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Teaching Modules for Steel Instruction. Advanced Flexure Design COMPOSITE BEAM THEORY SLIDES. Developed by Scott Civjan University of Massachusetts, Amherst. Composite Beams. Composite action accounts for the steel beam and floor slab working together to resist bending moments. - PowerPoint PPT Presentation

*Composite Beam TheoryDeveloped by Scott CivjanUniversity of Massachusetts, Amherst

Composite Beam Theory

Composite action accounts for the steel beam and floor slab working together to resist bending moments.Advantages over non-composite design:Increased strengthIncreased stiffnessFor given load conditions can achieve:Less steel requiredReduced steel depth*Composite Beam TheoryComposite Beams

Composite Beam Theory

Non-CompositeSlip at InterfaceTwo Neutral AxesMn= Mnconcrete+MnsteelI=Iconcrete + IsteelcccTTNA SteelNA CompositeNA ConcreteTFully CompositeAssumed no slip at InterfaceOne Neutral AxesMn>>Mnconcrete+MnsteelI>>Iconcrete+IsteelShear at interface transferred by shear connectors.*Composite Beam TheoryComposite Behavior

Composite Beam Theory

Composite Metal Deck Slabs most commonly used today.Advantages:Stay in place form.Slab shoring typically not required.Metal deck serves as positive reinforcement.Metal deck serves as construction platform.Flat Soffit Slabs typically, older construction.*Composite Beam TheorySlabs

Composite Beam Theory

beff = effective width of the slabFunction of: Span lengthDistance to nearest beamDistance to edge of slabs1s2s3beffedgeedge*Composite Beam TheoryEffective Width of Slabbeff

Composite Beam Theory

ts, slab thickness*Composite Beam TheorybeffFlat Soffit Slabs

Composite Beam Theory

*Composite Beam TheorybeffhrtcMetal Deck Slab - Ribs Parallel to Beam SpanAAhr=height of decktc=thickness of concrete above the deck

Composite Beam Theory

*Composite Beam TheorybeffhrAAMetal Deck Slab - Ribs Perpendicular to Beam Spantc

Composite Beam Theory

REFERENCES: COMPOSITE BEAMS

Steel Deck Institute web pagesNelson Headed Studs web pagesSteel Deck Manufacturer CatalogsThese can be found on-line

*Composite Beam Theory

Composite Beam Theory

Slab/Deck SpanGirderColumnBeam*Composite Beam TheoryTypical FramingPLAN

Composite Beam Theory

INSERT PHOTOS:

AISC Four Story Office BuildingPhoto Slide ShowsMetal Decking SlidesShear Studs Slides

*Composite Beam Theory

Composite Beam Theory

Flexural Strength*Composite Beam Theory

Composite Beam Theory

Positive Moment

The strength is determined as the plastic stress distribution on the composite section.Negative Moment

It typically is assumed that the concrete carries no tensile forces and reinforcement is minimal, therefore strength is identical to a bare steel section.*Composite Beam TheoryFlexural Strength

Composite Beam Theory

Fully Composite: The strength of either the floor slab in compression or the steel beam in tension is transferred at the interface. Partially Composite: The force transfer between the slab and beam is limited by the connectors. Positive Moment*Composite Beam TheoryFlexural Strength

Composite Beam Theory

Lateral Torsional Buckling is prevented by the slab (continuous bracing).Local Flange Buckling is minimized by the slab.In general, strength is controlled by Mp.*Composite Beam TheoryFlexural StrengthPositive Moment

Composite Beam Theory

INSERT INFORMATION: STRENGTH OF FULLY COMPOSITE BEAM SECTION CALCULATIONS

Handout on Calculations: FullyCompositeCalcs.PDF

*Composite Beam Theory

Composite Beam Theory

The bare steel section must support the temporary construction loads (before the concrete has set), or the steel beam must be shored until the composite section is effective. *Composite Beam TheoryFlexural Strength

Composite Beam Theory

Shear Transfer Between Slab and BeamTypically, provided by headed shear studs.Shear flow, n, is calculated along the interface between slab and beam.Minimal slip allows redistribution of forces among shear studs. Therefore, studs are uniformly distributed along the beam.The total shear flow, n, must be provided on each side of Mmax.*Composite Beam Theory

