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Steel beam design

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Tài liệu được biên soạn bởi RD Việt Nam - Công ty CPCN & TVTK Xây dựng RD …

Tài liệu được biên soạn bởi RD Việt Nam - Công ty CPCN & TVTK Xây dựng RD
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  • 1. ““Simple” Construction andSimple” Construction and Steel Beam DesignSteel Beam Design Dr M GillieDr M Gillie
  • 2. Some WebsitesSome Websites  www.access-steel.com/www.access-steel.com/ – ExamplesExamples – NCCI (Non-contradictory complementaryNCCI (Non-contradictory complementary information)information) – Scheme design etc.Scheme design etc. – Funded by steel manufacturersFunded by steel manufacturers  www.eurocodes.co.ukwww.eurocodes.co.uk
  • 3. Single Element DesignSingle Element Design  Many steel buildings designed on elementMany steel buildings designed on element by element basisby element basis  Typical office structuresTypical office structures  Beams, columns, connectionsBeams, columns, connections  Need bracing systemsNeed bracing systems  Distinct from framed buildings whereDistinct from framed buildings where elements cannot be separated so easilyelements cannot be separated so easily
  • 4. ““Simple” ConstructionSimple” Construction All connections pinned Bracing system needed Elements designed individually
  • 5. Floor slab spans between secondary beams Secondary beams span between primary beams (or columns) Primary beams span between columns Typical Floor SystemTypical Floor System
  • 6. Typical floor plan arrangements 6-9m 6-7.5m 3-4m Secondary beams Primary beams
  • 7. Concrete core for stability
  • 8. Typical Floor SystemTypical Floor System
  • 9. Non-composite Floors (first)Non-composite Floors (first)  No connection between steel and concreteNo connection between steel and concrete  Bending strength by simple addition (ignore concrete?Bending strength by simple addition (ignore concrete?  Lots of material working below yield stressLots of material working below yield stress  Quick to buildQuick to build  Pre-cast slabs often usedPre-cast slabs often used Concrete floor slab Steel beam
  • 10. Composite Floors (Later)Composite Floors (Later)  Connection between steel and concreteConnection between steel and concrete  Bending strength greatly enhancedBending strength greatly enhanced  Material working much closer to yield strengthMaterial working much closer to yield strength  Very efficient method of constructionVery efficient method of construction
  • 11. Steel BeamsSteel Beams  Beams very widely usedBeams very widely used  Needed for horizontal surfacesNeeded for horizontal surfaces  Defined as members that (principally) resistDefined as members that (principally) resist loads in bendingloads in bending  Fundamentals straightforward (1Fundamentals straightforward (1stst /2/2ndnd year)year)  Many potential buckling modes add complexityMany potential buckling modes add complexity in steelin steel  Composite beams often used – make effectiveComposite beams often used – make effective use floor slabs structurallyuse floor slabs structurally
  • 12. Different types of beamsDifferent types of beams  Open SectionOpen Section – Universal Beams D=1016 -127Universal Beams D=1016 -127 – Joists (Rolled Steel Joists – RSJs) D=254 – 76Joists (Rolled Steel Joists – RSJs) D=254 – 76 – Parallel Flange Channels D=430 – 100Parallel Flange Channels D=430 – 100 – Angles (Equal and Unequal)Angles (Equal and Unequal)  Hollow SectionHollow Section – Hot-finished Circular Hollow Sections D=500 - 27Hot-finished Circular Hollow Sections D=500 - 27 – Hot-finished Square Hollow Sections D=400 - 40Hot-finished Square Hollow Sections D=400 - 40 – Hot-finished Rectangular Sections D=500 - 50Hot-finished Rectangular Sections D=500 - 50  All the above Hollow Sections Cold FormedAll the above Hollow Sections Cold Formed  ASB (Asymmetric Beams) D=300 - 280ASB (Asymmetric Beams) D=300 - 280  Parallel Flange Channels D=430 - 100Parallel Flange Channels D=430 - 100  Beams with web openingsBeams with web openings – Castellated Universal Beams D=609 – 191Castellated Universal Beams D=609 – 191 – CellularCellular
  • 13. Universal Beams – I sectionsUniversal Beams – I sections  Optimised for bendingOptimised for bending about one axisabout one axis  Weak about otherWeak about other axisaxis  Widely usedWidely used  Mid-range spansMid-range spans  ALSO UniversalALSO Universal columns – H sectionscolumns – H sections
  • 14. Joist (RSJ)Joist (RSJ)  Similar to I-sectionsSimilar to I-sections  For smaller spansFor smaller spans
  • 15. Circular Hollow SectionCircular Hollow Section  Equal bendingEqual bending capacity about allcapacity about all axesaxes  AestheticAesthetic  Connections can beConnections can be trickytricky  Short to mediumShort to medium spansspans
