Composite Beam — Engineering Reference

AISC 360 Ch.I composite beam: effective slab width, PNA, phiMn, shear stud Qn. Full and partial composite action explained. Interactive calculator. Free.

Overview

A composite beam combines a steel W-shape with a 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 than either material alone. Composite beams are standard practice in steel-framed office buildings, parking garages, and industrial structures because they can support the same loads as non-composite beams 2-3 sizes heavier.

AISC 360-22 Chapter I governs composite beam design in the United States. The key concepts are effective slab width, plastic neutral axis (PNA) location, shear stud capacity, and the distinction between full and partial composite action.

Composite vs non-composite capacity comparison

Composite action typically adds 50-90% to bare steel capacity. Lighter beams benefit the most.

Effective slab width

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

• L/8 (one-eighth of the beam span)
• s/2 (half the center-to-center beam spacing)
• Distance to the slab edge

Effective width by span and spacing

For typical office construction (30 ft span, 10 ft spacing), total b_eff = 90 in.

Full composite action

Full composite action means enough shear studs are provided to develop the full compressive force in the concrete slab or the full tensile force in the steel section, whichever is smaller:

C = min(0.85 x f'c x b_eff x t_c, Fy x As)

where f'c is the concrete compressive strength, tc is the slab thickness above the deck ribs, and As is the steel cross-sectional area.

Partial composite action

Partial composite action uses fewer shear studs than required for full composite. AISC I3.2d requires a minimum of 25% composite action. In practice, 50-75% composite action is common because it provides 85-95% of full composite capacity with significantly fewer studs.

Capacity vs composite percentage

Below 50%, deflection serviceability often becomes the controlling limit state.

Shear stud capacity

The nominal strength of a single headed shear stud per AISC I8.2a is:

Qn = 0.5 x Asa x sqrt(f'c x Ec), capped at Rg x Rp x Asa x Fu

Shear stud capacity by diameter and concrete strength

Cap value controls for 3/4 in. studs in deck ribs with normal-weight concrete.

Rg and Rp factors

"Strong position" = stud on the side of the rib that bears against the deck flute in the direction of load. "Weak position" = opposite side. Rp = 0.75 for weak position reduces stud capacity by 25%.

Worked example — W16x26 composite beam

Given: W16x26 (As = 7.68 in^2, d = 15.7 in.), A992, span = 30 ft, beam spacing = 10 ft, 3 in. metal deck with 3.25 in. concrete topping (tc = 3.25 in.), f'c = 4 ksi, 3/4 in. shear studs.

1. Effective width: b_eff = min(30x12/8, 10x12/2) = min(45, 60) = 45 in. per side = 90 in. total.
2. Concrete compression: C_conc = 0.85 x 4 x 90 x 3.25 = 994 kip.
3. Steel tension: T_steel = 50 x 7.68 = 384 kip. Steel controls (PNA is in the slab).
4. Full composite moment: PNA is 384/(0.85 x 4 x 90) = 1.255 in. below top of slab. Moment arm = 7.85 + 3.0 + 3.25 - 0.628 = 13.47 in. Mn = 384 x 13.47 = 5173 kip-in = 431 kip-ft. phi x Mn = 388 kip-ft.
5. Studs required (full composite): N = 384 / 21.5 = 17.9 -> 18 studs per half-span (36 total).
6. At 50% composite: sum(Qn) = 0.50 x 384 = 192 kip. N = 192/21.5 = 8.9 -> 9 studs per half-span (18 total). phiMn approximately 315 kip-ft. This is 81% of full composite capacity with 50% of the studs.

Deflection calculation for composite beams

Lower-bound moment of inertia (AISC Table 3-20)

Using bare steel Ix for deflection overstates deflection by 80-140%. Always use ILB.

Construction-phase deflection

Before concrete cures, the bare steel beam supports wet concrete + construction loads. Check:

• Bare steel deflection under wet concrete <= L/360
• If it exceeds this, specify temporary shoring or a cambered beam

Lighter beams on longer spans almost always need shoring or camber for construction-phase deflection.

