Rehabilitation and maintenance of buildings - 02Karel Mike

12ContentsProperties of materialFailures of steel structuresTypes of refurbishmentMethods of reliability verificationBasis of member design of steel structuresBasis of joint designAssessment of steel structuresStrengthening of membersStrengthening and refurbishment of structuresRefurbishment of masonry structures using steelworkSeismic upgrading using steel structure

SAHC - SA5 Steel structures2010T.Vran, CTU in Prague23Methods of reliability verificationDesign based on experienceEmpirical attitudeAllowable stress methodOne safety factor Reduction of strengthActions not affectedMethod of limit statesReal probabilistic methodsMethod of partial safety factorsSemi-probabilistic method

SAHC - SA5 Steel structures2010T.Vran, CTU in Prague34Method of partial safety factorsPartial safety factors:material factors gMload factors gF

Ultimate Limit States ... gM 1, gF > 1Serviceability limit states ... gM = 1, gF = 1

Basis of Eurocodes

SAHC - SA5 Steel structures2010T.Vran, CTU in Prague45Partial safety factorsCharacteristic valuesPartial factors M, FReduction factors Design values

Partial factors cover:Disadvantageous deviations from characteristic valuesInaccuracy of action modelInaccuracy of structural model for analysisInaccuracy of transformation factorsSAHC - SA5 Steel structures2010T.Vran, CTU in Prague56EurocodesDesign codes (Eurocodes) European codes from1980 European Comittee for Standartization (CEN) from 1990 CR - member from 1998 Preliminary codes (ENV) European codes (EN) ENV - National application document (NAD) national specials EN - National annex, limited clausesSince 3/2010 should be valid in all CEN countriesSAHC - SA5 Steel structures2010T.Vran, CTU in Prague67Eurocodes EN EN 1990 Eurocode 0 Basis of Structural DesignEN 1991 Eurocode 1 Actions on structuresEN 1992 Eurocode 2 Design of concrete structuresEN 1993 Eurocode 3 Design of steel structures EN 1994 Eurocode 4 Design of composite steel and concrete structuresEN 1995 Eurocode 5 Design of timber structuresEN 1996 Eurocode 6 Design of masonry structuresEN 1997 Eurocode 7 Geotechnical designEN 1998 Eurocode 8 Design of structures for earthquake resistanceEN 1999 Eurocode 9 Design of aluminium structuresSAHC - SA5 Steel structures2010T.Vran, CTU in Prague78Eurocodes EN Partial safety factors gM = 1,00 (for steel)gM2 = 1,25

LoadingEffectService load(SLS)Extreme load(ULS)DeadfavourablegG = 1,0gG,min = 1,0unfavourablegG = 1,0gG,max = 1,35VariablegQ = 1,0gQ = 1,50SAHC - SA5 Steel structures2010T.Vran, CTU in Prague89ContentsProperties of materialFailures of steel structuresTypes of refurbishmentMethods of reliability verificationBasis of design of steel structuresAssessment of steel structuresStrengthening of membersStrengthening and refurbishment of structuresRefurbishment of masonry structures using steelworkSeismic upgrading using steel structure

SAHC - SA5 Steel structures2010T.Vran, CTU in Prague910Basis of design of steel structuresEurocode EN 1993 Design of steel structuresMethod of partial safety factors

Utilization of bi-linear stress-strain relation of steel

Axial tensionAxial compressionBendingShearCombinationSAHC - SA5 Steel structures2010T.Vran, CTU in Prague1011Axial tensionStress distribution:

(direct stress)

SAHC - SA5 Steel structures2010T.Vran, CTU in Prague1112Axial tensionResistance:full cross-section (plastic resistance)Npl.Rd=A fy / M0net cross-section at holes for fastenersNu.Rd=0,9 A netfu / M2

SAHC - SA5 Steel structures2010T.Vran, CTU in Prague1213Axial compressionDesign buckling resistance

Buckling factor :covers the effect of bucklingl (a depends on cross-section type)

SAHC - SA5 Steel structures2010T.Vran, CTU in Prague1314Axial compression BucklingStability collapsebuckling before fy is reached along cross-sectionMost frequent reason for collapse of S.S.

Perfect (ideal) member- stability problemReal member - buckling resistanceSAHC - SA5 Steel structures2010T.Vran, CTU in Prague1415Axial compression Stability of perfect memberStraight memberPinned endsCentric loadingSolution Euler 1744

SAHC - SA5 Steel structures2010T.Vran, CTU in Prague1516Axial compression Critical (Eulers) Force Critical Stress

Slenderness

SAHC - SA5 Steel structures2010T.Vran, CTU in Prague1617

Axial compression Buckling of Memberflexural or torsionalDouble axis symmetric profilesSlenderness y, z, zw

flexural or flexural-torsionalUniaxial symmetric profiles Slenderness y, yzw

flexural-torsionalNon-symmetrical profilesSlenderness yzw It is taken into account in simplified form

SAHC - SA5 Steel structures2010T.Vran, CTU in Prague1718Axial compression Buckling (effective) lengthUsing Eulers formula for general bar Buckling length:Length of basic member (pinned ends, constant compression force) of the same cross-section with equal critical force as examined member Lcr = b LSAHC - SA5 Steel structures2010T.Vran, CTU in Prague1819Axial compression Buckling lengthExample - CantileverEuler

