Patch Loading Resistance

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Stlbyggnad Kungliga Tekniska Hgskolan

Stlbalkars brfrmga vid intryckningorsakad av lokal momentbelastning

Patch Loading Resistance of steel girderssubjected to concentrated moments

Per HedmarkApril 2007

TRITA-BKN. Examensarbete 250 Stlbyggnad 2007 ISSN 1103-4297 ISRN KTH/BKN/EX250SE

Frord

FrordDetta examensarbete utfrdes vid avdelningen fr stlbyggnad , Institutionen fr Byggvetenskap p Kungliga Tekniska Hgskolan i Stockholm (KTH) under september till april 06/07. Arbetet r ett samarbete mellan SSAB och KTH. Handledare vid KTH har varit Bert Norlin och frn SSAB Eva Ptursson. Examinator r Bert Norlin. Jag vill ge ett stort tack till mina handledare som givit mig bra tips och ider. Fr deras tid och tlamod fr alla frgor och funderingar som uppkommit under arbetet. Jag vill speciellt tacka lektor Bert Norlin som alltid funnits till hands fr att ge ny inspiration till att fortstta kmpa.

Stockholm, Mars 2007

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Frord

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Sammanfattning

SammanfattningDetta examensarbete behandlar stlbalkar utsatta fr lokal intryckning orsakade av en lokal momentbelastning. Fr lastfallet finns nnu inga bra handrkningsmetoder, i plthandboken som ges ut av SSAB finns en berkningsmetod presenterad. Den r vldigt krnglig med mnga berkningssteg och diagram. Denna studie r inriktad p att utreda hur man kan rkna p belastningsfallet p ett enklare och bttre stt. Lastfallet uppkommer t.ex. d en lastgla svetsas till flnsen rakt ver livet p en balk. Om lastglan dras parallellt med balkens riktning s kan belastningen ses som tv komponenter, ett moment och en horisontalkraft. Momentet kommer att trycka in lastglan i balken och till slut blir det ett brott p.g.a. en blandning av att materialet flyter och att livet bucklar. I den hr rapporten behandlas bara momentdelen av lasten. Studien r gjord i tre steg. Frst byggdes en FE-modell i Abaqus. Denna modell verifierades mot fysiska frsk p lokal intryckning frn en vertikal kraft, eftersom inga frsk hittades p intryckning av ett lokalt moment. Som steg nummer tv anpassades FE-modellen till frsk med lokal intryckning frn ett moment. Ett antal experiment gjordes med variation av tv parametrar, livpltens tjocklek och lastglans lngd. Lastglan var vldigt styv eftersom den bara skulle skapa momentbelastningen. Sista steget var att utifrn resultaten ta fram en berkningsmodell fr lastfallet. FE-modellen som skapades fr testerna visade sig ge brfrmgor ca 10% under brfrmgan frn de fysiska frsken. Detta berodde mycket p att balken var knslig fr hur initialimperfektionerna sg ut och att frsta bucklingsmodens form anvndes vid modelleringen av de geometriska imperfektionerna. Berkningsmodellen utvecklades s att den skulle efterlikna den som gller fr lokal intryckning frn vertikal last i EN 1993-1-5. Detta fr att modellen skulle kunna anvndas som ett tillgg till EK3. Modellen utvecklades i tre delar, flytbrfrmgan, kritiska bucklingslasten och reduktionsfaktorn fr buckling. Modellen fr flytbrfrmgan togs fram analytiskt och fick en form som efterliknar den i EK3. Berkningsmetoden fr den kritiska bucklingslasten anvnder sig i princip av formlerna i EK3 frutom tv sm ndringar. Reduktionsfunktionen som valdes r en liten kning av funktionen i EK3 men resultaten ligger nd med bra marginal p skra sidan. Den kompletta berkningsmodellen ger resultat dr skerhetsmarginalen kar vid minskande lngd p lastglan. Den har utformats s att den r ltt att anvnda och vid jmfrelse med FE-frsk gav berkningsmodellen resultat p skra sidan fr alla balkar frutom ngra f av balkarna med lg slankhet.