Transformed section method and long-term deflection

The transformed section method converts the concrete slab into an equivalent steel area using the modular ratio n = Es / Ec. This allows standard steel section properties to be used for the composite section.

Modular ratio: n = 29,000 ksi / Ec where Ec = w_c^1.5 x 33 x sqrt(f'c) for normal-weight concrete (ACI 318). For 4 ksi normal-weight concrete: Ec = 145^1.5 x 33 x sqrt(4000) / 1000 = 3,830 ksi, so n = 29,000 / 3,830 = 7.6 (rounded to 8 for design). For 4 ksi lightweight concrete (wc = 115 pcf): Ec = 115^1.5 x 33 x sqrt(4000) / 1000 = 2,830 ksi, so n = 29,000 / 2,830 = 10.2 (rounded to 10).

Transformed slab width: b_tr = b_eff / n. For b_eff = 90 in with n = 8: b_tr = 90 / 8 = 11.25 in. This equivalent 11.25 in wide steel plate (same thickness as the slab) has the same axial stiffness as the 90 in wide concrete slab.

Moment of inertia of the transformed section: Calculate using the parallel axis theorem:

Itr = I_steel + A_steel x d1^2 + (b_tr x t_c^3 / 12) + (b_tr x t_c) x d2^2

where d1 = distance from steel centroid to composite centroid and d2 = distance from slab centroid to composite centroid. For a W16x26 with 90 in effective width, 3.25 in slab, n = 8: b_tr = 11.25 in, slab transformed area = 11.25 x 3.25 = 36.6 in2, steel area = 7.68 in2, total area = 44.3 in2. Composite neutral axis location from top of slab: y_bar = (36.6 x 1.625 + 7.68 x (3.25 + 15.7/2)) / 44.3 = (59.5 + 7.68 x 11.1) / 44.3 = (59.5 + 85.2) / 44.3 = 3.27 in below top of slab — approximately at the slab-to-beam interface. Itr ~ 720 in4 for this section (matching the full composite I_LB from AISC Table 3-20).

Long-term creep deflection: Under sustained dead loads (ceiling, MEP, flooring), concrete creeps, reducing the effective modulus and increasing deflection. Per AISC Commentary I3.2, use 2n (or 3n for heavily loaded floors) for sustained load deflections. For n = 8, use n_long = 16, giving b_tr_long = 90 / 16 = 5.63 in and a reduced I_tr_long. The creep deflection increment = delta_creep = M x L^2 / (8 x E x I_tr_long) - the same calculation as short-term deflection but with the reduced section. Total long-term deflection = immediate (pre-composite) + creep (sustained) + live load (short-term). For office buildings, the 2n creep approximation adds approximately 30-50% to the sustained load deflection.

Code comparison — composite beams

AISC 360-22 Chapter I: Composite Design Overview

AISC 360 Chapter I governs the design of composite members where steel sections act together with concrete to resist loads. For composite beams, the key provisions are:

• Section I3.1 — Assumptions for composite flexural members: concrete is uncracked in compression, steel yields in tension, full or partial composite action via shear studs.
• Section I3.2 — Positive moment region design: plastic stress distribution for compact sections, with the plastic neutral axis (PNA) location determined by the degree of composite action.
• Section I3.3 — Negative moment regions: concrete is cracked, reinforcement in the slab is engaged if studs are present and reinforcement is developed.
• Section I3.4 — Construction-phase loading: the bare steel beam must support wet concrete, deck, and construction live load before the slab gains strength.
• Section I4 — Composite column provisions (encased, filled).
• Section I6 — Composite slab provisions with formed steel deck.

