““Simple” Construction Simple” Construction andand

Steel Beam DesignSteel Beam Design

Dr M GillieDr M Gillie

Some WebsitesSome Websites

www.access-steel.com/www.access-steel.com/– ExamplesExamples– NCCI (Non-contradictory complementary NCCI (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

Single Element DesignSingle Element Design

Many steel buildings designed on Many steel buildings designed on element by element basiselement by element basis

Typical office structuresTypical office structures Beams, columns, connectionsBeams, columns, connections Need bracing systemsNeed bracing systems Distinct from framed buildings where Distinct from framed buildings where

elements cannot be separated so elements cannot be separated so easilyeasily

““Simple” ConstructionSimple” ConstructionAll connections pinned

Bracing systemneeded

Elements designedindividually

Floor slab spans betweensecondary beams

Secondary beamsspan between primarybeams (or columns)

Primary beamsspan betweencolumns

Typical Floor SystemTypical Floor System

Typical floor planarrangements

6-9m

6-7.5m

3-4m

Secondary beams

Primary beams

Concrete core forstability

Typical Floor SystemTypical Floor System

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

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

Steel BeamsSteel Beams

Beams very widely usedBeams very widely used Needed for horizontal surfacesNeeded for horizontal surfaces Defined as members that (principally) Defined as members that (principally)

resist loads in bendingresist loads in bending Fundamentals straightforward (1Fundamentals straightforward (1stst/2/2ndnd year) year) Many potential buckling modes add Many potential buckling modes add

complexity in steelcomplexity in steel Composite beams often used – make Composite beams often used – make

effective use floor slabs structurallyeffective use floor slabs structurally

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

Universal Beams – I sectionsUniversal Beams – I sections

Optimised for Optimised for bending about one bending about one axisaxis

Weak about other Weak about other axisaxis

Widely usedWidely used Mid-range spansMid-range spans ALSO Universal ALSO Universal

columns – H columns – H sectionssections

Joist (RSJ)Joist (RSJ)

Similar to I-sectionsSimilar to I-sections For smaller spansFor smaller spans

Circular Hollow SectionCircular Hollow Section

Equal bending Equal bending capacity about all capacity about all axesaxes

AestheticAesthetic Connections can be Connections can be

trickytricky Short to medium Short to medium

spansspans

Square Hollow SectionSquare Hollow Section

Equal bending Equal bending capacity about two capacity about two axesaxes

AestheticAesthetic Connections can be Connections can be

trickytricky Short to medium Short to medium

spansspans ALSO rectangular ALSO rectangular

hollow sectionshollow sections

Parallel Flange ChannelsParallel Flange Channels

Used in trussesUsed in trusses Small spansSmall spans Also equal angles Also equal angles

(EA)(EA) And unequal And unequal

angles (UA)angles (UA)

Open-web BeamsOpen-web Beams

Very efficientVery efficient Allow services to Allow services to

pass through holespass through holes Prone to complex Prone to complex

buckling behaviourbuckling behaviour Castellated, Castellated,

cellular or othercellular or other Weaker in shearWeaker in shear Long spansLong spans

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 Sometimes reduced by local-buckling

phenomenaphenomena Effects captured by section Class (determined Effects captured by section Class (determined

on geometrical ratios)on 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 Deflections and other serviceability criteria (can govern design)criteria (can govern design)

Where to check capacity?Where to check capacity?

Check at locations Check at locations of peak BM, SF, of peak BM, SF, deflection etc.deflection etc.

Different load cases Different load cases may result in may result in several checks several checks being neededbeing needed

BM

SF

Check bendingcapacity here

Check shear capacityat ends

Uniform load

Bending Capacity – Plastic Bending Capacity – Plastic HingeHinge

From earlier years plastic From earlier years plastic capacity, Mcapacity, Mpp has has– All material working at yield All material working at yield

stressstress- Depends on section Depends on section

geometry and…geometry and…- ……material strengthmaterial strength

- This is an upper-bound to This is an upper-bound to the section capacitythe section capacity

Cross-sectionStress-stateat plastic capacity

σy

Stress-statewhen local bucklinggoverns

< σy

yplp fWM

- Susceptibility to local buckling may reduce it- Susceptibility to local buckling may reduce it

Local-BucklingLocal-Buckling

Moment-Rotation BehaviourMoment-Rotation BehaviourM

om

ent

Mom

ent

RotationRotation

MMpp

MMyy

Class 4Class 4

Class 3Class 3Class 2Class 2

Class 1Class 1

What happens atpoint of max moment?

