Free Composite Beam Calculator -- Steel-Concrete Design

Design composite steel-concrete beams for floor systems in multi-story buildings and bridges. The calculator checks full and partial composite action, shear stud strength and layout, transformed section properties for both short-term and long-term loading, flexural capacity of the composite section, service-level deflection including concrete creep effects, and construction-phase checks for unshored erection. The analysis covers AISC 360-22 Section I3 (Composite Members), EN 1994-1-1 (Eurocode 4), AS 2327 (Composite Structures), and CSA S16 Section 17 (Composite Beams).

Composite beams achieve flexural capacity and stiffness far exceeding the steel beam alone by engaging the concrete slab as the compression element of the composite section. The concrete slab carries compression (replacing or supplementing the steel compression flange), while the steel beam carries tension. Shear studs welded to the steel beam top flange and embedded in the concrete slab transfer the horizontal shear at the interface, ensuring strain compatibility and composite action. Without adequate shear connection, the steel beam and slab would act as separate elements (non-composite), losing the stiffness benefit but still sharing load through their individual stiffnesses.

Composite beam types:

What this calculator does not cover: composite columns (encased or filled sections, per AISC 360 I2), composite connections and joint design, fire engineering of composite beams (reduced capacity at elevated temperatures), and pre-cambering for dead load deflection compensation.

How to Use This Calculator

Step 1 -- Select steel beam section. Choose a W-shape from the AISC database (W8 to W44 series). For floor beams, W14 to W24 are common; for girders, W21 to W30. The calculator retrieves section properties (As, d, Ix, Zx, bf, tf). For built-up sections, enter properties manually. Steel grade: typically A992 (Fy = 50 ksi, Fu = 65 ksi) for W-shapes.

Step 2 -- Define concrete slab. Enter the total slab thickness (deck rib height plus topping), concrete compressive strength f'c (3,000-5,000 psi typical for composite floor slabs), concrete density (normal-weight = 145 pcf or lightweight = 110-120 pcf), and whether welded wire fabric or rebar is provided for crack control. The modular ratio n = Es/Ec where Ec = wc^1.5 x 33 x sqrt(f'c) in psi, or Ec = wc^1.5 x 0.043 x sqrt(f'c) in MPa.

Step 3 -- Select metal deck profile. Enter deck rib height (1.5, 2, or 3 in for composite floor deck), rib width at the top, average flute width, and deck orientation relative to the beam (ribs perpendicular or parallel to the beam axis). Perpendicular ribs trigger shear stud reduction factors Rp and Rg per AISC 360 I3.2c. The effective slab width be is the minimum of beam span/8 (each side of beam centerline), half the distance to the adjacent beam web, and the slab overhang distance.

Step 4 -- Specify shear studs. Select stud diameter (3/4 in standard, 7/8 in for heavy composite), stud length (must extend at least 1.5 in above the top of the deck for 3/4 in studs), number of studs per rib (1 or 2), and stud layout (uniform spacing or concentrated near supports for partial-length composite). The nominal stud strength Qn is computed per AISC 360 Eq I3-3:

Qn = 0.5 x Asc x sqrt(f'c x Ec) ≤ Rg x Rp x Asc x Fu

where the first term is the concrete crushing limit and the second is the steel stud tensile rupture limit. Rg and Rp account for group effects and deck position per AISC 360 Table I3.2a.

Step 5 -- Enter loads for both phases. Construction phase (unshored): wet concrete weight, construction live load (20 psf per SDI), deck and beam self-weight, and any stored materials. Composite phase: superimposed dead load (partitions, ceiling, MEP, flooring), live load, and any special loads. The calculator checks the steel beam alone (construction) and the composite section (superimposed loads) separately.

Step 6 -- Review results. Output includes the transformed section properties (I_tr for short-term, I_tr_LT for long-term with 2n modular ratio), composite moment capacity (full and actual composite percentage), number of studs required and utilized, construction-phase steel DCR, composite flexure DCR, total deflection (DL + SDL creep + LL), and live load deflection vs L/360 limit.

Engineering Theory -- Composite Beam Behavior

Transformed Section Analysis

For elastic analysis (service-level deflection and stress checks), the concrete slab is transformed into an equivalent steel area by dividing the concrete width by the modular ratio n. The transformed section properties are computed about the centroid of the combined steel-plus-transformed-concrete section:

n = Es/Ec  (short-term, typically n = 8-10)
n_LT = 2n  (long-term, to account for concrete creep)

The transformed concrete width = be/n (or be/2n for long-term). The neutral axis location is found by equating first moments of area: y_bar = Sum(Ai x yi)/Sum(Ai) where Ai are the areas of the steel beam and the transformed concrete slab element.