Shear Stud Capacity per AISC 360

The nominal shear strength of a single stud embedded in a concrete slab (with or without metal deck) is:

Qn = min(0.5 * As * sqrt(f'c * Ec), As * Fu)    (AISC Eq. I3-3)

Where:

• As = Cross-sectional area of the stud (in2)
• f'c = Concrete compressive strength (psi)
• Ec = Modulus of elasticity of concrete = 57,000 * sqrt(f'c) (psi)
• Fu = Stud tensile strength (typically 65 ksi for ASTM A108 studs)

For studs in metal deck, apply reduction factors Rg and Rp per AISC 360 Section I3.2.2d:

Reduced stud capacity: Qn(reduced) = Rg _ Rp _ Qn

Partial vs. Full Composite Action

Partial composite (40-60%) is often the most economical choice because it provides 80-90% of full composite capacity with significantly fewer studs. The AISC minimum of 25% composite action ensures enough studs to maintain composite behavior reliably.

Metal Deck Types for Composite Construction

Higher gauge numbers (20 ga = 0.036 in, 22 ga = 0.030 in) are thinner. The rib geometry affects stud capacity through the Rg and Rp factors. Wider ribs allow more studs per rib, increasing total stud count and degree of composite action.

Composite beam design procedure — step by step

The AISC 360 Chapter I composite beam design workflow follows this sequence:

Step 1 — Determine effective slab width. Calculate b_eff per side = min(L/8, s/2, distance to slab edge). For a 30 ft span at 10 ft spacing: b_eff_total = 90 in.

Step 2 — Compute full composite horizontal shear. Vh' = min(0.85 x f'c x b_eff x t_c, Fy x A_s). The smaller of slab compression capacity and steel tension capacity governs.

Step 3 — Select stud type and compute Qn. Choose stud diameter (typically 3/4 in for most building applications). Calculate Qn = min(0.5 x Asa x sqrt(f'c x Ec), Rg x Rp x Asa x Fu). Apply the Rg and Rp reduction factors for deck rib geometry and stud position.

Step 4 — Determine degree of composite action. Choose between full composite (N = Vh'/Qn) or partial composite (typically 50-75%). Higher composite action increases capacity but requires more studs. Verify minimum 25% composite action per AISC I3.2d.

Step 5 — Locate the plastic neutral axis (PNA). For full composite: if C_conc >= T_steel, PNA is in the slab at depth a = T_steel / (0.85 x f'c x b_eff). If C_conc < T_steel, PNA is in the steel section. For partial composite: PNA is always in the steel section when sum(Qn) < T_steel.

Step 6 — Calculate nominal moment capacity Mn. Compute the moment of the compression and tension force couples about the PNA. The tension force is the full steel yield (or the portion below the PNA if PNA is in the steel). The compression includes slab compression plus any steel above the PNA.

Step 7 — Check deflection. Calculate pre-composite deflection using I_steel (unshored construction). Calculate composite deflection using I_LB from AISC Table 3-20 or the transformed section method. Apply creep multiplier (2n) for sustained loads. Verify total deflection <= L/240 (typical) and live load deflection <= L/360.

Step 8 — Check construction-phase strength. Verify the bare steel beam has adequate strength for wet concrete + construction live load per AISC I3.4. The bare steel must support 1.2 x (beam + deck + wet concrete) + 1.6 x construction LL without exceeding phi_b x Mn of the steel alone.

Step 9 — Distribute studs. Place studs uniformly along the beam span between the maximum moment and the supports. For symmetrical loading, place half the studs in each half-span. Verify rib clearance and stud-as-welded length (stud height must extend at least 1.5 in above the top of the deck ribs per AISC I8.1).

Step 10 — Check vibration. For floors with spans exceeding 25 ft or with low damping (open office, gymnasium), evaluate walking-induced vibration per AISC Design Guide 11. If the natural frequency is below 4 Hz (offices) or 8 Hz (sensitive equipment), increase beam size or add damping.

