Reliability assessments of concrete structures using non-linear finite element analyses

152 Pages·2017·29.75 MB·English

Reliability assessments of concrete
structures using non-linear finite
element analyses
Hanna Eklund
Astrid Skorve
Arne Strand
Civil and Environmental Engineering
Submission date: June 2017
Supervisor: Max Hendriks, KT
Co-supervisor: Morten Engen, KT
Jochen Köhler, IBM
Norwegian University of Science and Technology
Department of Structural Engineering

Department)of)Structural)Engineering) ) ) ))))))))))))))ACCESSIBILITY
Faculty(of(Engineering(Science(and(Technology(

NTNU6)Norwegian)University)of)Science)and)Technology)
(
(
(
(
MASTER)THESIS)2017)
(
(
SUBJECT(AREA:(( DATE:(( NO.(OF(PAGES:(
Structural(Design( 11.06.2017( 150(
(
(
TITLE:(
(
Reliability)Assessments)of)Concrete)Structures)using)Non6Linear)Finite)Element)
Analyses)
)
Pålitelighetsanalyser(av(betongkonstruksjoner(ved(bruk(av(ikkePlineære(
elementanalyser)
(
BY:(
(
(
(
Hanna(Eklund(
Astrid(Skorve(
Arne(Strand( (
SUMMARY:(
Reliability(assessment(of(slender(concrete(columns(using(NonPlinear(finite(element(analysis((NLFEA)(is(
studied(in(this(thesis.(Several(reliability(methods(in(combination(with(NLFEA(are(applied(and(discussed(to(
assess(the(consistency(of(the(Eurocode(design(calculations(in(regard(to(reliability.(
The(Eurocode(applies(the(safety(format(of(Partial(safety(factor((PSF)(which(assumes(a(linear(Limit(state(
function((LSF).(Using(NLFEA(may(result(in(a(nonPlinear(limit(state,(hence(violating(the(assumption(of(the(
PSF(method.(Still,(the(Eurocode(recommends(using(the(PSF(format(on(nonPlinear(problems(when(NLFEA(
are(conducted.( Current(research(on(concrete(structures(involves(formulating(new(safety(formats(that(are(
applicable(to(NLFEA(and(nonPlinear(LSFs.(
This(thesis(further(adapts(the(current(research(to(the(problem(of(slender(columns(subject(to(large(second(
order(effects.( The(reliability(is(assessed(by(a(response(surface(method(in(combination(with(first(and(
second(order(reliability(methods.(Both(NLFEA(and(an(analytic(approach(was(used(in(the(probabilistic(
design.(The(Monte(Carlo(method(was(applied(as(well(to(determine(the(accuracy(of(the(methods.(Five(
random(variables(were(introduced,(namely(the(concrete(compressive(strength,(the(reinforcement(yield(
strength,(the(concrete(stiffness,(the(eccentricity(of(the(load(and(the(load(itself.(The(material(and(geometric(
uncertainty(have(been(implemented,(while(some(considerations(were(made(towards(the(modelling(
uncertainty.(Safety(factors(applicable(to(several(case(configurations(were(also(sought(by(assessing(
different(concrete(grades(and(column(slenderness.(
Suggestions(for(improvements(in(a(future(version(of(Eurocode(2(is(given.(For(slender(columns,(it(may(seem(
advantageous(to(propose(a(new(set(of(safety(factors(that(are(calibrated(to(consider(second(order(effects.(In(
general,(safety(factors(associated(to(second(order(effects(should(be(increased,(and(safety(factors(
associated(to(the(crossPsectional(resistance(may(be(decreased(or(set(to(one.(
(
(
RESPONSIBLE(TEACHER:(Max(Hendriks(
(
SUPERVISOR(S):(Max(Hendriks,(Morten(Engen,(Jochen(Köhler(
(
CARRIED(OUT(AT:(Department(of(Structural(Engineering(
(

Department of Structural Engineering
FACULTY OF ENGINEERING
NTNU – Norwegian University of Science and Technology

MASTER THESIS 2017
for
Hanna Eklund, Astrid Skorve and Arne Strand

Reliability Assessments of Concrete Structures using Non-
Linear Finite Element Analyses
Pålitelighetsanalyser av betongkonstruksjoner ved bruk av ikke-lineære
elementanalyser

Concrete structures are normally designed using the partial safety factor (PSF) method.
Implicit in this method is the assumption of a linear limit state function (LSF), and this
permits the calibration of partial safety factors that account for the target reliability, and the
variability and assumed sensitivity of the respective basic variables. This approach
represents generically a large range of design situations today.

