Chapter 11 — Composite Beams (AISC 360-22 Chapter I)

1. Composite Action — Slip vs No-Slip

Picture two planks stacked with no fasteners, spanning between two supports, bent by a load. The bottom of the top plank stretches less than the top of the bottom plank — they slide relative to each other at the interface. This is non-composite behavior: each layer bends about its own centroid, and the combined stiffness is only the sum of the individual I's, EI₁ + EI₂. Now bolt the planks together tightly along their length. The interface can no longer slip; the two layers are forced to have the same strain at the interface, and the combined section behaves as a single deep member with a much larger transformed moment of inertia. That's composite action, and the "bolts" in a steel-concrete floor are the shear studs.

The horizontal shear flow at the interface is q = VQ/I_tr (elastic) — the studs must supply at least this shear per unit length everywhere along the beam, or in ultimate-strength (LRFD) terms, must supply a total horizontal force ΣQ_n at least equal to the smaller of the concrete or steel capacity between the point of zero moment and the point of maximum moment.

2. Effective Slab Width b_eff (§I3.1a)

Not all of a wide slab actually helps resist bending — stress fades away from the beam centerline due to shear lag. AISC caps the width on each side of the beam centerline that may be counted as effective.

• L_span — beam span, center-to-center of supports.
• s_beam — beam spacing (distance to the centerline of the adjacent parallel beam).
• At an edge beam, use the distance to the actual slab edge instead of s/2 on that side.
• Total effective width b_eff = sum of the two individual side widths (each independently limited).

What this means physically: a long-span, closely-spaced beam grid gets almost the full tributary width; a short-span, widely-spaced grid is capped by L/8 on each side and the extra slab width beyond that contributes nothing to bending strength (though it still carries gravity load to the beam).

3. Plastic Neutral Axis — Three Cases

Composite flexural strength (§I3.2a) is found the same way as a plastic-moment calculation for a bare shape — split the section into a compression zone and tension zone at full yield, and find where the two force resultants balance. The complication is that the compression zone is now concrete (weak in tension, strong-ish in compression, taken at a rectangular stress block of 0.85f'_c) sitting on top of a steel shape. Work down from the top of the slab, comparing the maximum available concrete compression force to the maximum available steel tension force:

1. PNA in the slab (most common for typical floor beams) — the full steel section yields in tension, T = A_sF_y, and only part of the slab depth a is needed in compression to balance it: C = 0.85f'_cb_effa = T.
2. PNA in the top flange — even using the ENTIRE slab depth in compression, C_slab < T_{full steel}. The PNA moves down into the flange; part of the flange goes into compression, adding to C, until equilibrium.
3. PNA in the web — heavy/deep steel section relative to a thin slab; the entire top flange plus part of the web must go into compression to balance the tension force in the rest of the web plus bottom flange.

In practice, AISC Manual Tables 3-19 (F_y = 50 ksi) tabulate φ_bM_n directly versus PNA location (rows labeled by distance Y1 below the top of steel) and percent composite action — this chapter shows the underlying hand calculation those tables automate.

4. Full vs Partial Composite Action

"Full" composite means enough studs are provided that the horizontal shear transferred, ΣQ_n, equals or exceeds the smaller of the two possible force limits — concrete crushing or steel yielding:

• A_c = effective concrete area = b_eff·t_c (concrete above the deck flutes only, ignore concrete inside/below ribs).
• A_s = area of the steel shape.
• Full composite: enough studs that ΣQ_n ≥ min(concrete, steel) — the PNA analysis of §3 above applies directly.
• Partial composite: fewer studs are provided (often to save cost when deflection, not strength, controls). Use ΣQ_n actually installed as the horizontal force V' in the PNA analysis — the effective compression block a becomes a = ΣQ_n/(0.85f'_cb_eff), smaller than the full-composite case, and M_n drops smoothly with % composite.
• AISC requires at least 25% composite action (ΣQ_n ≥ 0.25·min) for the interpolation approach in the Manual tables to be valid.

What this means physically: partial composite design trades some flexural strength for fewer, cheaper studs — a common owner-driven cost decision when the beam has strength to spare after other checks.

5. Shear Stud Strength Q_n (§I8.2a)

Each headed stud has a nominal shear (horizontal shear-transfer) capacity that is the lesser of the stud shearing off and the surrounding concrete crushing/splitting:

• A_sa — cross-sectional area of the stud shank (for a ¾″ stud, A_sa = 0.442 in²).
• E_c — concrete modulus, E_c = w_c^1.5·33·√f'_c (psi, w_c in pcf); for 145 pcf NWC at f'_c = 4 ksi, E_c ≈ 3,644 ksi.
• F_u — stud material tensile strength, typically 65 ksi.
• R_g — deck-geometry reduction factor (Table I8.2a): 1.0 for solid slab or one stud per rib with deck ∥ beam; 0.85 for two studs per rib; 0.7 for three-plus studs per rib.
• R_p — stud position factor: 0.75 for studs welded through deck (deck ⊥ or ∥, strong or weak position); 1.0 in a few specific favorable deck configurations noted in Table I8.2a — most practical designs use 0.75 (⊥ deck, "not through-deck welded in a haunch," standard case) or 0.6 (weak position, ⊥, unfavorable).

