----------------------------- | ------------------------------- | ------------------------------------ | ----------------------------- | ------------------------------ | | Effective flange width | I3.1a (L/8 per side) | Cl 5.4.1.2 (L_e/8 per side) | Cl 3.5.1 (L/8 each side) | Cl 17.3 (L/8 each side) | | Stud capacity | I3.2d (Eq. I3-3, I3-4) | Cl 6.6.3 (Eq. 6.21, 6.22) | Cl 8.3.2 (similar to AISC) | Cl 17.6 (similar to AISC) | | Stud reduction (deck ribs) | Table I3.2 (R_g, R_p) | Cl 6.6.4 (k_t reduction) | Cl 8.3.3 (R_g, R_p) | Cl 17.6.3 | | Steel contribution ratio | N/A | Cl 6.6.1 (0.25 <= eta <= 1.0) | N/A | N/A | | Full composite moment | I3.2c (plastic stress dist.) | Cl 6.2.1 (plastic or elastic) | Cl 5.3 (plastic stress dist.) | Cl 17.4 (plastic stress dist.) | | Partial composite moment | I3.2c(4) (linear interpolation) | Cl 6.2.1.3 (interpolation or m-k) | Cl 5.3.3 (interpolation) | Cl 17.4.3 | | Minimum composite action | 25% (I3.2c(4)) | eta >= 0.4 (unpropped), 0.25 (prop.) | 25% | 25% | | Steel shear capacity | I3.2b(3) (steel alone) | Cl 6.2.2 (steel alone for V) | Cl 5.4 (steel alone) | Cl 17.5 (steel alone) | | Construction stage (L/360 limit) | AISC DG3 Table 5.1 | Cl 7.2 (L/300 to L/500) | Cl 7.2 (L/350) | Cl 17.8 (L/360) | | Stud spacing limits | I3.2c(5) (6d longitudinal) | Cl 6.6.5 (5d longitudinal) | Cl 8.4 (6d longitudinal) | Cl 17.6.4 (6d) |

Key difference: EN 1994-1-1 is the only code entirely dedicated to composite steel-concrete construction. It provides more refined rules for partial interaction (interpolation method for ductile connectors, m-k method for non-ductile connectors) and explicitly requires a minimum degree of shear connection eta that depends on the beam span. AISC 360 is simpler — a single linear interpolation equation applies for all partial composite cases. AS 2327 closely follows AISC methodology but with Australian material standards (AS/NZS 3679.1 steel, AS 3600 concrete). CSA S16 §17 aligns with AISC but uses Canadian material properties and phi factors.

Step-by-Step Example

Problem: Design a composite floor beam for a 30 ft simply-supported span. Beam spacing = 10 ft (tributary width). W16x31 steel beam (A992, F_y = 50 ksi, A_s = 9.13 in^2, d = 15.9 in, I_x = 375 in^4, Z_x = 54.0 in^3). Slab: 4.5 in normal-weight concrete (f'_c = 4 ksi, w_c = 145 pcf) on 2 in metal deck (ribs perpendicular to beam). Studs: 3/4 in diameter, F_u = 65 ksi, one stud per rib. Unshored construction. Design code: AISC 360-22 LRFD.

Step 1 — Effective flange width: L/4 = 30*12/4 = 90 in. Beam spacing = 120 in. b_eff = min(90, 120) = 90 in.

Step 2 — Concrete above deck: Slab thickness above deck = 4.5 in. Deck depth = 2 in (rib). Total slab depth = 6.5 in.