Non-linear finite element analyses (NLFEA), if properly performed, provides the designer
with realistic estimates of the structural behavior. However, with NLFEA the LSF might
no longer be linear, and the underlying assumptions of the PSF method would then be
violated. Parts of current research in the concrete community is related to formulating
proper safety formats that are applicable in connection to NLFEA and possible non-linear
LSFs.

In this project, the problem will be elaborated on by studying a seemingly simple problem:
slender columns subjected to axial loading. Two 3.8 m long reinforced concrete columns
with similar geometries but different concrete grades are considered.

Supervisor(s): Max Hendriks, Jochen Köhler, Morten Engen
NTNU, 17.01. 2017

Preface
This MSc thesis is written as the final part of the master program of Civil Engineering at the
Norwegian University of Science and Technology in Trondheim. It is written for the Depart-
mentofStructuralEngineeringintheperiodfromJanuarytoJune2017.
ThethesisconcernsreliabilityassessmentofconcretestructuresusingNLFEA,andthefeasibil-
ity of Eurocode calculation methods regarding highly non-linear problems. Structural reliabil-
itywasarelativelynewfieldofstudyfortheauthors,sodiggingintoandtryingtocomprehend
themethodsandtheoryhasbeenagreatopportunityandchallenge. Thereliabilityassessments
performed in this thesis were conducted with self-developed, integrated procedures with Mat-
lab, Python, Diana and Command Prompt. The development was time consuming, but greatly
increasedtheunderstandingofthepotentialsandlimitationsofdifferentthemethods.
ThemasterthesishasbeensupervisedbyProfessorMaxHendriks,AssociateProfessorJochen
Köhler and PhD candidate Morten Engen at Multiconsult. Gratitude is extended towards our
supervisors for their patient and helpful guidance. We highly appreciate the good advice and
long, motivating discussions. We are also thankful for the the insight and knowledge our su-
pervisorssharedconcerningstructuralreliability,concretestructuresandinprogramming.
ThanksarealsoextendedtoPhDcandidateFinnIdarGrøttaGiskeatMulticonsultforvaluable
informationandunderstandingofthesecondorderreliabilitymethod.
Trondheim,11.06.2017
HannaEklund AstridSkorve ArneStrand
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Abstract
Reliability assessment of slender concrete columns using Non-linear finite element anal-
ysis (NLFEA) is studied in this thesis. Several reliability methods in combination with
NLFEAareappliedanddiscussedtoassesstheconsistencyoftheEurocodedesigncalcu-
lationsinregardtoreliability.
The Eurocode applies the safety format of Partial safety factor (PSF) method which as-
sumes a linear Limit state function (LSF). Using NLFEA may result in a non-linear limit
state, hence violating the underlying assumption of the PSF method. Still, the Eurocode
recommends using the PSF format on non-linear problems when NLFEA are conducted.
Current research on concrete structures involves formulating new safety formats that are
moreapplicabletoNLFEAandnon-linearLSFs.
This thesis further adapts the current research to the problem of slender columns subject
to large second order effects. The reliability is assessed by a response surface method in
combinationwithfirstandsecondorderreliabilitymethods. BothNLFEAandananalytic
approach was used in the probabilistic design. The Monte Carlo method was applied as
well to determine the accuracy of the methods. Five random variables were introduced,
namely the concrete compressive strength, the reinforcement yield strength, the concrete
stiffness, the eccentricity of the load and the load itself. The material and geometric un-
certaintyhavebeenimplemented,whilesomeconsiderationsweremadetowardsthemod-
ellinguncertainty. Safetyfactorsapplicabletoseveralcaseconfigurationswerealsosought
byassessingdifferentconcretegradesandcolumnslenderness.
Suggestions for improvements in a future version of Eurocode 2 is given. For slender
columns,itmayseemadvantageoustoproposeanewsetofsafetyfactorsthatarecalibrated
to consider second order effects. In general, safety factors associated to second order
effects should be increased, and safety factors associated to the cross-sectional resistance
maybedecreasedorsettoone.
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