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Sammanfattning

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Abstract

AbstractThis master thesis deals with steel girders subjected to patch loading caused by concentrated moments. There exist no good methods to calculate by hand the ultimate resistance for this load case. In tunnpltshandboken, (Handbook for sheet metal, which is published by SSAB), one calculation method is presented. Its however fairly difficult to use, because of many calculation steps and many graphs. This study concentrates on how to calculate the resistance for this load case in a better way. The load case arises for example when a small steel plate (attachment) is welded to the flange above the web of a girder and the attachment is pulled in a direction parallel to the beam. Its possible view the load as two components, a moment and a horizontal load. The moment will push the attachment into the girder and finally yielding in combination with web buckling will govern the ultimate resistance. In this report, only the moment part of the load is studied. This study was made in three steps. First an FE-model was built. This model was verified against physical tests on patch loading from a force acting perpendicular to the beam axis. This approach was taken because no tests were found for the load case with a local moment. As step number two the FE-model was numerically adjusted to work for tests with patch loading caused by a local moment. A number of experiments were made, for which two parameters were varied, the thickness of the web and the length of the attachment. The loaded attachment was made very stiff, because it should not be deformed in order to simulate a sharp concentrated moment. In the last step a hand calculation model was developed for the investigated load case. The FE-model that was created for comparison to the physical experiments gave resistances 10 % below the resistances, from the physical tests. This was mainly due to the sensitivity of the girder to initial imperfections and that the most severe buckling mode was used in the modeling of the imperfections. The handcalculation model was developed to imitate the one for patch loading in EN 1993-15 (EC3), because it may then work as an addition to EC3. The model was developed in three steps: yield resistance, critical elastic buckling load and the resistance function. The model for yield resistance is analytical and has a form equivalent to the one in EC3. The expressions for the critical elastic buckling load were taken as simple as possible, since they are the main area of this study. The method essentially uses the same equations as EC3 except from two small changes. The results are on the safe side but the safety margin increases when the length of the loaded attachment decreases and the slenderness of the web panel increase. Consequently formulas for calculating the critical load may be improved. The chosen reduction function was slightly increased compared to the function in EC3 but the results will still have a good safety margin. The complete model gives results where the safety margin increases as the length of the loaded attachment decreases. The calculation model was designed to be easy to use. In comparison to the FE-analysis, all the tested beams except a few with low slenderness gave results on the safe side.

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Abstract

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Beteckningar

Beteckningar

ss L a tw hw tf bf x fyw fyf sy F Fcr kF E Mu MR My Mp MpT Mpf

lngd p belastningsplatta lngd p balk avstnd mellan avstyvningar tjocklek p livet hjd p livet tjocklek p flnsen bredd p flnsen lngd frn flns till belastningspunkt flythllfasthet fr livet flythllfasthet fr flnsen lngd som antas plasticeras utanfr belastningsplattan kraft kritisk last bucklingskoefficient elasticitetsmodul tvrkontraktionstal brfrmgefunktion slankhetstal brottmoment frn FE-berkningar momentbrfrmga flytbrfrmga plastisk momentbrfrmga plastisk momentbrfrmga fr T-sektion plastisk momentbrfrmga fr flnsen

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Beteckningar

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Innehll

InnehllFrord ...................................................................................................................................... i Sammanfattning ....................................................................................................................iii Abstract .................................................................................................................................. v Beteckningar......................................................................................................................... vii Innehll.................................................................................................................................. ix 1. Introduktion.................................................................................................................... 1 1.1 Bakgrund ................................................................................................................ 1 1.2 Syfte och ml.......................................................................................................... 1 2. Teori ............................................................................................................................... 3 2.1 Introduktion............................................................................................................ 3 2.2 Plastisk analys ........................................................................................................ 3 2.3 Kritiska bucklingslasten ......................................................................................... 4 2.4 Brfrmgefunktionen ........................................................................................... 5 3. Finit elementmodell........................................................................................................ 7 3.1 Testmodell.............................................................................................................. 7 3.1.1 Fysiska frsk ................................................................................................ 7 3.1.2 Modell ............................................................................................................ 8 3.2 Slutgiltig modell I-balk ........................................................