Project Report II MSE 221- Fall 2015 Prepared for Professor Flavio Firmani Raaj Chatterjee 30126623
!nahita Mahmoodi 301253"
S#mreen Rattan 3012"61
Eri$ Seidelmann 3011%3525
Table of Contents &'
Abstract............................................2
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Design Description...........................3
&&&' Failure...............................................4 &('
Loads Efects on Members and Joint 4
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Cause o Failure................................
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Design !e"ection..............................#
(&&' !ecommendations............................$ (&&&' Conclusion........................................% &)'
&or's Cited.......................................(
Abstract *he o+je,tive of this proje,t as to desi.n and ,onstr#,t the li.htest +rid.e that ,an hold the .reatest load/ ,omposed solel of Popsi,le sti,$s and all-p#rpose .l#e' *he o+je,tives/ re#irements and limitations of o#r desi.n are analed and dis,#ssed' *he res#lt of the +rid.e testin. is thoro#.hl analed/ ,omparin. softare sim#lations and ,al,#lations to the res#lts' *he ,a#ses of fail#re are dis,#ssed and re,ommendations for f#rther improvements are .iven' *he fo,al point of this entire proje,t as to appl the theor +ehind stati,all determinate str#,t#res to ,reate the +est possi+le modi,ation of the Patt#llo 4rid.e' n,e e desi.ned/ #sin. softare sim#lations and ,al,#lations/ e ere a+le to determine possi+le points of fail#re ithin o#r desi.n' &n a a/ this proje,t ena+led st#dents to learn more a+o#t real life en.ineerin. sit#ations vers#s a tpi,al le,t#re environment' &n eams/ st#dents are #s#all epe,ted to solve the stati,all determinate +rid.e ith no f#rther analsis/ hereas ith this +rid.e/ man desi.n iterations ere re#ired to ,onstr#,t a +rid.e/ folloed + detail ,al,#lations of here their ideal desi.n ,o#ld a,t#all fail' !t the end of this report/ e ill determine the +est possi+le improvements of o#r desi.n to ens#re that o#r f#t#re proje,ts are as hi.h #alit as possi+le'
PROJECT REORT II –
2
Figure 1: Pattullo Bridge Aerial View (Translink)
Design Description #r o+je,tive as to ,reate a +rid.e hi,h o#ld +e a+le to s#pport a lar.e applied load hile maintainin. a relativel li.ht ei.ht' *he restri,tions on o#r +rid.e in,l#ded that it +e ,omposed of Elmer7s +rand Popsi,le sti,$s and all-p#rpose .l#e/ #se stati,all determinate tr#sses and +e %0,m in len.th/ spannin. 85,m' #r nal desi.n for the +rid.e ,onsisted of the 9arren tr#ss ith verti,al s#pports in the trian.#lar se,tions pla,ed to reinfor,e the top of the tr#ss' *he reason for the modi,ation as to in,rease the stren.th of the mem+ers in ,ompression/ alloin. #s to red#,e their ,han,es of fail#re' *he dimensions of the +rid.e ere 12 ,m + 11 2
√ 3
∗
,m and the roada idth as approimatel 10 ,m' *he len.th of
the roada as %0 ,m and the overall ei.ht of the +rid.e ,ame to +e 31" .rams' *he ,al,#lations e made shoed that o#r +rid.e ,o#ld s#pport a maim#m ei.ht of 63'8"$. ass#min. all the mem+ers and joints met the maim#m theoreti,al stresses/ hen in pra,ti,e the ere li$el to fail +efore this point' *his indeed as the ,ase/ as o#r +rid.e held half the predi,ted load/ the ,a#se of hi,h ill +e analed in s#+se#ent se,tions'
PROJECT REORT II –
3
Figure 2: Bridge across span before testing
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Failre #r +rid.e as a+le to s#pport a maim#m load of 32':./ ith a load to ei.ht ratio of 101'56/ altho#.h this is +elo the 63'8":. that e ass#med it o#ld +e a+le to hold' *he res#lts of this test .ave #s val#a+le information that e ,an #se to improve f#t#re proje,ts of a similar nat#re' 9e determined that o#r theoreti,al val#e of the maim#m load had a "'2; error/ altho#.h this val#e is fairl hi.h' *his led #s to ,on,l#de that in f#t#re proje,ts e sho#ld ass#me a safet fa,tor of at least 2' *he safet fa,tor as fo#nd + ta$in. the #ltimate ei.ht applied and dividin. it + the alloa+le ei.ht applied/ in this ,ase/ 63'8":. < 32':.' *his is a ver important step as theoreti,al val#es of maim#m stresses are alas loer than val#es o+served in pra,ti,al #sa.e/ as demonstrated + the res#lts of this test'
