Retrofit of Steel Moment Frame Connections

Composite Beam Theory

Developed by Scott Civjan

University of Massachusetts, Amherst

1

Composite Beams

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

For given load conditions can achieve:

Less steel required

Reduced steel depth

Composite Beam Theory 2

Composite Behavior

T c c

NA Concrete c

NA

Composite

NA Steel

T

Non-Composite

•Slip at Interface

•Two Neutral Axes

•

M n

= M nconcrete

+ M

•

I = I concrete

+ I nsteel steel

T

Fully Composite

•Assumed no slip at Interface

•One Neutral Axes

• M n

>>

•

I >> I

M nconcrete concrete

+ I

+ M nsteel steel

•Shear at interface transferred by shear connectors.


Slabs

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.


Effective Width of Slab b eff

= effective width of the slab

Function of: Span length

Distance to nearest beam

Distance to edge of slab b eff b eff edge s

1 s

2

Composite Beam Theory s

3 edge

5

Flat Soffit Slabs b eff t s

, slab thickness


Metal Deck Slab - Ribs Parallel to Beam Span b eff

A h r t c h r t c

= height of deck

= thickness of concrete above the deck

Composite Beam Theory

A

7

Metal Deck Slab - Ribs Perpendicular to Beam Span b eff

A h r t c

A


REFERENCES: COMPOSITE BEAMS

Steel Deck Institute web pages

Nelson Headed Studs web pages

Steel Deck Manufacturer Catalogs

These can be found on-line


Typical Framing

Girder

Column

Slab/Deck Span

PLAN


INSERT PHOTOS:

AISC Four Story Office Building

Photo Slide Shows

Metal Decking Slides

Shear 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.



Positive Moment

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

Lateral Torsional Buckling is prevented by the slab

(continuous bracing).

Local Flange Buckling is minimized by the slab.

In general, strength is controlled by M p

.


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.


Shear Transfer Between Slab and Beam

Typically, 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 M max

.



Compression

Force

Tension Force



Compression

Force

Tension Force


Shear Transfer Between Slab and Beam n

= shear flow



ν 

VQ

I tr n

= shear flow to be transferred by shear studs

V = Shear at the location considered

Q = first moment of inertia of area above the interface

I tr

= moment of inertia of the transformed cross section


Partially Composite Beam

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.



OF PARTIALLY COMPOSITE BEAM



PartiallyCompositeCalcs.PDF


Serviceability

For composite section deflections:

Transform section into equivalent steel section.

Compute center of gravity of transformed section.

Compute I tr of transformed section.


b eff

Serviceability b eff

/n t c h r t c h r

Note: modular ratio, n = E s

/E c

Composite Beam Transformed Beam


Shear Strength

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


Developed by Scott Civjan

University of Massachusetts, Amherst

28

Chapter I:

Composite Member Design

Composite Beam - AISC Manual 14th Ed 29

Slab effective width, b e

To each side of the beam, b e one-eighth beam span is limited by: one-half distance to adjacent beam distance to edge of slab

Lowest value controls.


Metal Deck Slab

≥0.5”

≥1.5” w r

≥ 2” steel beam w r h r t c

= average deck width

= height of deck

= thickness of concrete above the deck

Composite Beam - AISC Manual 14th Ed t c

≥ 2” h r

≤ 3”

31

Fully Composite Beam:

Bending Strength



f b

= 0.90 (

W b

= 1.67)



POSITIVE MOMENT

For h / t w



3 .

76

E

F y

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.



OF FULLY COMPOSITE BEAM



FullyCompositeCalcs.PDF



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.


Table 3-19

Nomenclature

(Pg. 3-14)

Y con a b e

6

7

4

5

Beam Flange Enlarged Detail

1

2

3

TFL t f

BFL a /2

Location of effective concrete flange force (

S

Q n

)

Y2

1

5

TFL(pt.1)

BFL(pt.5)

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



To reach fully composite strength, shear studs must transfer

S

Q n for Y1 = 0 (maximum value) listed in Table 3-19.

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


Shear Stud Strength


Strength of each stud, Q n

Equation I8-1

Q n



0 .

5 A sa f c

'E c



R g

R p

A sa

F u

0 .

5 A sa f c

'E c limits value to crushing of concrete around the shear stud.

R g

R p

A sa

F u limits value to strength of individual shear studs.


Q n



0 .

5 A sa f c

'E c



R g

R p

A sa

F u

A sa

= cross sectional area of shear stud

E

F u c

= modulus of elasticity of concrete

= shear stud minimum tensile strength

(typically 65ksi)

R g accounts for number of studs welded in each deck rib and w r

/ h r

.

Values are 1.0, 0.85 or 0.7.

R p 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.


Strength, Q n

, for one shear stud

Table 3-21


Limitations on shear stud placement for 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


Composite strength requires that shear studs transfer

S

Q n each side of the maximum moment in the span.

to

If

S

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


Partially Composite Beam:


F b

= 0.90 (

W b

= 1.67)



OF PARTIALLY COMPOSITE BEAM



PartiallyCompositeCalcs.PDF


Partially Composite Strength can be determined by using

Table 3-19.




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

S

Q n listed in Table 3-19.

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


Composite Beam: Shear Strength


SHEAR STRENGTH

It typically is assumed that the slab carries no shear forces.

Therefore, strength is identical to a bare steel section.


Composite Beam

Deflection Calculations



Fully Composite

I tr

= transformed section moment of inertia

Lower bound values of I tr are found in Table 3-20.

Values assume concrete area equal to

S

Q n

/ F y rather than actual area.



Partially Composite

I eff



I s



S

Q nr



I tr



I s



C f

Equation C-I3-4

I eff

I s

= effective moment of inertia

= moment of inertia of steel section only

I tr

ΣQ nr

= fully composite moment of inertia

= partially composite shear transfer

C f

= fully composite shear transfer




S eff



S s



S

Q nr



S tr

C f



S s



Equation C-I3-5

S eff

S s

= effective elastic section modulus

= elastic section modulus of steel section only

S tr

ΣQ nr

= fully composite elastic section modulus

= partially composite shear transfer

C f

= fully composite shear transfer




Table 3-20 can be used for lower bound values of I eff

.


Retrofit of Steel Moment Frame Connections

Flexural Strength

Chapter I:

Composite Member Design

Fully Composite Beam:

Bending Strength

Bending Strength

Shear Stud Strength

Partially Composite Beam:

Bending Strength

Composite Beam: Shear Strength

Composite Beam

Deflection Calculations

Related documents

Products

Support

Retrofit of Steel Moment Frame Connections

Flexural Strength

Chapter I:

Composite Member Design

Fully Composite Beam:

Bending Strength

Bending Strength

Shear Stud Strength

Partially Composite Beam:

Bending Strength

Composite Beam: Shear Strength

Composite Beam

Deflection Calculations

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