Composite Beam — Engineering Reference

AISC 360 Ch.I composite beam: effective slab width, PNA, φMn, 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.

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

For a typical interior beam with 10 ft spacing and 30 ft span: b_eff = min(30x12/8, 10x12/2, unlimited) = min(45, 60) = 45 in. per side, so 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, F_y x A_s)

where f'c is the concrete compressive strength, t_c is the slab thickness above the deck ribs, and A_s is the steel cross-sectional area. The plastic moment capacity is:

M_n = C x (d/2 + t_c/2 + h_r) (simplified, when PNA is in the slab)

where d is the steel beam depth and h_r is the deck rib height.

Partial composite action

Partial composite action uses fewer shear studs than required for full composite, producing a PNA location between the full composite position and the steel-only position. The degree of composite action is expressed as a percentage:

% Composite = sum(Q_n) / min(0.85 x f'c x b_eff x t_c, F_y x A_s) x 100

AISC I3.2d requires a minimum of 25% composite action. In practice, 50-75% composite action is common because it provides most of the strength benefit (typically 85-95% of full composite capacity) with significantly fewer studs. 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:

Q_n = 0.5 x A_sa x sqrt(f'c x E_c), capped at R_g x R_p x A_sa x F_u

where A_sa is the stud cross-sectional area, E_c = w_c^1.5 x sqrt(f'c) / 33 (for normal-weight concrete), R_g is the group factor (1.0 for one stud per rib, 0.85 for two studs), and R_p is the position factor (0.75 for studs in the weak position in deck ribs).

For a 3/4 in. diameter stud with f'c = 4 ksi normal-weight concrete: A_sa = 0.4418 in^2. Q_n = 0.5 x 0.4418 x sqrt(4 x 3644) = 0.5 x 0.4418 x 120.7 = 26.7 kip. Cap: 1.0 x 0.75 x 0.4418 x 65 = 21.5 kip (controls for studs in deck ribs).

Worked example — W16x26 composite beam

Given: W16x26 (A_s = 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 (t_c = 3.25 in.), f'c = 4 ksi, 3/4 in. shear studs.

Effective width: b_eff = min(30x12/8, 10x12/2) = min(45, 60) = 45 in. per side = 90 in. total.
Concrete compression: C_conc = 0.85 x 4 x 90 x 3.25 = 994 kip.
Steel tension: T_steel = 50 x 7.68 = 384 kip. Steel controls (PNA is in the slab).
Full composite moment: PNA is 384/(0.85 x 4 x 90) = 1.255 in. below the top of the slab. Moment arm = (15.7/2 + 3.0 + 3.25 - 1.255/2) = 7.85 + 3.0 + 3.25 - 0.628 = 13.47 in. M_n = 384 x 13.47 = 5173 kip-in = 431 kip-ft. phi x M_n = 388 kip-ft.
Studs required (full composite): N = 384 / 21.5 = 17.9 → 18 studs per half-span (36 total).
At 50% composite: sum(Q_n) = 0.50 x 384 = 192 kip. N = 192/21.5 = 8.9 → 9 studs per half-span (18 total). M_n (partial) from AISC Table 3-19 ≈ 350 kip-ft. phi x M_n ≈ 315 kip-ft. This is 81% of the full composite capacity with 50% of the studs.

Code comparison — composite beams

Feature	AISC 360 Ch. I	AS 2327	EN 1994-1-1	CSA S16 Cl. 17
Effective width	L/8, s/2, edge	L/8, s/2	L_e/8, s/2 (similar)	L/8, s/2
Stud capacity model	0.5 A_sa sqrt(f'c E_c)	Similar (AS 2327)	0.29 alpha d^2 sqrt(f_ck E_cm)	Similar to AISC
Minimum composite %	25%	25%	40% (EC4)	25%
Deck rib reduction	R_g x R_p factors	Reduction per rib geometry	k_t reduction factor	Similar to AISC
Deflection I_eff	Lower-bound I_LB (Table 3-20)	Effective I per composite %	Interpolation method	Effective I method

Common mistakes to avoid

Using the bare steel I_x for deflection — composite beams have I_eff = I_LB (lower-bound composite moment of inertia), which is typically 2-3 times the bare steel I_x. Using I_x massively overstates deflection and leads to oversized beams.
Ignoring construction-phase loading — before the concrete cures, the steel beam alone supports the wet concrete weight plus construction loads. The bare steel beam must be checked for strength and deflection during construction. If it fails this check, temporary shoring is required.
Placing studs in the wrong deck rib position — studs placed in the "weak" position (against the direction of the deck rib slope) have R_p = 0.75 rather than 1.0. Many studs in practice end up in the weak position, reducing their capacity by 25%.
Not checking vibration for long spans — composite floor systems with spans over 30 ft and light superimposed dead loads are prone to walking-induced vibration. Check per AISC Design Guide 11; the natural frequency should exceed 4 Hz for office buildings.
Assuming full composite when studs are spaced at deck rib limits — with 3 in. deck at 12 in. rib spacing, a maximum of one stud per rib limits the stud count to L/12 per half-span. For long spans, this may not provide enough studs for full composite action.

Run this calculation

Related references

Disclaimer

This page is for educational and reference use only. It does not constitute professional engineering advice. All design values must be verified against the applicable standard and project specification before use. The site operator disclaims liability for any loss arising from the use of this information.