The reliability of weight optimised steel portal frames

Stolk, Willem (2015-12)

Thesis (MEng)--Stellenbosch University, 2015.


ENGLISH ABSTRACT: Steel portal frame structures are traditionally designed in accordance with ultimate limit state criteria and then typically evaluated in terms of the serviceability limit state. The serviceability limit state often governs the design process, therefore it is important that appropriate deflection limits are used for the design of steel portal frames. The origin of deflection limits specified in some current codes of practice are unknown, while some codes do not even specify serviceability limit state deflections for portal frames, but rather leave the judgement of deflection limits to the engineer. The design of portal frame structures in accordance with certain deflection limits have no direct effect on the serviceability of the frame itself, however the deflection limits are used to protect the structure against other complicated serviceability demands. These demands include structural damage to non-structural members and connections as well as noticeable distressing deflections. When considering ultimate limit state, the definition of failure is fairly clear, however the distinction between serviceable and unserviceable are vague. It is therefore evident that the SCI advisory desk specified deflection limits, which are widely adopted, are mostly defined on experience. These specified limits may have a direct effect on the optimal weight and reliability of the structure. For the proposed study, a real-coded Genetic Algorithm which is part of the evolutionary algorithm family is used to determine the optimal or near optimal weight of steel portal frames. The proposed Genetic Algorithm based on the natural process, known as survival-of-the-fittest, selects the optimal universal beam section from a discrete set of available sections for columns and rafters. Furthermore, the algorithm will determine the optimal length of the haunch at the eaves as well as the optimal roof pitch. With the use of these four design variables, each portal frame has a possible 28.83 × 106 number of solutions. A total of 119 portal frames of different span to height ratios were optimised with the use of the proposed Genetic Algorithm. These 119 analyses were used to investigate the effect of the haunch length and roof pitch of the portal frame on the optimal weight. An overall average decrease in total weight of 9% were obtained when haunched rafters were used for portal frames. In terms of the roof pitch of portal frames, the conclusion was made that the roof pitch only has a significant effect on the optimal weight of portal frames with a span to height ratio larger than two. From the 119 analyses, 87% of the frames subjected to wind load were governed by the serviceability limit state. The reliability or safety index of each optimal steel portal frame will then be calculated with the use of the First Order Reliability Method (FORM), and compared to specified reliability values accepted in design codes of practice for ultimate and serviceability limit states. The value of the reliability index is dependent on the amount and quality of information that is available, therefore the theory and philosophy emphasize that the reliability or safety index becomes a design variable during the design phase of a structure. An average reliability index of β = 3.3 were obtained for optimal portal frames governed by the ultimate limit state which is greater than the target reliability index of β = 3.0 specified in SANS 10160-1:2011. For frames governed by the horizontal deflection limit, an average reliability index of β = 0.6 were obtained which is far less than the allowable target reliability index of β = 2.0 specified in SANS 10160-1:2011 for irreversible deflections.

AFRIKAANSE OPSOMMING: Staal portaalrame word tradisioneel in terme van die uiterste limietstaat ontwerp en daarna in terme van die diensbaarheid limietstaat geëvalueer. Die diensbaarheid limietstaat is gewoonlik die bepalende faktor tydens die ontwerp van portaalrame, daarom is dit belangrik geskikte defleksielimiete gebruik word. Die oorsprong van defleksielimiete wat in huidige ontwerpkodes gespesifiseer word, is onbekend, terwyl sommige ontwerpkodes die defleksielimiete aan die ingenieur se oordeel oorlaat. Die ontwerp van portaalrame, volgens sekere defleksielimiete, het geen direkte impak op die diensbaarheid van die raam self nie. Die defleksielimiete word wel gebruik om die portaalraam teen ander ingewikkelde diensbaarheidseise te beskerm. Hierdie eise sluit strukturele skade aan niestrukturele elemente en konneksies sowel as merkbare kommerwekkende defleksies in. Wanneer die uiterste limietstaat in ag geneem word, is die definisie van faling duidelik. Die onderskeid wat tussen die terme diensbaar en ondiensbaar getref word, is vaag. Dit is daarom verstaanbaar dat die defleksielimiete wat deur die SCI se adviserende instansie aanvaar is, meestal op ervaring gebaseer is. Hierdie limiete het ’n direkte invloed op die optimale gewig en betroubaarheid van die struktuur. Vir die voorgestelde studie word ’n Genetiese Algoritme, wat deel uitmaak van die evolusionêre algoritmiese familie, gebruik om ’n optimale portaalraam te vind. Die voorgestelde genetiese algoritme wat op die natuurlike proses, bekend as oorlewing van die sterkste, gebaseer is, kies ’n optimale universele balk vanuit ’n lys van beskikbare groottes. Dit word vir beide kolomme en balke gedoen. Die Genetiese Algoritme bepaal voorts die optimale lengte van die kolomskouers by die dakrante asook die optimale helling van die dak. ’n Totaal van 119 portaalrame van verskillende span tot hoogte verhoudings was geoptimiseer met behulp van die voorgestelde Genetiese Algoritme. Die 119 analises was gebruik om die effek van die kolomskouers en dakhelling van ’n portaalraam op die optimale gewig te ondersoek. ’n Totale afname in totale gewig van 9% is verkry wanneer kolomskouers gebruik was. In terme van die dakhelling van ’n portaalraam was die gevolgtrekking gemaak dat die dakhelling slegs ’n beduidende invloed op die optimale gewig van ’n portaal raam het vir rame met ’n span tot hoogte verhouding groter as twee. Van die 119 portaalrame word 87% van die rame beheer deur die diensbaarheid limietstaat. Die betroubaarheidsindeks, óf veiligheidsindeks, van die optimale portaalraam word deur die Eerste Orde Betroubaarheidsmetode (EOBM) bereken. Die voorgeskrewe betroubaarheidsindeks in ontwerpkodes vir die uiterste-en diensbaarheid limietstaat word dan hiermee vergelyk. Die waarde van die betroubaarheidsindeks is van die hoeveelheid en kwaliteit van inligting wat beskikbaar is afhanklik. Sodoende dui die teorie en filosofie daarop aan dat die betroubaarheidsindeks of veiligheidsindeks ’n ontwerpsveranderlike word tydens die ontwerpfase van ’n struktuur. ’n Gemiddelde betroubaarheidsindex van β = 3.3 was verkry vir rame wat beheer word deur die uiterste limietstaat. Hierdie betroubaarheidsindex is groter as die teiken betroubaarheidslimiet van β = 3.0 wat voorgeskryf is in SANS 10160-1:2011 en daarom aanvaarbaar. Vir rame wat beheer word deur die horisontal defleksie limietstaat, ’n gemiddelde betroubaarheidsindex van β = 0.6 was verky. Hierdie betroubaarheidsindex is laer as die teiken betroubaarheidsindex van β = 2.0 wat voorgeskryf is in SANS 10160-1:2011 vir onomkeerbare defleksies en daarom onaanvaarbaar.

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