CE331,Fall2010 Example:RoofTrussAnalysis 1/6

Inthisexample,aparallelchordsteelrooftrussisanalyzedfortypicaldeadandroofliveloads.Thephotobelowshowsatrussgirder(paintedgray)supportingtheroofofagymnasium.

Figure1.Trussgirders(gray)supportingbarjoists(white)supportingmetalroofdeckforagymnasium

Thetrussgirderinthephotoissupportedbycolumns(notseeninFigure1)andsupportsbarjoistsatthepanelpoints(chordconnections)andmidwaybetweenthepanelpoints.Asimilartrussgirderisanalyzedinthisexample,exceptthatthebarjoistsarelocatedatthepanelpointsonly.Informationabouttrussgirdermembersispresentedbelow.Table1.Trussgirdercomponents.

TypeMember Shape AvailableStrength(Pn)

Chords WT6x20 160k(compression)

Diagonals LL2.5x2.0x3/16 73k(tension)

Verticals LL2.5x2.5x3/16 43k(compression)

Thetotalweightoftrussgirder(selfweight)is4.05k,andthebarjoistsweigh9plf.Otherroofcomponentsarelistedbelow.Roof&Ceiling:

20gametaldeckWaterproofmembranewithgravel1thickPerliteinsulatingroofboardsHeating&coolingductworkSteelsuspendedceilingAcousticFiberBoard

CE331,Fall2010 Example:RoofTrussAnalysis 2/6

8@10

PlanView

FrontElevationView

6

barjoist

metaldecking

Side

Elevatio

nofRoo

fFraming

8@10

6

3@25

trussgirder

barjoists

trussgirder

column

3@25

ExampleRoofTrussAnalysis 3/6

Stability&Determinacy

assumethattrussisexternallystaticallydeterminateforgravityloads

Num_Forces =33+3= 36Num_Eqns =18x2= 36

thereforestable&determinate

DeadLoadRoof&CeilingWt: weight,psf

20gametaldeck 2.5Waterproofmembranewithgravel 5.5Fiberglassinsulation 0.7Heating&coolingductwork 4Steelsuspendedceiling 2AcoustisFiberBoard 1

Total 15.7 psf use 16 psf

StructuralModelofTruss

trussgirderselfwt 4.05 k =4.05k/(80ftx25ft)= 2.03 psf18.03 psf

barjoistwt 9 plf

PDint (deadloadataninteriorpanelpoint)

=18.025psfx25ftx10ft= 4.51 k dueroof,ceilingwt&trussgirder=9plfx25ft= 0.225 k duepurlinwt

4.73 kPDext (deadloadatanexteriorpanelpoint)

=18.025psfx25ftx10/2ft= 2.25 k dueroof,ceilingwt&trussgirder=9plfx25ft= 0.225 k duepurlinwt

2.48 k

7@4.73k2.48k 2.48k

StructuralModelofTruss

DeadLoadsonTrussGirder

ExampleRoofTrussAnalysis 4/6

LiveLoadRoofliveload=Lr=(20psf)R1 0.6

ExampleRoofTrussAnalysis 5/6

MaximumChordCompressiveForce

Drawdeflectedshapeofloadedtruss.Identifychordwithmax.compressiveforce.

Thetop"fibers"ofthebeamareincompression,and

thefibersinthemiddleofthebeamhavethemaximumcompression.

Therefore,thetopchordinthemiddleofthetrusshasthemax.compressiveforce.

CalculatetheforceinthetopchordofPanel#4

4@10.476k5 376 k

C

T

5.376k

5

R =[7(10.476k)+2(5.376k)]/2= 42.042 k

M aboutPt5=0:(f_top)(6ft)(42.042k5.376k)(4x10ft)+(3x10.476k)(20ft)=0

f_top 139.7 kinpanelsatmidspan

Checkthestrengthofthechords

factoredforceinmember(Pu)

ExampleRoofTrussAnalysis 6/6

MaximumDiagonalTensileForce

Lookingattheparallelchordtrussasifitwereabeam,themax.shearoccursnearthesupports

analagousbeam(assumeloadisuniformlydistributedalongbeam)

shear

bendingmoment

Therefore cut the truss in the first panel to calculate max diagonal forceTherefore,cutthetrussinthefirstpaneltocalculatemax.diagonalforce

5.38 k

6 ft 11.66 ft

10 ft

42.04 k

FV=0: 42.042k5.376k6/11.66xf_diag

f_diag 71.3 kinendpanels

CheckthestrengthofthediagonalsTu 71.3 k

TPn 73 k OK

f_diag