Composite Beam Design Guide — AISC 360 Chapter I

Effective Slab Width, Shear Studs, PNA Location, and Full vs. Partial Composite Action

Composite beam construction combines a steel W-shape with a reinforced concrete slab connected by headed shear studs to act as a single structural unit. The concrete slab resists compression while the steel section resists tension, producing a much larger effective moment arm and section modulus than either material alone. Composite beams are standard practice in steel-framed office buildings, parking garages, hospitals, and industrial structures. AISC 360-22 Chapter I (Design of Composite Members) governs composite beam design in the United States, with supplementary provisions in AISC Specification for Structural Steel Buildings Section I1 through I8.

PRELIMINARY — NOT FOR CONSTRUCTION. All results are for educational and reference use only. Must be independently verified by a licensed Professional Engineer (PE) or Structural Engineer (SE) before use in any project.

When to Use Composite Beams

Composite beams provide 50-90% more moment capacity than the equivalent non-composite bare steel beam, enabling lighter steel sections, shallower floor-to-floor heights, or longer spans. The cost premium for shear studs is small compared to the steel weight savings.

Composite vs Non-Composite Capacity Comparison

Lighter beams benefit the most from composite action. Heavier beams see diminishing returns because the bare steel capacity is already high and the concrete slab compression capacity is the limiting factor.

Effective Slab Width — AISC I3.1a

The effective slab width defines how much of the concrete floor slab participates in resisting compression. Per AISC 360 Section I3.1a, the effective width on each side of the beam centerline is the minimum of:

1. L/8 — one-eighth of the beam span (center-to-center of supports)
2. s/2 — one-half of the distance to the adjacent beam web (center-to-center beam spacing)
3. Distance to the slab edge — for exterior beams

The total effective width: b_eff = 2 * min(L/8, s/2, edge distance)

Example: Interior beam, 30 ft span (L = 360"), 10 ft beam spacing (s = 120"):

• L/8 = 360/8 = 45"
• s/2 = 120/2 = 60"
• b_eff per side = min(45", 60") = 45"
• Total b_eff = 2 x 45" = 90" = 7.5 ft

Edge beam example: Same span and spacing, but 5 ft to slab edge:

• b_eff interior side = 45"
• b_eff exterior side = min(45", 60") = 45" but limited by 5 ft = 60" → not limiting
• Total b_eff = 45" + 45" = 90"

The L/8 limit typically governs for longer spans and wider beam spacing (s/2 governs for closely spaced beams). The effective width is measured perpendicular to the beam span and applies to the full beam length per I3.1a, although the concrete stress distribution varies longitudinally.

Shear Stud Connectors — AISC I8

Stud Geometry and Material

Standard headed shear studs per AWS D1.1:

Stud diameter must not exceed 2.5 times the flange thickness per AISC I8.1: d_stud <= 2.5 * t_f. This prevents flange deformation during welding that could reduce fatigue life.

Nominal Shear Strength of One Stud — AISC I8.2a

For a stud embedded in a solid concrete slab (no metal deck):

Qn = 0.5 * Asa * sqrt(f'_c _ E_c) <= R_g _ Rp * Asa * F_u

Where:

• A_sa = cross-sectional area of stud shank (in^2)
• f'_c = concrete compressive strength (ksi)
• E_c = w_c^1.5 * sqrt(f'_c) per ACI 318 (ksi), with w_c in lb/ft^3
• For normal-weight concrete (w*c = 145 pcf): E_c = 33 * 145^1.5 _ sqrt(f'_c) / 1000 = 57,000 * sqrt(f'_c) / 1000
• F_u = 65 ksi specified minimum tensile strength of stud steel per AWS D1.1
• R_g = group effect factor (1.0 for one stud, 0.85 for two studs per rib, 0.70 for >=3)
• R_p = position effect factor for deck ribs

Example: 3/4" diameter stud in normal-weight 4 ksi concrete, solid slab (no deck, R_g = 1.0, R_p = 1.0):

