How is the effective slab width determined for composite beams per AISC 360?

AISC 360 Section I3.1a defines the effective width of the concrete slab flange on each side of the beam centerline as the minimum of: (1) one-eighth of the beam span L/8, (2) one-half the distance to the adjacent beam web s/2, or (3) the distance to the slab edge for exterior beams. The total effective width be is the sum of effective widths on both sides. For a typical interior beam at 30 ft span with 10 ft spacing: be per side = min(30x12/8, 10x12/2) = min(45, 60) = 45 in, giving total be = 90 in. The effective width limits the concrete area assumed to act compositely with the steel beam, preventing overestimation of the compression flange for widely spaced beams. For edge beams, the exterior effective width is limited to the actual slab overhang dimension.

How is shear stud capacity calculated per AISC 360?

AISC 360 Section I8.2a gives the nominal shear strength of headed steel stud anchors: Qn = 0.5 x Asc x sqrt(f'c x Ec) <= Rg x Rp x Asc x Fu, where Asc is the stud cross-sectional area, f'c is concrete compressive strength, Ec is concrete elastic modulus, Fu is stud tensile strength (typically 65 ksi), Rg is the group effect factor, and Rp is the position effect factor. For a 3/4 in diameter stud (Asc = 0.442 in^2) in 4 ksi normal-weight concrete (Ec = 3,605 ksi): Qn = 0.5 x 0.442 x sqrt(4 x 3605) = 26.5 kips, but limited by the stud tensile strength: 0.5 x 0.442 x 65 = 14.4 kips (if stud steel governs). For metal deck perpendicular to the beam with one stud per rib and wr/hr >= 1.5, Rg = 1.0 and Rp = 0.75, reducing Qn to approximately 10.8 kips for the steel-limited case. With stronger stud steel (Fu = 65 ksi), the concrete crushing limit of 21.5 kips typically governs for flat soffits. Minimum stud spacing is 6x stud diameter (4.5 in for 3/4 in studs); maximum is 36 in or 8x slab thickness.

What is partial composite action and when is it beneficial?

Partial composite action means the number of shear connectors is less than required for full composite action (V' < min(C, T) where C is the concrete crushing force and T is the steel yielding force). AISC 360 permits a minimum 25% composite ratio. At 25% composite, the PNA shifts into the steel beam (top flange or web), reducing the moment capacity but also reducing the number of studs needed. For a W16x26 composite beam at 30 ft span: full composite needs 26 studs per half beam for phi-Mn = 320 kip-ft (88% increase over bare steel); at 25% partial composite, only 7 studs are needed for phi-Mn = 210 kip-ft (24% increase). Partial composite is economical when full capacity isn't needed — the deflection is computed using the lower-bound moment of inertia ILB = Is + sqrt(Cf/Cfull) x (Icomp - Is), which accounts for slip at the interface. Key limitations: below 25% composite, the connection is too flexible for reliable horizontal shear transfer per AISC Commentary I3.2.

How does metal deck orientation affect composite beam design?

Metal deck orientation relative to the steel beam significantly affects stud capacity and placement. Perpendicular deck (ribs running across the beam, most common) requires stud reduction factors Rg and Rp from AISC I8.2a because studs are embedded in the narrower rib space. For one stud per rib: Rp = 0.75 for wr/hr >= 1.5, Rp = 0.60 for wr/hr < 1.5. For two studs per rib: Rp = 0.60 and Rg = 0.85. Parallel deck (ribs along the beam) eliminates rib reduction factors (Rg = Rp = 1.0) and provides more room for studs, but requires the deck ribs to be at least 2 in wide at the stud location. For perpendicular deck, studs are typically installed one per rib in the strong position (toward the beam web, providing greater concrete confinement and higher capacity). The deck profile also affects the concrete area above the ribs: for a 2 in deck with 3.25 in topping, only the topping concrete (above the ribs) is considered for the compression flange, and the deck itself is ignored for strength calculations per AISC I3.1a.

What is Composite Beam Calculator — Steel-Concrete AISC 360 Chapter I?

Steel-concrete composite beam design per AISC 360 Chapter I. Shear stud capacity, effective slab width, plastic moment, and lower-bound moment of inertia for partial composite action.

Composite Beam Design Calculator

Q: What is Composite Beam Calculator — Steel-Concrete AISC 360 Chapter I?

Steel-concrete composite beam design per AISC 360 Chapter I. Shear stud capacity, effective slab width, plastic moment, and lower-bound moment of inertia for partial composite action.

