalweightofbeaminitis10.5m.
Firstcrosssectionalareaofbeam=
(0.6x0.25)-(0.4x0.15)=0.09m2
Fromtableunitweightofconcrete=24kN/m3
Weightperunitlength=0.09x24=2.16kN/m
Totalweight=2.16x10.5=22.68kN
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Oftenwearedealingwithsheetmaterialsorweknowalayerthicknessoffloororroofbuildup.
Figureshereareperunitarea
Againwhenusingthesetypeofchartssomecareisneededtoensureyouhavethecorrectfigure,orthatitcorrespondswithyourdesign.
Unitweightofbasicsheetmaterials kN/m2Asphalt(19mm) 0.45Aluminiumroofsheeting 0.04Glass(singleglazing) 0.1Plasterboardandskim 0.15Raftersbattensroofingfelt 0.14Sand/cementscreed(25mm) 0.6Slates 0.6Timberfloorboards 0.15Plasteronwallface 0.3
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CalculatethedeadloadinkN/m2ofthefollowingfloorbuildup:
Timberfloorboards40mmsand/cementscreed125mmreinforcedconcreteslab
timberfloorboards =0.15screed =0.6x40/25=0.96concreteslab =0.125x24=3.00
dead load /m2 =4.11kN/m2
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ifwearedealingwithawallactingonabeamweareinterestedinloadperlinearunitofthebeam
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Inthisexamplecalculatetheloadpermetreonthebeam.Thebuildupisadoubleglazedwindowonacavitywallof102.5mmbrickouterfaceand100mmplasteredlightweightblock-workwhichis12kN/m3.
brickwork =1.2x0.1025x22 =2.71blockwork =1.2x0.1x12 =1.44plaster =1.2x0.3 =0.36doubleglazing =2x1.3x0.1 =0.26
loadonbeam =4.77kN/m
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Imposedloads-orliveloads,movableloadsthatactonthestructurewhenitisinuse.
People,furniture,cars,computersandmachineryareallimposedloads.
NormallyweconsiderimposedloadsasfloorandroofloadsTypicalfloorloads kN/m2Artgalleries 4.0Bankinghalls 3.0bars 5.0Carparks 2.5Classrooms 3.0Churches 3.0Computerlabs 3.5Dancehalls 5.0Factoryworkshop 5.0Foundaries 20.0Hotelbedrooms 2.0Offices(general) 2.5Offices(filing) 5.0Privatehouses 1.5Shops 4.0Theatres(fixedseats) 4.0
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Ifabarshouldbedesignedwithliveloadof5.0kN/m2andifanaveragepersonis80kghowmanypeopleareexpectedtobestandinginonesquaremetreoffloor?
Forceexertedbyoneperson =80x9.81 =785NNumberofpeopleperm2 =5000/785 =6.4people/m2
equivalentlyifyourhouseisdesignedwith1.5kN/m2andthetotalareawas22m2howmanypeoplecouldyouinvitetoaparty?
Forceexertedbyoneperson =785NNumberofpeopleperm2 =1500/785 =1.9people/m2Totalnumberofpeopleatparty =1.9x22 =42andabit.
certaintypesofdancingcancausedynamiceffectsthatincreasetheeffectofload.
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Calculatingimposedroofloads.
Whatyouneedtoknow:
1.Isaccesstotheroofprovided?(aloadofadjacentfloorareaisrequired)2.Predominantloadissnow. whichisdependanton geographicallocation heightabovesealevel shapeofroof windthatredistributessnowintodrifts
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EstimatinggroundsnowloadsinCanada.InfofromCanadianCryosphericInformationNetworkFindworstcasedepthandmultiplybydensity(kg/m3)and9.81
TablesinNationalBuildingCodeprovidefurtherdetails
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InUKsnowloadvariesfrom0.3kN/m2onsouthcoastto3.0kN/m2inScotland
CalculatingasnowloadinCanada.NationalBuildingCodePart44.1.7.