Step 3 — Shear stud capacity (3/4 in stud, one per rib, ribs perpendicular): Asa = pi * 0.75^2 / 4 = 0.442 in^2. Ec = 145^1.5 * sqrt(4000) = 1746 _ 63.25 = 3,490 ksi. Concrete limit: Q_n = 0.5 _ 0.442 _ sqrt(4 _ 3490) = 0.221 _ sqrt(13,960) = 0.221 _ 118.2 = 26.1 kips. Steel limit (with deck reduction): R*g = 1.0 (one stud per rib), R_p = 0.6 (ribs perpendicular, e_mid-ht >= 2 in). Q_n_steel = 1.0 * 0.6 _ 0.442 * 65 = 17.2 kips. Controlling Q_n = min(26.1, 17.2) = 17.2 kips per stud.

Step 4 — Number of studs for full composite action: Compression capacity of slab: Cconc = 0.85 * f'_c _ b_eff _ tslab_above_deck = 0.85 * 4 _ 90 _ 4.5 = 1,377 kips. Tension capacity of steel: Tsteel = A_s * Fy = 9.13 * 50 = 456.5 kips. C_f = min(1377, 456.5) = 456.5 kips (steel-controlled). N_full = C_f / Q_n = 456.5 / 17.2 = 26.6 → 28 studs (14 pairs).

Step 5 — Compression block depth (full composite): a = C*f / (0.85 * f'_c _ b_eff) = 456.5 / (0.85 _ 4 _ 90) = 456.5 / 306 = 1.49 in. PNA is in slab (a = 1.49 in < 4.5 in slab above deck). This is typically the most efficient case.

Step 6 — Full composite moment capacity: Mn = C_f * (d/2 + tslab_above_deck + h_deck - a/2) = 456.5 * (15.9/2 + 4.5 + 2 - 1.49/2) = 456.5 _ (7.95 + 6.5 - 0.745) = 456.5 _ 13.705 = 6,256 kip-in = 521.3 kip-ft. phi = 0.90. phi*M_n = 0.90 * 521.3 = 469.2 kip-ft.

Step 7 — Steel-only moment capacity (construction check): Mp_steel = F_y * Zx = 50 * 54.0 = 2,700 kip-in = 225 kip-ft. phi*M_n_steel = 0.90 * 225 = 202.5 kip-ft.

Step 8 — Partial composite (50% studs = 14 studs): Sum Qn = 14 * 17.2 = 240.8 kips. Mn_partial = M_s + (sum_Q_n / C_f) * (Mc - M_s) = 225 + (240.8/456.5) * (521.3 - 225) = 225 + 0.528 _ 296.3 = 225 + 156.4 = 381.4 kip-ft. phiM_n = 0.90 * 381.4 = 343.3 kip-ft (73% of full composite capacity with 50% of studs).

Step 9 — Factored demands (LRFD): Dead load: slab = 4.5/12 _ 145 _ 10 + deck self-weight ~2 psf _ 10 = 544 + 20 = 564 plf; beam SW = 31 plf; total DL = 595 plf. Superimposed DL (finishes, ceiling, MEP) = 15 psf _ 10 = 150 plf. Live load = 50 psf _ 10 = 500 plf (reducible per ASCE 7, but use unreduced for simplicity). w_u = 1.2_(595+150) + 1.6500 = 1.2745 + 800 = 894 + 800 = 1,694 plf = 1.69 klf. M_u = 1.69 * 30^2 / 8 = 190.1 kip-ft.

Step 10 — Utilization: Composite moment capacity = 469.2 kip-ft. M_u = 190.1 kip-ft. Utilization = 190.1 / 469.2 = 0.405 — full composite is over-designed. With partial composite (50% studs, 14 studs): 190.1 / 343.3 = 0.554 PASS with margin.

Construction-stage check (unshored): Wet concrete + deck + beam SW = 595 plf (assume deck provides some distributed load). Construction live load = 20 psf * 10 = 200 plf. w_construction = 1.2595 + 1.6200 = 714 + 320 = 1,034 plf. M_u_construction = 1.034 * 30^2 / 8 = 116.3 kip-ft. phi*M_n_steel = 202.5 kip-ft. Utilization = 116.3/202.5 = 0.574 PASS (unshored OK).

