# D1.C.9 Composite Beam Design per the AISC LRFD 3rd edition code

The design of composite beams per the 3rd edition of the American LRFD code has been implemented. The salient points of this feature are as follows:

### Nomenclature of composite beams

where
 t = thickness of slab As = area of steel beam fc = ultimate compressive strength of concrete b = effective slab width hr = rib height
Table 1. Composite Beam Design Parameters for AISC-LRFD
Parameter Name Default Value Description
RBH 0.0 in. Rib height for steel form deck.
EFFW Value used in analysis Effective width of the slab.
FPC Value used in analysis Ultimate compressive strength of the concrete slab.

## Theoretical Basis

1. Find the maximum compressive force carried by concrete as:

0.85 fc⋅b⋅t

2. Find the maximum tensile force carried by the steel beam as:

As . fy

Tensile strength of concrete is ignored.

3. If step 1 produces a higher value than step 2, plastic neutral axis (PNA) is in the slab. Else, it is in the steel beam.

Location of the Plastic Neutral Axis (PNA) defines the moment capacity:

• Case 1: PNA in the slab

Find the depth of the PNA below the top of the slab as:

0.85fc⋅b⋅a = As⋅fy

Rearranging terms:

a = As⋅fy/(0.85fc⋅b)

### Plastic neutral axis in the concrete slab

Lever arm

e = d/2 + hr + t - a/2

Moment Capacity

ϕb(As⋅fy)e

• Case 2: PNA in Steel Beam

 Cs + Cb = Tb

where Cs = compressive force in slab = 0.85fc⋅b⋅t Cb = compressive force in steel beam Tb = tensile force in steel beam

Since the magnitude of Cb + |Tb| = As⋅fy

Substituting for Tb = (As⋅fy - Cb) gives:

Cs+ Cb = As⋅fy - Cb

Rearranging terms:

Cb= (As⋅fy - Cs)/2

Determine whether the PNA is within the top flange of the steel beam or inside the web:

where Cf = maximum compressive force carried by the flange = Af⋅fy Af = area of the flange

If Cf ≥ Cb, the PNA lies within the flange (Case 2A)

If Cf < Cb, the PNA lies within the web (Case 2B)

• Case 2A: PNA in Flange of Steel Beam

Calculate:

y = Cf/(bf⋅fy)

where bf = width of the flange

The point of action of the tensile force is the centroid of the steel are below the PNA. After find that point, e1 and e2 can be calculated.

### Plastic neutral axis falls within the top flange

Moment Capacity

ϕb(Cf⋅e1 + Cs⋅e2)

• Case 2B: PNA in Web of Steel Beam

### Plastic neutral axis falls within the web

where Cw = compressive force in the web = Cb - Cf g = Cw/(tw⋅fy) tw = thickness of the web

The point of action of the tensile force is the centroid of the steel area below the PNA. After finding that point, e1, e2, and e3 can be calculated.

Moment Capacity

ϕb(Cs⋅e2 + Cf⋅e1 + Cw⋅e3)

Utilization Ratio = Applied Moment / Moment Capacity

## Notes

1. Rib Height is the distance from top of flange of steel beam to lower surface of concrete.

2. If the slab is flush on top of the steel beam, set the Rib Height to zero.

### Steel deck form ribs

3. For moments which cause tension in the slab (called positive moments in STAAD.Pro convention), design of the beam is presently not carried out.

4. Shear connectors are presently not designed.

5. Member selection is presently not carried out.

6. In order to design a member as a composite beam, the member property specification during the analysis phase of the data must contain the CM attribute. See TR.20.1 Assigning Properties from Steel Tables for details.

## Example

```STAAD SPACE
…
MEMBER PROPERTY
1 TA CM W12X26 CT 6.0 FC 4.0 CW 40.0
…
PERFORM ANALYSIS
…
PARAMETER
CODE LRFD
RBH 5.0 MEMB 1
CHECK CODE MEMB 1
FINISH```