S=Ss (CbxCwxCsxCa)+Sr
Snowloadperm2
groundsnowloadinkPa(kN/m2)
roofsnowloadfactor=0.8???
windexposurefactor
slopefactor
accumulationfactor
associatedrainload
NationalBuildingCodeofCanadaappendixcfortablesofclimaticinformation
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windexposurefactor
is1.0butcanbereducedto0.75orinexposedareasnorthoftreelineto0.5 if buildingisanexposedlocationandexposedonallsides noobstructionsaroundbuilding noobstructionsonroofsuchasparapet snowcannotdriftontorooffromadjacentsurfaces
slopefactorbasedonroofangleaandsurfacetype. is1.0ifa30 is0ifa>70
ifroofisaslipperysurface(wheresnowandiceslideoff)
slopefactor is1.0ifa15 is0ifa>60
NationalBuildingCodeofCanadaappendixcfortablesofclimaticinformation
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accumulationfactor
is1.0 exceptwhen forlargeflatroofswhen 1.2x[1-(30/l)2]butnotlessthan1.0forroofswithwindfactor=1.0 1.6x[1-(120/l)2]butnotlessthan1.0forroofswithwindfactor=0.75or0.5
w=smallerplandimension L=largerplandimension and lis2xw-(w2/L)inmetres
canbeassignedothervalueswhen: roofshapesarearched,curvedordomes snowloadsinvalleys snowdriftsfromanotherroof projectionsonadjacentroofs snowslidingordrainagefromadjacentroofs
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Theresmore:
inrealityfullandpartialloadinghastobeconsidered
Inadditiontotheloadcalculationaboveroofsofslopelessthan15andarchedorcurvedroofsmustbedesignedwithaccumulationfactor1.0ononeportionwhilehalfthatloadisappliedtotheremainder.
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Calculatesnowloadonthisroofstructure
Whatisthesnowloadpermetrelengthoftruss?
Whatisthetotalsnowloadononerooftruss?
Whatistheloadpermetreonthesupportingwall?Assumethatloadsfromtrussesareevenlydistributed
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CalculatesnowloadforHalifaxS
groundsnowHalifax=1.7
snowloadfactor=0.8
windexposurefactor=1.0
slopefactor=(70-40)/40=0.75
accumulationfactor=1.0
rainloadHalifax=0.5
S=1.7x(0.8x1x0.75x1)+0.5
S=1.52kN/m2
Snowloadperm2
groundsnowloadinkPa(kN/m2)
roofsnowloadfactor=0.8???
windexposurefactor
slopefactor
accumulationfactor
associatedrainload
S=Ss (CbxCwxCsxCa)+Sr
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Trussesareat0.6mcentres
Sosnowloadpermetrelengthoftrussis:
0.6x1.52=0.9kN/m
Noteloadisverticalso1mdimen-sionismeasuredhorzontally
For7mtrussloadis
7x0.9=6.4kN
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Loadpermonwall=1.52x3.5=5.32kN/m
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Windloadsactnormal(orperpendicular)tobuildingsurfaces
windscancausepressureorsuction.
Forthisreasonbuildingstructuresmustresisthorizontalforcesaswellasverticalforces.
Inadditionsomelightweightstructurescanbesubjecttoupliftforcesfromthewindsoneedtobead-equatelyhelddown.
Windloadslikesnowloadsvarydependingon:
geographiclocation degreeofexposure buildingheightandsize buildingshape winddirectioninrelationstostructure positiveornegativepressuresinthebuilding
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Fastermovingaircreateslowerpressure(bernoullieffect)asinplanewings.
Thesameprinciplecausesforcestoactonbuildingsurfaces.
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Structureforresistingwindloads
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Theseprinciplesshouldbewellunderstoodbynowifnot
Lookat: FrancisChing.BuildingConstructionIllustrated
EdwardAllen.ArchitectsStudioCompanion
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Forstructuraldesignitisoftennecessarytoconsiderseveralloadcasesduetothewindblowingfromdifferentdirections.
DesigningabuildinginHalifaxcalculatingwindloads.NationalBuildingCodeofCanadaPart44.1.8.
p=qxCexCgxCp
externalpressureactingstaticallyandnormaltosurface
referencevelocitypressure
exposurefactor
gusteffectfactor
externalpressurecoefficient
NationalBuildingCodeofCanadaappendixcfortablesofclimaticinformation
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netpressureonasurfaceisthedifferencebetweeninternalandexternal
similartoexternalpressureinternalpressureiscalculatedaccordingtotheNBC
p=qxCexCgxCp
internalpressureactingstaticallyandnormaltosurface
referencevelocitypressure
exposurefactor
gusteffectfactor
internalpressurecoefficient
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referenceveloctypressurethreeareshownintable1in10,1in30,1in100
theseareprobabilitiesofpressureoccuring
so1in10isusedforcladdingandstucturaldesignforvibrationanddeflection
1in30forstructuralstrength
post-disasterbuldingsusethe1in100pressurevalues.
exposurefactor
exposureincreasewithheightheightm exposurefactor>0and6and12and20and30and44and
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gustfactor
1.0or2.0forinternalpressurestobefoundsomewhereinthe500pagesofappendixA!! welluse1.0fornow.
