One-Way Beam Shear: ACI 318-19 (§22.5) vs. Eurocode 2 (§6.2)
The 45-degree Vc + Vs model in ACI versus Eurocode's variable angle truss model—explained without the headache.
How These Two Standards Actually Compare
ACI 318 assumes diagonal shear cracks always form at 45° and lets you add the concrete contribution (Vc) and stirrup contribution (Vs) together. Eurocode 2 takes a different approach: once a beam needs shear links, you ignore the concrete contribution completely (VRd,c = 0), but you are allowed to flatten the compression strut angle θ down to 21.8° (cot θ = 2.5)—which activates 2.5 times more stirrups across the crack.
At first glance, dropping Vc in Eurocode sounds ultra-conservative. In practice, multiplying your stirrup capacity by cot θ = 2.5 more than makes up for losing Vc in moderate-to-heavily loaded beams. Where Eurocode requires extra care is at the end supports: flattening the strut angle θ increases the horizontal tension force in your bottom longitudinal bars.
At a Glance: Side-by-Side Cheat Sheet
Quick reference table of notation, safety factors, and design assumptions.
| Parameter | ACI 318-19 §22.5 | Eurocode 2 §6.2 | What It Means in Practice |
|---|---|---|---|
| Shear Resistance Model | Additive: Vn = Vc + Vs (Fixed 45° truss) | Variable Strut Inclination: VRd = VRd,s (with 1.0 ≤ cot θ ≤ 2.5) | In Eurocode, concrete and stirrup capacities are not added together. |
| Crack / Strut Angle (θ) | Fixed at 45° (cot θ = 1.0) | Designer chooses θ between 21.8° (cot θ = 2.5) and 45° (cot θ = 1.0) | Using cot θ = 2.5 cuts required stirrup area by up to 60% before web crushing governs. |
| Effective Shear Depth | Effective depth d | Internal lever arm z ≈ 0.9d | Eurocode uses z = 0.9d directly in the stirrup spacing equation. |
| Maximum Shear (Web Crushing) | Vs,max = 0.66√f'c · bw · d (SI) | VRd,max = αcw · bw · z · ν1 · fcd / (cot θ + tan θ) | Flatter strut angles (cot θ = 2.5) lower the web-crushing ceiling VRd,max. |
Governing Equations Side-by-Side
Direct comparison of the core code formulas and what each term represents.
1. Shear Capacity with Vertical Stirrups
Concrete capacity Vc (updated in 2019 to include longitudinal steel ratio ρw and size effect λs) stays active alongside the stirrups.
Concrete contribution is omitted, but cot θ scales the stirrup efficiency up to 2.5× until diagonal web crushing (VRd,max) is reached.
Practical Notes When Converting Designs
Real-world rules of thumb and the most common conversion mistake to avoid.
How Eurocode Designers Pick cot θ
In everyday office practice, engineers start by setting cot θ = 2.5 to minimize stirrups. If the applied shear VEd exceeds VRd,max at cot θ = 2.5, you gradually steepen the angle toward 45° (cot θ = 1.0) to gain more web-crushing capacity.
The Shift Rule (Curtailment of Bottom Bars)
Because a flatter compression strut pushes harder horizontally, Eurocode 2 requires an additional tensile force ΔFtd = 0.5 · VEd · cot θ to be anchored by the bottom longitudinal bars at supports.
ACI 318-19 Changed Vc for Lightly Reinforced Members
If you are used to the classic ACI 318-14 rule (Vc = 2√f'c · bw · d in psi, or 0.17√f'c in MPa), note that ACI 318-19 replaced it when Av < Av,min. For thick slabs or beams with low longitudinal steel ρw, the 2019 ACI Vc equation now gives lower capacities—much closer to Eurocode 2.