The transformed moment of inertia I_tr = Sum(Ii + Ai x (y_bar - yi)^2). For a typical composite floor beam (W18x35 with 90-inch effective slab width at 6.25-inch total thickness, n ≈ 9): the transformed concrete area contributes approximately 30-50% of the total I_tr, more than doubling the steel-only moment of inertia. This stiffness increase reduces live load deflection proportionally.

Full vs Partial Composite Action

The horizontal shear force V' (kip) that must be transferred between the slab and steel beam to achieve the composite section's full plastic moment is the smaller of:

V'_steel = As x Fy  (steel beam yields in tension)
V'_concrete = 0.85 x f'c x be x ts  (concrete slab crushes in compression)

For a W18x35 with As = 10.3 in^2 and Fy = 50 ksi: V'_steel = 515 kips. For a 90-inch slab at 4 ksi: V'_concrete = 0.85 x 4 x 90 x 6.25 = 1,913 kips. The steel controls: only 515 kips of horizontal shear transfer is needed to develop the full composite plastic moment before the steel yields.

The number of shear studs required for full composite action: N = V'_steel / (phi x Qn). For 3/4-inch studs at Qn = 17.2 kips and phi = 0.85: N = 515 / (0.85 x 17.2) = 35 studs. With 2 studs per rib at 12-inch rib spacing and a 15-foot half-span, 30 stud positions are available -- not enough for full composite. The beam is partially composite, which is perfectly acceptable.

For partial composite, the actual composite percentage = (N_provided / N_required_full) x 100%. The composite moment capacity is linearly interpolated between the steel-only moment (0% composite) and the full composite moment (100% composite), per AISC 360 Commentary I3.2. At 25% composite (the code minimum), the moment capacity is approximately steel_Mn + 0.25 x (composite_Mn - steel_Mn).

Plastic Stress Distribution (AISC 360 I3.2)

The composite beam's plastic moment is determined by the plastic stress distribution, assuming the steel beam is fully yielded in tension (or in compression above the PNA) and the concrete slab develops a uniform stress block of 0.85 x f'c over a depth a. The plastic neutral axis (PNA) depth is found from horizontal force equilibrium:

Case 1 -- PNA in the slab (most common for floor beams): a = As x Fy / (0.85 x f'c x be). If a ≤ ts (topping thickness above the deck ribs), the PNA lies in the slab. The composite plastic moment is:

Mn = As x Fy x (d/2 + ts - a/2)

Case 2 -- PNA in the steel beam top flange (deeper beams or thin slabs): a exceeds ts and the compression block extends into the steel beam top flange. The PNA is found by equilibrating the forces: the concrete slab compression (0.85 x f'c x be x ts) plus the steel flange compression (bf x (a - ts) x Fy) equals the steel tension below. The moment is computed by summing moments of these forces about the PNA.

Shear Stud Design per AISC 360 I3.5

The nominal shear strength Qn of a single headed stud anchor is per AISC 360 Eq I3-3:

Qn = 0.5 x Asc x sqrt(f'c x Ec) ≤ Rg x Rp x Asc x Fu

For a 3/4-inch stud (Asc = 0.442 in^2) in 4,000 psi normal-weight concrete (Ec = 33 x 145^1.5 x sqrt(4,000)/1,000 = 3,605 ksi): sqrt(f'c x Ec) = sqrt(4 x 3,605) = sqrt(14,420) = 120.1 ksi. Qn = 0.5 x 0.442 x 120.1 = 26.5 kips.

Upper bound: Rg x Rp x 0.442 x 65. Rg = 1.0 (one stud per rib), Rp = 0.6 (weak position, deck ribs perpendicular). Rg x Rp = 0.6. Qn_max = 0.6 x 0.442 x 65 = 17.2 kips.

Governing Qn = 17.2 kips (the stud position reduction governs for weak-position studs). For strong-position studs (Rp = 0.75), Qn = 21.6 kips. For parallel ribs (Rp = 1.0, Rg = 1.0), Qn = 26.5 kips (concrete crushing governs).

