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# Comparative study of the equivalent moment factor between international steel design specifications

Smalberger, Hermanus Johannes Wessels (2014-12)

Thesis (MEng)--Stellenbosch University, 2014.

Thesis

ENGLISH ABSTRACT: Lateral-torsional buckling (LTB) is an important failure mode that needs to be taken into account during the design of steel beams. The fundamental equation for determining the elastic critical moment of a beam was derived with the assumption that the beam is subjected to a uniform bending moment distribution. Loads on steel structures generate a great variety of bending moment distributions. The effect of the bending moment distribution is taken into account by a parameter known as the equivalent moment factor. The procedure outlined in the South African National Standard for limit-states design of hot-rolled steel work, SANS 10162-1:2011, for determining the equivalent moment factor was originally developed for a bending moment that is uniformly or linearly distributed, however it is currently used for all bending moment distributions. A Finite Element (FE) model was developed in this investigation for determining the equivalent moment factor. The numerical model included residual stresses and initial geometric imperfections commonly found in hot-rolled steel beams. To validate the assumptions made during the development of the FE model an in-depth experimental investigation was conducted on simply supported beams. Three different load configurations were considered in the experimental study in order to simulate various bending moment distributions. A comparison of the equivalent moment factor between the numerical results and the results obtained from various steel specifications, including SANS 10162-1:2011, was carried out in an attempt to quantify the positive and negative attributes of the various methods employed by steel design specifications. The experimental investigation concluded that the FE model is able to successfully represent a simply supported beam with realistic characteristics that include residual stresses and imperfections. The comparative study illustrated that for a bending moment distribution with a constant moment gradient, SANS 10162-1:2011 provides excellent results. However, for the other distributions considered in this investigation highly conservative results were obtained for the equivalent moment factor. The relevance of these findings were made clear by considering three design cases found in steel structures. The resistance moment of the beams in each of these cases was calculated according to each of the steel specifications. It was found that the use of a highly conservative procedure for determining the equivalent moment factor can lead to the uneconomical design of a structure.

AFRIKAANSE OPSOMMING: Laterale-torsie knik is ’n belangrike falings modus wat in ag geneem moet word tydens die ontwerp van staal balke. Die fundamentele vergelyking vir die bepaling van die elastiese kritieke moment van ’n balk is afgelei met die aanname dat die balk onderworpe is aan ’n eenvormige buigmoment verdeling. Belastings op staalstrukture genereer ’n groot verskeidenheid van buigmoment verdelings. Die effek van hierdie buigmoment verdelings word in ag geneem deur ’n parameter wat bekend staan as die ekwivalente moment faktor. Die prosedure uiteengesit in die Suid-Afrikaanse Nasionale Standaard vir die ontwerp van warm-gewalste staalwerk, SANS 10162-1:2011, vir die bepaling van hierdie faktor is oorspronklik ontwikkel vir ’n buigmoment wat uniform of linieêr verdeel is oor die lengte van die balk, maar dit word tans gebruik vir alle buigmoment verdelings. ’n Eindige Element (FE) model is ontwikkel in hierdie ondersoek vir die bepaling van die ekwivalente moment faktor. Die numeriese model sluit die residuele spannings en aanvanklike geometriese imperfeksies wat in die algemeen teenwoordig is in warm-gewalste profiele in. Die aannames wat gemaak is tydens die ontwikkeling van die FE model is bevestig met ’n in diepte eksperimentele ondersoek oor die gedrag van eenvoudig opgelegde balke. Drie verskillende las konfigurasies is oorweeg in die eksperimentele studie om verskeie buigmoment verspreidings na te boots. ’n Vergelyking van die ekwivalente moment faktor tussen die numeriese resultate en die resultate verkry van verskeie staal spesifikasies, insluitend SANS 10162-1:2011, is uitgevoer in ’n poging om die positiewe en negatiewe eienskappe van die verskillende metodes wat gebruik word in verskillende staal ontwerp spesifikasies, te kwantifiseer. Die eksperimentele ondersoek het tot die gevolgtrekking gelei dat die FE model in staat is om ’n eenvoudige opgelegte balk te verteenwoordig, met realistiese eienskappe wat residuele spannings en imperfekies insluit. Die vergelykende studie toon dat SANS 10162-1:2011 uitstekende resultate bied vir ’n buigmoment verdeling met ’n konstante moment gradiënt. Dit was egter gevind dat vir ander verdelings wat in hierdie ondersoek oorweeg is, SANS 10162-1:2011 hoogs konserwatiewe resultate bied. Die toepaslikheid van hierdie bevindinge is duidelik gemaak deur drie ontwerp gevalle wat algemeen in staalstrukture gevind word te bestudeer. Die weerstandsmoment is in elk van die gevalle bereken volgens elke staal spesifikasies. Daar is gevind dat die gebruik van ’n hoogs konserwatiewe prosedure vir die bepaling van die ekwivalente moment faktor kan lei tot die ontwerp van ’n onekonomiese struktuur.

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