Quick answer: A W16x26 beam (Fy = 50 ksi) with 3.25-inch lightweight concrete slab on 1.5-inch composite deck (f'c = 4 ksi), spanning 30 ft at 5 ft spacing, needs approximately 26 studs (3/4" dia x 3.5") for full composite action. The full composite phi-Mn is about 320 kip-ft -- nearly double the 170 kip-ft capacity of the bare steel beam. At 25% minimum partial composite, phi-Mn drops to about 210 kip-ft with only 7 studs. Use the calculator below for exact AISC 360 Chapter I checks.

Composite Beam Capacity Comparison

Composite Ratio	Studs Needed (3/4" dia)	phi-Mn (kip-ft)	Increase vs Bare Steel
Bare steel (non-composite)	0	170	--
25% (AISC minimum)	7	~210	+24%
50% partial	13	~250	+47%
75% partial	20	~290	+71%
100% full composite	26	~320	+88%

Beam: W16x26, Fy=50ksi, 30ft span, 5ft spacing, 4ksi LW concrete on 1.5" deck.

Key Design Steps Per AISC 360 Chapter I

1. Effective slab width (AISC I3.1a): be = min(L/8, s/2, edge distance) on each side of the beam centerline. For a W16x26 at 30 ft span, 5 ft spacing: be = min(30x12/8, 5x12/2) = min(45, 30) = 30 in per side = 60 in total.

2. Shear stud capacity (AISC I3.3): Qn = 0.5 x Asc x sqrt(f'c x Ec) <= 0.5 x Asc x Fu (stud tensile strength) For 3/4" dia stud (Asc = 0.44 in^2), f'c = 4 ksi, Ec = 2700 ksi (NW): Qn = 0.5 x 0.44 x sqrt(4 x 2700) = 21.5 kips per stud.

3. Full composite stud count: C = 0.85 x f'c x be x ts = 0.85 x 4 x 60 x 4.75 = 969 kips (concrete crushing) T = As x Fy = 7.68 x 50 = 384 kips (steel yielding) -- governs N = T / Qn = 384 / 21.5 = 17.9 -- use 18 studs minimum per half beam (36 total for symmetric loading).

4. Plastic neutral axis location: If PNA is in the slab: a = C / (0.85 x f'c x be). If a <= ts, PNA is in the slab and phi-Mn = C x (d/2 + ts - a/2) x phi (phi = 0.90).

5. Lower-bound moment of inertia (for deflection): ILB = Is + sqrt(Cf/Cfull) x (Icomp - Is), where Cf/Cfull is the composite ratio. Used for partially composite beams to account for stud slip.

Partial Composite Action

AISC 360 allows minimum 25% composite ratio. Partial composite means fewer studs (lower cost) but:

Reduced moment capacity
PNA shifts into the steel beam (may be in top flange or web)
Deflection increases (use ILB, not Icomp)
The beam must still be checked as non-composite for construction stage (unshored)

How the Calculator Works

The calculator uses the plastic stress distribution method from AISC 360 Section I3.2a. The compressive force in the slab is limited by the lesser of concrete crushing, steel yielding, or total shear stud capacity. The PNA is located by force equilibrium. For partial composite, the stud capacity limits the compression force and the PNA shifts into the steel section.

Worked Example — Full Composite Beam Design

Problem: Design a W18x35 (A992, Fy = 50 ksi) composite beam for a 30 ft span. The beam spacing is 8 ft on center. The slab is 2-inch composite deck with 4 inches of normal-weight concrete (f'c = 4,000 psi, total slab = 6 inches). Service dead load = 25 psf (above slab), service live load = 80 psf.

Step 1 — Effective slab width

be per side = min(L/8, s/2) = min(30×12/8, 8×12/2) = min(45, 48) = 45 in
Total effective width: be = 2 × 45 = 90 in

Effective slab depth: ts = 6.0 in (total slab above beam top flange)
Concrete area: Ac = be × ts = 90 × 6.0 = 540 in²

Step 2 — Material properties

W18x35: As = 10.3 in², d = 17.70 in, bf = 6.00 in
A992: Fy = 50 ksi
Concrete: f'c = 4,000 psi, Ec = 57,000 × √4000 = 3,605 ksi (NW)
Steel: E = 29,000 ksi

Step 3 — Shear stud capacity (AISC I8.2a)

3/4" diameter headed studs: Asc = π×0.75²/4 = 0.442 in²

Qn = 0.5 × Asc × √(f'c × Ec) = 0.5 × 0.442 × √(4 × 3605)
Qn = 0.5 × 0.442 × 120.1 = 26.5 kips

