How to design a composite beam

A steel beam under a concrete slab carries load on its own. Weld shear studs to its top flange so the slab can't slip, and the two act together: the concrete takes the compression, the steel the tension. The composite beam is typically 1.5–2.5 times stronger and 2–3 times stiffer than the bare steel — which means lighter beams, shallower floors, and a new set of checks.

#How composite action works

• Effective width — only part of the slab works with the beam: in AISC, L/8 each side but not more than half the distance to the next beam (and not beyond the slab edge).
• Shear studs transfer the horizontal force between steel and slab. Full composite action needs studs for the smaller of the slab compression and the steel tension; partial composite action uses fewer studs and gets a lower moment.
• Construction stage — in unshored construction the wet concrete is carried by the steel beam alone before the slab hardens. That stage often governs the steel size.

#Worked example (AISC 360)

Office floor beams spanning 9.0 m, simply supported, at 3.0 m centres, under a 130 mm solid slab, f′_c = 28 MPa, A992 steel F_y = 345 MPa, unshored. Finishes 1.0 kPa, office live load 2.4 kPa.

#Loads

D = (0.13 × 25 + 1.0) × 3.0 + 0.38 (beam) = 13.13 kN/m; L = 2.4 × 3.0 = 7.2 kN/m.

#Construction stage first

The steel alone carries the dead load (the deck or formwork braces the top flange). W14×22 has Z_x = 544 × 10³ mm³: φM_p = 0.9 × 544 000 × 345 = 169 kN·m, against 1.4D: 1.4 × 13.07 × 81 / 8 = 185 kN·m → 1.09 ✗. The composite beam would have been fine — the bare steel during the pour is not.

Next size up, W14×26 (A = 4950 mm², d = 353 mm, Z_x = 659 × 10³ mm³): φM_p = 204.5 kN·m, 1.4D → 186 kN·m → 0.91 ✓.

#Composite stage

b_eff = min(9000/4, 3000) = 2250 mm. The slab could carry 0.85 × 28 × 2250 × 130 = 6962 kN, the steel only A_sF_y = 4950 × 345 = 1708 kN, so C = 1708 kN and the neutral axis is in the slab:

276 / 447 = 0.62 ✓ — more than twice the bare steel's strength.

#Studs

Ø19 headed studs (A_sa = 283.5 mm², F_u = 450 MPa) in a solid slab, E_c = 4700√28 = 24 870 MPa:

Full composite action: 1708 / 118 = 14.4 → 15 studs each side of midspan, 30 in all. Since 0.62 leaves margin, partial composite action with fewer studs would pass too — the fewest that still meet strength, deflection and the minimum degree of composite action is the economic answer.

Eurocode 4: the same plastic method (EN 1994-1-1 6.2.1) with f_cd = 0.85 f_ck/γ_c, b_eff = L_e/8 each side, and stud resistance P_Rd as the smaller of shank shear and concrete crushing, divided by γ_V = 1.25.

#Floor vibration (AISC Design Guide 11)

Light, long-span composite floors can pass every strength check and still feel lively when people walk. DG11 estimates the floor's natural frequency from the deflection Δ of the beam and girder under the supported weight, and the peak acceleration a person causes:

For example, Δ = 15 mm gives f_n = 0.18 × √(9810/15) = 4.6 Hz; with β = 0.03 and W = 400 kN, a_p/g = 0.29 × e^−1.61 / 12 = 0.48 % — just within the office limit. Heavier or stiffer floors (higher W or f_n) feel calmer.

#Design it in Struxt3D

1. Open a steel building with floor slabs — the Multi-storey frame in steel.
2. Turn composite design on in Design settings › Composite beams (steel beams under a concrete slab: studs, unshored), and Floor vibration for the DG11 walking check with the limits of the chosen floor use.
3. Run the design (F6). Steel beams under the slab are designed simply supported over their span, unshored: the dead load on the steel alone at construction, then the composite section for the strength combinations.
4. Read the Composite beams table: the composite beam, number of studs, degree of composite action, governing check, clause, combination and ratio. The vibration result appears in the table's note.
5. Inspect a beam — its inspector has an As a composite beam section next to the steel member check.

#Common mistakes

• Skipping the construction stage in unshored floors.
• Using the full slab width instead of the effective width.
• Forgetting vibration on long, light spans.
• Counting composite action in hogging zones — the slab is in tension there and cracks.