Worked Example: W21x44 Composite Beam

Given:

• Beam: W21x44 (A992, Fy = 50 ksi), span L = 30 ft
• Slab: 3.25 in lightweight concrete (f'c = 4,000 psi, wc = 115 pcf) on 2 in metal deck (total slab = 5.25 in)
• Effective width be = min(L/4, s/2) = min(30*12/4, 120/2) = min(90, 60) = 60 in
• Studs: 3/4 in diameter x 5 in, ASTM A108 (Fu = 65 ksi)
• Loading: SDL = 20 psf, construction LL = 20 psf, floor LL = 80 psf

Step 1: Steel beam properties (W21x44)

A = 13.0 in2,  d = 20.7 in,  bf = 6.50 in,  tf = 0.451 in,  tw = 0.351 in
Ix = 843 in4,  Sx = 81.4 in3,  Zx = 95.4 in3

Step 2: Concrete slab properties

Ec = 57,000 * sqrt(4,000) = 3,605,000 psi = 3,605 ksi
Aslab = be * ts = 60 * 3.25 = 195 in2 (solid concrete above deck)

Step 3: Full composite horizontal shear

V's = As * Fy = 13.0 * 50 = 650 kips (steel beam yield force)
V'c = 0.85 * f'c * Aslab = 0.85 * 4.0 * 195 = 663 kips (concrete slab compression)
V'h = min(V's, V'c) = min(650, 663) = 650 kips

Step 4: Single stud capacity (Qn)

As_stud = pi/4 * (0.75)^2 = 0.442 in2
Qn = min(0.5 * 0.442 * sqrt(4.0 * 3605), 0.442 * 65)
   = min(0.5 * 0.442 * 120.1, 28.7)
   = min(26.6, 28.7) = 26.6 kips per stud

With deck reduction (Rg = 1.0, Rp = 1.0, strong position):
Qn_eff = 26.6 kips per stud

Step 5: Stud count for full composite

N_full = V'h / Qn_eff = 650 / 26.6 = 24.4 → use 25 studs per half-beam = 50 studs total

Step 6: Use 50% composite (25 studs total)

V'h(50%) = 25 * 26.6 = 665 kips... wait, that's 50 studs = full.
50% composite = 25 studs total (12-13 per half)
Vr = 25 * 26.6 / 2 = 13 studs per side * 26.6 = 346 kips (approximately 50% of 650)
C = min(Vr, 0.85*f'c*Aslab, As*Fy) = min(346, 663, 650) = 346 kips
a = C / (0.85 * f'c * be) = 346 / (0.85 * 4.0 * 60) = 1.70 in

Step 7: PNA depth from top of slab

PNA is in the steel beam (partial composite).
Moment arm from slab compression to PNA:
a = 1.70 in (concrete stress block depth)
T = C = 346 kips (tension in steel)

For simplified partial composite moment capacity:

Mn_approx = C * (d/2 + ts - a/2)
          = 346 * (20.7/2 + 3.25 - 1.70/2)
          = 346 * (10.35 + 3.25 - 0.85)
          = 346 * 12.75 = 4,412 in-kips = 368 ft-kips

phi * Mn = 0.90 * 368 = 331 ft-kips

Step 8: Factored demand

wu = 1.2 * (self-weight + SDL) + 1.6 * LL
   = 1.2 * (0.050 + 0.020) * 30 + 1.6 * 0.080 * 30
   = 1.2 * 2.1 + 1.6 * 2.4 = 2.52 + 3.84 = 6.36 klf

Mu = wu * L^2 / 8 = 6.36 * 30^2 / 8 = 716 ft-kips

Demand (716 ft-kips) > Capacity (331 ft-kips)
→ Need more studs or larger beam. At full composite:
Mn = Mp = Zx * Fy + C * (partial) ... full composite gives Mn ≈ Mp ≈ 95.4 * 50 = 4,770 in-kips
phi * Mn = 0.90 * 4,770 / 12 = 358 ft-kips ... still insufficient.

→ Increase beam to W21x62 or reduce span. This illustrates the importance of checking composite capacity against actual demand.

Worked Example — Deflection of W18x35 composite beam

Given: W18x35 (Ix = 510 in4), span = 30 ft, spacing = 10 ft, b_eff = 90 in, 3.25 in slab (4 ksi NWC), 3/4 in studs at 50% composite. Check total deflection under service loads.

