Composite Members

Introduction to composite steel-concrete construction.
Composite construction synergistically combines the high tensile strength, ductility, and rapid erection speed of structural steel with the massive compressive strength, stiffness, and fire resistance of concrete. The most ubiquitous application is a steel beam physically connected to a concrete floor slab via shear connectors, forcing them to act as a single, unified structural element.

Composite Beams

The fundamental mechanics of composite floor systems.
A steel beam supporting a concrete slab acts as a massive T-beam only if the two materials are forced to act together. Without a physical connection, the concrete slab simply slips over the top flange of the steel beam as it bends, and they act as two independent, much weaker beams.

Key Components of a Composite Beam System

  • Steel Beam: Typically a standard W-shape. Because the concrete slab will handle almost all the compression, the top flange of the steel beam is technically redundant. However, it is required for stability during construction and to provide a surface for welding the shear connectors.
  • Concrete Slab: Usually reinforced concrete cast over a profiled (corrugated) steel deck. The deck acts as permanent formwork and bottom tensile reinforcement for the slab itself spanning between beams.
  • Shear Connectors: Headed steel studs (typically 3/4" diameter) welded through the steel deck directly to the top flange of the steel beam. These studs physically embed into the concrete, preventing horizontal slip between the slab and the beam, thus transferring the horizontal shear forces required for composite action.

Construction Phases: Shored vs. Unshored

How the beam is supported during the concrete pour determines its critical design stages.
  • Unshored Construction: The most common and economical method. The steel beam alone must support its own weight, the weight of the wet (uncured) concrete, the metal deck, and temporary construction live loads (workers, equipment). The steel beam must be designed to carry these loads independently. After the concrete cures (fc′f'_c is reached), the composite section supports all superimposed dead loads (ceilings, flooring) and the full occupancy live load.
  • Shored Construction: Temporary shores (props) support the steel beam at intervals during pouring. The steel beam carries almost no load. The composite section must support the entire load (including the slab's massive dead weight) once the shores are removed. This results in a smaller steel beam but higher construction costs and delays due to shoring removal.

Effective Width of the Concrete Flange (beb_e)

Determining how much of the slab acts with the beam.
The entire width of the floor slab cannot be assumed to act compositely with a single beam. Due to shear lag in the concrete, the compressive stress is highest directly over the beam and dissipates outward. AISC limits the effective width (beb_e) of the concrete slab contributing to the composite section to the minimum of:
  • One-eighth of the beam span (L/8L/8) on each side of the beam centerline. (Total width = L/4L/4).
  • One-half the distance to the adjacent beam (S/2S/2) on each side. (Total width = SS, the beam spacing).
  • The distance to the edge of the slab.

Elastic Analysis: Transformed Section Method

Calculating properties for serviceability (deflection) checks.
To calculate elastic properties (deflection, elastic stress under service loads), the composite section of two different materials is artificially transformed into an equivalent section of a single material (usually steel) using the modular ratio nn.
n=EsEcn = \frac{E_s}{E_c} btr=benb_{tr} = \frac{b_e}{n}
Where btrb_{tr} is the transformed width of the concrete slab, effectively turning the 3000−40003000-4000 psi concrete into a very narrow strip of 29,00029,000 ksi steel. The moment of inertia of this transformed section (ItrI_{tr}) is used to calculate deflections. However, concrete creeps over time under sustained dead loads, reducing its effective stiffness. A modified modular ratio (2n2n or 3n3n) is often used for calculating long-term dead load deflections.

Plastic Moment Capacity (MnM_n)

Calculating the ultimate flexural strength using plastic analysis.
At the ultimate limit state (factored loads), the composite beam is assumed to be fully plastic. The entire steel section yields either in tension or compression (FyF_y), and the effective width of the concrete slab yields uniformly in compression at 0.85fc′0.85f'_c (the Whitney stress block).
The location of the Plastic Neutral Axis (PNA)—the line separating tension from compression—determines the exact stress distribution. Because the concrete slab is massive, the PNA is almost always much higher than the geometric centroid of the steel beam.
  • Case 1: PNA in the Concrete Slab. The entire steel beam is yielding in tension (AsFyA_s F_y). A portion of the concrete slab depth (aa) is in compression (0.85fc′bea0.85 f'_c b_e a). This is the most common and efficient case. MnM_n is simply the tension force times the moment arm between the centroids of the two blocks.
  • Case 2: PNA in the Steel Top Flange. The concrete is fully in compression, and the top sliver of the steel flange is also in compression. The rest of the steel is in tension.
  • Case 3: PNA in the Steel Web. A deep compression block extends down into the steel web. This usually only occurs with very thick steel flanges or very thin/weak concrete slabs.