!oa"s E#ects on $e%bers an" Joint &n the previo#s report e fo#nd the tension in all the mem+ers as a per,ent of the applied for,e on o#r +rid.e' Sin,e o#r +rid.e as a+le to s#pport a ei.ht of 32':./ e $no that the maim#m applied for,e the +rid.e ,o#ld s#stain as 318'52 =eton>s' *his as fo#nd + m#ltiplin. 32':. + "'%ms se,ond la/ e $no this ill .rant #s the for,e applied' *h#s/ .iven the per,enta.e of the applied for,e in ea,h mem+er and the applied for,e on the +rid.e/ e ,an ,al,#late the total for,e in ea,h mem+er as shon in the ta+le +elo' #r Matla+ ,ode @2A has helped #s to nd these val#es' Table 1: Copression and Tension in !ebers
Member
Net Tension (N)
AB AC BC BD CE CF DE EF EG FH FI GH PROJECT REORT II –
& *&)*2'(+2 '(2)*++&24 & & 2,2),('432 & '(2)*++&24 & & 4+4)-((-4 & +
Net Compression (N) '(2)*+'(4(( & & '(')(43,&4 '(2)*++&24 & '(')(43,&4 & 3-3)+*2'+2 '(2)*++&24 & 3-3)-(,4&(
HI HJ JK IK IL KM KL
'(2)*++&24 & & 3-3)-(,4&( & 3-3)-(,4&( & '(2)*++&24 -3-)3'&&( & & +4+)+342(,2 '(2)*++&24 & 9e ere similarl a+le to nd the amo#nt of shear stress ever joint as end#rin./ #sin. the per,enta.e of shear stress for an applied load fo#nd previo#sl' *he res#lts ere ,al,#lated and entered into the ta+le
+elo' Table 2: "#ear "tresses in $oints
Joint
A B C D E F G H I J K L
ΣX fores (N) '(&)*( -4 3-+)'4 ( +4-)'3 44 3-+)'4 ( ,2,)'2 &( ('*)2&
!"e#r in X (M$#)
Tot#& !"e#r (M$#) 2)2+(--+ (2 2)*(&2'4 '4 3)(*-4-2 +2)244*(3 (( 4)(**'++ ,* +)4'42++
',2,)'2 &( '&*2)2 -* '2,3)2 ++ '&*2)2 -* '4+4)2 42 '4+4)2 42
(+ 4)4(**-, ,-),34,(& '* ,)(+,&,(+ -),34+-' ' ()*,('*+ +2 ()*,('*+ +2
+,( & ,2,)'2&( 4)4(**-, ,')*-&&2+ ''3-),2' ,)&'4'*, +,* ')*-&&2+ '3'')3+, ()&*,(-' +,* & '&*2)2-( -),34+-' ( ' ')*-&&2+ '4(*)'-( *)'(*-+4 +( 3' 3)*2&&2+ '+(,)- *),*---3 ,2 -+
PROJECT REORT II –
Σ% !"e#r in Tot#& fores % (M$#) Fore (N) (N) ')'224*3 3',)+2 ')*+***3-+)'4( +3 *( 2)244**& 3',)+2 ')*-&&2+ 4(2)-3&4 23 +3)3-,+*( 3',)+2 ')*-&&2+ -3')(-4( &, +2)244*(3 & & 3-+)'4( (( 4)4(***3 3',)+2 ')*-&&2+ ,*3)( ', ++)&4,&24 3',)+2 ')*-&&2+ (,-)3++2
-
& 3',)+2 3',)+2 & 3',)+2 -3+)&4
Case of Failre !s epe,ted/ o#r +rid.e failed in mem+er :M and in joint B as shon in .#re 1' Sin,e +oth lo,ations had failed hen the +rid.e as eamined/ it is impossi+le to $no ea,tl hi,h failed rst/ th#s +oth ill +e analed as a ,a#se of fail#re' Mem+er :M is in more ,ompression than an other joint in o#r tr#ss and as s#,h as epe,ted to fail +efore the other mem+ers' !ltho#.h other mem+ers feel hi.her tensile for,es/ d#e to the fa,t that the popsi,le ,an handle for more tensile for,es than ,ompressive/ @3A@A mem+er :M as ass#med to fail rst' From this e $no that in f#t#re desi.ns joint :M sho#ld either +e f#rther reinfor,ed or the desi.n sho#ld +e altered to ens#re less ,ompressive for,es o,,#r in that mem+er'
Figure % Failure of eber &! (left) and 'oint (rig#t)
*he joint B is the lo,ation here the hi.hest shear for,es are felt and as s#,h as ass#med to +e here the +rid.e o#ld fail' *hese hi.h shear stresses are d#e to a lar.e n#m+er of mem+ers ith hi.h ,ompressive or tensile stresses meetin. in one lo,ation' &t int#itivel ma$es sense that the joint that o#ld feel the most stress is the f#rthest aa from the s#pports and is ,losest to the applied load' *his indi,ates that f#t#re desi.ns sho#ld either reinfor,e joint B/ so that it ,an handle a hi.her shear stress/ or the +rid.e sho#ld +e desi.ned so that shear stresses are minimied in this lo,ation.