Check upper limit: Qn ≤ 0.5 × Asc × Fu = 0.5 × 0.442 × 65 = 14.4 kips
→ Qn = 14.4 kips (stud tensile strength governs for high-strength studs)

With deck rib reduction (1 stud per rib, perpendicular deck, wr/hr = 2.5/2 = 1.25):
Rg = 1.0, Rp = 0.75 (for one stud, wr/hr < 1.5 would be worse)
Qn_actual = 14.4 × 1.0 × 0.75 = 10.8 kips per stud (conservative)

Use Qn = 21.5 kips for flat soffit (no deck reduction for this example).

Step 4 — Full composite stud count

C = 0.85 × f'c × Ac = 0.85 × 4 × 540 = 1,836 kips (concrete crushing)
T = As × Fy = 10.3 × 50 = 515 kips (steel yielding) → GOVERNS

N_full = T / Qn = 515 / 21.5 = 24.0 studs per half beam → 24 studs per half
Use 25 studs per half beam (50 total for symmetric loading) to exceed full composite.

Step 5 — Plastic moment capacity

PNA in the slab (a ≤ ts):
  a = T / (0.85 × f'c × be) = 515 / (0.85 × 4 × 90) = 1.68 in < 6.0 in ✓

Moment arm: d/2 + ts - a/2 = 17.70/2 + 6.0 - 1.68/2 = 8.85 + 6.0 - 0.84 = 14.01 in

φMn = 0.90 × T × (d/2 + ts - a/2) = 0.90 × 515 × 14.01 = 6,496 kip-in = 541 kip-ft

Step 6 — Demand check

Factored load: wu = 1.2 × (25 + slab weight) + 1.6 × 80
Slab weight: 6/12 × 150 = 75 psf + beam weight: 35/8 = 4.4 psf = 79.4 psf
wu = 1.2 × (25 + 79.4) + 1.6 × 80 = 1.2 × 104.4 + 128 = 125.3 + 128 = 253.3 lb/ft

Mu = wu × L² / 8 = 0.253 × 30² / 8 = 28.5 kip-ft...
Actually: Mu = 0.2533 × 900 / 8 = 28.5 kip-ft

Wait — wu in kips/ft = 0.253 kip/ft
Mu = 0.253 × 30² / 8 = 0.253 × 112.5 = 28.5 kip-ft

φMn / Mu = 541 / 28.5 = 19.0 → WELL OK (beam is oversized for this span)

This is typical — the W18x35 at 30 ft span has substantial excess composite capacity.

Step 7 — Deflection check (lower-bound EI)

Non-composite: Is = 510 in⁴ (W18x35 bare steel)
Fully composite: Icomp ≈ 2,200 in⁴ (concrete slab + steel beam, transformed)
25% partial: ILB = Is + √(0.25) × (Icomp - Is) = 510 + 0.5 × 1,690 = 1,355 in⁴

Live load deflection:
Δ_LL = 5 × w_LL × L⁴ / (384 × E × I)
w_LL = 80/1000 × 8 = 0.64 kip/ft (total LL on tributary width)
Δ_LL = 5 × 0.64 × 30⁴ × 1728 / (384 × 29000 × 1355) = 5 × 0.64 × 810000 × 1728 / 15081600000
Δ_LL = 0.30 in

L/360 = 30 × 12 / 360 = 1.0 in → 0.30 < 1.0 ✓

Even at 25% composite, the deflection is well within limits.

Stud Layout Patterns

Symmetric uniform layout (most common)

Studs placed uniformly from each support toward midspan.
Number per half beam = N/2 (rounded up).

For 25 studs per half beam at 30 ft span:
  Beam length per half = 180 in
  Spacing = 180 / 25 = 7.2 in ≈ 7 in on center
  Actual studs = 180/7 = 25.7 → 26 studs per half

Minimum spacing: 6× stud diameter = 6 × 0.75 = 4.5 in
Maximum spacing: 36 in or 8× slab thickness (AISC I8.3)

Strong/weak stud placement

Strong position: studs placed in the "strong" position (toward the near side
of the deck rib, closer to the beam web) per SDI and stud manufacturer.

Weak position: studs placed on the far side of the rib.
Capacity reduction of approximately 10-15% for weak-position studs.

Most specifications require strong-position placement.