Full plastic capacity

Reduced capacity

< σy

σy

Section ClassificationSection Classification

Class 1Class 1

(Plastic)(Plastic)Class 2Class 2

(Compact(Compact))

Class 3 Class 3

(Semi-(Semi-compact)compact)

Class 4 Class 4 (Slender)(Slender)

Large Large plastic plastic rotationsrotations

Full-Full-plasticplastic

Moment, Moment, small small rots.rots.

Full-elasticFull-elastic

momentmoment< elastic < elastic momentmoment

Shear CapacityShear Capacity Shear capacity normally doesn’t govern but…Shear capacity normally doesn’t govern but… … … must be checked and may be important in must be checked and may be important in

short, deep beamsshort, deep beams Normally assumed that shear carried by web Normally assumed that shear carried by web

only, Aonly, Avv

Max shear stresses given by fMax shear stresses given by fyy//√√3 (from von 3 (from von mises yield criterion)mises yield criterion)

Therefore shear capacity related to ATherefore shear capacity related to Av v ffyy//√√3 3 Combined shear and moment should be Combined shear and moment should be

checked too: rarely a problemchecked too: rarely a problem

Global buckling - Global buckling - Lateral-Torsional BucklingLateral-Torsional Buckling

Dead weight load applied vertically

Buckled position

Unloaded position

Clamped at root

Lateral-Torsional BucklingLateral-Torsional Buckling

Mid-span sectionMid-span section PlanPlan

Beam – unrestrained laterallyBeam – unrestrained laterally

Some sections Some sections more affected more affected by L-T buckling by L-T buckling than othersthan others– Hollow sections Hollow sections

unaffectedunaffected

Mb/Mp

Lateral-Torsional Buckling Lateral-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 ignored L-T buckling can be ignored– Beams stiff in torsion or minor axis bending not Beams stiff in torsion or minor axis bending not

susceptible to L-T bucklingsusceptible to L-T buckling If beam restrained against lateral movement - If beam restrained against lateral movement -

OKOK

L-T buckling capacity(simple case!)

5.0

2

2

2

2

zZ

wzb EI

GJL

I

I

L

EIM

Depends on many things!

Note 1/L2 and stiffness terms

Eurocode 3- LayoutEurocode 3- Layout Remember designing for Remember designing for E<R (from EN 1990)

Sections 1+2: Introductory sectionsSections 1+2: Introductory sections– Coordinate axesCoordinate axes

Section 3: Material data Section 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 Overall buckling capacity 6.3 (strength of whole

members)members)– Serviceability checks 7.3 Serviceability checks 7.3

Eurocode Design of “Simple” Eurocode Design of “Simple” BeamsBeams

E<RBending 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 etcBending resistance from 6.2.5Shear resistance from 6.2.6Bending + Shear from 6.2.8

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 calculating Various means of calculating χχ all complex – depend on all 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

Avoiding L-T BucklingAvoiding L-T Buckling

Some forms of section not susceptible Some forms of section not susceptible 6.3.2.1(2)6.3.2.1(2)

Lateral restraint to compression flange Lateral 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 Can be provided by flooring, purlins, bracing

etcetc– Bracing needs to be provided at minimal Bracing needs to be provided at minimal

intervalsintervals– Expression 6.59 gives test for sufficient bracingExpression 6.59 gives test for sufficient bracing

Real Beam BehaviourReal Beam BehaviourBendingCapacity

Slenderness

Mp

Plastic failure

“Complex”behaviour

How do we calculate real bendingcapacity in this region where L-T buckling occur?

Behaviour close totheoretical predictions

Calculating L-T Buckling Calculating L-T Buckling LoadLoad

yyLTRdb fWM ,

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

yyLT M

fW

Bending capacity

Theoretical L-T buckling moment - difficult

Accounts for geometry, load condition, imperfections etc.

Calculating L-T Buckling Calculating L-T Buckling LoadLoad

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 Examples available of Access-Steel

websitewebsite– Simply-supported laterally unrestrained Simply-supported laterally unrestrained

beambeam– Simply-supported beam with lateral Simply-supported beam with lateral

restraint at load-pointrestraint at load-point

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 Use appropriate techniques (earlier

years) to calculate deflectionsyears) to calculate deflections Not different partial safety factorsNot different partial safety factors Other serviceability criteria may Other serviceability criteria may

applyapply