Long-Term Deflection and Creep

Concrete creep under sustained dead load increases the beam deflection over time by a factor of approximately 2.0 to 3.0 compared to the initial dead load deflection. AISC 360 I3.6 addresses creep through the use of a long-term modular ratio n_LT = 2n for the sustained dead load portion. The total deflection is:

Delta_total = Delta_DL_unshored(steel only) + Delta_SDL_creep(n_LT = 2n) + Delta_LL(n = short-term)

The effective moment of inertia I_eff used for the sustained load portion is computed with n_LT = 2 x n (approximately 16-20 for normal-weight concrete). This halves the transformed slab width, raising the neutral axis and reducing the composite moment of inertia by approximately 15-25% compared to the short-term I_tr.

Worked Example -- Office Floor Composite Beam

Problem: Design a composite floor beam for a 30 ft x 30 ft bay office building. Beams at 10 ft o.c. (so be = min(30 x 12/4, 10 x 12, N/A) = min(90, 120) = 90 in). Slab: 3-inch composite deck (20 ga) with 3.25-inch normal-weight concrete topping (total 6.25 in), f'c = 4,000 psi. Unshored construction. Superimposed DL = 15 psf, LL = 50 psf. Steel beam: trial W18x35 (A992, Fy = 50 ksi, As = 10.3 in^2, d = 17.7 in, Ix = 510 in^4, Zx = 66.5 in^3).

Step 1 -- Construction phase (steel beam alone). Slab self-weight: (3 in deck + 3.25 in topping) ≈ 46 psf equivalent for NWC. Beam self-weight = 35 plf x (trib 10 ft) = 3.5 psf. Total construction dead load = 46 + 3.5 = 49.5 psf. Construction LL = 20 psf. Factored construction load = 1.2 x 49.5 + 1.6 x 20 = 59.4 + 32.0 = 91.4 psf x 10 ft trib = 0.914 klf. M_construction = 0.914 x 30^2/8 = 102.8 kip-ft. Steel beam strength: phi_Mn = 0.90 x 50 x 66.5/12 = 249 kip-ft. DCR = 102.8/249 = 0.41. Passes.

Step 2 -- Composite section properties (short-term). n = Es/Ec = 29,000/(33 x 145^1.5 x sqrt(4,000)/1,000) = 29,000/3,605 = 8.04, use n = 8. Transformed slab width = 90/8 = 11.25 in. Concrete area (transformed) = 11.25 x 6.25 = 70.3 in^2. (For ribbed deck, the effective thickness accts for the solid portion above ribs plus the rib concrete weighted by rib area ratio. Simplified approach: use total slab depth with a weighted average thickness.)

Simplified: effective concrete thickness above deck ribs = 3.25 in (topping only, ribs contribute mostly stiffness below the PNA and are neglected in the simplified approach). Area_transformed = 11.25 x 3.25 = 36.6 in^2. Composite centroid (from top of slab): y_bar = (36.6 x 1.625 + 10.3 x (3.25 + 17.7/2))/ (36.6 + 10.3) = (59.5 + 10.3 x 12.1)/46.9 = (59.5 + 124.6)/46.9 = 184.1/46.9 = 3.93 in from top. I_tr = I_steel + As x (d/2 + ts - y_bar)^2 + (be/n) x ts^3/12 + (be/n) x ts x (y_bar - ts/2)^2 = 510 + 10.3 x (8.85 + 3.25 - 3.93)^2 + 11.25 x 3.25^3/12 + 11.25 x 3.25 x (3.93 - 1.625)^2 = 510 + 10.3 x (8.16)^2 + 32.2 + 36.6 x (2.31)^2 = 510 + 10.3 x 66.6 + 32.2 + 36.6 x 5.32 = 510 + 686 + 32.2 + 194.7 = 1,423 in^4. Compare to steel-only Ix = 510 in^4 -- composite action increases stiffness by 179%.

Step 3 -- Composite flexure (plastic). V'_steel = 10.3 x 50 = 515 kips. V'_concrete = 0.85 x 4 x 90 x 3.25 = 995 kips. Steel controls. a = 515/(0.85 x 4 x 90) = 515/306 = 1.68 in < 3.25 in topping. PNA in slab. Mn = 515 x (17.7/2 + 3.25 - 1.68/2)/12 = 515 x (8.85 + 3.25 - 0.84)/12 = 515 x 11.26/12 = 483 kip-ft. phi_Mn = 0.90 x 483 = 435 kip-ft.

Step 4 -- Factored superimposed moment. w_SDL_factored = 1.2 x 15/1,000 x 10 = 0.180 klf. w_LL_factored = 1.6 x 50/1,000 x 10 = 0.800 klf. Total w_super = 0.980 klf. M_super = 0.980 x 30^2/8 = 110.3 kip-ft. DCR_flexure = 110.3/435 = 0.25. Passes easily. Flexure is not the governing check.