Frequently Asked Questions

What is partial composite action? Partial composite action means the number of shear connectors is less than required for full composite action, so the horizontal shear transfer between the steel beam and concrete slab is limited by the stud capacity rather than by yielding or crushing. AISC allows a minimum of 25% composite action. Partial composite reduces the moment capacity but also reduces the number of studs needed, which can be more economical when full capacity is not required.

How is the lower-bound moment of inertia calculated? The lower-bound moment of inertia ILB is used for deflection calculations of partially composite beams. It accounts for the slip at the steel-concrete interface by interpolating between the non-composite moment of inertia (steel section alone) and the fully composite moment of inertia, based on the ratio of actual stud capacity to full composite capacity. AISC provides the formula in Commentary Section I3.2.

What determines the effective slab width? AISC 360 Section I3.1a defines the effective width of the concrete slab flange as the minimum of: beam span divided by 8 (each side), half the beam spacing, or the distance to the slab edge. This limits the slab width assumed to act compositely with the beam and prevents overestimating the concrete compression flange for widely spaced beams.

What is the minimum number of shear studs required? AISC 360 requires a minimum composite ratio of 25%, meaning the total stud capacity must be at least 25% of the lesser of As×Fy or 0.85×f'c×Ac. Below this threshold, the connection is too flexible to reliably transfer horizontal shear, and deflection predictions become unreliable. For typical office floor beams (W16 to W21 sections at 25-35 ft spans), this translates to approximately 4-8 studs per half beam.

How does concrete type affect composite beam capacity? Lightweight concrete (110 pcf) reduces the slab self-weight by 25-30% compared to normal-weight concrete (150 pcf), which reduces dead load and improves deflection performance. However, lightweight concrete also has a lower elastic modulus (Ec ≈ 60-70% of NW), which reduces the transformed section properties and slightly reduces the composite moment capacity. The stud capacity Qn is also lower for lightweight concrete because Ec is lower. The net effect is that lightweight concrete is preferred for long-span beams where deflection governs, while normal-weight concrete gives slightly higher moment capacity.

What are shored vs unshored composite beams? Shored construction uses temporary props to support the beam during concrete placement, so the beam carries only the composite section weight after the concrete cures. Unshored construction lets the bare steel beam carry the wet concrete weight during construction. Unshored is more common because it avoids the cost and scheduling of shoring, but it requires checking the bare steel beam for construction-stage loads and the composite section for full-service loads. The composite capacity is the same either way — only the stress history differs.

What is the construction stage check for unshored composite beams? During construction, before the concrete has cured, the bare steel beam must support the wet concrete, metal deck, construction loads, and its own weight. AISC 360 requires checking the bare steel beam for construction-stage loads per ASCE 37 (typically 50 psf construction live load plus the wet concrete and deck weight). The bare beam must satisfy strength, stability (lateral-torsional buckling with the unbraced length determined by deck attachment), and deflection limits (typically L/240 for construction dead load to avoid ponding effects in the wet concrete).

How does deck orientation affect composite beam capacity? Metal deck can be oriented perpendicular or parallel to the beam. Perpendicular deck (ribs running across the beam) is most common and requires rib reduction factors for stud capacity (Rg and Rp factors from AISC I8.2a) because the studs must be embedded in the narrower rib space. Parallel deck (ribs running along the beam) provides more room for studs and eliminates rib reduction factors. For perpendicular deck, studs are typically placed one per rib in the strong position. The number of studs per rib is limited: 1 stud per rib at less than 2:1 rib aspect ratio, 2 studs at 2:1 or greater.

What fire rating considerations apply to composite beams? Composite beams in rated floor assemblies must maintain their load-carrying capacity for the specified fire duration. The steel beam is the critical element because it loses strength at elevated temperatures. Common fire protection methods include spray-applied fire-resistant material (SFRM), intumescent paint, and encasement in concrete. For a typical 2-hour rated assembly with a W16x26 composite beam, approximately 1/2 to 3/4 inch of SFRM is required on the steel beam surfaces. The slab thickness, concrete type, and steel deck profile are part of the rated assembly and must match the tested configuration from the UL or Intertek directory.

What is the difference between a composite beam and a non-composite beam with the same steel section? A composite beam develops significantly higher moment capacity and stiffness than the same steel section acting non-compositely. For a W16x26, the non-composite phi-Mn is approximately 170 kip-ft and the moment of inertia is 301 in^4. With full composite action and a 5-inch slab, phi-Mn increases to approximately 320 kip-ft (88% increase) and the effective moment of inertia increases to approximately 1,800 in^4 (500% increase). This means composite beams deflect much less and can span farther for the same section size, or use a lighter steel section for the same span and load.

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