Designing A Fanlike Structure

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1 Designing A Fnlike Sruure To proeed wih his lesson, lik on he Nex buon here or he op of ny pge. When you re done wih his lesson, lik on he Conens buon here or he op of ny pge o reurn o he lis of lessons. This is he seel roof sruure of he Sugr Airpor, designed by Von Gerkn, Mrg, und Prner. The olumn rees re spilly rih exmple of fnlike sruure. Despie heir orgni pperne, he olumns nd brnhes re rrnged so s o rry he roof lods in ompression wih lile or no bending fores. The muliple brnhes of eh ree gher fores from mny direions nd merge hem ino fewer nd fewer resulns unil hey join ls ino single fore in he min runk. This lesson demonsres he use of grphil ehniques o design plnr, fnlike sruure h is boh sruurlly effiien nd esheilly sisfying.

2 Designing A Fnlike Sruure Hinge 9 f Hinge Hinge The Problem: This is n iniil ide for he roof of overed mrke building. The sruure will be mde of seel pipes wih welded onneions. The uniform ded lod plus live lod is esimed o be ips eh inerior node long he op hord, nd ips eh end node. We will insll hree hinges s shown. These will elimine mos inidenl sresses used by emperure movemen nd foundion selemen. They will lso mke i esier for us o find he fores in he sruure.

3 Designing A Fnlike Sruure How effiien is he form of his sruure A good wy o begin looking his sruure is o mke simplified free-body digrm of he exernl fores h on i. Beuse i is symmeril nd hinged he ener, we only need o look one hlf of he sruure. Noie h he righmos lod on his digrm, he ener lod on he whole sruure, hs been hlved from ips in he previous digrm o ips here. This is beuse when onsidering hlf he sruure, only hlf of he ener lod is rried by eiher side.

4 Designing A Fnlike Sruure W = 4ips The lods on he op of he lef hlf of he sruure n be represened in simplified form by single fore, W, h is equl o he sum of he lods, 4ips, nd h s verilly he ener of his hlf.

5 Designing A Fnlike Sruure W = 4ips H Nex we onsider he fore h s on his hlf of he sruure ross he pin he op of he sruure. Under uniform lod, he pin will exer only horizonl fore, H, his poin. The lines of ion of H nd W inerse poin. If here were symmeril grviy lods, or lerl lods, ing on he sruure, he fore he op ener pin ould hve veril omponen s well. If lods suh s hese were o be invesiged, more deiled nlysis of he line of ion of fore H would be required.

6 Designing A Fnlike Sruure W = 4ips H There is only one oher exernl fore h s on he lef hlf: reion R, whose line of ion mus pss hrough he hinge he bse of he olumn. If he hlf-sruure is in equilibrium, he line of ion of R mus lso pss hrough poin, he inerseion of he lines of ion of he oher wo exernl fores. R

7 Designing A Fnlike Sruure W = 4ips H = 18.ips Now h we know he direions of ll hree exernl fores nd he mgniude of one of hem, we n find he mgniudes of he oher wo by onsruing Fore Polygon o sle. H = 18.ips R = 1. kips R = 1. kips W = 4ips Fore Polygon

8 Designing A Fnlike Sruure W Nonxil Column Lod H The line of ion of reion R does no lie long he veril line of he olumn. This mens h he olumn is no xilly loded. The olumn is subjeed o bending momens by his nonxil lod. H = 18.ips R R = 1. kips W = 4ips Fore Polygon

9 Designing A Fnlike Sruure Momen Digrm W Node n H The bending momen ny poin in he xis of he olumn n be qunified s he veril omponen of R, whih is 4ips, imes he horizonl disne beween h poin nd he line of ion of R. I rehes mximum node n. H = 18.ips R R = 1. kips W = 4ips Fore Polygon

10 Designing A Fnlike Sruure W n H The nonxil lod will use bending in he olumn nd in he rdiing members bove. While we ould hiken he olumn nd rdiing members o enble hem o resis hese bending fores, we n sve meril if we modify he shpe of he sruure in suh wy h is members experiene only xil lods. H = 18.ips R R = 1. kips W = 4ips Fore Polygon

11 Designing A Fnlike Sruure W n H One wy o do his would be o keep node n where i is, while moving he bse hinge unil he olumn lies long line hrough poins nd n. This produes rher wkwrd sruure h hs high horizonl nd reive fores (H nd R), s we see from he Fore Polygon. Furhermore, people would end o bump heir heds on he seeply inlined olumns. H = 40.7 kips R R =.9 kips W = 4ips Fore Polygon

