🎓 Lesson 9
D3
EC2 vs ACI: Comparative Design of a Cantilever Slab
EC2 and ACI are two different rulebooks engineers use to design reinforced concrete slabs, beams, and columns — like choosing between metric and imperial tools for the same job.
🎯 Learning Objectives
- ✓ Compare EC2 and ACI 318 design assumptions for flexural capacity of cantilever slabs
- ✓ Calculate ultimate moment resistance (M<sub>Rd</sub> or M<sub>n</sub>) using both codes for identical geometry and reinforcement
- ✓ Explain how differences in material partial factors (γ<sub>c</sub>, γ<sub>s</sub>) and strength reduction factors (φ) affect required steel area
- ✓ Apply EC2’s rectangular stress block parameters (λ = 0.8, η = 1.0) and ACI’s (α<sub>1</sub> = 0.85 for f'<sub>c</sub> ≤ 28 MPa) to compute neutral axis depth
- ✓ Analyze why EC2 typically yields ~5–10% more conservative steel requirements than ACI for thin cantilever slabs under similar loading
📖 Why This Matters
Cantilever slabs — such as blast shelter roofs, overhanging mine access platforms, or retaining wall copings — are common in mining infrastructure. Choosing between EC2 and ACI isn’t academic: it affects material costs, constructability, international project compliance, and even liability in cross-border contracts. Understanding *how* and *why* each code arrives at different steel solutions ensures you design safely, economically, and credibly — whether your project is in Johannesburg, Santiago, or Jakarta.
📘 Core Principles
Both EC2 and ACI adopt a simplified rectangular stress block for concrete in compression and assume plane sections remain plane. However, EC2 defines design concrete strength as f<sub>cd</sub> = f<sub>ck</sub>/γ<sub>c</sub> (γ<sub>c</sub> = 1.5 for persistent design), and steel as f<sub>yd</sub> = f<sub>yk</sub>/γ<sub>s</sub> (γ<sub>s</sub> = 1.15). ACI uses nominal strengths f'<sub>c</sub> and f<sub>y</sub>, then applies a strength reduction factor φ = 0.9 for flexure. EC2’s stress block has fixed λ = 0.8 and η = 1.0; ACI uses α<sub>1</sub> = 0.85 (reduced linearly for f'<sub>c</sub> > 28 MPa). Crucially, EC2 mandates minimum cover based on exposure class and diameter (e.g., XC1 → 20 mm), while ACI specifies cover by member type and exposure (e.g., 30 mm for exterior slabs). These distinctions compound in slender elements like cantilevers, where serviceability (deflection, cracking) often governs over strength.
📐 Ultimate Moment Resistance
The nominal moment capacity of a singly reinforced rectangular section depends on equilibrium of compressive force in concrete and tensile force in steel. While both codes use C = T, their expressions for concrete compressive force and lever arm differ due to stress block definitions and safety factors.
💡 Worked Example
Problem: Design a 200 mm thick cantilever slab (b = 1000 mm) spanning 1.8 m, supporting g<sub>k</sub> = 4.5 kN/m² (dead) + q<sub>k</sub> = 3.0 kN/m² (live). Concrete: C30/37 (f<sub>ck</sub> = 30 MPa); Steel: B500B (f<sub>yk</sub> = 500 MPa). Effective depth d = 165 mm. Calculate required A<sub>s</sub> per EC2 and ACI.
1.
Step 1: Determine design bending moment — EC2: M<sub>Ed</sub> = 1.35×g<sub>k</sub> + 1.5×q<sub>k</sub> = 10.58 kN·m/m; ACI: M<sub>u</sub> = 1.2×g<sub>k</sub> + 1.6×q<sub>k</sub> = 10.20 kN·m/m.
2.
Step 2: EC2 — f<sub>cd</sub> = 30/1.5 = 20 MPa; f<sub>yd</sub> = 500/1.15 = 435 MPa; solve 0.8×x×1000×20 = A<sub>s</sub>×435 → x = 0.0272A<sub>s</sub>; then M<sub>Rd</sub> = A<sub>s</sub>×435×(165 − 0.4×0.0272A<sub>s</sub>) = 10.58×10⁶ → A<sub>s</sub> = 168 mm²/m.
3.
Step 3: ACI — f'<sub>c</sub> = 30 MPa → α<sub>1</sub> = 0.85; φ = 0.9; solve 0.85×30×a×1000 = A<sub>s</sub>×500 → a = 0.0196A<sub>s</sub>; then M<sub>n</sub> = A<sub>s</sub>×500×(165 − 0.5×0.0196A<sub>s</sub>); φM<sub>n</sub> = 10.20×10⁶ → A<sub>s</sub> = 154 mm²/m.
4.
Step 4: Verify minimum reinforcement — EC2 requires A<sub>s,min</sub> = 0.26(f<sub>ctm</sub>/f<sub>yk</sub>)bd = 0.26×2.9/500×1000×165 = 249 mm²/m → governs; ACI requires A<sub>s,min</sub> = (3√f'<sub>c</sub>/f<sub>y</sub>)bd = (3√30/500)×1000×165 = 162 mm²/m → OK.
Answer:
EC2 governs with A<sub>s</sub> = 249 mm²/m (using H8 @ 200 mm c/c = 251 mm²/m); ACI permits A<sub>s</sub> = 154 mm²/m but must meet min requirement → also governs at 162 mm²/m. Thus, EC2 demands ~54% more steel than ACI's strength-based result — highlighting how minimum rules and partial factors dominate in thin members.
🏗️ Real-World Application
In the 2022 redesign of the ventilation shaft canopy at the Tschudi Copper Mine (Chile), engineers compared EC2 (for EU equipment supplier compliance) and ACI 318-19 (for local construction approval). The 2.2 m cantilever slab, exposed to aggressive mine atmosphere (XC4 per EC2 / severe exposure per ACI), required 35 mm cover. EC2’s higher γ<sub>c</sub> and γ<sub>s</sub>, combined with stricter crack width limits (w<sub>max</sub> = 0.3 mm vs ACI’s 0.4 mm), led to 12% more top steel and tighter bar spacing — increasing rebar cost by 8% but eliminating post-construction epoxy injection for surface cracks observed in prior ACI-designed canopies.