Copyright 2010 Pearson Education South Asia Pte LtdChapter 6 : Structural Analysis1. Simple Trusses2. The Method o !oints". #ero$%orce Mem&ers'. The Method o SectionsAPPLICATIONS%or a gi(en truss geometry and load) ho* can you determine the orces in the truss mem&ers and thus &e a&le to select their si+es,Trusses are commonly used to supportroos.A more challenging -uestion is) that or a gi(en load) ho* can *e design the trusses. geometry to minimi+e cost,APPLICATIONS /continued0Trusses are also used in a (ariety o structures li1e cranes and the rames o aircrat or the space station.2o* can you design a light *eight structure satisying load) saety) cost speciications) is simple to manuacture) and allo*s easy inspection o(er its lietime,Copyright 2010 Pearson Education South Asia Pte Ltd6.1 Simple Trusses3A truss composed o slender mem&ers 4oined together at their end pointsPlanar Trusses3Planar trusses used to support roos and &ridges35oo load is transmitted to the truss at 4oints &y means o a series o purlinsCopyright 2010 Pearson Education South Asia Pte LtdPlanar Trusses /26 truss03 The analysis o the orces de(eloped in the truss mem&ers is 263 Similar to roo truss) the &ridge truss loading is also coplanarCopyright 2010 Pearson Education South Asia Pte LtdAssumptions or 6esign1. 7All loadings are applied at the 4oint8$ 9eight o the mem&ers neglected2. 7The mem&ers are 4oined together &y smooth pins8 $ Assume connections pro(ided the center lines o the 4oining mem&ers are concurrentCopyright 2010 Pearson Education South Asia Pte LtdSimple Truss3 %orm o a truss must &e rigid to pre(ent collapse3 The simplest orm that is rigid or sta&le is a triangleCopyright 2010 Pearson Education South Asia Pte Ltd6.2 The Metho o! "oints3%or truss analysis) *e need to 1no* the orce in each mem&er3%orces in the mem&ers are internal orces3%or e:ternal orce mem&ers) e-uations o e-uili&rium can &e applied3%orce system acting at each 4oint is coplanar and concurrent /analysis &ased on e-uili&ium o a particle03 ;%: < 0 and ;%y < 0 must &e satisied or e-uili&riumCopyright 2010 Pearson Education South Asia Pte LtdProcedure or Analysis3 6ra* the %=6 o 4oint *ith not more than 2 un1no*n orces3 %ind the e:ternal reactions at the truss support i necessary.3 6etermine the correct sense o orce in the mem&er3 >rient the : and y a:es3 Apply ;%: < 0 and ;%y < 0Copyright 2010 Pearson Education South Asia Pte Ltd#$ample 6.16etermine the orce in each mem&er o the truss and indicate *hether the mem&ers are in tension or compression.Copyright 2010 Pearson Education South Asia Pte LtdSolution32 un1no*n mem&er orces at 4oint =32 un1no*n orces and 1 un1no*n reaction orce at 4oint C /total " un1no*n032 un1no*n mem&er orces and 2 un1no*n reaction orces at point A /total ' un1no*n0%or !oint =)Copyright 2010 Pearson Education South Asia Pte Ltd%or !oint C)%or !oint A)Copyright 2010 Pearson Education South Asia Pte Ltd3 %=6 o each pin sho*s the eect o all the connected mem&ers and e:ternal orces applied to the pin3 %=6 o each mem&er sho*s only the eect o the end pins on the mem&erCopyright 2010 Pearson Education South Asia Pte Ltd6.% &ero'(orce Mem)ers3Method o 4oints is simpliied using +ero$orce mem&ers3#ero$orce mem&ers are supports *ith no loading at 4oint.35ule ? 1@ 9hen 2 mem&ers orm a truss 4oint. =othmem&ers are non$collinear and no e:ternal orce or support reaction is applied to the 4oint) then &oth the mem&ers are +ero$orce mem&ers5ule ? 23 9hen " mem&ers orm a truss 4oint) t*o are collinear and the third is non$collinear then "rdmem&er /non$collinear0 is a +ero$orce mem&er pro(ided no e:ternal orce or support reaction is applied to the 4oint.Copyright 2010 Pearson Education South Asia Pte LtdCopyright 2010 Pearson Education South Asia Pte Ltd#$ample 6.*Asing the method o 4oints) determine all the +ero$orce mem&ers o the %in1 roo truss. Assume all 4oints are pin connected.Copyright 2010 Pearson Education South Asia Pte LtdSolution%or !oint B)BC is a +ero$orce mem&er. %or !oint 6)Copyright 2010 Pearson Education South Asia Pte LtdSolution%or !oint %)Copyright 2010 Pearson Education South Asia Pte LtdSolution%2C satisy ;%y < 0 and thereore 2C is not a +ero$orce mem&er. APPLICATIONSLong trusses are oten used to construct large cranes and large electrical transmission to*ers.The method o 4oints re-uires that many 4oints &e analy+ed &eore *e can determine the orces in the middle o a large truss.So another method to determine those orces is helpul.Copyright 2010 Pearson Education South Asia Pte Ltd6.* The Metho o! Sections3Ased to determine the loadings *ithin a &ody3C a &ody is in e-uili&rium) any part o the &ody is in e-uili&rium3To ind orces *ithin mem&ers) an imaginary section is used to cut each mem&er into 2 and e:pose each internal orce as e:ternalCopyright 2010 Pearson Education South Asia Pte Ltd3 Consider the truss and section a$a as sho*n3 Mem&er orces are e-ual and opposite to those acting on the other part D Ee*ton.s La*Copyright 2010 Pearson Education South Asia Pte LtdProcedure or Analysis%ree$=ody 6iagram3 6ecide the section o the truss 3 6etermine the truss.s e:ternal reactions i re-uired.3 6ra* %=6 o the sectioned truss *hich has the least num&er o orces acting on it3 Assume the sense o an un1no*n mem&er orce as in tension /orce directed a*ay rom the mem&er03 Ase e-uili&rium e-uations to sol(e mem&er orces at the cut session /"E>E or " un1no*n0E-uations o E-uili&rium3 Summed moments a&out a point 3 6etermine the " un1no*n orces rom the " E>E or 26 truss analysis.Copyright 2010 Pearson Education South Asia Pte Ltd#$ample 6.+6etermine the orce in mem&ers BE) BC) and =C o the truss. Cndicate *hether the mem&ers are in tension or compression.Copyright 2010 Pearson Education South Asia Pte LtdSolution3Choose section a$a since it cuts through the three mem&ers36ra* %=6 o the entire trussCopyright 2010 Pearson Education South Asia Pte Ltd3 6ra* %=6 or the section portion#,AMPL#a0 Ta1e a cut through mem&ers F!) F6 and C6.&0 9or1 *ith the let part o the cut section. 9hy,c0 6etermine the support reactions at A. 9hat are they,d0 Apply the E$o$E to ind the orces in F!) F6 and C6.-i.en: Loads as sho*n on the truss. (in: The orce in mem&ers F!) F6) and C6.Plan:+6./ 0N+6./ 0N