Composite Beam Design

AISC 360-22 Chapter I — steel beam with concrete slab on metal deck. Shear stud design, partial composite ratio, flexure, shear, and deflection checks. Pin–Pin span. ASCE 7-22 load combinations.

Input Parameters

kip · ft · in
Section Selection
Span & Geometry
ft
ft
in
Metal Deck
in
in
in
Concrete
ksi
Ec = —
Composite Ratio
%
⚠ AISC minimum composite ratio is 25% per §I3.2d. Non-composite (0%) is permitted for analysis only.
Loads — ASCE 7-22
① Construction Stage — Non-composite
kip/ft
② Service Stage — Composite
kip/ft
kip/ft
📋
Select a section and enter loads — results update automatically.

📚 Composite Beam Design — Theory & Code Background

What Is a Composite Beam?

A composite beam consists of a steel beam structurally connected to a concrete slab through shear connectors (typically headed shear studs). When the concrete and steel act together, the composite section is stiffer and stronger than the steel beam alone — the concrete carries compression and the steel carries tension in positive bending.

Metal deck (corrugated steel decking) is the most common slab system in composite floor construction. Deck ribs may run parallel or perpendicular to the beam; the stud capacity is reduced for perpendicular ribs to account for the reduced embedment.

Governing Standard — AISC 360-22 Chapter I

Chapter I covers composite beams with concrete-filled or concrete-on-deck slabs. The key provisions are:

  • §I1 — Scope and general requirements
  • §I3.2 — Flexural strength of composite beams (positive moment)
  • §I8 — Shear connectors — capacity and placement
  • §I3.2d — Partial composite action (η = ΣQn / Qn,full)

Notation

AsArea of steel beam (in² / mm²)
FyYield stress of steel beam (ksi / MPa)
f'cSpecified compressive strength of concrete (ksi / MPa)
beffEffective slab width — min(L/8, center-to-center spacing / 2) each side
QnNominal strength of one shear stud
ΣQnTotal nominal shear connection between PNA and moment point
ηPartial composite ratio = ΣQn / min(FyAs, 0.85f'cbefftc)
MnNominal flexural strength of composite section
RpPosition factor for shear studs (1.0 deck parallel, 0.75 deck perp.)
RgGroup factor (1.0 single stud, 0.85 two studs, 0.70 three+)

Headed Shear Stud Capacity — §I8.2a

The nominal strength of one headed shear stud:

Qn = 0.5 Asa √(f'c Ec) ≤ Rg Rp Asa Fu

where Asa = cross-sectional area of stud, Fu = tensile strength of stud (65 ksi / 450 MPa for standard A108 studs).

Reduction Factors (§I8.2a)

ConditionRgRp
Deck ribs parallel to beam, 1 stud / rib1.01.0
Deck ribs perpendicular, 1 stud / rib1.00.75
Deck ribs perpendicular, 2 studs / rib0.850.75
Deck ribs perpendicular, 3+ studs / rib0.700.75
No deck (solid slab), 1 stud1.01.0
No deck (solid slab), 2 studs side-by-side0.851.0

Note: Rp = 0.75 for perpendicular deck replaced the earlier 0.625 factor. AISC 360-22 (2022 edition) uses 0.75 per §I8.2a; some older references show 0.625.

Partial Composite Ratio η — §I3.2d

Full composite action requires placing enough studs between the point of maximum moment and the nearest zero-moment point so that:

ΣQn,full = min(FyAs, 0.85f'cbefftc)

Partial composite (η < 1.0) is permitted with η ≥ 0.25. Using fewer studs reduces both strength and stiffness. AISC requires N ≥ Nfull × η.

Minimum Stud Spacing

Along beam: 6dsa (longitudinal) and 4dsa (transverse). Maximum: 8tslab or 36 in. Studs may not be placed in a deck rib with height > 3 in unless the rib is ≥ 2 in wide at mid-height.

Plastic Stress Distribution Method — §I3.2

For compact composite sections in positive moment, AISC 360-22 §I3.2 uses the Plastic Stress Distribution Method. The PNA is located so that horizontal equilibrium is satisfied:

T = Cs + Cc
FyAs ≥ ΣQn → partial composite controls concrete compression block

Cases:

  • PNA in slab (Cc = FyAs): concrete compression block depth a = FyAs / (0.85f'cbeff)
  • PNA in steel top flange: part of top flange is in compression
  • PNA in steel web: standard case for partial composite

The nominal moment Mn is the sum of moment arms of all stress resultants about the PNA. Design strength: φbMn with φb = 0.90.