Composite Beam Theory

*Composite Beam TheoryShear Transfer Between Slab and BeamCompression ForceTension Force

Composite Beam Theory

*Composite Beam TheoryShear Transfer Between Slab and BeamCompression ForceTension Force

Composite Beam Theory

*Composite Beam TheoryShear Transfer Between Slab and Beamn = shear flow

Composite Beam Theory

=shear flow to be transferred by shear studsV=Shear at the location consideredQ=first moment of inertia of area above the interfaceItr=moment of inertia of the transformed cross section*Composite Beam TheoryShear Transfer Between Slab and Beam

Composite Beam Theory

Consider when fully composite strength is greater than required. This may occur when:The shape is based on construction loads.The shape is based on architectural constraints.The lightest shape has excess strength.*Composite Beam TheoryPartially Composite Beam

Composite Beam Theory

INSERT INFORMATION: STRENGTH OF PARTIALLY COMPOSITE BEAM SECTION CALCULATIONS

Handout on Calculations: PartiallyCompositeCalcs.PDF

*Composite Beam Theory

Composite Beam Theory

For composite section deflections: Transform section into equivalent steel section.Compute center of gravity of transformed section.Compute Itr of transformed section.*Composite Beam TheoryServiceability

Composite Beam Theory

*Composite Beam TheorybefftchrComposite Beambeff/ntchrTransformed BeamServiceabilityNote:modular ratio, n = Es/Ec

Composite Beam Theory

It typically is assumed that the slab carries no shear forces, therefore composite strength is identical to that of a bare steel section.*Composite Beam TheoryShear Strength

Composite Beam Theory

*Developed by Scott CivjanUniversity of Massachusetts, Amherst

Composite Beam Theory

Composite Beam - AISC Manual 14th EdChapter I: Composite Member Design*

Composite Beam Theory

Composite Beam - AISC Manual 14th EdSlab effective width, beTo each side of the beam, be is limited by:one-eighth beam spanone-half distance to adjacent beamdistance to edge of slab

Lowest value controls.*

Composite Beam Theory

Composite Beam - AISC Manual 14th EdMetal Deck Slabwr 2tc 2hr 3*1.50.5wr = average deck widthhr=height of decktc=thickness of concrete above the decksteel beam

Composite Beam Theory

Composite Beam - AISC Manual 14th EdFully Composite Beam: Bending Strength*

Composite Beam Theory

Composite Beam - AISC Manual 14th Edfb = 0.90 (Wb = 1.67)*Bending Strength

Composite Beam Theory

Composite Beam - AISC Manual 14th EdPOSITIVE MOMENT

For h/tw

The strength is determined as the plastic stress distribution of the composite section.(*Note: All current ASTM A6 W, S and HP shapes satisfy this limit.)NEGATIVE MOMENT

It is typically assumed that the concrete carries no tensile forces and reinforcement is minimal, therefore strength is identical to a bare steel section.*Bending Strength

Composite Beam Theory

Composite Beam - AISC Manual 14th EdINSERT INFORMATION: STRENGTH OF FULLY COMPOSITE BEAM SECTION CALCULATIONS

Handout on Calculations: FullyCompositeCalcs.PDF

*

Composite Beam Theory

Composite Beam - AISC Manual 14th EdFully Composite Strength can be determined by using Table 3-19.Y2 - Calculated per handoutY1 = 0 if PNA in the slab,Calculated per handout if PNA in the beam flange or web.*Bending Strength

Composite Beam Theory

Composite Beam - AISC Manual 14th EdTable 3-19 Nomenclature(Pg. 3-14)beaYcona/2Y2Location of effective concrete flange force (SQn)TFL(pt.1)BFL(pt.5)67Y1 = Distance from top of steel flange to any of the seven tabulated PNA locations4 Eq. spaces1245TFLBFLtf*Beam Flange Enlarged Detail15

Composite Beam Theory

Composite Beam - AISC Manual 14th EdTo reach fully composite strength,shear studs must transfer SQn for Y1 = 0 (maximum value) listed in Table 3-19.