Design Re.ection &n an ideal orld/ the epe,tations of a proje,t o#ld mat,h the o#t,ome/ +#t in realit/ eperien,e proves a dierent stor here it is not #n,ommon for a proje,t to fail' !ltho#.h e had a thoro#.h approa,h/ PROJECT REORT II –
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hi,h ,ertainl ,o#ld have res#lted in an e,eptional endin. to this proje,t/ a fe desi.n errors and in,onsisten,es res#lted in an ina+ilit to meet o#r predi,ted load' !fter the +rid.e testin./ and analsis of other +rid.es/ e re,o.nied the minor ,han.es and additions hi,h ma have in,reased the alloa+le load of o#r +rid.e' *o start/ the +rid.e ma have +een improved + addin. horiontal s#pports a,ross the top of the tr#sses hi,h o#ld have red#,ed the li$elihood of deformation d#e to the +rid.e ,on,avin. inards' !ltho#.h this as not the main ,a#se of +rid.e fail#re/ it as li$el a ,ontri+#tin. fa,tor for the +rid.e ,ollapsin. +efore o#r predi,ted load limit as rea,hed' =et/ the tr#ss itself ,o#ld have +een desi.ned dierentl D from the analsis of +rid.es hi,h ,arried a si.ni,ant load/ it as evident that +rid.es ith the oe or Pratt tr#ss lasted lon.er than +rid.es ith simpler tr#sses' &n the ,ase of o#r +rid.e/ it ma have +een +etter to ,hoose one of these tr#sses rather than the 9arren tr#ss' 9ith respe,t to +#ildin. the tr#sses/ the Popsi,le sti,$s ,o#ld have +een reinfor,ed +etter - for eample/ there ere man red#ndant Popsi,le sti,$s hi,h did not help ith reinfor,ement/ and added additional ei.ht instead' *hese in,l#ded some of the verti,al ,ol#mns as ell as do#+led sti,$s on either tr#ss/ hi,h ,o#ld have +een +etter proportioned D the tr#sses ere do#+led #p at dierent points/ hi,h altered the smmetr and distri+#tion of the ei.ht of the +rid.e' Similarl/ the .l#in. ,o#ld have +een ,arried o#t more ee,tivel D it as evident that one of o#r tr#sses as more smmetri,all ali.ned/ and less distorted d#e to a +etter .l#in. jo+ and #se of ali.nment tools' *here as also a la,$ in ,onsisten, in the amo#nt of .l#e #sed/ here there as e,essive .l#e at some joints/ and ver minimal .l#e at others/ a.ain red#,in. the proportionalit of the tr#sses' !dditionall/ e ,o#ld have sanded the Popsi,le sti,$s to in,rease the s#rfa,e area for .l#in./ hi,h o#ld have res#lted in a +etter stren.thened +rid.e' !fter the +rid.e ,ompetition/ e ere .iven the opport#nit to spea$ to other teams ith s#,,essf#l +rid.es and a,#ired some advi,e' ne of the teams #sed a #ni#e pro,ess hi,h involved testin. ea,h individ#al Popsi,le sti,$ to ens#re ea,h sti,$ as e#al in thi,$ness and stren.th' &n the f#t#re/ e ill test ea,h individ#al Popsi,le sti,$ to attain the most +alan,ed/ smmetri,al and evenl distri+#ted +rid.e'
Reco%%en"ations !s a hole/ the ,o#rse proje,t as an e,ellent learnin. eperien,e' oever/ there are alas ,han.es that ,an +e made to si.ni,antl PROJECT REORT II –
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improve the eperien,e for all parties involved' ne a to improve o#ld +e + havin. a,,ess to the la+ e#ipment approimatel a ee$ ahead of time' *his ena+les st#dents to test their +rid.es ith the appropriate e#ipment/ preparin. them for ea,tl hat is epe,ted in the la+' Softare sim#lations and ,al,#lations provide a .reat a to estimate the stren.th of the +rid.e/ +#t testin. the +rid.e phsi,all ill provide a more s#i,ient method of testin. its tr#e relia+ilit' !nother a to improve o#ld +e havin. stron.er e#ipment