• A_sa = pi * 0.75^2 / 4 = 0.442 in^2
• Ec = 33 * 145^1.5 _ sqrt(4.0) / 1000 = 33 _ 1746 _ 2 / 1000 = 3,834 ksi (use simplified 57sqrt(f'_c)1000 for US units: 57sqrt(4000) * 1000 = 3,605 ksi)
• Q*n_concrete = 0.5 * 0.442 _ sqrt(4 _ 3605) = 0.5 _ 0.442 * 120.1 = 26.5 kips
• Q*n_steel = 1.0 * 1.0 _ 0.442 * 65 = 28.7 kips
• Q_n = min(26.5, 28.7) = 26.5 kips

Note: For studs in composite deck with ribs perpendicular to the beam, the concrete contribution is multiplied by a reduction factor R_p:

Rp = 0.6 * (wr / h_r) * [(H_s / h_r) - 1.0] <= 1.0 for perpendicular ribs

Where w*r = average rib width, h_r = rib height, H_s = stud height after welding (typically h_r + 1.5" minimum per I8.2c). For typical 3" deep deck with 6" ribs: R_p = 0.6 * (6/3) _ [(5/3) - 1.0] = 0.6 _ 2 _ 0.667 = 0.80. This reduces the stud capacity by approximately 20% compared to a solid slab.

Number of Studs Required

For full composite action: N_full = V_h / Q_n where V_h is the total horizontal shear to be transferred between the point of maximum moment and the point of zero moment. Per AISC I3.2d:

V*h_full = min(0.85 * f'_c _ A_c, A_s * F_y)

Where A_c = b_eff * t_slab (effective slab area in compression), A_s = area of steel beam.

For partial composite action: N_partial = degree * N_full, where the degree of shear connection (eta) must be >= 25% per I3.2d(1). Partial composite moment capacity:

M_sp = M_s_bare + (n/N_full) * (M_s_full - M_s_bare)

Linear interpolation is conservative and permitted per AISC Commentary I3.2d.

Plastic Neutral Axis (PNA) Location

The PNA location is the key to determining composite moment capacity. Per AISC I3.2d, two cases exist:

Case 1 — PNA in Concrete Slab (a <= t_slab)

This occurs when the concrete compression capacity exceeds the steel tensile capacity: 0.85 _ f'_c _ beff * tslab >= A_s * F_y. The steel beam is entirely in tension.

Compression block depth: a = (As * Fy) / (0.85 * f'_c * b_eff)

Moment arm: d1 = d/2 + t_slab - a/2 (measured from top of slab to centroid of steel in tension)

Nominal moment capacity: Mn = A_s * Fy * d1

Criteria: a <= t_slab (PNA within slab depth). If a > t_slab, go to Case 2.

Case 2 — PNA in Steel Beam (a > t_slab)

This occurs when the steel beam capacity is larger than the slab compression capacity. The PNA drops into the steel flange or web. The steel beam is partially in compression above the PNA and in tension below.

Concrete compression: C*c = 0.85 * f'_c _ b_eff * t_slab

Steel tension required: T = A_s * F_y

Steel compression required for equilibrium: C_s = (T - C_c) / 2 (half in compression, half adjusting for concrete)

The PNA location is solved for by iterating through the steel cross-section to find the depth where C_c + C_s_above_PNA = T_s_below_PNA. The moment capacity is then:

Mn = C_c * dcc + C_s * d_cs + T_s * d_ts

where d_cc, d_cs, d_ts are the moment arms from the compressive and tensile force resultants to the PNA.

For W-shapes, closed-form equations exist in AISC Manual Part 3 for both cases.

Worked Example — Interior Composite Beam

Design: 30 ft span interior composite beam, 10 ft beam spacing, 4.5" lightweight concrete slab on 3" metal deck (total slab = 7.5" from top of beam), f'_c = 4 ksi, F_y = 50 ksi, 3/4" diameter studs, 25% partial composite action for economy.

