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1Composite Beam Theory

Developed by Scott Civjan

University of Massachusetts, Amherst

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Composite action accounts for the steel beam and floor slab

working together to resist bending moments.

Advantages over non-composite design:

Increased strength

Increased stiffness

Composite Beams

For given load conditions can achieve:

Less steel required

Reduced steel depth

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c

cc

NA Steel

NA

CompositeNA Concrete

T

Composite Behavior

Non-Composite

Slip at Interface

Two Neutral Axes

Mn=Mnconcrete+MnsteelI =Iconcrete +Isteel

Fully Composite

Assumed no slip at Interface

One Neutral Axes

Mn >>Mnconcrete+MnsteelI >>Iconcrete+IsteelShear at interface transferred

by shear connectors.

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Composite Metal Deck Slabs most commonly used today.

Advantages:Stay in place form.

Slab shoring typically not required.

Slabs

Metal deck serves as construction platform.

Flat Soffit Slabs typically, older construction.

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beff = effective width of the slab

Function of: Span length

Distance to nearest beamDistance to edge of slab

b

Effective Width of Slab

b

s1 s2 s3edge edge

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ts, slab thickness

beff

Flat Soffit Slabs

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beff

hrtc

Metal Deck Slab - Ribs Parallel to Beam Span

A

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A

hr = height of deck

tc = thickness of concrete above the deck

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beff

hr

A

Metal Deck Slab - Ribs Perpendicular to Beam Span

tc

8Composite Beam Theory

A

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REFERENCES: COMPOSITE BEAMS

Steel Deck Institute web pages

Steel Deck Manufacturer Catalogs

These can be found on-line

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GirderColumn

Beam

Typical Framing

Slab/Deck Span

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PLAN

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INSERT PHOTOS:

AISC Four Story Office Building

Photo Slide ShowsMetal Decking Slides

Shear Studs Slides

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Flexural Strength

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Positive Moment

The strength is determined as the plastic stressdistribution on the composite section.

Flexural Strength

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.

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Fully Composite: The strength of either the floor slab in

compression or the steel beam in tension is transferred at

the interface.

Positive Moment

Flexural Strength

Partially Composite: The force transfer between the slab

and beam is limited by the connectors.

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Lateral Torsional Buckling is prevented by the slab

(continuous bracing).

Flexural Strength

Positive Moment

Local Flange Buckling is minimized by the slab.

In general, strength is controlled byMp.

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INSERT INFORMATION: STRENGTHOF FULLY COMPOSITE BEAM

SECTION CALCULATIONS

Handout on Calculations:

FullyCompositeCalcs.PDF

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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

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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 ofMmax.

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Shear Transfer Between Slab and Beam

Compression

Force

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Tension Force

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Shear Transfer Between Slab and Beam

Compression

Force

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Tension Force

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Shear Transfer Between Slab and Beam

= shear flow

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tr

VQ

I=

Shear Transfer Between Slab and Beam

= shear flow to be transferred by shear studs

V= Shear at the location considered

Q = first moment of inertia of area above the interface

Itr= moment of inertia of the transformed cross section

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Consider when fully composite strength is greater than required.This may occur when:

The shape is based on construction loads.

Partially Composite Beam

e s ape s ase on arc ec ura cons ra n s.

The lightest shape has excess strength.

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INSERT INFORMATION: STRENGTHOF PARTIALLY COMPOSITE BEAM

SECTION CALCULATIONS

Handout on Calculations:

PartiallyCompositeCalcs.PDF

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For composite section deflections:

Transform section into equivalent steel section.Compute center of gravity of transformed section.

ComputeItrof transformed section.

Serviceability

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beff

tchr

beff/n

tchr

Serviceability

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Composite Beam Transformed Beam

modular ratio, n =Es/Ec

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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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