Cantilever

Lcr = 2 L =2

SAHC - SA5 Steel structures2010T.Vran, CTU in Prague1920Axial compression Buckling resistance of real memberImperfectionsGeometric imperfectionsInitial curvature of the member axis,excentricity of the loading positionDeviation from the theoretical shape of the cross-sectionMaterial imperfectionsResidual stresses Due to the welding, straightening or coolingStructural imperfectionsImperfect function of hinges or fixed connectionsSAHC - SA5 Steel structures2010T.Vran, CTU in Prague2021Axial compression Results of experiments of compression members

SAHC - SA5 Steel structures2010T.Vran, CTU in Prague2122Axial compression Buckling factora imperfection factordepends on type of cross-section

SAHC - SA5 Steel structures2010T.Vran, CTU in Prague2223Axial compression Buckling factor

SAHC - SA5 Steel structures2010T.Vran, CTU in Prague2324

Global analysis of structure Statically determinate structuresStatically indeterminate structuresElastic analysisPlastic analysisPlastification of the part of the structure

Idealised stress-strain relation SAHC - SA5 Steel structures2010T.Vran, CTU in Prague2425

Global analysis of structure Elastic analysis Material satisfies Hookes law = EFor steel under the yield point fy

Ideal stress-strain diagram SAHC - SA5 Steel structures2010T.Vran, CTU in Prague2526Global analysis of structure Plastic analysisTwo steps:Plastic check of governing cross-sectionPlastic global analysisAt redundant structuresDevelopment of plastic mechanism

SAHC - SA5 Steel structures2010T.Vran, CTU in Prague2627Global analysis of structure Step by step plastification of I cross sectionDevelopment of plastic mechanismSufficient rotation capacity of cross section

SAHC - SA5 Steel structures2010T.Vran, CTU in Prague2728Global analysis of structure Utilization of cross section

SAHC - SA5 Steel structures2010T.Vran, CTU in Prague2829Global analysis Utilization of cross sectionElasto-elasticDistribution of internal forces based on elastic analysisUtilization of structural cross section elasticElasto-plasticDistribution of internal forces based on elastic analysisMaximally loaded cross section utilized plasticallyPlasto-plasticDistribution of internal forces based on plastic analysisAt plastic joints is cross section plastified

SAHC - SA5 Steel structures2010T.Vran, CTU in Prague2930Classification of cross sectionclass 1:Plastic hinges Plastic redistribution of inner forces Plasto-plastic analysisclass 2:Fully plastifiedLimited rotation capacity Elasto-plastic analysisclass 3:It is possible to reach the yield point at edge fibres Elasto-elastic analysisclass 4:slender, at compression stresses buckle earlier before the yield is reached Elasto-elastic analysis

SAHC - SA5 Steel structures2010T.Vran, CTU in Prague3031Classification of cross section Definition of cross-section classClassification for all parts with compression stressFor every compressed part according to b/t ratiob ... width of sheett ... thickness of sheetMaximum class (scr,min) governs

SAHC - SA5 Steel structures2010T.Vran, CTU in Prague3132

SAHC - SA5 Steel structures2010T.Vran, CTU in Prague3233Classification of cross section Cross section of class 4Plate bucklingIdeal cross-section Replacement of real width with effective widths

SAHC - SA5 Steel structures2010T.Vran, CTU in Prague3334Bending, shear Bending resistance MRdShear resistance VRd

SAHC - SA5 Steel structures2010T.Vran, CTU in Prague3435Bending, shearDesign bending resistanceInfluence of cross-section class

1., 2. class 3. class 4. class

fyd = fy/gM0

SAHC - SA5 Steel structures2010T.Vran, CTU in Prague3536Bending, shearDesign shear resistanceAv shear areaSmall shear:VEd 0,5 Vpl,Rd combination M+V is neglectedLarge shearVEd > 0,5 Vpl,Rd combination M+V is considered

SAHC - SA5 Steel structures2010T.Vran, CTU in Prague3637Bending, shearM+V - Large shearReduction of strength on shear area:

for symmetrical cross-section along y-y :

SAHC - SA5 Steel structures2010T.Vran, CTU in Prague3738BendingLateral-torsional buckling

SAHC - SA5 Steel structures2010T.Vran, CTU in Prague3839Relative slenderness

BendingResistance with lateral-torsional bucklingfor cross section of class 1 a 2for cross section of class 3for cross section of class 4

SAHC - SA5 Steel structures2010T.Vran, CTU in Prague3940

BendingBeams not subjected to lat.-torsional bucklingLateral restraint of compression flange

Beam bended in the direction of smaller rigidity

Torsional rigidity of beam is high (closed cross section)

SAHC - SA5 Steel structures2010T.Vran, CTU in Prague4041Serviceability limit statescheck relevant especially for beams

DeflectionsVibrations

Reversible behaviour is requiredElastic behaviour SAHC - SA5 Steel structures2010T.Vran, CTU in Prague4142

Serviceability limit states DeflectionsBending stiffness: E I

max ... resultant deflection 2 ... deflection due to variable load 0 ... chamber of beam 1 ... deflection due to dead loadSAHC - SA5 Steel structures2010T.Vran, CTU in Prague4243Serviceability limit states Recommended limit deflectionsLimits should be agreedJust recommendations in National annexesRefurbishment proper judgement of designerLimits according to ENV:

LoadingfloorsroofstotalL/250L/200variableL/300 (L/350)L/250SAHC - SA5 Steel structures2010T.Vran, CTU in Prague43