  • 16. Square Hollow SectionSquare Hollow Section  Equal bending capacityEqual bending capacity about two axesabout two axes  AestheticAesthetic  Connections can be tricConnections can be tric  Short to medium spansShort to medium spans  ALSO rectangular holloALSO rectangular hollow sectionssections
  • 17. Parallel Flange ChannelsParallel Flange Channels  Used in trussesUsed in trusses  Small spansSmall spans  Also equal anglesAlso equal angles (EA)(EA)  And unequal anglesAnd unequal angles (UA)(UA)
  • 18. Open-web BeamsOpen-web Beams  Very efficientVery efficient  Allow services to passAllow services to pass through holesthrough holes  Prone to complexProne to complex buckling behaviourbuckling behaviour  Castellated, cellularCastellated, cellular or otheror other  Weaker in shearWeaker in shear  Long spansLong spans
  • 19. Design of Steel BeamsDesign of Steel Beams  Local behaviour - cross-section checksLocal behaviour - cross-section checks  In simple cases given by full-plastic momentIn simple cases given by full-plastic moment  Sometimes reduced by local-buckling phenomenaSometimes reduced by local-buckling phenomena  Effects captured by section Class (determined onEffects captured by section Class (determined on geometrical ratios)geometrical ratios)  Also heck shear capacity (rarely governs)Also heck shear capacity (rarely governs)  Global behaviourGlobal behaviour – Check lateral-torsional bucklingCheck lateral-torsional buckling  Deflections and other serviceability criteriaDeflections and other serviceability criteria (can govern design)(can govern design)
  • 20. Where to check capacity?Where to check capacity?  Check at locations ofCheck at locations of peak BM, SF,peak BM, SF, deflection etc.deflection etc.  Different load casesDifferent load cases may result in severalmay result in several checks being neededchecks being needed BM SF Check bending capacity here Check shear capacity at ends Uniform load
  • 21. Bending Capacity – PlasticBending Capacity – Plastic HingeHinge From earlier years plasticFrom earlier years plastic capacity, Mcapacity, Mpp hashas – All material working at yieldAll material working at yield stressstress - Depends on section geometryDepends on section geometry and…and… - ……material strengthmaterial strength - This is an upper-bound to theThis is an upper-bound to the section capacitysection capacity Cross-section Stress-state at plastic capacity σy Stress-state when local buckling governs < σy yplp fWM = - Susceptibility to local buckling may reduce it- Susceptibility to local buckling may reduce it
  • 22. Local-BucklingLocal-Buckling
  • 23. Moment-Rotation BehaviourMoment-Rotation BehaviourMomentMoment RotationRotation MMpp MMyy Class 4Class 4 Class 3Class 3 Class 2Class 2 Class 1Class 1 What happens at point of max moment? Full plastic capacity Reduced capacity < σy σy
  • 24. Section ClassificationSection Classification Class 1Class 1 (Plastic)(Plastic) Class 2Class 2 (Compact)(Compact) Class 3Class 3 (Semi-compact)(Semi-compact) Class 4Class 4 (Slender)(Slender) LargeLarge plasticplastic rotationsrotations Full-plasticFull-plastic Moment,Moment, small rots.small rots. Full-elasticFull-elastic momentmoment < elastic< elastic momentmoment
  • 25. Shear CapacityShear Capacity  Shear capacity normally doesn’t govern but…Shear capacity normally doesn’t govern but…  …… must be checked and may be important inmust be checked and may be important in short, deep beamsshort, deep beams  Normally assumed that shear carried by webNormally assumed that shear carried by web only, Aonly, Avv  Max shear stresses given by fMax shear stresses given by fyy//√√3 (from von3 (from von mises yield criterion)mises yield criterion)  Therefore shear capacity related to ATherefore shear capacity related to Avv ffyy//√√33  Combined shear and moment should beCombined shear and moment should be checked too: rarely a problemchecked too: rarely a problem
  • 26. Global buckling -Global buckling - Lateral-Torsional BucklingLateral-Torsional Buckling Dead weight load applied vertically Buckled position Unloaded position Clamped at root
  • 27. Lateral-Torsional BucklingLateral-Torsional Buckling Mid-span sectionMid-span section PlanPlan Beam – unrestrained laterallyBeam – unrestrained laterally
  • 28.  Some sectionsSome sections more affected bymore affected by L-T buckling thanL-T buckling than othersothers – Hollow sectionsHollow sections unaffectedunaffected Mb/Mp