12 Designing A Fnlike Sruure W n' n H Anoher lernive would be o keep he bse hinge in is originl loion, bu o move node n o n', poin on he line of ion of R. This lernive looks less wkwrd hn he previous one nd hs lower fores, bu i sill doesn' look very greful. H = 18.ips R R = 1. kips W = 4ips Fore Polygon

13 Designing A Fnlike Sruure n'' W n If we move node n o poin n'', whih lies on he line of ion of W, he olumn beomes veril nd he horizonl fore he op hinge disppers ompleely. This is very logil, effiien onfigurion for his sruure, hough perhps no very exiing. Cn we find wy o give i more drmi shpe wihou subsnilly reduing is effiieny H = 0 R R = 4ips W = 4ips Fore Polygon

14 Designing A Fnlike Sruure n''' W n H If we move node n o n''', while keeping he olumn xis ligned on poin, he sruure suddenly ppers o ke wing. The Fore Polygon shows h he horizonl fore H is smll nd he reion R is only bi lrger hn lod W. For very smll srifie in effiieny, we hve found muh more exiing shpe for he sruure. H = 9.ips R W = 4ips R= 48.9 kips Fore Polygon

15 Designing A Fnlike Sruure R H Finding he fores in he sruure: If you re lredy fmilir wih grphil nlysis of russes, you know how o find he fores in his russ. We begin wih free body digrm of he sruure. Eh inerior node long he op hord rries n exernl grviy lod of ips. Eh end node rries hlf of his, ips. All oher exernl fores ing on he russ, in his se H nd R, re dded o he digrm.

16 Designing A Fnlike Sruure B 1 C E D 4 F K G J Fore JK We pply inervl noion o he. The olumn fore is KA, nd he horizonl fore is JK. A Fore KA

17 Designing A Fnlike Sruure B 1 C E D 4 F K G J The Lod Line is ringle, jk. A b Tringle jk ppers in differen orienion from he Fore Polygon we onsrued erlier beuse he fores hve been summed in differen order. Lod Line k d e f g j

18 Designing A Fnlike Sruure B 1 A C D 4 E F K G J Beginning wih members 1 nd b1, nd progressing hrough he reminder of he russ, we onsru he omplee Fore Polygon. We lso use he Fore Polygon o deermine he hrer of he fores (ension or ompression) in he russ members. b 1 Fore Polygon k d e f g j 4

19 Designing A Fnlike Sruure B 1 A C D 4 E F K G J The Fore Polygon ells us immediely by is omp shpe h member fores re probbly resonble in mgniude. b 1 Fore Polygon k d e f g j 4

20 Designing A Fnlike Sruure B 1 A C D 4 E F K 18-8¼ G J Knowing he lengh of he members in he russ, nd he mgniude nd hrer of heir fores, we n ssign pproxime required sizes of seel pipe for eh by looking in ble of seel pipe olumn piies, suh s in he Mnul of Seel Consruion. b 1 For exmple, member 4- is 18-8¼ long, nd is subjeed o ompressive fore of 1.1 kips. The Mnul of Seel Consruion ells us h his fore n be rried wih ½ sndrd seel pipe. Fore Polygon k d e f g j kips

21 Designing A Fnlike Sruure Sru Anoher lernive: Anoher possible onfigurion for his sruure would be o minin is originl shpe, bu o dd ompression sru he bse of he fns. The simplified free body digrm shows how his would work: The ounerlokwise momen produed by W nd R would be blned by he lokwise momen of H nd H'. The olumn would experiene only n xil fore. W H H' R Simplified Free Body Digrm

22 Designing A Fnlike Sruure B A 1 G F E D C 4 K H J The Fore Polygon for his sruure shows h member fores re muh higher hn in he previous lernive, whose Fore Polygon is lso shown he sme sle for purposes of omprison. Previous Alernive 1 b 4 d e f Fore Polygon g h,k j

23 Designing A Fnlike Sruure W H Thus our bes design for he mrke roof ppers o be he one wih he olumns h slope inwrd slighly. We n experimen furher wih he olumn slope if we wish, king re o keep he xis of he olumn ligned on poin so h ll he member fores re xil. R Fore Polygon k b d e f g j 1 4

24 Designing A Fnlike Sruure B 1 A C D 4 E F G H 48.9 kips 48.9 kips Q 7 J K 8 9 L M N Clik on he Conens buon o begin new lesson. Clik on he imge of he Sugr Airpor o reurn o he beginning of his lesson P Beuse he lods nd sruure re symmeril, we n lso refle he Fore Polygon for he hlf-sruure o onsru Fore Polygon for he omplee sruure. q Fore Polygon 7 b d e f g h j k l m n p

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