Teaching Modules for Steel Instruction

1Composite Beam Theory

Developed by Scott CivjanUniversity of Massachusetts, Amherst

Composite action accounts for the steel beam and floor slab working together to resist bending moments.

Advantages over non-composite design:Increased strengthIncreased stiffness

For given load conditions can achieve:Less steel requiredReduced steel depth


Composite Beams

Non-Composite•Slip at Interface•Two Neutral Axes•Mn= Mnconcrete+Mnsteel

•I = Iconcrete + Isteel

c

cc

T T

NA Steel

NA Composite

NA ConcreteT

Fully Composite•Assumed no slip at Interface•One Neutral Axes•Mn >> Mnconcrete+Mnsteel

•I >> Iconcrete+Isteel

•Shear at interface transferred by shear connectors.


Composite Behavior

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.


Slabs

beff = effective width of the slabFunction of: Span length

Distance to nearest beamDistance to edge of slab

s1 s2s3

beff

edge edge


Effective Width of Slab

beff

ts, slab thickness


beff

Flat Soffit Slabs


beff

hrtc

Metal Deck Slab - Ribs Parallel to Beam Span

A

A

hr = height of decktc = thickness of concrete above the deck


beff

hr

A

A

Metal Deck Slab - Ribs Perpendicular to Beam Span

tc

REFERENCES: COMPOSITE BEAMS

Steel Deck Institute web pagesNelson Headed Studs web pagesSteel Deck Manufacturer Catalogs

These can be found on-line


Slab/Deck Span

GirderColumn

Bea

m


Typical Framing

PLAN

INSERT PHOTOS:

AISC Four Story Office BuildingPhoto Slide ShowsMetal Decking SlidesShear Studs Slides


Flexural Strength


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.


Flexural Strength

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


Flexural Strength

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.


Flexural Strength

Positive Moment

INSERT INFORMATION: STRENGTH OF FULLY COMPOSITE BEAM SECTION CALCULATIONS

Handout on Calculations: FullyCompositeCalcs.PDF


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.


Flexural Strength

Shear Transfer Between Slab and Beam

Typically, provided by headed shear studs.

Shear flow, 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, must be provided on each side of Mmax.




Compression Force

Tension Force



Compression Force

Tension Force



= shear flow

= 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

νtr

VQ

I



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.


Partially Composite Beam

INSERT INFORMATION: STRENGTH OF PARTIALLY COMPOSITE BEAM SECTION CALCULATIONS

Handout on Calculations: PartiallyCompositeCalcs.PDF


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


Serviceability


beff

tchr

Composite Beam

beff/n

tc

hr

Transformed Beam

Serviceability

Note:modular ratio, n = Es/Ec

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


Shear Strength

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Developed by Scott CivjanUniversity of Massachusetts, Amherst

Composite Beam - AISC Manual 14th Ed

Chapter I: Composite Member Design

29


Slab effective width, be

To 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.

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Metal Deck Slab

wr ≥ 2”

tc ≥ 2”

hr ≤ 3”

31

≥1.5”

≥0.5”

wr = average deck widthhr = height of decktc = thickness of concrete above the deck

steel beam


Fully Composite Beam: Bending Strength

32


b = 0.90 (b = 1.67)

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Bending Strength


POSITIVE 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.)

yF

E.763

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.

34

Bending Strength


INSERT INFORMATION: STRENGTH OF FULLY COMPOSITE BEAM SECTION CALCULATIONS

Handout on Calculations: FullyCompositeCalcs.PDF

35


Fully Composite Strength can be determined by using Table 3-19.

Y2 - Calculated per handout

Y1 = 0 if PNA in the slab,Calculated per handout if PNA in the beam flange or web.

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Bending Strength


Table 3-19 Nomenclature(Pg. 3-14)

be

aYcon

a/2

Y2

Location of effective concrete flange force (Qn)

TFL(pt.1)

BFL(pt.5)6

7 Y1 = Distance from top of steel flange to any of the seven tabulated PNA locations4

Eq.

spa

ces 1

2

3

4

5

TFL

BFL

tf

37

Beam Flange Enlarged Detail

15


To reach fully composite strength,shear studs must transfer Qn for Y1 = 0 (maximum value) listed in Table 3-19.

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

38

Bending Strength


Shear Stud Strength

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limits value to strength of individual shear studs.

Strength of each stud, QnEquation I8-1

usapgccsan FARR'EfA.Q 50

limits value to crushing of concrete around the shear stud.

usapg FARR

40

ccsa 'EfA.50


Asa = 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.

41

usapgccsan FARR'EfA.Q 50


Strength, Qn, for one shear studTable 3-21

42


Limitations on shear stud placementfor shear studs placed in metal decking:

Center-Center Spacing: > 4 times diameter≤ 8 times slab thickness≤ 36 inches

Shear Stud Diameter: ≤ 3/4”≤ 2.5 times flange thickness unless over web

43


Composite strength requires that shear studs transfer Qn to each side of the maximum moment in the span.

If Qn strength of the shear studs is inadequate to provide fully composite action, the beam is partially composite.

44


Partially Composite Beam: Bending Strength

b = 0.90 (b = 1.67)

45


INSERT INFORMATION: STRENGTH OF PARTIALLY COMPOSITE BEAM SECTION CALCULATIONS

Handout on Calculations: PartiallyCompositeCalcs.PDF

46


Partially Composite Strength can be determined by using Table 3-19.


47



Partially Composite Action is limited by the total strength of shear studs.

Qn listed in Table 3-19.

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

48


Composite Beam: Shear Strength

49


SHEAR STRENGTH

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

50


Composite Beam Deflection Calculations

51


Deflection CalculationsFully Composite

Itr = transformed section moment of inertia

Lower bound values of Itr are found in Table 3-20.Values assume concrete area equal to Qn/Fy rather than actual area.

52


Deflection Calculations Partially Composite

Equation C-I3-4 strf

nrseff II

C

QII

Ieff = effective moment of inertiaIs = moment of inertia of steel section onlyItr = fully composite moment of inertiaΣQnr= partially composite shear transferCf = fully composite shear transfer

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Equation C-I3-5 strf

nrseff SS

C

QSS

Seff = effective elastic section modulusSs = elastic section modulus of steel section onlyStr = fully composite elastic section modulusΣQnr= partially composite shear transferCf = fully composite shear transfer

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Table 3-20 can be used for lower bound values of Ieff.

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Teaching Modules for Steel Instruction