Step 1 — Loads and moments:

• Slab (4.5" LW concrete @ 110 pcf + 3" deck @ 2 psf): DL_slab = 4.5/12 * 110 + 2 = 43 psf + self-weight of deck
• Superimposed DL (mech, ceiling, partitions): SDL = 15 psf
• Live load (office): LL = 50 psf + 20 psf partitions = 70 psf
• Tributary width = 10 ft
• w_DL = (43 + 15) * 10 + beam weight = 580 plf + beam weight
• w_LL = 70 * 10 = 700 plf
• M_DL = w_DL * L^2 / 8 (steel beam alone resists pre-composite DL)
• M_LL = w_LL * L^2 / 8 (composite section resists LL)

Step 2 — Try W18x35 (A_s = 10.3 in^2, d = 17.7", I_x = 510 in^4, b_f = 6.00", t_f = 0.425")

• w_beam = 35 plf
• Total DL = 580 + 35 = 615 plf
• M_DL = 0.615 * 30^2 / 8 = 69.2 kip-ft (bare steel)
• M_LL = 0.700 * 30^2 / 8 = 78.8 kip-ft (composite)
• M_u = 1.269.2 + 1.678.8 = 83.0 + 126.1 = 209.1 kip-ft
• Check bare steel: phi*M_n_W18x35 = 249 kip-ft > 209.1 → OK non-composite too, but composite will provide reserve capacity for vibration and deflection

Step 3 — Effective slab width:

• L/8 = 360"/8 = 45" per side
• s/2 = 120"/2 = 60" per side
• b_eff = 2 * 45 = 90"

Step 4 — Check PNA case:

• afull = A_s * Fy / (0.85 * f'_c _ b_eff) = 10.3 _ 50 / (0.85 _ 4 _ 90) = 515 / 306 = 1.68"
• t_slab = 4.5" (concrete above deck only — deck concrete is in tension zone and neglected)
• a = 1.68" < 4.5" → PNA in slab (Case 1) — full composite action

Step 5 — Full composite moment capacity:

• d1 = d/2 + t_slab - a/2 = 17.7/2 + 4.5 - 1.68/2 = 8.85 + 4.5 - 0.84 = 12.51"
• Mn_full = A_s * Fy * d1 / 12 = 10.3 _ 50 _ 12.51 / 12 = 537 kip-ft
• phi = 0.90 per AISC I3.2
• phi*M_n_full = 0.90 * 537 = 483 kip-ft

Step 6 — Partial composite (25%):

• eta = 0.25
• M_s_25 = M_bare + 0.25 * (M_full - M_bare)
• M_bare = phi*M_n_W18x35 = 249 kip-ft
• M_s_25 = 249 + 0.25 * (483 - 249) = 249 + 58.5 = 307.5 kip-ft
• Check: M_u = 209.1 kip-ft < 307.5 kip-ft → OK

Step 7 — Number of studs required:

• V*h_full = min(0.85 * 4 _ 90 _ 4.5, 10.3 _ 50) = min(1,377, 515) = 515 kips
• Q_n per stud (reduced for deck ribs): For 3/4" stud with deck ribs perpendicular:
  • R*p = 0.6 * (wr/hr) _ (Hs/hr - 1.0). Assume wr = 6", hr = 3", Hs = 5"
  • R*p = 0.6 * 2 _ (5/3 - 1.0) = 0.6 _ 2 _ 0.667 = 0.80
  • Q_n_concrete = 26.5 kips (from earlier calculation)
  • Qn = 0.80 * 26.5 = 21.2 kips (check upper bound: Rg * Rp * Asa * F*u = 1.0 * 0.80 _ 0.442 * 65 = 23.0 kips, not governing)
• N_full = V_h_full / Q_n = 515 / 21.2 = 24.3 → 26 studs total (13 pairs)
• N_25 = 0.25 * 26 = 6.5 → 8 studs (4 pairs, spaced evenly between max moment and zero moment)
• Minimum degree = 25% → 25% * 26 = 6.5 studs minimum. 8 studs > 6.5 → OK

Step 8 — Deflection checks:

• Pre-composite DL deflection (bare W18x35): delta*1 = 5 * 0.615 _ 30^4 _ 12^3 / (384 _ 29000 * 510) = 0.48" = L/750 < L/360 → OK
• Composite LL deflection: Itransformed (short-term n = E_s/E_c = 29000/3605 = 8.04). The transformed slab width = b_eff/n = 90/8.04 = 11.2". Compute transformed I_x_comp (with slab area 4.5" x 11.2" = 50.4 in^2 at top of composite section). Approximating: I_comp ≈ 2.0 * Isteel = 2.0 * 510 = 1,020 in^4 for quick hand check. delta*LL = 5 * 0.700 _ 30^4 _ 12^3 / (384 _ 29000 * 1020) = 0.33" = L/1090 < L/360 → OK
• Total long-term: use n_LT = 2*n = 16.08, I_comp_LT ≈ 1.5 * I_steel = 765 in^4. delta_total ≈ 0.48 (DL1) + 0.25 (SDL) + 0.33 (LL) = 1.06" = L/340 > L/240 → OK, but consider camber = 0.75" to offset.