Deflection — construction (wet concrete only, service): deltaDL = 5 * (0.595 klf) _ (3012)^4 / (384 * 29000 _ 375) = 5 _ 0.595 * 1.679610^9 / (384 _ 29000 _ 375 * 1000) [convert klf to kip/in: 0.595/12 = 0.0496 k/in] Actually: w = 0.595 klf = 0.0496 k/in. delta = 50.0496*(360)^4 / (38429000375) = 5*0.0496*1.6796e9 / 4.176e9 = 4.165e8 / 4.176e9 = 0.10 in = L/3600 — well within L/360 = 1.0 in limit.

Result: W16x31 with 14 pairs of 3/4 in studs (28 total) at uniform spacing achieves 0.55 utilization in partial composite. Construction stage governs beam size for unshored condition but is well within capacity. Full composite would require 28 pairs (56 studs) with minimal practical benefit given the low utilization.

Common Design Mistakes

• Selecting the steel beam for composite capacity without checking the construction stage: The steel beam alone supports the wet concrete weight in unshored construction. For spans over 25 ft, construction-stage deflection often controls beam size more than composite-stage strength. A W16x31 may be adequate for composite strength at 30 ft span but the construction deflection of the bare steel beam may exceed L/360, wasting concrete due to ponding.
• Applying deck reduction factors incorrectly for stud strength: When ribs are perpendicular to the beam, the R_p factor (0.6 for one stud per rib, 0.75 for two studs per rib) dramatically reduces stud capacity — a single 3/4 in stud drops from 21.9 kips (solid slab) to 13.1 kips (perpendicular ribs). Designers sometimes forget this reduction, leading to under-designed stud layouts.
• Using the gross concrete thickness instead of thickness above the deck for compression: The concrete in the metal deck ribs is below the neutral axis for typical PNA-in-slab cases and does not contribute to compression. Only the concrete above the top of the deck is effective in compression. Using the total slab thickness overestimates capacity.
• Neglecting long-term creep effects on deflection: Under sustained dead load, concrete creeps — the modular ratio effectively doubles or triples over time (2n or 3n). This means the composite section stiffness for long-term dead load deflection is significantly lower than for short-term live load. A beam that passes the live-load deflection check at n = 8 may fail the total-load check at 3n = 24.
• Assuming the effective flange width is the full beam spacing: The L/8 limit often controls for long-span beams. For a 40 ft beam, L/4 = 120 in = 10 ft, so maximum effective width is 10 ft regardless of beam spacing. For a beam at 15 ft spacing, the effective width is only 10 ft — the outer 2.5 ft of slab on each side is not effective in composite action. This reduces the compression block and the moment capacity proportionally.
• Ignoring stud ductility requirements for partial composite design: AISC limits partial composite design to cases where the studs are ductile (sufficient deformation capacity to redistribute shear along the beam). Non-ductile studs (e.g., studs in very high-strength concrete, or studs with very low h/d ratios) may not achieve the necessary slip for the linear interpolation method to be valid. EN 1994-1-1 explicitly requires a minimum stud deformation capacity of 6 mm for the interpolation method.

Frequently Asked Questions

What is the difference between shored and unshored composite construction? In shored construction, temporary supports are placed under the steel beam during concrete placement, so the wet concrete weight is carried by the shores rather than the steel beam. After the concrete cures, the shores are removed and the composite section carries all loads (dead + live). This allows lighter steel beams and eliminates the construction-stage deflection check. In unshored construction, the steel beam alone supports the wet concrete weight, and the composite section only carries loads applied after curing (superimposed dead + live). Shoring is more expensive in labor and schedule but produces a more efficient final design. For spans over ~30 ft, shoring is often worth the additional cost because the steel savings outweigh the shoring cost.