Composite Section: Plastic Neutral Axis (PNA)

PNA
$C$
$T$
  • Controlling Shear Transfer ($V'$): 500 kips
  • PNA Location: Case 2: PNA in Steel Flange
  • Increasing the number of shear studs or concrete strength forces the PNA higher into the slab, increasing the moment arm and the flexural capacity.

Horizontal Shear Transfer ($V')

The critical force the shear studs must carry.
For full composite action to exist, the shear connectors must be capable of transferring the maximum possible horizontal shear force (V′V') between the point of maximum positive moment (midspan) and the point of zero moment (the support). This force is simply the lesser of the maximum compressive force the concrete can carry, or the maximum tensile force the steel can carry.
The total required horizontal shear force (V′V') is the minimum of:
  1. Concrete Crushing Strength: 0.85fc′Ac0.85 f'_c A_c (where AcA_c is the solid concrete area within the effective width).
  2. Steel Yielding Strength: AsFyA_s F_y (where AsA_s is the total area of the steel beam).
The total strength of all the shear studs provided between the support and midspan (∑Qn\sum Q_n) must equal or exceed this V′V' value for Full Composite Action.

Shear Connectors (QnQ_n)

The strength of individual headed stud anchors.
The nominal shear strength of one headed stud anchor embedded in solid concrete is based on either the stud shearing off or the concrete crushing around it.
Qn=0.5Ascfc′Ec≤RgRpAscFuQ_n = 0.5 A_{sc} \sqrt{f'_c E_c} \le R_g R_p A_{sc} F_u
Where:
  • AscA_{sc} = Cross-sectional area of the stud shank.
  • fc′f'_c = Concrete compressive strength.
  • EcE_c = Concrete modulus of elasticity (wc1.5fc′w_c^{1.5} \sqrt{f'_c}).
  • FuF_u = Minimum tensile strength of the stud (typically 65 ksi).
  • RgR_g and RpR_p = Crucial reduction factors (AISC Section I3.2d) that account for the geometry of the metal deck (rib orientation, number of studs per rib) and the stud's position within the deck rib. If the deck ribs run perpendicular to the beam, the stud is weaker because there is less solid concrete bearing against it.

Partial Composite Action

If the number of studs provided (∑Qn\sum Q_n) is less than V′V', the beam is in Partial Composite Action. The flexural strength is reduced, but it is often still significantly higher than the bare steel beam. The minimum allowed composite action is 25% (i.e., ∑Qn≥0.25V′\sum Q_n \ge 0.25 V').

Partial Composite Action and Steel Deck Orientation

Designing for situations where full composite behavior is unachievable or unnecessary.
Achieving 100% composite action means providing enough shear studs (∑Qn\sum Q_n) to fully develop the maximum possible plastic moment capacity of the steel beam or the compressive capacity of the concrete slab, whichever is smaller.
However, full composite action is often not required to satisfy strength limits, or it may be physically impossible to fit the required number of studs on the beam flange due to spacing constraints. In these cases, Partial Composite Action is utilized.

Partial Composite Action Limitations

In partial composite design, fewer studs are used. The shear transferred at the interface is governed by the actual strength of the provided studs (∑Qn\sum Q_n), which becomes the limiting factor in the plastic moment calculation.
AISC requires that the partial composite action must be at least 25% (∑Qn≥0.25×min(Cc,Ts)\sum Q_n \ge 0.25 \times \text{min}(C_c, T_s)). Below 25%, the slip at the interface becomes excessive, the shear studs become prone to fatigue or sudden failure, and the deflection predictions become highly inaccurate.