Step 1 — Loads (service level):

Pre-composite (on bare steel): w_D1 = beam 0.035 + deck 0.015 + wet conc 0.050 = 0.100 klf
Superimposed dead (composite): w_D2 = 0.020 klf (ceiling + MEP)
Live (composite): w_L = 0.080 klf

Step 2 — Pre-composite deflection (bare steel Ix = 510 in4):

delta_D1 = 5 x 0.100 x 30^4 x 1728 / (384 x 29000 x 510) = 1.18 in
L/delta = 360/1.18 = 305 — exceeds L/360 (1.00 in) — camber or shoring needed

Step 3 — Composite section properties at 50% composite: n = 8 (NWC 4 ksi), b_tr = 90/8 = 11.25 in (full slab width for transformed section). At 50% composite, I_LB from AISC Table 3-20 is approximately 950 in4.

Step 4 — Superimposed dead load deflection (composite, I_LB = 950 in4):

delta_D2 = 5 x 0.020 x 30^4 x 1728 / (384 x 29000 x 950) = 0.14 in

Step 5 — Long-term creep deflection (use 2n = 16, I_tr_creep ~ 750 in4):

delta_creep = 5 x 0.020 x 30^4 x 1728 / (384 x 29000 x 750) = 0.17 in

Creep adds approximately 0.03 in (21% increase) to the SDL deflection.

Step 6 — Live load deflection (composite, I_LB = 950 in4):

delta_L = 5 x 0.080 x 30^4 x 1728 / (384 x 29000 x 950) = 0.55 in
L/delta = 360/0.55 = 655 — well under L/360 limit

Step 7 — Total long-term deflection:

delta_total = delta_D1 + delta_D2 + delta_creep + delta_L
            = 1.18 + 0.14 + 0.17 + 0.55 = 2.04 in
L/delta_total = 360/2.04 = 176 — exceeds typical L/240 limit (1.50 in)

However, the pre-composite deflection (1.18 in) is typically offset by camber. If the beam is cambered 1.25 in, the net total deflection reduces to delta_total_net = (2.04 - 1.25) = 0.79 in — acceptable.

Vibration of composite floor systems

Composite floor vibration is a serviceability concern for long-span beams (25 ft+) and open bay areas without partitions. AISC Design Guide 11 provides the analytical framework:

Natural frequency of a composite beam:

f = 0.18 x sqrt(g / delta_D)    (Hz)

where g = 386 in/s2 and delta_D = dead load deflection (in) including the beam self-weight, slab, ceiling, MEP, and 10% of the live load as mass. For the W18x35 composite beam above with camber-adjusted delta_D = 0.31 in:

f = 0.18 x sqrt(386 / 0.31) = 0.18 x 35.3 = 6.4 Hz

This exceeds 4 Hz (the minimum for office occupancy per DG11 Table 2.1) but falls short of 8 Hz (required for sensitive equipment areas). For a gymnasium or open workspace with a 30 ft span, the same beam would have f ~ 5.0-5.5 Hz — borderline for comfort.

Walking excitation amplitude:

a_p = (P0 x e^(-0.35 x fn)) / (beta x W)    (in/s2 peak acceleration)

where P0 = 65 lb (walking force amplitude for 1st harmonic), beta = modal damping ratio (2% for open office with ceiling, 5% for fully furnished office with partitions), and W = effective panel weight. For f = 6.4 Hz, beta = 0.03 (typical open office with furniture):

a_p = (65 x e^(-0.35 x 6.4)) / (0.03 x (0.100 x 30 x 10)) = (65 x 0.106) / (0.03 x 30) = 6.89 / 0.9 = 7.7 in/s2

Per DG11, peak acceleration limit for office occupancy is 0.5% of g = 0.005 x 386 = 1.93 in/s2. The calculated 7.7 in/s2 exceeds this limit — heavier beam or increased damping is needed.