Step 9 — Stud layout:

• 8 studs for 25% partial composite per half-span (16 total for full span)
• Spacing = L_half / 4 = 15 ft / 4 = 3.75 ft (45") between pairs
• Max spacing per AISC I8.2d: 8 _ t_slab = 8 _ 4.5 = 36" → adjust to 4 pairs = 3.75 ft pair spacing, or use 6 pairs (24 total studs) for tighter spacing

Construction Considerations

Shoring vs Unshored Construction

• Shored: Temporary supports carry the fresh concrete weight until the concrete reaches 75% of f'_c. The composite section resists all dead + live loads. Provides the most efficient composite design but adds shoring cost and construction schedule impact.
• Unshored: The bare steel beam carries the fresh concrete dead load alone. Only superimposed dead loads and live loads are resisted by the composite section. More common in practice because it avoids shoring cost and schedule delays. Pre-cambering is recommended for unshored construction to offset dead load deflections.

Camber Recommendations

Pre-camber the steel beam to offset approximately 75-80% of the pre-composite dead load deflection. For the W18x35 example: camber = 0.75 * 0.48" = 0.36" → specify 3/8" camber. AISC Code of Standard Practice Section 6.3.2 requires cambers less than 3/4" to be specified in 1/4" increments.

Metal Deck Orientation

• Deck ribs perpendicular to beam: R_p reduction applies per I8.2a (most common for floor beams)
• Deck ribs parallel to beam: No R_p reduction, but minimum stud height and spacing rules change per I8.2c. The stud must extend at least 1.5" above the top of the deck.

Frequently Asked Questions

What is the minimum concrete strength for composite beam design?

AISC I1.2 requires a minimum f'_c of 3 ksi for normal-weight concrete and 4 ksi for lightweight concrete in composite beams. Lower strengths reduce shear stud capacity (Qn depends on sqrt(f'_c)) and increase the required slab thickness to develop the full compression capacity.

How does lightweight concrete affect composite beam design?

Lightweight concrete (90-120 pcf) reduces the modulus of elasticity E_c, which reduces shear stud capacity by approximately 15-25% compared to normal-weight concrete at the same f'_c. The AISC I8.2a equation for Qn uses E_c explicitly, so the reduction is computed directly. Lightweight concrete also requires a higher minimum f'_c (4 ksi vs 3 ksi) per AISC I1.2. The density factor lambda per ACI 318 is not used in the AISC stud strength equation — only w_c enters through E_c.

Can I use composite beams with metal deck parallel to the beam?

Yes. Per AISC I8.2c, when deck ribs are parallel to the beam, the R_p factor equals 1.0 (no reduction), but the stud height must extend at least 1.5" above the deck surface after welding, and the minimum stud length is 4" to engage adequate embedment. The studs are typically welded through the deck or placed in deck openings. The stud diameter is limited to 2.5*t_f regardless of orientation.

What is the fire rating for composite steel beams?

Composite beams achieve fire resistance through the concrete slab acting as a heat sink and the steel section being partially shielded. Unprotected composite beams achieve 1-hour fire resistance per UL assembly D902 for restrained assemblies with 3.25" minimum slab thickness. For 2-hour and 3-hour ratings, spray-applied fireproofing (SFRM) or intumescent coating is applied to the exposed steel surfaces. The composite action itself does not change the fire protection requirements — the fire rating is determined by the steel temperature during the fire exposure, which is a function of the section factor W/D (weight per foot divided by heated perimeter) per AISC Design Guide 19.

Related Pages

• Composite Beam Reference — Overview and capacity comparison tables
• Steel Beam Capacity Calculator — Beam design per AISC 360
• Concrete on Steel Deck — Floor deck and slab systems
• Bolted Connections — Connection design for composite beams
• Deflection Control — Serviceability limits per IBC and AISC

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