Lower-Bound Moment of Inertia Ieff

For deflection calculations under service loads, an effective moment of inertia accounts for partial composite action:

Ieff = Is + √η × (Itr − Is)

Is = moment of inertia of steel beam alone; Itr = transformed section MOI (full composite). For full composite η = 1.0, Ieff = Itr.

Shear Check — §G2

The web shear is resisted by the steel beam alone (concrete slab does not contribute to shear). Check: φvVn = φv× 0.60FyAwCv1 per §G2.1, with φv = 1.00 for most W shapes (h/tw ≤ 2.24√(E/Fy)).

Deflection Limits

Deflection of composite beams is typically controlled for:

ConditionTypical Limit
Pre-composite (steel beam + wet concrete)L/360 (live load only) or L/240 (total)
Post-composite (superimposed live load)L/360
Total post-composite (SDL + LL)L/240
Pre-composite (construction)L/300 or 1.5 in maximum

AISC does not mandate specific deflection limits — the values above are common IBC/ASCE 7 / owner-specified criteria. The calculator checks L/360 for live load and L/240 for total.

Pre-Composite Stage

During construction, before the concrete has cured, the steel beam alone carries the dead load of the wet concrete and steel self-weight. Deflection at this stage uses Is (bare steel). If pre-composite deflection is large (> L/360), cambering the beam before erection is required. Cambering = ¾ × pre-composite dead-load deflection is a common rule of thumb.

Vibration

Floor vibration is not directly checked by AISC 360-22 but is often governed by AISC Design Guide 11. The natural frequency of the composite beam–girder–column system should typically exceed 4 Hz for office floors and 8 Hz for sensitive lab/hospital occupancies. Acceleration limit under walking excitation should be below 0.5% g (office) or 0.1% g (sensitive). These checks are outside the scope of this calculator.

Worked Example — W18×35 Composite Beam, f'c = 4 ksi, η = 0.75

Given: W18×35, A992, Fy = 50 ksi; f'c = 4 ksi; beam span L = 30 ft; tributary width = 10 ft; beff = min(30/8, 10/2) = 3.75 ft each side → total beff = 7.5 ft = 90 in; slab tc = 3.5 in above deck; deck ribs perpendicular, hr = 3 in; ¾ in × 4.5 in headed studs (Asa = 0.4418 in²); η = 0.75; wDL = 1.5 kip/ft, wLL = 1.5 kip/ft.

Step 1 — Stud Capacity (§I8.2a)

Ec = 33×1451.5×√4≈ 3644 ksi
0.5 Asa √(f'cEc) = 0.5×0.4418×√(4×3644)= 26.7 kips
RgRpAsaFu = 1.0×0.75×0.4418×65= 21.5 kips ← governs
Qn= 21.5 kips

Step 2 — Full Composite Horizontal Shear

FyAs = 50 × 10.3= 515 kips (W18×35: As=10.3 in²)
0.85f'cbefftc = 0.85×4×90×3.5= 1071 kips
Qn,full = min(515, 1071)= 515 kips
ΣQn = η × Qn,full = 0.75 × 515= 386 kips
N studs each half = 386 / 21.5= 18 studs (→ 36 total)

Step 3 — Flexural Strength Mn

Concrete compression block: a = ΣQn / (0.85f'cbeff) = 386/(0.85×4×90)= 1.26 in (in slab)
PNA in steel top flange (check: FyAs−ΣQn = 515−386 = 129 kips → small part of flange in compression)
Mp,steel = ZxFy = 66.5×50/12= 277 kip-ft
Mn,composite (by PSDM)≈ 443 kip-ft
φbMn = 0.90 × 443= 399 kip-ft

Step 4 — Demand

wu = 1.2×1.5 + 1.6×1.5 = 1.8 + 2.4= 4.2 kip/ft
Mu = wuL²/8 = 4.2×30²/8= 473 kip-ft
D/C = 473 / 399= 1.18 — NG (increase η or section)

To pass: increase η to 1.0 → φbMn ≈ 490 kip-ft → D/C ≈ 0.97 OK. Or select W21×44.