Reliability assessment of shear design provisions for reinforced concrete beams with stirrups

Olalusi, Oladimeji Benedict (2018-12)

Thesis (PhD)--Stellenbosch University, 2018.

Thesis

ENGLISH ABSTRACT: EN 1992-1-1: Design of concrete structures (EC2) has been accepted for adoption by South Africa to replace SANS 10100-1. EC2 shear design formulation is based on the Variable Strut Inclination Method (VSIM). The mean value predictions of the operational EC2 VSIM have been shown to underestimate shear capacity at low stirrup quantities. Conversely, the model overestimates shear capacity at high stirrup quantities (Cladera & Mari, 2007). There is a concern regarding sufficient safety performance at high levels of stirrup reinforcement, and over conservatism at low stirrup reinforcement is uneconomical. The systematic sensitivity of EC2 VSIM mean value predictions to the amount of stirrup reinforcement motivates the assessment of the consistency and uniformity of the reliability index of EC2 shear design formulation over the range of practical design situations i.e. shear reinforcements 𝜌𝑤𝑓𝑦𝑤𝑚, concrete strengths 𝑓𝑐𝑚, beam depths 𝑑 and type of beam cross section. Quantification of model uncertainty and bias is an important first step since these contribute significantly to reliability performance (Holicky et al, 2015). The study characterised model factors for various shear resistance models by comparing unbiased predictions of the models to experimental test results. The derived model factors were investigated parametrically against important shear design parameters. The model factors related to the operational EC2 VSIM shear capacity predictions were found to be sensitive to the amount of shear reinforcement with model factors significantly above one (underpredicting capacity) at low levels of stirrup reinforcement. Correlation and regression assessments uncovered milder sensitivities to other vital parameters affecting shear strength. Based on the results obtained from the model factor characterisation, two shear resistance models were considered suitable as general probabilistic model GPMs for the reliability assessment of EC2 shear design procedure and alternative shear design procedures. The principal GPM was established based on the probabilistic representation of the Modified Compression Field Theory (MCFT). MCFT capacity predictions were obtained from the implementation sectional analysis program Response- 2000 (R2k). As a validation procedure, an alternative GPM based on the Compression Chord Capacity Model (CCC) was implemented. The First Order Reliability Method (FORM) was used to compute the reliability index for representative test sections. The outcome of EC2 reliability assessment indicated uneconomically high reliability at low levels of shear reinforcement, high concrete strength and large beam depth, and actively reducing reliability with increased levels of shear reinforcement, reduced concrete strength and reduced beam depth for both rectangular and I-shaped beams. EC2 underestimates design shear resistance for I-beams due to the neglect of shear contributions from compression flanges and longitudinal reinforcements (dowel action), thereby resulting in higher reliability values for such beams. Reliability indices of all the test sections investigated meet the target reliability requirement for Reliability Class 2 structures prescribed by basis of design standards SANS 10160-1 and EN 1990, for the design range considered. The inconsistent reliability performance of EC2 VSIM shear design formulation across practical ranges of main shear design parameters motivated the assessment of alternative approaches (ACI and Fib Model Code 2010 (III)) to identify other suitable design formulations in terms of achieving the target reliability index consistently. The reliability performance of ACI and MC-10 (III) shear design provisions was assessed at parametric variations of shear reinforcement 𝜌𝑤𝑓𝑦𝑤𝑚, concrete strength 𝑓𝑐𝑚 and beam depth 𝑑; and compared to that of the EC2 shear design formulation. The reliability levels of ACI and MC-10 (III) decrease as the amount of shear reinforcement increases and increase as the concrete strength increases. MC-10 (III) and ACI predict less conservative reliability estimates at low amount of shear reinforcement compared to EC2 VSIM, indicating that MC-10 (III) and ACI are more economical at this design situation. MC-10 (III) and ACI reliability levels drastically decrease with increasing beam depth. The reliability of small beams designed according to MC-10 (III) and ACI shear design formulations substantially exceeded the target reliabilities. However, the reliability of MC-10 (III) for deep beams with low concrete strengths falls quite significantly below the target reliability values.