Steel Deck Rib Orientation

In modern building construction, concrete slabs are rarely cast on flat plywood. They are cast on corrugated formed steel decking. The orientation of the deck ribs relative to the steel beam profoundly affects the strength of the shear studs:
  • Deck Ribs Perpendicular to Beam: The most common scenario for filler beams. The stud is welded through the deck into the beam flange, sitting inside the deck rib. The concrete surrounding the stud is weaker because of the void space created by the ribs. A severe reduction factor (Rg×RpR_g \times R_p) must be applied to the nominal stud strength (QnQ_n).
  • Deck Ribs Parallel to Beam: Common for girders. The concrete around the stud is typically solid and continuous. The stud strength reduction is minimal or non-existent, provided the deck is split over the girder to allow solid concrete encasement.

Continuous Composite Beams

Behavior in negative moment regions.
In continuous beams (spanning over an interior support), the bending moment reverses. The top flange is in tension, and the bottom flange is in compression.
  • The concrete slab is useless in tension (it cracks).
  • Therefore, in the negative moment region, the composite section consists only of the steel beam plus the longitudinal steel reinforcing bars (rebar) embedded in the slab within the effective width. The concrete itself is ignored.
  • The steel beam's bottom flange, now in massive compression, must be carefully checked for local buckling and lateral-torsional buckling (since the bottom flange is typically unbraced).

Composite Columns

Combining steel and concrete for massive axial capacity.
Composite columns are heavily used in high-rise buildings and are categorized into two types:
  1. Encased Composite Columns: A structural steel shape (W-shape) completely surrounded by reinforced concrete, including longitudinal rebar and transverse ties (hoops).
  2. Filled Composite Columns: A Hollow Structural Section (HSS round, square, or rectangular tube) completely filled with concrete.

Advantages of Composite Columns

  • Increased Axial Capacity: The concrete carries a massive portion of the compressive load (0.85fc′Ac0.85 f'_c A_c).
  • Increased Buckling Resistance: The concrete drastically increases the effective bending stiffness (EIeffEI_{eff}), delaying global Euler buckling.
  • Local Buckling Prevention: In filled columns, the concrete core prevents the thin steel HSS walls from buckling inward. In encased columns, the concrete encasement prevents the W-shape flanges from buckling outward.
  • Fire Protection: Encased columns inherently provide excellent fireproofing for the steel core. Filled columns provide some fire resistance due to the thermal mass of the concrete core.
  • Formwork Elimination: For filled columns, the steel HSS acts as permanent, structural formwork, speeding up construction significantly.

Design Approach (AISC Chapter I2)

The design follows the same fundamental buckling principles as bare steel columns (Chapter E) but uses modified, equivalent properties to account for the multiple materials.
  • Nominal Axial Compressive Strength (PoP_o): The theoretical squash load (length = 0). It is the sum of the yield strengths of all components: Po=AsFy+AsrFyr+0.85Acfc′P_o = A_s F_y + A_{sr} F_{yr} + 0.85 A_c f'_c (where AsrA_{sr} is the area of longitudinal rebar).
  • Effective Stiffness (EIeffEI_{eff}): The modified bending stiffness used to calculate the elastic buckling load (PeP_e). The concrete's contribution is reduced by a factor (C1C_1 or C3C_3) to account for cracking and creep. EIeff=EsIs+EsIsr+C1EcIcEI_{eff} = E_s I_s + E_s I_{sr} + C_1 E_c I_c
  • The calculated PoP_o and PeP_e are then plugged into the standard AISC column buckling equations (the 0.6580.658 or 0.8770.877 formulas) to determine the final design strength ϕPn\phi P_n.
Key Takeaways
  • Composite beams use headed shear studs welded through the metal deck to ensure the concrete slab and steel beam act as a single unit, massively increasing flexural capacity and stiffness compared to bare steel.
  • The beam's design criteria differ depending on whether construction is shored or unshored. Unshored steel beams must be independently strong enough to carry the massive wet concrete load.
  • The Plastic Neutral Axis (PNA) dictates the ultimate stress distribution. In an optimized design, the PNA lies within the concrete slab, meaning the entire steel beam yields in tension.
  • Shear connectors (QnQ_n) transfer the horizontal shear force (V′V'); their strength is heavily reduced (RgR_g, RpR_p) if the metal deck ribs run perpendicular to the beam.
  • In continuous beams over supports (negative moment), the concrete cracks and is ignored; only the steel beam and slab rebar provide strength.
  • Composite columns (encased or filled) provide vastly higher axial capacity and better buckling resistance due to the added compressive area and stiffness (EIeffEI_{eff}) of the concrete core/encasement.
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