Step 5 -- Shear stud design. Required number of studs for full composite = V'_steel/(phi x Qn) = 515/(0.85 x 17.2) = 35 studs. With studs at 2 per rib, deck ribs at 12 in o.c., half-span = 15 ft = 15 ribs. Available stud positions = 15 x 2 = 30 studs per half-span. Number provided per beam = 30 x 2 half-spans = 60 studs total. N_provided_per_half = 30 > N_req_per_half = 17.5. The beam achieves full composite action with comfortable margin (30 provided vs 18 required per half-span).

Check minimum composite: 25% x 35 = 9 studs. 30 >> 9. OK.

Step 6 -- Deflection check. Live load (service): w_LL_service = 0.050 x 10 = 0.500 klf. Delta_LL = 5 x 0.500 x 30^4 x 1,728/(384 x 29,000 x 1,423) = 5 x 0.500 x 810,000 x 1,728/(384 x 29,000 x 1,423) = 3,499,200,000/(15,813,000,000) = 0.22 in = L/1,636. Limit: L/360 = 30 x 12/360 = 1.0 in. Passes with large margin. The composite stiffness makes deflection nearly negligible for this span.

Creep deflection: long-term modular ratio n_LT = 16. I_tr_LT ≈ 1,080 in^4 (computed with n=16). Delta_SDL = 5 x 0.015 x 10 x 30^4 x 1,728/(384 x 29,000 x 1,080) = 0.073 in. Total deflection = steel-only construction DL (from initial camber, if any) + creep SDL + LL = approximately 0.4 in total. Well within L/240 limit. Passes.

Result: W18x35 composite beam with 3.25-inch normal-weight concrete topping on 3-inch composite deck. 60 shear studs (3/4 in dia, 2 per rib, 30 ribs per beam). Full composite action achieved. Deflection far below limits due to high composite stiffness. The beam is construction-strength controlled; composite action provides abundant reserve for superimposed loads.

Frequently Asked Questions

What is partial composite action and when is it used?

Partial composite action means fewer shear studs than required for full composite action are provided. AISC 360 I3.2a permits a minimum of 25% composite action. Using fewer studs reduces flexural capacity and stiffness approximately linearly with the composite percentage but saves stud installation cost. The neutral axis moves upward in partial composite beams, and deflections increase, so serviceability (deflection, vibration) often governs the minimum stud count. Partial composite is most economical when the beam is significantly oversized for strength and more studs would provide diminishing returns.

How does metal deck orientation affect shear stud strength?

Deck ribs perpendicular to the beam axis require stud capacity reduction factors Rp and Rg per AISC 360 Table I3.2a. For one stud per rib in weak position: Rp = 0.6, Rg = 1.0, reducing stud capacity by 40% compared to a stud in a solid slab. For two studs per rib: Rg = 0.85, Rp = 0.6, reducing capacity by 49%. For deck ribs parallel to the beam, the stud is through the deck at the rib valley, and Rp = Rg = 1.0 (no reduction), though the stud must be placed to avoid interference with the deck reinforcing.

What is the minimum slab thickness for composite beams?

AISC 360 I3.2c requires a minimum slab thickness of 2 inches above the top of the metal deck ribs for composite action with studs. For 3/4-inch and smaller studs, the stud must extend at least 1-1/2 inches above the top of the deck. For 7/8-inch and larger studs, a minimum 3-inch topping above the deck is required. The total slab depth (deck + topping) is typically 4-1/2 to 7-1/2 inches for composite floor systems, with a practical minimum of 4 inches to accommodate stud welding through the deck.

What happens if a beam has zero shear studs (non-composite)?

With zero shear studs, the concrete slab and steel beam act as independent parallel elements. The slab contributes its own stiffness but does not increase the steel beam's section properties. The steel beam alone resists all flexure, and the slab deflection equals the beam deflection. Non-composite beams require deeper or heavier steel sections, but this can be economical where the slab is precast (no wet concrete for stud embedment), where the floor is temporary, or where composite action cannot be reliably developed (e.g., slabs exposed to deicing chemicals).

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Disclaimer (Educational Use Only)

This page is provided for general technical information and educational use only. It does not constitute professional engineering advice. All structural designs must be independently verified by a licensed Professional Engineer (PE) or Structural Engineer (SE) registered in the project jurisdiction. The site operator disclaims all liability for any loss or damage arising from the use of this page or the associated calculator tool. Results are preliminary -- not for construction.