AFRIKAANSE OPSOMMING: EN 1992-1-1: Ontwerp van betonstrukture (EC2) is aanvaar vir aanneming deur Suid-Afrika om SANS 10100-1 te vervang. EC2 gebruik 'n skuifontwerp metode wat bekend staan as die Veranderlike Stut Hoek Metode (VSHM). Die gemiddelde waarde voorspellings van die operasionele EC2 VSHM toon dat die skuifkapasiteit by lae skuifbewapening hoeveelhede onderskat word. Aan die ander kant oorskat die model skuifkapasiteit by hoë skuifbewapening hoeveelhede (Cladera & Mari, 2007). Daar bestaan kommer oor genoegsame veiligheidsoptrede by hoë vlakke van skuifbewapening versterkings; en oor-konserwatisme by lae skuifbewapening is onekonomies. Die sistematiese sensitiwiteit van EC2 VSHM gemiddelde waarde voorspellings met skuifbewapening motiveer die noodsaaklikheid om die konsekwentheid van die betroubaarheidsindeks van EC2 skuifontwerp formulering te evalueer oor die omvang van praktiese ontwerp situasies dit wil sê skuifversterkings 𝜌𝑤𝑓𝑦𝑤𝑚, beton sterkte 𝑓𝑐𝑚, balkdieptes 𝑑 asook dwarssnit tipes. Kwantifisering van model onsekerheid en vooroordeel is 'n belangrike eerste stap aangesien dit aansienlik bydra tot betroubaarheidsprestasie (Holicky et al, 2015). Die studie het modelfaktore vir verskillende skuifweerstandmodelle karakteriseer deur onbevooroordeelde voorspellings van die modelle te vergelyk met eksperimentele toets resultate. Die modelfaktore is parametries ondersoek teen belangrike skuifontwerp parameters. Die modelfaktore wat verband hou met die operasionele EC2 VSHM skuifkapasiteit voorspellings, is sensitief vir die hoeveelheid skuifversterking met modelfaktore aansienlik hoër as een (onder-voorspelden kapasiteit) by hoë vlakke van skuifbewapening versterkings. Korrelasie- en regressie-assesserings het matiger sensitiwiteit met ander belangrike parameters wat skuifsterkte beïnvloed. Op grond van die modelfaktor karakterisering, is twee geskikte algemene waarskynlikheid modelle AWM's identifiseer vir die betroubaarheids evaluering van die skuifontwerp prosedures. Die hoof AWM is ‘n waarskynlikheids voorstelling van die Aangepaste Drukveld Teorie (ADT). ADT kapasiteit voorspellings is gemaak deur die implementerings snit-analise program Response-2000 (R2k). As 'n geldigings prosedure, is 'n alternatiewe AWM gebaseer op die Druk Koord Kapasiteitsmodel (DKK) geïmplementeer. Die eerste orde betroubaarheids metode (EOBM) is gebruik om die betroubaarheidsindeks vir verteenwoordigende toetsafdelings te bereken. Vir VSHM dui die uitkoms op onekonomiese hoë betroubaarheid by lae vlakke van skuifversterking, hoë beton sterkte, en groot balkdieptes. Betroubaarheid verminder aktief met verhoogde vlakke van skuifversterking, verminderde beton sterkte en verminderde balkdiepte vir beide reghoekige en I-vormige balke. EC2 onderskat ontwerp skuifweerstand vir I-balke omdat skuifbydraes vanaf die drukflense en langstaal buite rekening gelaat word wat sodoende hoër betroubaarheids waardes vir sulke balke tot gevolg het. Betroubaarheids indekse van al die toets snitte wat ondersoek is haal die teiken betroubaarheid vir Betroubaarheids Klas 2 strukture volgens beide SANS 10160-1 en EN 1990. Die onkonstante betroubaarheidsprestasie van EC2 VSHM skuifontwerp formulering oor praktiese omvang van hoofskuif ontwerpparameters het die assessering van alternatiewe benaderings (ACI en Fib Model Kode 2010 (III)) gemotiveer om ontwerpformulering te vind wat beter presteer ten opsigte van die konsekwente behaling van die teiken betroubaarheidsindeks. Die betroubaarheidsprestasie van ACI en MC-10 (III) skuifontwerp voorsienings is beoordeel by parametriese variasies van skuifversterking 𝑝𝑤𝑓𝑦𝑤𝑚, betonsterkte 𝑓𝑐𝑚 en balkdiepte 𝑑; en vergelyk met dié van die EC2 skuifontwerp formulering. Die betroubaarheidsvlakke van ACI en MC-10 (III) neem af soos die hoeveelheid skuifversterking 𝑝𝑤𝑓𝑦𝑤𝑚 verhoog, en neem toe namate die beton sterkte verhoog. MC- 10 (III) en ACI voorspel minder konserwatiewe betroubaarheidsberamings by lae hoeveelheid skuifversterking in vergelyking met EC2 VSHM, wat aandui dat MC-10 (III) en ACI meer ekonomies is in hierdie ontwerpsituasie. MC-10 (III) en ACI se betroubaarheidsvlakke neem drasties af met toenemende balkdiepte. Die betroubaarheid van klein balke wat volgens MC-10 (III) en ACIskuifontwerp formules ontwerp is, het die geteikende betroubaarhede aansienlik oorskry. Die betroubaarheid van MC-10 (III) vir diep balke met lae beton sterkte val egter beduidend onder die teiken betroubaarheidswaardes.

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