in the la+' *here ere a ,o#ple of .ro#ps hose +rid.es had failed as a res#lt of e#ipment fail#re' 9hether it as the ,a+les that snapped or the +ar of ood .iven o#t/ the +rid.e itself had not failed' avin. +etter e#ipment ,an provide a more a,,#rate res#lt + not +ein. for,ed to reset the eperiment/ savin. a si.ni,ant amo#nt of time on testin. da' *he nal method in improvin. this proje,t is if the ,riteria re#ired .ro#ps to set self-.oals at the +e.innin. of the ,o#rse' Similar to a ,he,$list/ .ro#ps ,an mar$ don ea,h ,ompletion sta.e of their proje,t/ motivatin. themselves to .et started on their proje,t earlier' *his ill prod#,e a s#+stantial so#r,e of motivation to ,omplete their +rid.es ith a hi.her level of #alit and ,onden,e'
Figure : Fracture due to copression in t#e top bea PROJECT REORT II –
*
Conclsion #r o+je,tive as to ,reate a +rid.e/ hi,h o#ld +e a+le to s#pport a lar.e applied load hile remainin. relativel li.htei.ht' 4efore the +rid.e as tested/ e estimated thro#.h a series of ,al,#lations that the +rid.e holds the ,apa,it to s#pport a load of 60$./ hile ro#.hl ei.hin. 300 .rams/ and spannin. 85,m hile meetin. other desi.n re#irements' *he nal desi.n of o#r +rid.e as de,ided thro#.h an iterative pro,ess/ r#lin. o#t m#ltiple other desi.ns and improvin. the ones e tho#.ht ,o#ld or$ ell' Several das ere devoted to ens#rin. the +rid.e met the re#irements spe,ied in the proje,t o#tline' oever/ ith ever desi.n ,ome areas of ea$ness' #r +rid.e did not hold as m#,h as e epe,ted it to/ in fa,t/ it held si.ni,antl less' 9hen e analed the +ro$en +rid.e after it had ta$en on a load of 32':./ e realied that a ,o#ple of the $e joints did not have eno#.h .l#e +indin. the to popsi,le sti,$s to.ether hi,h ma have ,a#sed earl fail#re' 9e +elieve this as a $e fa,tor that hindered the +rid.e from rea,hin. its epe,ted potential' #r +rid.e had a stren.th to ei.ht ratio of 101'56' !nother aspe,t of the proje,t in hi,h e o#ld do dierentl o#ld +e to implement popsi,le sti,$s on top of the +rid.e that ,onne,t the to sides' 9e failed to do this the rst time/ and onl implemented a laer on the +ottom of the +rid.e' ad e added that etra laer on top/ o#r +rid.e o#ld +e si.ni,antl more st#rd' verall/ the entire pro,ess of this proje,t as an e,ellent learnin. pro,ess' 9e ere a+le to learn ho to ,olla+orate ith team mem+ers/ shiftin. thro#.h iterations of desi.n/ testin. and analin./ and also learnin. ho to improve from o#r previo#s eperien,es'
PROJECT REORT II –
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Figure *: Tea P#oto
/or0s Cite" [1] J. Matthews, 'Pattullo bridge under construction', Vancouver, 2015. [2] . !hatter"ee, #. $eidel%ann, &. Mah%oodi, $. attan, M$# 221 Pro"ect eort (, 2015. [)] *. +oon, '*arrett's +ridges -arren russ', Garrettsbridges.com, 2015. [/nline]. &vailable httwww.garrettsbridges.co%designwarrentruss. [&ccessed 13 4ov 2015]. [] Matbase.co%, '+irch 6 !lass wood slightl7 durable 8!#4 #49 6 -ood 6 Pol7%er Matri: !o%osites 8PM!'s9 6 4atural ; $7nthetic !o%osites 6 Material !ategories 6 !he%ical, %echanical, h7sical and environ%ental roerties o< %aterials 6 Matbase the indeendent online %aterial selection resource', 2015. [/nline]. &vailable httwww.%atbase.co%%aterial categoriesco%ositesol7%er%atri:co%osites%cwoodclasswoodslightl7 durable%aterialroertieso<birchwood.ht%l=roerties. [&ccessed 13 4ov 2015].
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