2.0forthebuildingasawholeandmainstructuralmembers
2.5forsmallelements
externalandinternalpressurecoefficients
againappendixAwelluse1.0fornow.
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Forcesduetowindonsimplebuilding
externalpressurep=qxCexCgxCp
1in30yearPressureHalifax=0.52kPa(kN/m2)
Wallsbelow6msoexposurefactoris0.9
Gustfactor=2.0externaland1.0internal
Pressurecoefficient=1.0
externalp=0.52x0.9x2.0x1.0=0.936kN/m2
internalp=0.52x0.9x1.0x1.0=0.468kN/m2
so0.936-0.468=0.468kN/m2actingnormaltoverticalsurfaceswindward
and0.936+0.468=1.4kN/m2leeward
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Forcesduetowindonsimplebuilding
externalpressurep=qxCexCgxCp
1in30yearPressureHalifax=0.52kPa(kN/m2)
Roofabove6msoexposurefactoris1.0
Gustfactor=2.0externaland1.0internal
Pressurecoefficient=1.0
externalp=0.52x1.0x2.0x1.0=1.04kN/m2
internalp=0.52x1.0x1.0x1.0=0.52kN/m2
1.04kN/m2actingnormaltoverticalsurfacesatrooflevel
normaltoroof1.04xSin(40)=0.67 windward=0.67-0.52=0.15kN/m2 leeward=0.67+0.52=1.19(suction)
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Nextup:Acoupleofotherloadtypes(toknowabout)UniformandpointloadsSafetyfactorsCalculatingloadonbeamsLoadpaths
PinJointedstructures
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A couple of other load types (to know about)Uniform and point loadsSafety factors Calculating load on beamsLoad paths
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Hydrostatic pressure loads from soils and liquids
Increases linearly with depth.
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Application of safety factors to loads
Loads discussed are realistic estimates of loads or characteristic loads
when checking ultimate strength characteristic loads are increased by multiplying by a safety factor.
The result is the design load.Safety factors
load combination dead imposed winddead and imposed 1.4 or 1.0 1.6 -dead and wind 1.4 or 1.0 - 1.4dead, imposed and wind 1.2 1.2 1.2
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For example
to obtain the maximum compressive design in the support at Btwo load combinations should be checked and the larger value used
1.4 x dead + 1.6 imposed
or
1.2 x dead + 1.2 x imposed + 1.2 wind
to obtain maximum tensile design load in the support at A
we need to minimise the effect of the dead and imposed loads by using
1.0 x dead + 1.4 x wind
A B
wind
imposed roof
imposed floor
dead load
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Point load (kN)
Uniformly distributed load (kN/m)
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Calculating loads on beams
Example
Building type - officeFloor construction = 4.11kN/m2Perimeter wall construction = 4.77kN/m2self weight of beams = 0.6 kN/m
safety factors are 1.4 for dead load and 1.6 for live load to find design load
design load kN/m2floor 1.4 x 4.11 5.75wall 1.4 x 4.77 6.68beams 1.4 x 0.6 0.84imposed 1.6 x 2.5 4.00
total design floor load = 5.75 + 4.00 = 9.75kN/m2
B6
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Beam B1 (8m span)supports a total width of 6m
load from floor = 9.75 x 6 = 58.50kN/mself weight of beam = 0.84 kN/m
design UDL = 59.34 kN/m
symmetry indicates reactions will be equal
reaction = (59.34 x 8) / 2 = 237.4 kN
beam B2 is the same as B1
B6
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Beam B3 suports a 3m width of floor plus the perimeter wall
Load from floor = 3 x 9.75 = 29.25 kN/mload from wall = 6.68kN/mself weight of beam = 0.86kN/m
total design UDL = 36.79kN/m
symmetry indicates reactions will be equal
reaction = (36.9 x 8) /2 = 147.6kN
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Beam B4 has same UDL as B1 and B2 but span is 6m
B6
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Beam B6
Supports perimeter wall and a point load from the reaction of B2.
Load from wall = 6.68kN/mself weight of beam = 0.86kN/m
design UDL = 7.54kN/m
design point load = 237.4kN
Reaction from symmetry
= ((7.54 x 12) + 237.4) / 2 = 163.9kN
B6
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Now work out reactions for B5
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Load paths
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Working through load path for a simple sign.
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03Loads03LoadsPart2