Limit StatesFlexureElasticPlasticStability (buckling)ShearDeflectionFatigueSupports

FlexureElasticPlasticStability (buckling)LRFDASD

Flexure - ElasticS=I/c : Section Modulus (Tabulated Value)

Flexure - Plastic

Flexure - PlasticZ=(0.5A)a : Plastic Section Modulus (Tabulated Value)

Mp = Acfy = Atfy = fy (0.5A) a = Mp=Zfy

Mp/ My =Z/SFor shapes that are symmetrical about the axis of bending the plastic and elastic neutral axes are the sameC=TAcfy=AtfyAc=At

Flexure - StabilityMp is reached and section becomes fully plastic

Or

Flange Local Buckling (FLB) Elastically or InelasticallyWeb Local Buckling (WLB) Elastically or Inelastically

Lateral Torsional Buckling (LTB) Elastically or Inelastically

A beam has failed when:

Flexure - StabilitySlenderness ParameterFLB

l=bf/2tfWLB

l=h/twLTB

l= Lb /ry

Flexure - StabilityFLB and WLB (Section B5 Table B4.1)Evaluate Moment Capacity for Different lFLB

l=bf/2tfWLB

l=h/tw

Slenderness Parameter - Limiting ValuesAISC B5 Table B4.1 pp 16.1-16

Slenderness Parameter - Limiting ValuesAISC B5 Table B4.1 pp 16.1-17

Slenderness Parameter - Limiting ValuesAISC B5 Table B4.1 pp 16.1-18

Flexure - StabilityFLB and WLB (Section B5 Table B4.1)

FLB

l=bf/2tfWLB

l=h/tw

Bending Strength of Compact ShapesLateral Torsional Buckling

Bending Strength of Compact Shapes

Bending Strength of Compact ShapesLaterally Supported Compact Beams

Bending Strength of Compact Shapes

Bending Strength of Compact ShapesElastic Buckling

Elastic BucklingCb = factor to account for non-uniform bending within the unbraced lengthABCMmaxSee AISC table 3-1 p 3.10

Elastic Buckling

Elastic Buckling

Elastic BucklingCb = factor to account for non-uniform bending within the unbraced lengthRm=1 for doubly symmetric cross sections and singly symmetric subject to single curvature

Elastic BucklingCb = factor to account for non-uniform bending within the unbraced length

Elastic BucklingCb = factor to account for non-uniform bending within the unbraced lengthho = distance between flange centroids = d-tf

Bending Strength of Compact Shapes

Bending Strength of Compact ShapesInelastic BucklingLinear variation between Mp and Mr

Nominal Flexural Strength Compact Shapes

Nominal Flexural Strength NON-Compact ShapesMost W- M- S- and C- shapes are compact

A few are NON-compact

NONE is slender

Webs of ALL hot rolled shapes in the manual are compactFLB and LTB

Built-Up welded shapes can have non-compact or slender websFLB, WLB, LTB (AISC F4 and F5)

Nominal Flexural Strength NON-Compact ShapesWLB

Design of Beams - Limit StatesFlexureElasticPlasticStability (buckling)ShearDeflection

Design for Shear

Large concentrated loads placed near beam supportsRigid connection of beams and columns with webs on the same planeNotched or coped beamsHeavily loaded short beamsThin webs in girders

Design for ShearV: Vertical shear at the section under considerationQ: First moment about of neutral axis of area of the cross section between point of interest and top or bottom of section (depends on y)I: Moment of inertia of sectionb: width of section at point of interest

Design for ShearWeb fails before flangesd/b=2Error ~3%d/b=1Error ~12%d/b=1/4Error 100%Small width bNominal Strength if no buckling:Average Shear Stress

Design for ShearYieldingInelastic BucklingElastic BucklingFailure of Web due to Shear:h/twh/tw>260 Stiffeners are requiredAppendix F2

Design for ShearAISC Specs G pp 16.1-64Shear Strength must be sufficient to satisfyresistance factor for shear=0.9nominal shear strengthdepends on failure modemaximum shear based on the controlling combination for factored loadsLRFDSafety factormaximum shear based on the controlling combination for service loadsASD

AISC Spec requirements for ShearCv depends on whether the limit state is web yielding, web inelastic buckling or web elastic buckling

AISC Spec requirements for ShearSpecial Case for Hot Rolled I shapes withMost W shapes with

AISC Spec requirements for Shear Chapter GAll other doubly and singly symmetric shapes except round HSS

DEFLECTIONSAISC Specs Chapter LServiceability Limit StateUse deflection formulas in AISC Part 3 Or standard analytical or numerical methods

Calculate due to UNFACTORED (service) loadsGoverning Building Code, IBC etcDeflections due to Service LoadsLimiting Value

Design Shear is rarely a problem in rolled steel beamsusual practice

Design for Flexure and Check for Shear and DeflectionsOrDesign for Deflections and Check for Flexure and Shear

DesignCompute Required Moment Strength Mu or MaWeight of Beam can be assumed and verified or ignored and checked after member is selected

Select shape that satisfies strength requirements

Assume shape, compute strength, compare with required, revise if necessary orUse beam design aids in Part 3 of the Manual

Check Shear and deflections