  • 29. Lateral-Torsional BucklingLateral-Torsional Buckling Resistance?Resistance?  Complex and real situation worse thereforeComplex and real situation worse therefore – Design approach semi-empiricalDesign approach semi-empirical  If MIf Mpp<M<Mbb L-T buckling can be ignoredL-T buckling can be ignored – Beams stiff in torsion or minor axis bending notBeams stiff in torsion or minor axis bending not susceptible to L-T bucklingsusceptible to L-T buckling  If beam restrained against lateral movement - OKIf beam restrained against lateral movement - OK L-T buckling capacity (simple case!) 5.0 2 2 2 2       += zZ wz b EI GJL I I L EI M π π Depends on many things! Note 1/L2 and stiffness terms
  • 30. Eurocode 3- LayoutEurocode 3- Layout  Remember designing forRemember designing for E<R (from EN 1990)  Sections 1+2: Introductory sectionsSections 1+2: Introductory sections – Coordinate axesCoordinate axes  Section 3: Material dataSection 3: Material data  Section 5: Analysis of structuresSection 5: Analysis of structures – Analysis methodsAnalysis methods – Section classificationSection classification  Section 6: How to calculate strength of structuresSection 6: How to calculate strength of structures – Partial safety factors on strengthPartial safety factors on strength – Section capacity 6.2 (cross-section “local” strength)Section capacity 6.2 (cross-section “local” strength) – Overall buckling capacity 6.3 (strength of whole members)Overall buckling capacity 6.3 (strength of whole members) – Serviceability checks 7.3Serviceability checks 7.3
  • 31. Eurocode Design of “Simple” BeamsEurocode Design of “Simple” Beams E<R Bending moment (or shear force) Bending strength of beam (or shear strength) Material details from EN1993 Table 3.1  fy normally of most interest Classification of cross-section from Table 5.3 etc Bending resistance from 6.2.5 Shear resistance from 6.2.6 Bending + Shear from 6.2.8
  • 32. L-T Buckling - DesignL-T Buckling - Design  First try and avoid it (this is commonest and easiest)First try and avoid it (this is commonest and easiest) – Lateral restraintLateral restraint – choice of sectionchoice of section  Use simplified methods in Eurocode 3 clause 6.3.2.4Use simplified methods in Eurocode 3 clause 6.3.2.4  Use factor on bending strengthUse factor on bending strength – χχWWyyffyy//γγmm – Various means of calculatingVarious means of calculating χχ all complex – depend onall complex – depend on  Section typeSection type  Moment distributionMoment distribution  LoadingLoading  RestraintRestraint – Semi-empirical methods neededSemi-empirical methods needed – Eurocode rather vague, need NCCI or text book tooEurocode rather vague, need NCCI or text book too
  • 33. Avoiding L-T BucklingAvoiding L-T Buckling  Some forms of section not susceptible 6.3.2.1(2)Some forms of section not susceptible 6.3.2.1(2)  Lateral restraint to compression flangeLateral restraint to compression flange 6.3.2.1(2), 6.3.2.4 (1)B6.3.2.1(2), 6.3.2.4 (1)B – Can be provided by flooring, purlins, bracing etcCan be provided by flooring, purlins, bracing etc – Bracing needs to be provided at minimal intervalsBracing needs to be provided at minimal intervals – Expression 6.59 gives test for sufficient bracingExpression 6.59 gives test for sufficient bracing
  • 34. Real Beam BehaviourReal Beam Behaviour Bending Capacity Slenderness Mp Plastic failure “Complex” behaviour How do we calculate real bending capacity in this region where L-T buckling occur? Behaviour close to theoretical predictions
  • 35. Calculating L-T Buckling LoadCalculating L-T Buckling Load yyLTRdb fWM χ=, Use knock-down factor on section bending resistance (eqn 6.55)Use knock-down factor on section bending resistance (eqn 6.55) Χ (chi) a function of the slenderness of the beam (eqn 6.56) cr yy LT M fW =λ Bending capacity Theoretical L-T buckling moment - difficult Accounts for geometry, load condition, imperfections etc.
  • 36. Calculating L-T Buckling LoadCalculating L-T Buckling Load  ComplexComplex  Code gives only very basic guidanceCode gives only very basic guidance – See NCCI and commentary in ExtractsSee NCCI and commentary in Extracts  Examples available of Access-Steel websiteExamples available of Access-Steel website – Simply-supported laterally unrestrained beamSimply-supported laterally unrestrained beam – Simply-supported beam with lateral restraint atSimply-supported beam with lateral restraint at load-pointload-point
  • 37. ServiceabilityServiceability  Deflections need to be limitedDeflections need to be limited  Guidance given in section 7.2Guidance given in section 7.2  Use appropriate techniques (earlier years)Use appropriate techniques (earlier years) to calculate deflectionsto calculate deflections  Not different partial safety factorsNot different partial safety factors  Other serviceability criteria may applyOther serviceability criteria may apply

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