How many shear studs do I need — full or partial composite? The answer depends on the demand-to-capacity ratio of the composite section. If the composite moment capacity with full interaction far exceeds the factored demand (utilization < 0.6), partial composite action will likely be adequate and more economical. The minimum degree of composite action is 25% per AISC 360. A practical approach: (a) compute the required moment capacity (M_u), (b) compute steel-only capacity (phiM_s), (c) the composite action must bridge the gap: required composite contribution = M_u - phiM_s, (d) solve for required sum_Q_n from the interpolation equation, (e) divide by Q_n per stud. Often, 40-60% composite action is the economical range. For uniformly loaded beams, shear studs can be spaced uniformly; for beams with concentrated loads or varying shear, studs should be concentrated near the supports where shear flow is highest.

How does metal deck orientation affect composite beam design? Metal deck ribs can be oriented parallel or perpendicular to the steel beam. Parallel ribs: the concrete in the ribs runs alongside the beam, so the ribs do not interrupt the compression block. The full slab thickness (including ribs) can be used for compression, and stud reduction factors R_g = 1.0, R_p = 0.75 (for ribs parallel, e_mid-ht requirement must still be met). Perpendicular ribs: the ribs create "valleys" in the concrete compression zone; only the concrete above the deck top is effective in compression, and studs in the rib have reduced capacity (R_p = 0.6 for one stud per rib). Parallel rib orientation is structurally more efficient but requires coordination with the deck span direction — deck typically spans the shorter direction, so parallel ribs occur when the beam is perpendicular to the deck span.

What is the modular ratio and why does it matter for composite beams? The modular ratio n = E_s / E_c converts the concrete area into an equivalent steel area for elastic analysis. For normal-weight concrete (f'_c = 4 ksi), E_c = 145^1.5 * sqrt(4000) = 3,490 ksi, and E_s = 29,000 ksi, so n = 29,000/3,490 = 8.3 (typically rounded to 8). A transformed section property (I_tr) is computed by dividing the concrete area by n, which places the concrete at an equivalent stiffness to steel. The modular ratio affects the elastic neutral axis location and the section modulus — a lower n (stiffer concrete) moves the neutral axis upward, increasing the section modulus to the bottom flange. For long-term deflection, creep reduces the effective concrete stiffness, so the modular ratio is increased to 2n or 3n, which lowers I_tr and increases long-term deflection.

When does the plastic neutral axis fall in the steel beam rather than in the slab? The plastic neutral axis (PNA) falls in the steel beam when the concrete compression capacity exceeds the steel tension capacity: 0.85f'_cb_efft_slab > A_sF_y. For typical floor beams with a 4.5 in slab and 90 in effective width, C_conc = 0.854904.5 = 1,377 kips. The PNA will be in the slab for any steel section with A_sF_y < 1,377 kips (i.e., A_s < 27.5 in^2 for F_y = 50 ksi). This covers most W-shapes up to about W24x94. For heavier sections (W24x104, W27x114, etc.), the PNA drops into the top flange or web. When the PNA is in the steel, the moment arm is reduced (center of concrete compression to center of steel tension is smaller), and the moment capacity per pound of steel becomes less efficient — this is one reason composite beams typically use lighter steel sections than non-composite alternatives.

How does fire rating affect composite beam design? Composite beams typically achieve fire ratings through one of three approaches: (a) unprotected steel with the slab acting as a heat sink — the concrete slab absorbs heat from the top flange while the bottom flange is exposed. The beam can achieve 1-hour ratings without spray-applied fireproofing if the slab thickness and beam mass are adequate (per UL assemblies), (b) spray-applied fire-resistive material (SFRM) on the exposed bottom flange and web, which adds cost and construction time, or (c) partially encased composite beams where concrete is cast between the flanges, providing inherent fire resistance. The fire limit state requires reduced material strengths at elevated temperature (steel retains ~50% strength at 550 deg C) and reduced loads per the fire load combination (typically 1.0D + 0.5L). EN 1994-1-2 provides comprehensive fire design rules for composite beams.

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