Remedial measures for excessive vibration:

• Increase beam size (stiffer = higher frequency, lower amplitude)
• Add damping (full-height partitions interrupt footfall paths)
• Increase slab thickness (adds mass but reduces frequency slower than it reduces amplitude)
• Use staggered beam layout to break floor panel resonance
• Avoid cantilevers and large open bays without cross-framing

Common mistakes to avoid

1. Using the bare steel Ix for deflection — composite beams have I_eff = I_LB, which is typically 2-3 times the bare steel Ix. Using Ix massively overstates deflection and leads to oversized beams.
2. Ignoring construction-phase loading — before the concrete cures, the steel beam alone supports the wet concrete weight plus construction loads. Check bare steel beam for strength and deflection during construction.
3. Placing studs in the wrong deck rib position — studs in the "weak" position have Rp = 0.75 rather than 1.0, reducing capacity by 25%. Specify stud position on drawings.
4. Not checking vibration for long spans — composite floor systems with spans over 30 ft are prone to walking-induced vibration. Check per AISC Design Guide 11; natural frequency should exceed 4 Hz for offices.
5. Assuming full composite when studs are limited by deck ribs — with 3 in. deck at 12 in. rib spacing, one stud per rib limits total stud count. For long spans, this may not provide enough studs for full composite action.

Frequently asked questions

What is the advantage of composite construction? A composite beam uses the concrete slab (which must be there anyway) to resist compression, allowing the steel beam to be 2-3 sizes lighter than a non-composite beam for the same load and span.

What is partial composite action? Using fewer shear studs than required for full composite. The beam still works as a composite section, but the PNA shifts toward the steel. 50% composite provides 80-85% of full composite capacity with 50% fewer studs.

Do I always need shear studs? No. For short spans with light loads, non-composite design may be more economical when the cost of stud welding exceeds the savings from a lighter beam. Check both options.

What is the minimum stud count? AISC requires enough studs for at least 25% composite action. Below this, the connection between slab and beam is insufficient to reliably develop composite behavior.

How do I handle negative moment regions? In continuous beams, negative moment regions have the slab in tension. Shear studs in negative moment regions contribute only if the slab reinforcement is developed across the support. Design negative moment regions as non-composite unless adequate reinforcement is provided.

What is I_LB and why does it matter? Lower-bound moment of inertia from AISC Table 3-20. It's the minimum composite I for the given degree of composite action. Use it for deflection calculations instead of bare steel Ix.

How does the transformed section method work for composite beams?

The transformed section method converts the concrete slab to an equivalent steel area so the entire composite section can be analyzed using steel section properties. The modular ratio n = Es / Ec converts concrete to equivalent steel: b_tr = b_eff / n. For a 30 ft span beam with 4 ksi normal-weight concrete, n = 8 and a 90 in effective slab reduces to b_tr = 11.25 in. The transformed moment of inertia is then calculated using the parallel axis theorem across both the steel beam and the transformed slab area: Itr = I_steel + A_steel x d1^2 + (b_tr x t_c^3 / 12) + (b_tr x t_c) x d2^2, where d1 and d2 are the distances from each component centroid to the composite neutral axis. This Itr is used for deflection calculations. For long-term creep deflection under sustained loads, use 2n (double the modular ratio) to account for concrete creep, which reduces the transformed slab width and increases predicted deflection by 30-50%.

What is the vibration criteria for composite floor systems?

AISC Design Guide 11 provides composite floor vibration criteria based on natural frequency and peak acceleration. The natural frequency is estimated as f = 0.18 x sqrt(g/delta_D) where delta_D is the dead load deflection including 10% of the live load as mass. Minimum acceptable frequencies: 4 Hz for office occupancy, 6 Hz for retail, 8 Hz for sensitive equipment or operating rooms. Peak acceleration from walking excitation: a_p = (P0 x e^(-0.35 x f)) / (beta x W) where P0 = 65 lb (walking force), beta = damping ratio (2-5%), and W = effective panel weight. The acceptable acceleration limit is 0.5% of g for offices (1.93 in/s2). Remedial options for excessive vibration include increasing beam stiffness, adding full-height partitions for damping, increasing slab thickness, or using staggered beam layouts to break panel resonance.

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Related references

• Beam Sizes
• Beam Formulas
• Deflection Limits
• Floor Vibration
• Precast Composite
• Castellated Beam
• Steel Section Types
• Steel Grades
• How to Verify Calculations

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