This is equivalent to value C* in calculations (handout).*Bending Strength

Composite Beam Theory

Composite Beam - AISC Manual 14th EdShear Stud Strength*

Composite Beam Theory

Composite Beam - AISC Manual 14th Edlimits value to strength of individual shear studs.Strength of each stud, QnEquation I8-1

limits value to crushing of concrete around the shear stud.*

Composite Beam Theory

Composite Beam - AISC Manual 14th EdAsa=cross sectional area of shear studEc=modulus of elasticity of concreteFu=shear stud minimum tensile strength (typically 65ksi)Rg accounts for number of studs welded in each deck rib and wr/hr.Values are 1.0, 0.85 or 0.7.

Rp accounts for deck rib orientation with respect to the beam, stud engagement in the concrete above the rib, and weak or strong stud location.Values are 0.75 or 0.6.*

Composite Beam Theory

Composite Beam - AISC Manual 14th EdStrength, Qn, for one shear studTable 3-21*

Composite Beam Theory

Composite Beam - AISC Manual 14th EdLimitations on shear stud placementfor shear studs placed in metal decking:Center-Center Spacing:>4 times diameter8 times slab thickness36 inches

Shear Stud Diameter:3/42.5 times flange thickness unless over web*

Composite Beam Theory

Composite Beam - AISC Manual 14th EdComposite strength requires that shear studs transfer SQn to each side of the maximum moment in the span.If SQn strength of the shear studs is inadequate to provide fully composite action, the beam is partially composite.*

Composite Beam Theory

Composite Beam - AISC Manual 14th EdPartially Composite Beam: Bending Strength

Fb = 0.90 (Wb = 1.67)*

Composite Beam Theory

Composite Beam - AISC Manual 14th EdINSERT INFORMATION: STRENGTH OF PARTIALLY COMPOSITE BEAM SECTION CALCULATIONS

Handout on Calculations: PartiallyCompositeCalcs.PDF

*

Composite Beam Theory

Composite Beam - AISC Manual 14th EdPartially Composite Strength can be determined by using Table 3-19.Y1 - Calculated per handout*Y2 - Calculated per handout

Composite Beam Theory

Composite Beam - AISC Manual 14th EdPartially Composite Action is limited by the total strength of shear studs.

SQn listed in Table 3-19.

This is equivalent to value C* in calculations (handout).*

Composite Beam Theory

Composite Beam - AISC Manual 14th EdComposite Beam: Shear Strength*

Composite Beam Theory

Composite Beam - AISC Manual 14th Ed

SHEAR STRENGTH

It typically is assumed that the slab carries no shear forces. Therefore, strength is identical to a bare steel section.*

Composite Beam Theory

Composite Beam - AISC Manual 14th EdComposite Beam Deflection Calculations*

Composite Beam Theory

Composite Beam - AISC Manual 14th EdDeflection CalculationsFully Composite Itr = transformed section moment of inertiaLower bound values of Itr are found in Table 3-20.Values assume concrete area equal to SQn/Fy rather than actual area.*

Composite Beam Theory

Composite Beam - AISC Manual 14th EdDeflection Calculations Partially CompositeEquation C-I3-4Ieff= effective moment of inertiaIs=moment of inertia of steel section onlyItr=fully composite moment of inertiaQnr=partially composite shear transferCf=fully composite shear transfer*

Composite Beam Theory

Composite Beam - AISC Manual 14th EdDeflection Calculations Partially CompositeEquation C-I3-5Seff= effective elastic section modulusSs=elastic section modulus of steel section onlyStr=fully composite elastic section modulusQnr=partially composite shear transferCf=fully composite shear transfer*

Composite Beam Theory

Composite Beam - AISC Manual 14th EdDeflection Calculations Partially CompositeTable 3-20 can be used for lower bound values of Ieff.*

Composite Beam Theory

***************************************Note that this indicates that push-out of a stud through a rib could be minimized by increasing Fu of the stud, which is not realistic. The equations assume standard materials.****************