For a common case — ¾ in. dia. stud, deck ⊥ to the beam, standard weak-position welding, 3 in. deck, f'_c = 4 ksi NWC, one stud per rib — Q_n works out to roughly 17–21 kips depending on R_p; the AISC Manual Table 3-21 tabulates common combinations directly so hand computation of Eq. I8-1 is rarely needed in practice, but every input above should be checked against the actual deck/stud submittal.

6. Deck Orientation Effects

Steel deck ribs run either parallel or perpendicular to the supporting beam, and this changes both A_c and Q_n:

• Deck ⊥ to beam (most common for filler beams) — ribs interrupt the slab, so only concrete above the deck flutes (t_c) counts for A_c; studs sit inside individual ribs, subject to R_g, R_p reductions above.
• Deck ∥ to beam (typical for girders) — the rib runs along the beam, so the concrete inside the rib directly over the beam can be included in A_c if the rib width w_r ≥ 2 in.; R_g = R_p = 1.0 unless the average rib width < 2 in.

7. Horizontal Shear Force Transfer & Stud Layout

Studs need not be uniformly spaced by calculation — AISC only requires the CUMULATIVE ΣQ_n between any point and the nearest point of zero moment to be at least equal to the moment demand at that point (§I8.3), but uniform spacing between the maximum-moment section and each end is standard practice and satisfies this automatically for typical uniform-load beams.

8. Construction Stage (Unshored) Checks

Unless temporary shoring is specified, the steel beam alone — with zero composite action — must carry the wet concrete weight, the metal deck, and a construction live load (commonly 20 psf per ASCE 7 / SDI) before the concrete has cured enough to act compositely.

Lateral bracing of the compression (top) flange during the pour is provided only by the deck attachment and temporary shoring/edge form ties — this must be verified separately (often more conservative L_b than the final composite condition, where the hardened slab braces the top flange continuously).

9. Shear Strength — Steel Web Alone

Composite action increases flexural (bending) capacity dramatically, but it does essentially nothing for shear — the concrete slab is not relied upon to resist beam shear. AISC takes the ENTIRE beam shear on the bare steel web, exactly as in Chapter G, regardless of composite percentage:

10. Deflection with the Lower-Bound Moment of Inertia I_LB

For live-load (post-composite) deflection, using the fully-transformed elastic I_tr over-predicts stiffness for a partial-composite or a not-yet-fully-cracked section. AISC Commentary provides the lower-bound moment of inertia I_LB — a closed-form transformed-section value based on the actual PNA location for the installed ΣQ_n, giving a conservative (slightly larger) deflection than the fully elastic transformed section:

• I_x, A_s, d — bare steel shape properties.
• Y₂ — distance from top of steel to the top of the slab (t_c + t_deck, or slab top to steel top).
• Y_ENA — distance from bottom of the steel section (or top of steel, per Manual convention) to the elastic neutral axis of the transformed section, computed from ΣQ_n/F_y acting as an "equivalent concrete area at the top of steel."
• AISC Manual Table 3-20 tabulates I_LB directly for standard W-shapes vs percent composite — matching this formula.

What this means physically: I_LB is always between I_x (bare steel, lower bound) and I_tr (fully composite elastic, upper bound) — it recognizes that concrete cracking and imperfect stud slip make the beam a little less stiff than idealized elastic transformed-section theory predicts.

Design Workflow

1. Determine b_eff from span and beam spacing (§I3.1a).
2. Compute A_c = b_eff·t_c and both limiting horizontal shear forces 0.85f'_cA_c and F_yA_s; take the smaller as the full-composite target V'.
3. Select a trial stud size/spacing, compute Q_n per Eq. I8-1 with the correct R_g, R_p for the deck orientation, and determine ΣQ_n installed.
4. Locate the PNA using the actual ΣQ_n (full or partial) and compute φ_bM_n; compare to M_u.
5. Check bare-steel shear φ_vV_n against V_u (composite action does not help shear).
6. Check the UNSHORED construction stage: bare beam φ_bM_p and Δ_constr against wet-concrete + construction live load, including top-flange bracing during the pour.
7. Check post-composite live-load deflection using I_LB against the applicable limit (Ch. 18) and specify camber if needed.

Additional Design Aids & Stratified Equations

📖 Using the AISC Manual — Composite Beams

Companion reference: Manual Part 3 — Table 3-19 (composite W-shapes with concrete slab) & 3-20 (lower-bound φM_n) & 3-21 (shear-stud strength Q_n). In practice, engineers rarely compute every quantity from first principles — the AISC Steel Construction Manual (16th Ed.) tabulates φR_n (or R_n/Ω) for every rolled shape so you can pick a member in seconds. Formulas remain essential for understanding, verifying, and for anything the tables do not cover.

Typical workflow: pick required φM_n → enter Table 3-19 at Y₂≈5.5″ (4.5″ slab − 1″ compression) → find lightest W meeting φM_n at 100% composite → from Table 3-21 count studs. Done.