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Load Calculations
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Loads
Dead loadsImposed loads floor roofDeterminingloadpermandm2Wind
Structurestransmitloadsfromoneplacetoanother
Wheredoloadscomefrom
Deadloads-permanentandstationary
StructureitselfPlantandequipment
Someroughfigures(notethatvaluesaresubjecttovariationdependingonspecifcmaterialtype)Alsonotevaluesareforcesperunitvolumenotmassperunitvolume.
UnitWeightsofbaiscconstructionmaterials kN/m3Aluminium 24Brick 22Concrete 24Steel 70Timber 6
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
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
CalculatethedeadloadinkN/m2ofthefollowingfloorbuildup:
Timberfloorboards40mmsand/cementscreed125mmreinforcedconcreteslab
timberfloorboards =0.15screed =0.6x40/25=0.96concreteslab =0.125x24=3.00
dead load /m2 =4.11kN/m2
ifwearedealingwithawallactingonabeamweareinterestedinloadperlinearunitofthebeam
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
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
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.
Calculatingimposedroofloads.
Whatyouneedtoknow:
1.Isaccesstotheroofprovided?(aloadofadjacentfloorareaisrequired)2.Predominantloadissnow. whichisdependanton geographicallocation heightabovesealevel shapeofroof windthatredistributessnowintodrifts
EstimatinggroundsnowloadsinCanada.InfofromCanadianCryosphericInformationNetworkFindworstcasedepthandmultiplybydensity(kg/m3)and9.81
TablesinNationalBuildingCodeprovidefurtherdetails
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
windexposurefactor
is1.0butcanbereducedto0.75orinexposedareasnorthoftreelineto0.5 if buildingisanexposedlocationandexposedonallsides noobstructionsaroundbuilding noobstructionsonroofsuchasparapet snowcannotdriftontorooffromadjacentsurfaces
slopefactorbasedonroofangleaandsurfacetype. is1.0ifa30 is0ifa>70
ifroofisaslipperysurface(wheresnowandiceslideoff)
slopefactor is1.0ifa15 is0ifa>60
NationalBuildingCodeofCanadaappendixcfortablesofclimaticinformation
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
Theresmore:
inrealityfullandpartialloadinghastobeconsidered
Inadditiontotheloadcalculationaboveroofsofslopelessthan15andarchedorcurvedroofsmustbedesignedwithaccumulationfactor1.0ononeportionwhilehalfthatloadisappliedtotheremainder.
Calculatesnowloadonthisroofstructure
Whatisthesnowloadpermetrelengthoftruss?
Whatisthetotalsnowloadononerooftruss?
Whatistheloadpermetreonthesupportingwall?Assumethatloadsfromtrussesareevenlydistributed
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
Trussesareat0.6mcentres
Sosnowloadpermetrelengthoftrussis:
0.6x1.52=0.9kN/m
Noteloadisverticalso1mdimen-sionismeasuredhorzontally
For7mtrussloadis
7x0.9=6.4kN
Loadpermonwall=1.52x3.5=5.32kN/m
Windloadsactnormal(orperpendicular)tobuildingsurfaces
windscancausepressureorsuction.
Forthisreasonbuildingstructuresmustresisthorizontalforcesaswellasverticalforces.
Inadditionsomelightweightstructurescanbesubjecttoupliftforcesfromthewindsoneedtobead-equatelyhelddown.
Windloadslikesnowloadsvarydependingon:
geographiclocation degreeofexposure buildingheightandsize buildingshape winddirectioninrelationstostructure positiveornegativepressuresinthebuilding
Fastermovingaircreateslowerpressure(bernoullieffect)asinplanewings.
Thesameprinciplecausesforcestoactonbuildingsurfaces.
Structureforresistingwindloads
Theseprinciplesshouldbewellunderstoodbynowifnot
Lookat: FrancisChing.BuildingConstructionIllustrated
EdwardAllen.ArchitectsStudioCompanion
Forstructuraldesignitisoftennecessarytoconsiderseveralloadcasesduetothewindblowingfromdifferentdirections.
DesigningabuildinginHalifaxcalculatingwindloads.NationalBuildingCodeofCanadaPart44.1.8.
p=qxCexCgxCp
externalpressureactingstaticallyandnormaltosurface
referencevelocitypressure
exposurefactor
gusteffectfactor
externalpressurecoefficient
NationalBuildingCodeofCanadaappendixcfortablesofclimaticinformation
netpressureonasurfaceisthedifferencebetweeninternalandexternal
similartoexternalpressureinternalpressureiscalculatedaccordingtotheNBC
p=qxCexCgxCp
internalpressureactingstaticallyandnormaltosurface
referencevelocitypressure
exposurefactor
gusteffectfactor
internalpressurecoefficient
referenceveloctypressurethreeareshownintable1in10,1in30,1in100
theseareprobabilitiesofpressureoccuring
so1in10isusedforcladdingandstucturaldesignforvibrationanddeflection
1in30forstructuralstrength
post-disasterbuldingsusethe1in100pressurevalues.
exposurefactor
exposureincreasewithheightheightm exposurefactor>0and6and12and20and30and44and
gustfactor
1.0or2.0forinternalpressurestobefoundsomewhereinthe500pagesofappendixA!! welluse1.0fornow.
2.0forthebuildingasawholeandmainstructuralmembers
2.5forsmallelements
externalandinternalpressurecoefficients
againappendixAwelluse1.0fornow.
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
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)
Nextup:Acoupleofotherloadtypes(toknowabout)UniformandpointloadsSafetyfactorsCalculatingloadonbeamsLoadpaths
PinJointedstructures
A couple of other load types (to know about)Uniform and point loadsSafety factors Calculating load on beamsLoad paths
Hydrostatic pressure loads from soils and liquids
Increases linearly with depth.
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
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
Point load (kN)
Uniformly distributed load (kN/m)
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
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
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
Beam B4 has same UDL as B1 and B2 but span is 6m
B6
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
Now work out reactions for B5
Load paths
Working through load path for a simple sign.
03Loads03LoadsPart2